Daily Papers

Language confusion -- where large language models (LLMs) generate unintended languages against the user's need -- remains a critical challenge, especially for English-centric models. We present the first mechanistic interpretability (MI) study of language confusion, combining behavioral benchmarking with neuron-level analysis. Using the Language Confusion Benchmark (LCB), we show that confusion points (CPs) -- specific positions where language switches occur -- are central to this phenomenon. Through layer-wise analysis with TunedLens and targeted neuron attribution, we reveal that transition failures in the final layers drive confusion. We further demonstrate that editing a small set of critical neurons, identified via comparative analysis with multilingual-tuned models, substantially mitigates confusion without harming general competence or fluency. Our approach matches multilingual alignment in confusion reduction for most languages and yields cleaner, higher-quality outputs. These findings provide new insights into the internal dynamics of LLMs and highlight neuron-level interventions as a promising direction for robust, interpretable multilingual language modeling.

While alignment algorithms are now commonly used to tune pre-trained language models towards a user's preferences, we lack explanations for the underlying mechanisms in which models become ``aligned'', thus making it difficult to explain phenomena like jailbreaks. In this work we study a popular algorithm, direct preference optimization (DPO), and the mechanisms by which it reduces toxicity. Namely, we first study how toxicity is represented and elicited in a pre-trained language model, GPT2-medium. We then apply DPO with a carefully crafted pairwise dataset to reduce toxicity. We examine how the resulting model averts toxic outputs, and find that capabilities learned from pre-training are not removed, but rather bypassed. We use this insight to demonstrate a simple method to un-align the model, reverting it back to its toxic behavior.

Despite superior reasoning prowess demonstrated by Large Language Models (LLMs) with Chain-of-Thought (CoT) prompting, a lack of understanding prevails around the internal mechanisms of the models that facilitate CoT generation. This work investigates the neural sub-structures within LLMs that manifest CoT reasoning from a mechanistic point of view. From an analysis of LLaMA-2 7B applied to multistep reasoning over fictional ontologies, we demonstrate that LLMs deploy multiple parallel pathways of answer generation for step-by-step reasoning. These parallel pathways provide sequential answers from the input question context as well as the generated CoT. We observe a striking functional rift in the middle layers of the LLM. Token representations in the initial half remain strongly biased towards the pretraining prior, with the in-context taking over abruptly in the later half. This internal phase shift manifests in different functional components: attention heads that write the answer token predominantly appear in the later half, attention heads that move information along ontological relationships appear exclusively in the initial half, and so on. To the best of our knowledge, this is the first attempt towards mechanistic investigation of CoT reasoning in LLMs.

While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and reasoning tasks -- but mathematical understanding is lagging substantially behind. Recent lines of work have begun studying representational aspects of this question: that is, the size/depth/complexity of attention-based networks to perform certain tasks. However, there is no guarantee the learning dynamics will converge to the constructions proposed. In our paper, we provide fine-grained mechanistic understanding of how transformers learn "semantic structure", understood as capturing co-occurrence structure of words. Precisely, we show, through a combination of experiments on synthetic data modeled by Latent Dirichlet Allocation (LDA), Wikipedia data, and mathematical analysis that the embedding layer and the self-attention layer encode the topical structure. In the former case, this manifests as higher average inner product of embeddings between same-topic words. In the latter, it manifests as higher average pairwise attention between same-topic words. The mathematical results involve several assumptions to make the analysis tractable, which we verify on data, and might be of independent interest as well.

Large language models are increasingly used to process documents and facilitate question-answering on them. In our paper, we extract mechanistic circuits for this real-world language modeling task: context-augmented language modeling for extractive question-answering (QA) tasks and understand the potential benefits of circuits towards downstream applications such as data attribution to context information. We extract circuits as a function of internal model components (e.g., attention heads, MLPs) using causal mediation analysis techniques. Leveraging the extracted circuits, we first understand the interplay between the model's usage of parametric memory and retrieved context towards a better mechanistic understanding of context-augmented language models. We then identify a small set of attention heads in our circuit which performs reliable data attribution by default, thereby obtaining attribution for free in just the model's forward pass. Using this insight, we then introduce ATTNATTRIB, a fast data attribution algorithm which obtains state-of-the-art attribution results across various extractive QA benchmarks. Finally, we show the possibility to steer the language model towards answering from the context, instead of the parametric memory by using the attribution from ATTNATTRIB as an additional signal during the forward pass. Beyond mechanistic understanding, our paper provides tangible applications of circuits in the form of reliable data attribution and model steering.

A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.

In the field of antibody engineering, an essential task is to design a novel antibody whose paratopes bind to a specific antigen with correct epitopes. Understanding antibody structure and its paratope can facilitate a mechanistic understanding of its function. Therefore, antibody structure prediction from its sequence alone has always been a highly valuable problem for de novo antibody design. AlphaFold2, a breakthrough in the field of structural biology, provides a solution to predict protein structure based on protein sequences and computationally expensive coevolutionary multiple sequence alignments (MSAs). However, the computational efficiency and undesirable prediction accuracy of antibodies, especially on the complementarity-determining regions (CDRs) of antibodies limit their applications in the industrially high-throughput drug design. To learn an informative representation of antibodies, we employed a deep antibody language model (ALM) on curated sequences from the observed antibody space database via a transformer model. We also developed a novel model named xTrimoABFold to predict antibody structure from antibody sequence based on the pretrained ALM as well as efficient evoformers and structural modules. The model was trained end-to-end on the antibody structures in PDB by minimizing the ensemble loss of domain-specific focal loss on CDR and the frame-aligned point loss. xTrimoABFold outperforms AlphaFold2 and other protein language model based SOTAs, e.g., OmegaFold, HelixFold-Single, and IgFold with a large significant margin (30+\% improvement on RMSD) while performing 151 times faster than AlphaFold2. To the best of our knowledge, xTrimoABFold achieved state-of-the-art antibody structure prediction. Its improvement in both accuracy and efficiency makes it a valuable tool for de novo antibody design and could make further improvements in immuno-theory.

Research in mechanistic interpretability seeks to explain behaviors of machine learning models in terms of their internal components. However, most previous work either focuses on simple behaviors in small models, or describes complicated behaviors in larger models with broad strokes. In this work, we bridge this gap by presenting an explanation for how GPT-2 small performs a natural language task called indirect object identification (IOI). Our explanation encompasses 26 attention heads grouped into 7 main classes, which we discovered using a combination of interpretability approaches relying on causal interventions. To our knowledge, this investigation is the largest end-to-end attempt at reverse-engineering a natural behavior "in the wild" in a language model. We evaluate the reliability of our explanation using three quantitative criteria--faithfulness, completeness and minimality. Though these criteria support our explanation, they also point to remaining gaps in our understanding. Our work provides evidence that a mechanistic understanding of large ML models is feasible, opening opportunities to scale our understanding to both larger models and more complex tasks.

We investigate the internal behavior of Transformer-based Large Language Models (LLMs) when they generate factually incorrect text. We propose modeling factual queries as Constraint Satisfaction Problems and use this framework to investigate how the model interacts internally with factual constraints. Specifically, we discover a strong positive relation between the model's attention to constraint tokens and the factual accuracy of its responses. In our curated suite of 11 datasets with over 40,000 prompts, we study the task of predicting factual errors with the Llama-2 family across all scales (7B, 13B, 70B). We propose SAT Probe, a method probing self-attention patterns, that can predict constraint satisfaction and factual errors, and allows early error identification. The approach and findings demonstrate how using the mechanistic understanding of factuality in LLMs can enhance reliability.

Interpretability provides a toolset for understanding how and why neural networks behave in certain ways. However, there is little unity in the field: most studies employ ad-hoc evaluations and do not share theoretical foundations, making it difficult to measure progress and compare the pros and cons of different techniques. Furthermore, while mechanistic understanding is frequently discussed, the basic causal units underlying these mechanisms are often not explicitly defined. In this paper, we propose a perspective on interpretability research grounded in causal mediation analysis. Specifically, we describe the history and current state of interpretability taxonomized according to the types of causal units (mediators) employed, as well as methods used to search over mediators. We discuss the pros and cons of each mediator, providing insights as to when particular kinds of mediators and search methods are most appropriate depending on the goals of a given study. We argue that this framing yields a more cohesive narrative of the field, as well as actionable insights for future work. Specifically, we recommend a focus on discovering new mediators with better trade-offs between human-interpretability and compute-efficiency, and which can uncover more sophisticated abstractions from neural networks than the primarily linear mediators employed in current work. We also argue for more standardized evaluations that enable principled comparisons across mediator types, such that we can better understand when particular causal units are better suited to particular use cases.

Large language models (LLMs) excel on a variety of reasoning benchmarks, but previous studies suggest they sometimes struggle to generalize to unseen questions, potentially due to over-reliance on memorized training examples. However, the precise conditions under which LLMs switch between reasoning and memorization during text generation remain unclear. In this work, we provide a mechanistic understanding of LLMs' reasoning-memorization dynamics by identifying a set of linear features in the model's residual stream that govern the balance between genuine reasoning and memory recall. These features not only distinguish reasoning tasks from memory-intensive ones but can also be manipulated to causally influence model performance on reasoning tasks. Additionally, we show that intervening in these reasoning features helps the model more accurately activate the most relevant problem-solving capabilities during answer generation. Our findings offer new insights into the underlying mechanisms of reasoning and memory in LLMs and pave the way for the development of more robust and interpretable generative AI systems.

Refusal mechanisms in large language models (LLMs) are essential for ensuring safety. Recent research has revealed that refusal behavior can be mediated by a single direction in activation space, enabling targeted interventions to bypass refusals. While this is primarily demonstrated in an English-centric context, appropriate refusal behavior is important for any language, but poorly understood. In this paper, we investigate the refusal behavior in LLMs across 14 languages using PolyRefuse, a multilingual safety dataset created by translating malicious and benign English prompts into these languages. We uncover the surprising cross-lingual universality of the refusal direction: a vector extracted from English can bypass refusals in other languages with near-perfect effectiveness, without any additional fine-tuning. Even more remarkably, refusal directions derived from any safety-aligned language transfer seamlessly to others. We attribute this transferability to the parallelism of refusal vectors across languages in the embedding space and identify the underlying mechanism behind cross-lingual jailbreaks. These findings provide actionable insights for building more robust multilingual safety defenses and pave the way for a deeper mechanistic understanding of cross-lingual vulnerabilities in LLMs.

Central to our understanding of chemical reactivity is the principle of mass conservation, which is fundamental for ensuring physical consistency, balancing equations, and guiding reaction design. However, data-driven computational models for tasks such as reaction product prediction rarely abide by this most basic constraint. In this work, we recast the problem of reaction prediction as a problem of electron redistribution using the modern deep generative framework of flow matching. Our model, FlowER, overcomes limitations inherent in previous approaches by enforcing exact mass conservation, thereby resolving hallucinatory failure modes, recovering mechanistic reaction sequences for unseen substrate scaffolds, and generalizing effectively to out-of-domain reaction classes with extremely data-efficient fine-tuning. FlowER additionally enables estimation of thermodynamic or kinetic feasibility and manifests a degree of chemical intuition in reaction prediction tasks. This inherently interpretable framework represents a significant step in bridging the gap between predictive accuracy and mechanistic understanding in data-driven reaction outcome prediction.

Despite the growing use of transformer models in computer vision, a mechanistic understanding of these networks is still needed. This work introduces a method to reverse-engineer Vision Transformers trained to solve image classification tasks. Inspired by previous research in NLP, we demonstrate how the inner representations at any level of the hierarchy can be projected onto the learned class embedding space to uncover how these networks build categorical representations for their predictions. We use our framework to show how image tokens develop class-specific representations that depend on attention mechanisms and contextual information, and give insights on how self-attention and MLP layers differentially contribute to this categorical composition. We additionally demonstrate that this method (1) can be used to determine the parts of an image that would be important for detecting the class of interest, and (2) exhibits significant advantages over traditional linear probing approaches. Taken together, our results position our proposed framework as a powerful tool for mechanistic interpretability and explainability research.

Language models learn a great quantity of factual information during pretraining, and recent work localizes this information to specific model weights like mid-layer MLP weights. In this paper, we find that we can change how a fact is stored in a model by editing weights that are in a different location than where existing methods suggest that the fact is stored. This is surprising because we would expect that localizing facts to specific model parameters would tell us where to manipulate knowledge in models, and this assumption has motivated past work on model editing methods. Specifically, we show that localization conclusions from representation denoising (also known as Causal Tracing) do not provide any insight into which model MLP layer would be best to edit in order to override an existing stored fact with a new one. This finding raises questions about how past work relies on Causal Tracing to select which model layers to edit. Next, we consider several variants of the editing problem, including erasing and amplifying facts. For one of our editing problems, editing performance does relate to localization results from representation denoising, but we find that which layer we edit is a far better predictor of performance. Our results suggest, counterintuitively, that better mechanistic understanding of how pretrained language models work may not always translate to insights about how to best change their behavior. Our code is available at https://github.com/google/belief-localization

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general syntax of structural recursion, coupled with two different frameworks for understanding their semantics -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art large language models (LLMs) to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function.

Fine-tuning adapts pretrained models for specific tasks but poses the risk of catastrophic forgetting (CF), where critical knowledge from pretraining is overwritten. To address the issue of CF in a general-purpose framework, we propose Low-damage Knowledge Implanting (LoKI), a parameter-efficient fine-tuning (PEFT) technique that utilizes recent mechanistic understanding of how knowledge is stored in transformer architectures. We compare LoKI against state-of-the-art PEFT methods in two real-world fine-tuning scenarios. The results show that LoKI demonstrates significantly better preservation of general capabilities. At the same time, its task-specific performance is comparable to or even surpasses that of full parameter fine-tuning and these PEFT methods across various model architectures. Our work bridges the mechanistic insights of LLMs' knowledge storage with practical fine-tuning objectives, enabling an effective balance between task-specific adaptation and the retention of general-purpose capabilities.

While large language models based on the transformer architecture have demonstrated remarkable in-context learning (ICL) capabilities, understandings of such capabilities are still in an early stage, where existing theory and mechanistic understanding focus mostly on simple scenarios such as learning simple function classes. This paper takes initial steps on understanding ICL in more complex scenarios, by studying learning with representations. Concretely, we construct synthetic in-context learning problems with a compositional structure, where the label depends on the input through a possibly complex but fixed representation function, composed with a linear function that differs in each instance. By construction, the optimal ICL algorithm first transforms the inputs by the representation function, and then performs linear ICL on top of the transformed dataset. We show theoretically the existence of transformers that approximately implement such algorithms with mild depth and size. Empirically, we find trained transformers consistently achieve near-optimal ICL performance in this setting, and exhibit the desired dissection where lower layers transforms the dataset and upper layers perform linear ICL. Through extensive probing and a new pasting experiment, we further reveal several mechanisms within the trained transformers, such as concrete copying behaviors on both the inputs and the representations, linear ICL capability of the upper layers alone, and a post-ICL representation selection mechanism in a harder mixture setting. These observed mechanisms align well with our theory and may shed light on how transformers perform ICL in more realistic scenarios.

Interpretability can improve the safety, transparency and trust of AI models, which is especially important in healthcare applications where decisions often carry significant consequences. Mechanistic interpretability, particularly through the use of sparse autoencoders (SAEs), offers a promising approach for uncovering human-interpretable features within large transformer-based models. In this study, we apply Matryoshka-SAE to the radiology-specialised multimodal large language model, MAIRA-2, to interpret its internal representations. Using large-scale automated interpretability of the SAE features, we identify a range of clinically relevant concepts - including medical devices (e.g., line and tube placements, pacemaker presence), pathologies such as pleural effusion and cardiomegaly, longitudinal changes and textual features. We further examine the influence of these features on model behaviour through steering, demonstrating directional control over generations with mixed success. Our results reveal practical and methodological challenges, yet they offer initial insights into the internal concepts learned by MAIRA-2 - marking a step toward deeper mechanistic understanding and interpretability of a radiology-adapted multimodal large language model, and paving the way for improved model transparency. We release the trained SAEs and interpretations: https://huggingface.co/microsoft/maira-2-sae.

The transcriptional response to genetic perturbation reveals fundamental insights into complex cellular systems. While current approaches have made progress in predicting genetic perturbation responses, they provide limited biological understanding and cannot systematically refine existing knowledge. Overcoming these limitations requires an end-to-end integration of data-driven learning and existing knowledge. However, this integration is challenging due to inconsistencies between data and knowledge bases, such as noise, misannotation, and incompleteness. To address this challenge, we propose ALIGNED (Adaptive aLignment for Inconsistent Genetic kNowledgE and Data), a neuro-symbolic framework based on the Abductive Learning (ABL) paradigm. This end-to-end framework aligns neural and symbolic components and performs systematic knowledge refinement. We introduce a balanced consistency metric to evaluate the predictions' consistency against both data and knowledge. Our results show that ALIGNED outperforms state-of-the-art methods by achieving the highest balanced consistency, while also re-discovering biologically meaningful knowledge. Our work advances beyond existing methods to enable both the transparency and the evolution of mechanistic biological understanding.

Predicting high-dimensional or extreme multilabels, such as in medical coding, requires both accuracy and interpretability. Existing works often rely on local interpretability methods, failing to provide comprehensive explanations of the overall mechanism behind each label prediction within a multilabel set. We propose a mechanistic interpretability module called DIctionary Label Attention (\method) that disentangles uninterpretable dense embeddings into a sparse embedding space, where each nonzero element (a dictionary feature) represents a globally learned medical concept. Through human evaluations, we show that our sparse embeddings are more human understandable than its dense counterparts by at least 50 percent. Our automated dictionary feature identification pipeline, leveraging large language models (LLMs), uncovers thousands of learned medical concepts by examining and summarizing the highest activating tokens for each dictionary feature. We represent the relationships between dictionary features and medical codes through a sparse interpretable matrix, enhancing the mechanistic and global understanding of the model's predictions while maintaining competitive performance and scalability without extensive human annotation.

The ability of neural networks to represent more features than neurons makes interpreting them challenging. This phenomenon, known as superposition, has spurred efforts to find architectures that are more interpretable than standard multilayer perceptrons (MLPs) with elementwise activation functions. In this note, I examine bilinear layers, which are a type of MLP layer that are mathematically much easier to analyze while simultaneously performing better than standard MLPs. Although they are nonlinear functions of their input, I demonstrate that bilinear layers can be expressed using only linear operations and third order tensors. We can integrate this expression for bilinear layers into a mathematical framework for transformer circuits, which was previously limited to attention-only transformers. These results suggest that bilinear layers are easier to analyze mathematically than current architectures and thus may lend themselves to deeper safety insights by allowing us to talk more formally about circuits in neural networks. Additionally, bilinear layers may offer an alternative path for mechanistic interpretability through understanding the mechanisms of feature construction instead of enumerating a (potentially exponentially) large number of features in large models.

Spider silks are remarkable materials characterized by superb mechanical properties such as strength, extensibility and lightweightedness. Yet, to date, limited models are available to fully explore sequence-property relationships for analysis and design. Here we propose a custom generative large-language model to enable design of novel spider silk protein sequences to meet complex combinations of target mechanical properties. The model, pretrained on a large set of protein sequences, is fine-tuned on ~1,000 major ampullate spidroin (MaSp) sequences for which associated fiber-level mechanical properties exist, to yield an end-to-end forward and inverse generative strategy. Performance is assessed through: (1), a novelty analysis and protein type classification for generated spidroin sequences through BLAST searches, (2) property evaluation and comparison with similar sequences, (3) comparison of molecular structures, as well as, and (4) a detailed sequence motif analyses. We generate silk sequences with property combinations that do not exist in nature, and develop a deep understanding the mechanistic roles of sequence patterns in achieving overarching key mechanical properties (elastic modulus, strength, toughness, failure strain). The model provides an efficient approach to expand the silkome dataset, facilitating further sequence-structure analyses of silks, and establishes a foundation for synthetic silk design and optimization.

Understanding the mechanisms behind Large Language Models (LLMs) is crucial for designing improved models and strategies. While recent studies have yielded valuable insights into the mechanisms of textual LLMs, the mechanisms of Multi-modal Large Language Models (MLLMs) remain underexplored. In this paper, we apply mechanistic interpretability methods to analyze the visual question answering (VQA) mechanisms in the first MLLM, Llava. We compare the mechanisms between VQA and textual QA (TQA) in color answering tasks and find that: a) VQA exhibits a mechanism similar to the in-context learning mechanism observed in TQA; b) the visual features exhibit significant interpretability when projecting the visual embeddings into the embedding space; and c) Llava enhances the existing capabilities of the corresponding textual LLM Vicuna during visual instruction tuning. Based on these findings, we develop an interpretability tool to help users and researchers identify important visual locations for final predictions, aiding in the understanding of visual hallucination. Our method demonstrates faster and more effective results compared to existing interpretability approaches. Code: https://github.com/zepingyu0512/llava-mechanism

Understanding how features evolve across layers in deep neural networks is a fundamental challenge in mechanistic interpretability, particularly due to polysemanticity and feature superposition. While Sparse Autoencoders (SAEs) have been used to extract interpretable features from individual layers, aligning these features across layers has remained an open problem. In this paper, we introduce SAE Match, a novel, data-free method for aligning SAE features across different layers of a neural network. Our approach involves matching features by minimizing the mean squared error between the folded parameters of SAEs, a technique that incorporates activation thresholds into the encoder and decoder weights to account for differences in feature scales. Through extensive experiments on the Gemma 2 language model, we demonstrate that our method effectively captures feature evolution across layers, improving feature matching quality. We also show that features persist over several layers and that our approach can approximate hidden states across layers. Our work advances the understanding of feature dynamics in neural networks and provides a new tool for mechanistic interpretability studies.

The integration of Rotary Position Embedding (RoPE) in Multimodal Diffusion Transformer (MMDiT) has significantly enhanced text-to-image generation quality. However, the fundamental reliance of self-attention layers on positional embedding versus query-key similarity during generation remains an intriguing question. We present the first mechanistic analysis of RoPE-based MMDiT models (e.g., FLUX), introducing an automated probing strategy that disentangles positional information versus content dependencies by strategically manipulating RoPE during generation. Our analysis reveals distinct dependency patterns that do not straightforwardly correlate with depth, offering new insights into the layer-specific roles in RoPE-based MMDiT. Based on these findings, we propose a training-free, task-specific image editing framework that categorizes editing tasks into three types: position-dependent editing (e.g., object addition), content similarity-dependent editing (e.g., non-rigid editing), and region-preserved editing (e.g., background replacement). For each type, we design tailored key-value injection strategies based on the characteristics of the editing task. Extensive qualitative and quantitative evaluations demonstrate that our method outperforms state-of-the-art approaches, particularly in preserving original semantic content and achieving seamless modifications.

Large Language Models (LLMs) have demonstrated unprecedented capabilities across various natural language processing tasks. Their ability to process and generate viable text and code has made them ubiquitous in many fields, while their deployment as knowledge bases and "reasoning" tools remains an area of ongoing research. In geography, a growing body of literature has been focusing on evaluating LLMs' geographical knowledge and their ability to perform spatial reasoning. However, very little is still known about the internal functioning of these models, especially about how they process geographical information. In this chapter, we establish a novel framework for the study of geospatial mechanistic interpretability - using spatial analysis to reverse engineer how LLMs handle geographical information. Our aim is to advance our understanding of the internal representations that these complex models generate while processing geographical information - what one might call "how LLMs think about geographic information" if such phrasing was not an undue anthropomorphism. We first outline the use of probing in revealing internal structures within LLMs. We then introduce the field of mechanistic interpretability, discussing the superposition hypothesis and the role of sparse autoencoders in disentangling polysemantic internal representations of LLMs into more interpretable, monosemantic features. In our experiments, we use spatial autocorrelation to show how features obtained for placenames display spatial patterns related to their geographic location and can thus be interpreted geospatially, providing insights into how these models process geographical information. We conclude by discussing how our framework can help shape the study and use of foundation models in geography.

Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for behavioral studies. However, these studies do not provide insights into the internal mechanisms driving the observed capabilities. To improve our understanding of the internal mechanisms of transformers, we present a comprehensive mechanistic analysis of a transformer trained on a synthetic reasoning task. We identify a set of interpretable mechanisms the model uses to solve the task, and validate our findings using correlational and causal evidence. Our results suggest that it implements a depth-bounded recurrent mechanisms that operates in parallel and stores intermediate results in selected token positions. We anticipate that the motifs we identified in our synthetic setting can provide valuable insights into the broader operating principles of transformers and thus provide a basis for understanding more complex models.

Mathematical reasoning in large language models (LMs) has garnered significant attention in recent work, but there is a limited understanding of how these models process and store information related to arithmetic tasks within their architecture. In order to improve our understanding of this aspect of language models, we present a mechanistic interpretation of Transformer-based LMs on arithmetic questions using a causal mediation analysis framework. By intervening on the activations of specific model components and measuring the resulting changes in predicted probabilities, we identify the subset of parameters responsible for specific predictions. This provides insights into how information related to arithmetic is processed by LMs. Our experimental results indicate that LMs process the input by transmitting the information relevant to the query from mid-sequence early layers to the final token using the attention mechanism. Then, this information is processed by a set of MLP modules, which generate result-related information that is incorporated into the residual stream. To assess the specificity of the observed activation dynamics, we compare the effects of different model components on arithmetic queries with other tasks, including number retrieval from prompts and factual knowledge questions.

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

Text-to-image (T2I) diffusion models rely on encoded prompts to guide the image generation process. Typically, these prompts are extended to a fixed length by adding padding tokens before text encoding. Despite being a default practice, the influence of padding tokens on the image generation process has not been investigated. In this work, we conduct the first in-depth analysis of the role padding tokens play in T2I models. We develop two causal techniques to analyze how information is encoded in the representation of tokens across different components of the T2I pipeline. Using these techniques, we investigate when and how padding tokens impact the image generation process. Our findings reveal three distinct scenarios: padding tokens may affect the model's output during text encoding, during the diffusion process, or be effectively ignored. Moreover, we identify key relationships between these scenarios and the model's architecture (cross or self-attention) and its training process (frozen or trained text encoder). These insights contribute to a deeper understanding of the mechanisms of padding tokens, potentially informing future model design and training practices in T2I systems.

Large neural models are increasingly deployed in high-stakes settings, raising concerns about whether their behavior reliably aligns with human values. Interpretability provides a route to internal transparency by revealing the computations that drive outputs. We argue that interpretability especially mechanistic approaches should be treated as a design principle for alignment, not an auxiliary diagnostic tool. Post-hoc methods such as LIME or SHAP offer intuitive but correlational explanations, while mechanistic techniques like circuit tracing or activation patching yield causal insight into internal failures, including deceptive or misaligned reasoning that behavioral methods like RLHF, red teaming, or Constitutional AI may overlook. Despite these advantages, interpretability faces challenges of scalability, epistemic uncertainty, and mismatches between learned representations and human concepts. Our position is that progress on safe and trustworthy AI will depend on making interpretability a first-class objective of AI research and development, ensuring that systems are not only effective but also auditable, transparent, and aligned with human intent.

Understanding training dynamics and feature evolution is crucial for the mechanistic interpretability of large language models (LLMs). Although sparse autoencoders (SAEs) have been used to identify features within LLMs, a clear picture of how these features evolve during training remains elusive. In this study, we: (1) introduce SAE-Track, a novel method to efficiently obtain a continual series of SAEs; (2) mechanistically investigate feature formation and develop a progress measure for it ; and (3) analyze and visualize feature drift during training. Our work provides new insights into the dynamics of features in LLMs, enhancing our understanding of training mechanisms and feature evolution.

Transformers exhibit impressive capabilities but are often regarded as black boxes due to challenges in understanding the complex nonlinear relationships between features. Interpreting machine learning models is of paramount importance to mitigate risks, and mechanistic interpretability is in particular of current interest as it opens up a window for guiding manual modifications and reverse-engineering solutions. In this work, we introduce contextual decomposition for transformers (CD-T), extending a prior work on CD for RNNs and CNNs, to address mechanistic interpretation computationally efficiently. CD-T is a flexible interpretation method for transformers. It can capture contributions of combinations of input features or source internal components (e.g. attention heads, feed-forward networks) to (1) final predictions or (2) the output of any target internal component. Using CD-T, we propose a novel algorithm for circuit discovery. On a real-world pathology report classification task: we show CD-T distills a more faithful circuit of attention heads with improved computational efficiency (speed up 2x) than a prior benchmark, path patching. As a versatile interpretation method, CD-T also exhibits exceptional capabilities for local interpretations. CD-T is shown to reliably find words and phrases of contrasting sentiment/topic on SST-2 and AGNews datasets. Through human experiments, we demonstrate CD-T enables users to identify the more accurate of two models and to better trust a model's outputs compared to alternative interpretation methods such as SHAP and LIME.

Robust tooling and publicly available pre-trained models have helped drive recent advances in mechanistic interpretability for language models. However, similar progress in vision mechanistic interpretability has been hindered by the lack of accessible frameworks and pre-trained weights. We present Prisma (Access the codebase here: https://github.com/Prisma-Multimodal/ViT-Prisma), an open-source framework designed to accelerate vision mechanistic interpretability research, providing a unified toolkit for accessing 75+ vision and video transformers; support for sparse autoencoder (SAE), transcoder, and crosscoder training; a suite of 80+ pre-trained SAE weights; activation caching, circuit analysis tools, and visualization tools; and educational resources. Our analysis reveals surprising findings, including that effective vision SAEs can exhibit substantially lower sparsity patterns than language SAEs, and that in some instances, SAE reconstructions can decrease model loss. Prisma enables new research directions for understanding vision model internals while lowering barriers to entry in this emerging field.

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to gain mechanistic insights into the phenomenon of abrupt learning by studying RNNs trained to perform diverse short-term memory tasks. In these tasks, RNN training begins with an initial search phase. Following a long period of plateau in accuracy, the values of the loss function suddenly drop, indicating abrupt learning. Analyzing the neural computation performed by these RNNs reveals geometric restructuring (GR) in their phase spaces prior to the drop. To promote these GR events, we introduce a temporal consistency regularization that accelerates (bioplausible) training, facilitates attractor formation, and enables efficient learning in strongly connected networks. Our findings offer testable predictions for neuroscientists and emphasize the need for goal-agnostic secondary mechanisms to facilitate learning in biological and artificial networks.

Large language models (LLMs) have made remarkable progress in various domains, yet they often suffer from repetitive text generation, a phenomenon we refer to as the "Repeat Curse". While previous studies have proposed decoding strategies to mitigate repetition, the underlying mechanism behind this issue remains insufficiently explored. In this work, we investigate the root causes of repetition in LLMs through the lens of mechanistic interpretability. Inspired by recent advances in Sparse Autoencoders (SAEs), which enable monosemantic feature extraction, we propose a novel approach, "Duplicatus Charm", to induce and analyze the Repeat Curse. Our method systematically identifies "Repetition Features" -the key model activations responsible for generating repetitive outputs. First, we locate the layers most involved in repetition through logit analysis. Next, we extract and stimulate relevant features using SAE-based activation manipulation. To validate our approach, we construct a repetition dataset covering token and paragraph level repetitions and introduce an evaluation pipeline to quantify the influence of identified repetition features. Furthermore, by deactivating these features, we have effectively mitigated the Repeat Curse.

Compositional relational reasoning (CRR) is a hallmark of human intelligence, but we lack a clear understanding of whether and how existing transformer large language models (LLMs) can solve CRR tasks. To enable systematic exploration of the CRR capability of LLMs, we first propose a new synthetic benchmark called Generalized Associative Recall (GAR) by integrating and generalizing the essence of several tasks in mechanistic interpretability (MI) study in a unified framework. Evaluation shows that GAR is challenging enough for existing LLMs, revealing their fundamental deficiency in CRR. Meanwhile, it is easy enough for systematic MI study. Then, to understand how LLMs solve GAR tasks, we use attribution patching to discover the core circuits reused by Vicuna-33B across different tasks and a set of vital attention heads. Intervention experiments show that the correct functioning of these heads significantly impacts task performance. Especially, we identify two classes of heads whose activations represent the abstract notion of true and false in GAR tasks respectively. They play a fundamental role in CRR across various models and tasks. The dataset and code are available at https://github.com/Caiyun-AI/GAR.

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. Despite the significant gain in performance achieved via these protocols, the underlying mechanisms of stepwise inference have remained elusive. To address this, we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. Despite is simplicity, we find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy tradeoff in model generations as sampling temperature varies; (iii) a simplicity bias in the model's output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.

Modern language models can imitate complex patterns through few-shot learning, enabling them to complete challenging tasks without fine-tuning. However, imitation can also lead models to reproduce inaccuracies or harmful content if present in the context. We study harmful imitation through the lens of a model's internal representations, and identify two related phenomena: "overthinking" and "false induction heads". The first phenomenon, overthinking, appears when we decode predictions from intermediate layers, given correct vs. incorrect few-shot demonstrations. At early layers, both demonstrations induce similar model behavior, but the behavior diverges sharply at some "critical layer", after which the accuracy given incorrect demonstrations progressively decreases. The second phenomenon, false induction heads, are a possible mechanistic cause of overthinking: these are heads in late layers that attend to and copy false information from previous demonstrations, and whose ablation reduces overthinking. Beyond scientific understanding, our results suggest that studying intermediate model computations could be a promising avenue for understanding and guarding against harmful model behaviors.

The mechanisms by which reasoning training reshapes LLMs' internal computations remain unclear. We study lightweight steering vectors inserted into the base model's residual stream and trained with a reinforcement-learning objective. These vectors match full fine-tuning performance while preserving the interpretability of small, additive interventions. Using logit-lens readouts and path-patching analyses on two models, we find that (i) the last-layer steering vector acts like a token-substitution bias concentrated on the first generated token, consistently boosting tokens such as "To" and "Step"; (ii) the penultimate-layer vector leaves attention patterns largely intact and instead operates through the MLP and unembedding, preferentially up-weighting process words and structure symbols; and (iii) middle layers de-emphasize non-English tokens. Next, we show that a SAE isolates features associated with correct generations. We also show that steering vectors (i) transfer to other models, (ii) combine across layers when trained in isolation, and (iii) concentrate magnitude on meaningful prompt segments under adaptive token-wise scaling. Taken together, these results deepen understanding of how trained steering vectors shape computation and should inform future work in activation engineering and the study of reasoning models.

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns: a diagonal and homogeneous pattern in the key-query (KQ) weights, and a last-entry-only and zero-sum pattern in the output-value (OV) weights. Remarkably, these patterns consistently appear from gradient-based training starting from random initialization. Our analysis reveals that such emergent structures enable multi-head attention to approximately implement a debiased gradient descent predictor -- one that outperforms single-head attention and nearly achieves Bayesian optimality up to proportional factor. Furthermore, compared to linear transformers, the softmax attention readily generalizes to sequences longer than those seen during training. We also extend our study to scenarios with non-isotropic covariates and multi-task linear regression. In the former, multi-head attention learns to implement a form of pre-conditioned gradient descent. In the latter, we uncover an intriguing regime where the interplay between head number and task number triggers a superposition phenomenon that efficiently resolves multi-task in-context learning. Our results reveal that in-context learning ability emerges from the trained transformer as an aggregated effect of its architecture and the underlying data distribution, paving the way for deeper understanding and broader applications of in-context learning.

Layer-wise normalization (LN) is an essential component of virtually all transformer-based large language models. While its effects on training stability are well documented, its role at inference time is poorly understood. Additionally, LN layers hinder mechanistic interpretability by introducing additional nonlinearities and increasing the interconnectedness of individual model components. Here, we show that all LN layers can be removed from every GPT-2 model with only a small increase in validation loss (e.g. +0.03 cross-entropy loss for GPT-2 XL). Thus, LN cannot play a substantial role in language modeling. We find that the amount of fine-tuning data needed for LN removal grows sublinearly with model parameters, suggesting scaling to larger models is feasible. We release a suite of LN-free GPT-2 models on Hugging Face. Furthermore, we test interpretability techniques on LN-free models. Direct logit attribution now gives the exact direct effect of individual components, while the accuracy of attribution patching does not significantly improve. We also confirm that GPT-2's "confidence neurons" are inactive in the LN-free models. Our work clarifies the role of LN layers in language modeling, showing that GPT-2-class models can function without LN layers. We hope that our LN-free analogs of the GPT-2 family of models will enable more precise interpretability research and improve our understanding of language models.

In-context learning is a powerful emergent ability in transformer models. Prior work in mechanistic interpretability has identified a circuit element that may be critical for in-context learning -- the induction head (IH), which performs a match-and-copy operation. During training of large transformers on natural language data, IHs emerge around the same time as a notable phase change in the loss. Despite the robust evidence for IHs and this interesting coincidence with the phase change, relatively little is known about the diversity and emergence dynamics of IHs. Why is there more than one IH, and how are they dependent on each other? Why do IHs appear all of a sudden, and what are the subcircuits that enable them to emerge? We answer these questions by studying IH emergence dynamics in a controlled setting by training on synthetic data. In doing so, we develop and share a novel optogenetics-inspired causal framework for modifying activations throughout training. Using this framework, we delineate the diverse and additive nature of IHs. By clamping subsets of activations throughout training, we then identify three underlying subcircuits that interact to drive IH formation, yielding the phase change. Furthermore, these subcircuits shed light on data-dependent properties of formation, such as phase change timing, already showing the promise of this more in-depth understanding of subcircuits that need to "go right" for an induction head.

Mechanistic Interpretability (MI) promises a path toward fully understanding how neural networks make their predictions. Prior work demonstrates that even when trained to perform simple arithmetic, models can implement a variety of algorithms (sometimes concurrently) depending on initialization and hyperparameters. Does this mean neuron-level interpretability techniques have limited applicability? We argue that high-dimensional neural networks can learn low-dimensional representations of their training data that are useful beyond simply making good predictions. Such representations can be understood through the mechanistic interpretability lens and provide insights that are surprisingly faithful to human-derived domain knowledge. This indicates that such approaches to interpretability can be useful for deriving a new understanding of a problem from models trained to solve it. As a case study, we extract nuclear physics concepts by studying models trained to reproduce nuclear data.

Understanding the decision-making processes of neural networks is a central goal of mechanistic interpretability. In the context of Large Language Models (LLMs), this involves uncovering the underlying mechanisms and identifying the roles of individual model components such as neurons and attention heads, as well as model abstractions such as the learned sparse features extracted by Sparse Autoencoders (SAEs). A rapidly growing line of work tackles this challenge by using powerful generator models to produce open-vocabulary, natural language concept descriptions for these components. In this paper, we provide the first survey of the emerging field of concept descriptions for model components and abstractions. We chart the key methods for generating these descriptions, the evolving landscape of automated and human metrics for evaluating them, and the datasets that underpin this research. Our synthesis reveals a growing demand for more rigorous, causal evaluation. By outlining the state of the art and identifying key challenges, this survey provides a roadmap for future research toward making models more transparent.

The greatest ambition of mechanistic interpretability is to completely rewrite deep neural networks in a format that is more amenable to human understanding, while preserving their behavior and performance. In this paper, we attempt to partially rewrite a large language model using simple natural language explanations. We first approximate one of the feedforward networks in the LLM with a wider MLP with sparsely activating neurons - a transcoder - and use an automated interpretability pipeline to generate explanations for these neurons. We then replace the first layer of this sparse MLP with an LLM-based simulator, which predicts the activation of each neuron given its explanation and the surrounding context. Finally, we measure the degree to which these modifications distort the model's final output. With our pipeline, the model's increase in loss is statistically similar to entirely replacing the sparse MLP output with the zero vector. We employ the same protocol, this time using a sparse autoencoder, on the residual stream of the same layer and obtain similar results. These results suggest that more detailed explanations are needed to improve performance substantially above the zero ablation baseline.

Large language models (LLMs) trained on huge corpora of text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often mysterious, and different prompts can elicit different capabilities through in-context learning. We propose a framework that enables us to analyze in-context learning dynamics to understand latent concepts underlying LLMs' behavioral patterns. This provides a more nuanced understanding than success-or-failure evaluation benchmarks, but does not require observing internal activations as a mechanistic interpretation of circuits would. Inspired by the cognitive science of human randomness perception, we use random binary sequences as context and study dynamics of in-context learning by manipulating properties of context data, such as sequence length. In the latest GPT-3.5+ models, we find emergent abilities to generate seemingly random numbers and learn basic formal languages, with striking in-context learning dynamics where model outputs transition sharply from seemingly random behaviors to deterministic repetition.

As artificial intelligence models have exploded in scale and capability, understanding of their internal mechanisms remains a critical challenge. Inspired by the success of dynamical systems approaches in neuroscience, here we propose a novel framework for studying computations in deep learning systems. We focus on the residual stream (RS) in transformer models, conceptualizing it as a dynamical system evolving across layers. We find that activations of individual RS units exhibit strong continuity across layers, despite the RS being a non-privileged basis. Activations in the RS accelerate and grow denser over layers, while individual units trace unstable periodic orbits. In reduced-dimensional spaces, the RS follows a curved trajectory with attractor-like dynamics in the lower layers. These insights bridge dynamical systems theory and mechanistic interpretability, establishing a foundation for a "neuroscience of AI" that combines theoretical rigor with large-scale data analysis to advance our understanding of modern neural networks.

The fundamental units of internal representations in large language models (LLMs) remain undefined, limiting further understanding of their mechanisms. Neurons or features are often regarded as such units, yet neurons suffer from polysemy, while features face concerns of unreliable reconstruction and instability. To address this issue, we propose the Atoms Theory, which defines such units as atoms. We introduce the atomic inner product (AIP) to correct representation shifting, formally define atoms, and prove the conditions that atoms satisfy the Restricted Isometry Property (RIP), ensuring stable sparse representations over atom set and linking to compressed sensing. Under stronger conditions, we further establish the uniqueness and exact ell_1 recoverability of the sparse representations, and provide guarantees that single-layer sparse autoencoders (SAEs) with threshold activations can reliably identify the atoms. To validate the Atoms Theory, we train threshold-activated SAEs on Gemma2-2B, Gemma2-9B, and Llama3.1-8B, achieving 99.9% sparse reconstruction across layers on average, and more than 99.8% of atoms satisfy the uniqueness condition, compared to 0.5% for neurons and 68.2% for features, showing that atoms more faithfully capture intrinsic representations of LLMs. Scaling experiments further reveal the link between SAEs size and recovery capacity. Overall, this work systematically introduces and validates Atoms Theory of LLMs, providing a theoretical framework for understanding internal representations and a foundation for mechanistic interpretability. Code available at https://github.com/ChenhuiHu/towards_atoms.

Mechanistic interpretability aims to understand the computational mechanisms underlying neural networks' capabilities in order to accomplish concrete scientific and engineering goals. Progress in this field thus promises to provide greater assurance over AI system behavior and shed light on exciting scientific questions about the nature of intelligence. Despite recent progress toward these goals, there are many open problems in the field that require solutions before many scientific and practical benefits can be realized: Our methods require both conceptual and practical improvements to reveal deeper insights; we must figure out how best to apply our methods in pursuit of specific goals; and the field must grapple with socio-technical challenges that influence and are influenced by our work. This forward-facing review discusses the current frontier of mechanistic interpretability and the open problems that the field may benefit from prioritizing.

Mechanistic interpretability seeks to understand the internal mechanisms of machine learning models, where localization -- identifying the important model components -- is a key step. Activation patching, also known as causal tracing or interchange intervention, is a standard technique for this task (Vig et al., 2020), but the literature contains many variants with little consensus on the choice of hyperparameters or methodology. In this work, we systematically examine the impact of methodological details in activation patching, including evaluation metrics and corruption methods. In several settings of localization and circuit discovery in language models, we find that varying these hyperparameters could lead to disparate interpretability results. Backed by empirical observations, we give conceptual arguments for why certain metrics or methods may be preferred. Finally, we provide recommendations for the best practices of activation patching going forwards.

Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features, often hypothesized to manifest as low-dimensional subspaces of activations. Specifically, recent studies have explored subspace interventions (such as activation patching) as a way to simultaneously manipulate model behavior and attribute the features behind it to given subspaces. In this work, we demonstrate that these two aims diverge, potentially leading to an illusory sense of interpretability. Counterintuitively, even if a subspace intervention makes the model's output behave as if the value of a feature was changed, this effect may be achieved by activating a dormant parallel pathway leveraging another subspace that is causally disconnected from model outputs. We demonstrate this phenomenon in a distilled mathematical example, in two real-world domains (the indirect object identification task and factual recall), and present evidence for its prevalence in practice. In the context of factual recall, we further show a link to rank-1 fact editing, providing a mechanistic explanation for previous work observing an inconsistency between fact editing performance and fact localization. However, this does not imply that activation patching of subspaces is intrinsically unfit for interpretability. To contextualize our findings, we also show what a success case looks like in a task (indirect object identification) where prior manual circuit analysis informs an understanding of the location of a feature. We explore the additional evidence needed to argue that a patched subspace is faithful.

Mechanistic interpretability aims to understand the behavior of neural networks by reverse-engineering their internal computations. However, current methods struggle to find clear interpretations of neural network activations because a decomposition of activations into computational features is missing. Individual neurons or model components do not cleanly correspond to distinct features or functions. We present a novel interpretability method that aims to overcome this limitation by transforming the activations of the network into a new basis - the Local Interaction Basis (LIB). LIB aims to identify computational features by removing irrelevant activations and interactions. Our method drops irrelevant activation directions and aligns the basis with the singular vectors of the Jacobian matrix between adjacent layers. It also scales features based on their importance for downstream computation, producing an interaction graph that shows all computationally-relevant features and interactions in a model. We evaluate the effectiveness of LIB on modular addition and CIFAR-10 models, finding that it identifies more computationally-relevant features that interact more sparsely, compared to principal component analysis. However, LIB does not yield substantial improvements in interpretability or interaction sparsity when applied to language models. We conclude that LIB is a promising theory-driven approach for analyzing neural networks, but in its current form is not applicable to large language models.

Mechanistic interpretability is the program of explaining what AI systems are doing in terms of their internal mechanisms. I analyze some aspects of the program, along with setting out some concrete challenges and assessing progress to date. I argue for the importance of propositional interpretability, which involves interpreting a system's mechanisms and behavior in terms of propositional attitudes: attitudes (such as belief, desire, or subjective probability) to propositions (e.g. the proposition that it is hot outside). Propositional attitudes are the central way that we interpret and explain human beings and they are likely to be central in AI too. A central challenge is what I call thought logging: creating systems that log all of the relevant propositional attitudes in an AI system over time. I examine currently popular methods of interpretability (such as probing, sparse auto-encoders, and chain of thought methods) as well as philosophical methods of interpretation (including those grounded in psychosemantics) to assess their strengths and weaknesses as methods of propositional interpretability.

Gradient descent is the method of choice for training large artificial intelligence systems. As these systems become larger, a better understanding of the mechanisms behind gradient training would allow us to alleviate compute costs and help steer these systems away from harmful behaviors. To that end, we suggest utilizing the circuit perspective brought forward by mechanistic interpretability. After laying out our intuition, we illustrate how it enables us to design a curriculum for efficient learning in a controlled setting. The code is available at https://github.com/facebookresearch/pal.

Mechanistic Interpretability aims to reverse engineer the algorithms implemented by neural networks by studying their weights and activations. An obstacle to reverse engineering neural networks is that many of the parameters inside a network are not involved in the computation being implemented by the network. These degenerate parameters may obfuscate internal structure. Singular learning theory teaches us that neural network parameterizations are biased towards being more degenerate, and parameterizations with more degeneracy are likely to generalize further. We identify 3 ways that network parameters can be degenerate: linear dependence between activations in a layer; linear dependence between gradients passed back to a layer; ReLUs which fire on the same subset of datapoints. We also present a heuristic argument that modular networks are likely to be more degenerate, and we develop a metric for identifying modules in a network that is based on this argument. We propose that if we can represent a neural network in a way that is invariant to reparameterizations that exploit the degeneracies, then this representation is likely to be more interpretable, and we provide some evidence that such a representation is likely to have sparser interactions. We introduce the Interaction Basis, a tractable technique to obtain a representation that is invariant to degeneracies from linear dependence of activations or Jacobians.

Recent work has shown that language models (LMs) have strong multi-step (i.e., procedural) reasoning capabilities. However, it is unclear whether LMs perform these tasks by cheating with answers memorized from pretraining corpus, or, via a multi-step reasoning mechanism. In this paper, we try to answer this question by exploring a mechanistic interpretation of LMs for multi-step reasoning tasks. Concretely, we hypothesize that the LM implicitly embeds a reasoning tree resembling the correct reasoning process within it. We test this hypothesis by introducing a new probing approach (called MechanisticProbe) that recovers the reasoning tree from the model's attention patterns. We use our probe to analyze two LMs: GPT-2 on a synthetic task (k-th smallest element), and LLaMA on two simple language-based reasoning tasks (ProofWriter & AI2 Reasoning Challenge). We show that MechanisticProbe is able to detect the information of the reasoning tree from the model's attentions for most examples, suggesting that the LM indeed is going through a process of multi-step reasoning within its architecture in many cases.

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems.

Transformer-based language models excel at both recall (retrieving memorized facts) and reasoning (performing multi-step inference), but whether these abilities rely on distinct internal mechanisms remains unclear. Distinguishing recall from reasoning is crucial for predicting model generalization, designing targeted evaluations, and building safer interventions that affect one ability without disrupting the other.We approach this question through mechanistic interpretability, using controlled datasets of synthetic linguistic puzzles to probe transformer models at the layer, head, and neuron level. Our pipeline combines activation patching and structured ablations to causally measure component contributions to each task type. Across two model families (Qwen and LLaMA), we find that interventions on distinct layers and attention heads lead to selective impairments: disabling identified "recall circuits" reduces fact-retrieval accuracy by up to 15\% while leaving reasoning intact, whereas disabling "reasoning circuits" reduces multi-step inference by a comparable margin. At the neuron level, we observe task-specific firing patterns, though these effects are less robust, consistent with neuronal polysemanticity.Our results provide the first causal evidence that recall and reasoning rely on separable but interacting circuits in transformer models. These findings advance mechanistic interpretability by linking circuit-level structure to functional specialization and demonstrate how controlled datasets and causal interventions can yield mechanistic insights into model cognition, informing safer deployment of large language models.

We study neural network loss landscapes through the lens of mode connectivity, the observation that minimizers of neural networks retrieved via training on a dataset are connected via simple paths of low loss. Specifically, we ask the following question: are minimizers that rely on different mechanisms for making their predictions connected via simple paths of low loss? We provide a definition of mechanistic similarity as shared invariances to input transformations and demonstrate that lack of linear connectivity between two models implies they use dissimilar mechanisms for making their predictions. Relevant to practice, this result helps us demonstrate that naive fine-tuning on a downstream dataset can fail to alter a model's mechanisms, e.g., fine-tuning can fail to eliminate a model's reliance on spurious attributes. Our analysis also motivates a method for targeted alteration of a model's mechanisms, named connectivity-based fine-tuning (CBFT), which we analyze using several synthetic datasets for the task of reducing a model's reliance on spurious attributes.

Methods for knowledge editing and unlearning in large language models seek to edit or remove undesirable knowledge or capabilities without compromising general language modeling performance. This work investigates how mechanistic interpretability -- which, in part, aims to identify model components (circuits) associated to specific interpretable mechanisms that make up a model capability -- can improve the precision and effectiveness of editing and unlearning. We find a stark difference in unlearning and edit robustness when training components localized by different methods. We highlight an important distinction between methods that localize components based primarily on preserving outputs, and those finding high level mechanisms with predictable intermediate states. In particular, localizing edits/unlearning to components associated with the lookup-table mechanism for factual recall 1) leads to more robust edits/unlearning across different input/output formats, and 2) resists attempts to relearn the unwanted information, while also reducing unintended side effects compared to baselines, on both a sports facts dataset and the CounterFact dataset across multiple models. We also find that certain localized edits disrupt the latent knowledge in the model more than any other baselines, making unlearning more robust to various attacks.

Large Language Models (LLMs) display striking surface fluency yet systematically fail at tasks requiring symbolic reasoning, arithmetic accuracy, and logical consistency. This paper offers a structural diagnosis of such failures, revealing a persistent gap between comprehension and competence. Through controlled experiments and architectural analysis, we demonstrate that LLMs often articulate correct principles without reliably applying them--a failure rooted not in knowledge access, but in computational execution. We term this phenomenon the computational split-brain syndrome, where instruction and action pathways are geometrically and functionally dissociated. This core limitation recurs across domains, from mathematical operations to relational inferences, and explains why model behavior remains brittle even under idealized prompting. We argue that LLMs function as powerful pattern completion engines, but lack the architectural scaffolding for principled, compositional reasoning. Our findings delineate the boundary of current LLM capabilities and motivate future models with metacognitive control, principle lifting, and structurally grounded execution. This diagnosis also clarifies why mechanistic interpretability findings may reflect training-specific pattern coordination rather than universal computational principles, and why the geometric separation between instruction and execution pathways suggests limitations in neural introspection and mechanistic analysis.

A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons often encode multiple concepts has motivated a shift toward analyzing directions in activation space. A key question is how to find directions that capture interpretable features in an unsupervised manner. Current methods rely on dictionary learning with sparse autoencoders (SAEs), commonly trained over residual stream activations to learn directions from scratch. However, SAEs often struggle in causal evaluations and lack intrinsic interpretability, as their learning is not explicitly tied to the computations of the model. Here, we tackle these limitations by directly decomposing MLP activations with semi-nonnegative matrix factorization (SNMF), such that the learned features are (a) sparse linear combinations of co-activated neurons, and (b) mapped to their activating inputs, making them directly interpretable. Experiments on Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs and a strong supervised baseline (difference-in-means) on causal steering, while aligning with human-interpretable concepts. Further analysis reveals that specific neuron combinations are reused across semantically-related features, exposing a hierarchical structure in the MLP's activation space. Together, these results position SNMF as a simple and effective tool for identifying interpretable features and dissecting concept representations in LLMs.

Organic reaction mechanisms are the stepwise elementary reactions by which reactants form intermediates and products, and are fundamental to understanding chemical reactivity and designing new molecules and reactions. Although large language models (LLMs) have shown promise in understanding chemical tasks such as synthesis design, it is unclear to what extent this reflects genuine chemical reasoning capabilities, i.e., the ability to generate valid intermediates, maintain chemical consistency, and follow logically coherent multi-step pathways. We address this by introducing oMeBench, the first large-scale, expert-curated benchmark for organic mechanism reasoning in organic chemistry. It comprises over 10,000 annotated mechanistic steps with intermediates, type labels, and difficulty ratings. Furthermore, to evaluate LLM capability more precisely and enable fine-grained scoring, we propose oMeS, a dynamic evaluation framework that combines step-level logic and chemical similarity. We analyze the performance of state-of-the-art LLMs, and our results show that although current models display promising chemical intuition, they struggle with correct and consistent multi-step reasoning. Notably, we find that using prompting strategy and fine-tuning a specialist model on our proposed dataset increases performance by 50% over the leading closed-source model. We hope that oMeBench will serve as a rigorous foundation for advancing AI systems toward genuine chemical reasoning.

As large language models (LLMs) grow more powerful, concerns around potential harms like toxicity, unfairness, and hallucination threaten user trust. Ensuring beneficial alignment of LLMs with human values through model alignment is thus critical yet challenging, requiring a deeper understanding of LLM behaviors and mechanisms. We propose opening the black box of LLMs through a framework of holistic interpretability encompassing complementary bottom-up and top-down perspectives. The bottom-up view, enabled by mechanistic interpretability, focuses on component functionalities and training dynamics. The top-down view utilizes representation engineering to analyze behaviors through hidden representations. In this paper, we review the landscape around mechanistic interpretability and representation engineering, summarizing approaches, discussing limitations and applications, and outlining future challenges in using these techniques to achieve ethical, honest, and reliable reasoning aligned with human values.

Mechanistic interpretability methods aim to identify the algorithm a neural network implements, but it is difficult to validate such methods when the true algorithm is unknown. This work presents InterpBench, a collection of semi-synthetic yet realistic transformers with known circuits for evaluating these techniques. We train these neural networks using a stricter version of Interchange Intervention Training (IIT) which we call Strict IIT (SIIT). Like the original, SIIT trains neural networks by aligning their internal computation with a desired high-level causal model, but it also prevents non-circuit nodes from affecting the model's output. We evaluate SIIT on sparse transformers produced by the Tracr tool and find that SIIT models maintain Tracr's original circuit while being more realistic. SIIT can also train transformers with larger circuits, like Indirect Object Identification (IOI). Finally, we use our benchmark to evaluate existing circuit discovery techniques.

Interpretability research aims to bridge the gap between empirical success and our scientific understanding of the inner workings of large language models (LLMs). However, most existing research focuses on analyzing a single mechanism, such as how models copy or recall factual knowledge. In this work, we propose a formulation of competition of mechanisms, which focuses on the interplay of multiple mechanisms instead of individual mechanisms and traces how one of them becomes dominant in the final prediction. We uncover how and where mechanisms compete within LLMs using two interpretability methods: logit inspection and attention modification. Our findings show traces of the mechanisms and their competition across various model components and reveal attention positions that effectively control the strength of certain mechanisms. Code: https://github.com/francescortu/comp-mech. Data: https://huggingface.co/datasets/francescortu/comp-mech.

A basic question within the emerging field of mechanistic interpretability is the degree to which neural networks learn the same underlying mechanisms. In other words, are neural mechanisms universal across different models? In this work, we study the universality of individual neurons across GPT2 models trained from different initial random seeds, motivated by the hypothesis that universal neurons are likely to be interpretable. In particular, we compute pairwise correlations of neuron activations over 100 million tokens for every neuron pair across five different seeds and find that 1-5\% of neurons are universal, that is, pairs of neurons which consistently activate on the same inputs. We then study these universal neurons in detail, finding that they usually have clear interpretations and taxonomize them into a small number of neuron families. We conclude by studying patterns in neuron weights to establish several universal functional roles of neurons in simple circuits: deactivating attention heads, changing the entropy of the next token distribution, and predicting the next token to (not) be within a particular set.

Traditional white-box methods for creating adversarial perturbations against LLMs typically rely only on gradient computation from the targeted model, ignoring the internal mechanisms responsible for attack success or failure. Conversely, interpretability studies that analyze these internal mechanisms lack practical applications beyond runtime interventions. We bridge this gap by introducing a novel white-box approach that leverages mechanistic interpretability techniques to craft practical adversarial inputs. Specifically, we first identify acceptance subspaces - sets of feature vectors that do not trigger the model's refusal mechanisms - then use gradient-based optimization to reroute embeddings from refusal subspaces to acceptance subspaces, effectively achieving jailbreaks. This targeted approach significantly reduces computation cost, achieving attack success rates of 80-95\% on state-of-the-art models including Gemma2, Llama3.2, and Qwen2.5 within minutes or even seconds, compared to existing techniques that often fail or require hours of computation. We believe this approach opens a new direction for both attack research and defense development. Furthermore, it showcases a practical application of mechanistic interpretability where other methods are less efficient, which highlights its utility. The code and generated datasets are available at https://github.com/Sckathach/subspace-rerouting.

Activation patching is a popular mechanistic interpretability technique, but has many subtleties regarding how it is applied and how one may interpret the results. We provide a summary of advice and best practices, based on our experience using this technique in practice. We include an overview of the different ways to apply activation patching and a discussion on how to interpret the results. We focus on what evidence patching experiments provide about circuits, and on the choice of metric and associated pitfalls.

Labeling neural network submodules with human-legible descriptions is useful for many downstream tasks: such descriptions can surface failures, guide interventions, and perhaps even explain important model behaviors. To date, most mechanistic descriptions of trained networks have involved small models, narrowly delimited phenomena, and large amounts of human labor. Labeling all human-interpretable sub-computations in models of increasing size and complexity will almost certainly require tools that can generate and validate descriptions automatically. Recently, techniques that use learned models in-the-loop for labeling have begun to gain traction, but methods for evaluating their efficacy are limited and ad-hoc. How should we validate and compare open-ended labeling tools? This paper introduces FIND (Function INterpretation and Description), a benchmark suite for evaluating the building blocks of automated interpretability methods. FIND contains functions that resemble components of trained neural networks, and accompanying descriptions of the kind we seek to generate. The functions are procedurally constructed across textual and numeric domains, and involve a range of real-world complexities, including noise, composition, approximation, and bias. We evaluate new and existing methods that use language models (LMs) to produce code-based and language descriptions of function behavior. We find that an off-the-shelf LM augmented with only black-box access to functions can sometimes infer their structure, acting as a scientist by forming hypotheses, proposing experiments, and updating descriptions in light of new data. However, LM-based descriptions tend to capture global function behavior and miss local corruptions. These results show that FIND will be useful for characterizing the performance of more sophisticated interpretability methods before they are applied to real-world models.

There is a substantial body of literature examining the mathematical reasoning capabilities of large language models (LLMs), particularly their performance on precise arithmetic operations in autoregressive architectures. However, their ability to perform approximate reasoning in informal, fast-paced mathematical operations has received far less attention, especially among non-autoregressive decoder models. Our work addresses this gap by introducing StreetMath, a benchmark designed to evaluate models' approximation abilities under real-world approximation scenarios. We conduct extensive evaluations across different LLM architectures: Qwen3-4B-Instruct-2507, Qwen3-4B-Thinking-2507, Dream-v0-Instruct-7B, Falcon-Mamba-7B-Instruct, and Mamba-GPT-3B. Furthermore, we apply mechanistic interpretability techniques to probe their internal computational states. Our analysis reveals that LLMs generally attempt to compute exact values or invoke external tools even in tasks that call for approximation. Moreover, while models sometimes reach the correct answer in early layers or steps, they still consume more tokens when solving approximation tasks. Additional experiments indicate that exact and approximate arithmetic operations rely on largely separate neural components. Drawing upon research on cognitive psychology, we argue that LLMs do not exhibit cognitive miserliness in the same way humans do in street math settings. We open source our work https://github.com/ctseng777/StreetMath

Universality is a key hypothesis in mechanistic interpretability -- that different models learn similar features and circuits when trained on similar tasks. In this work, we study the universality hypothesis by examining how small neural networks learn to implement group composition. We present a novel algorithm by which neural networks may implement composition for any finite group via mathematical representation theory. We then show that networks consistently learn this algorithm by reverse engineering model logits and weights, and confirm our understanding using ablations. By studying networks of differing architectures trained on various groups, we find mixed evidence for universality: using our algorithm, we can completely characterize the family of circuits and features that networks learn on this task, but for a given network the precise circuits learned -- as well as the order they develop -- are arbitrary.

The chemical reaction recommendation is to select proper reaction condition parameters for chemical reactions, which is pivotal to accelerating chemical science. With the rapid development of large language models (LLMs), there is growing interest in leveraging their reasoning and planning capabilities for reaction condition recommendation. Despite their success, existing methods rarely explain the rationale behind the recommended reaction conditions, limiting their utility in high-stakes scientific workflows. In this work, we propose ChemMAS, a multi-agent system that reframes condition prediction as an evidence-based reasoning task. ChemMAS decomposes the task into mechanistic grounding, multi-channel recall, constraint-aware agentic debate, and rationale aggregation. Each decision is backed by interpretable justifications grounded in chemical knowledge and retrieved precedents. Experiments show that ChemMAS achieves 20-35% gains over domain-specific baselines and outperforms general-purpose LLMs by 10-15% in Top-1 accuracy, while offering falsifiable, human-trustable rationales, which establishes a new paradigm for explainable AI in scientific discovery.

In a recent paper, Erasmus et al. (2021) defend the idea that the ambiguity of the term "explanation" in explainable AI (XAI) can be solved by adopting any of four different extant accounts of explanation in the philosophy of science: the Deductive Nomological, Inductive Statistical, Causal Mechanical, and New Mechanist models. In this chapter, I show that the authors' claim that these accounts can be applied to deep neural networks as they would to any natural phenomenon is mistaken. I also provide a more general argument as to why the notion of explainability as it is currently used in the XAI literature bears little resemblance to the traditional concept of scientific explanation. It would be more fruitful to use the label "understandable AI" to avoid the confusion that surrounds the goal and purposes of XAI. In the second half of the chapter, I argue for a pragmatic conception of understanding that is better suited to play the central role attributed to explanation in XAI. Following Kuorikoski & Ylikoski (2015), the conditions of satisfaction for understanding an ML system are fleshed out in terms of an agent's success in using the system, in drawing correct inferences from it.

Through considerable effort and intuition, several recent works have reverse-engineered nontrivial behaviors of transformer models. This paper systematizes the mechanistic interpretability process they followed. First, researchers choose a metric and dataset that elicit the desired model behavior. Then, they apply activation patching to find which abstract neural network units are involved in the behavior. By varying the dataset, metric, and units under investigation, researchers can understand the functionality of each component. We automate one of the process' steps: to identify the circuit that implements the specified behavior in the model's computational graph. We propose several algorithms and reproduce previous interpretability results to validate them. For example, the ACDC algorithm rediscovered 5/5 of the component types in a circuit in GPT-2 Small that computes the Greater-Than operation. ACDC selected 68 of the 32,000 edges in GPT-2 Small, all of which were manually found by previous work. Our code is available at https://github.com/ArthurConmy/Automatic-Circuit-Discovery.

Circuit analysis of any certain model behavior is a central task in mechanistic interpretability. We introduce our circuit discovery pipeline with Sparse Autoencoders (SAEs) and a variant called Transcoders. With these two modules inserted into the model, the model's computation graph with respect to OV and MLP circuits becomes strictly linear. Our methods do not require linear approximation to compute the causal effect of each node. This fine-grained graph identifies both end-to-end and local circuits accounting for either logits or intermediate features. We can scalably apply this pipeline with a technique called Hierarchical Attribution. We analyze three kinds of circuits in GPT-2 Small: bracket, induction, and Indirect Object Identification circuits. Our results reveal new findings underlying existing discoveries.

For centuries, researchers have sought out ways to connect disparate areas of knowledge. While early scholars (Galileo, da Vinci, etc.) were experts across fields, specialization has taken hold later. With the advent of Artificial Intelligence, we can now explore relationships across areas (e.g., mechanics-biology) or disparate domains (e.g., failure mechanics-art). To achieve this, we use a fine-tuned Large Language Model (LLM), here for a subset of knowledge in multiscale materials failure. The approach includes the use of a general-purpose LLM to distill question-answer pairs from raw sources followed by LLM fine-tuning. The resulting MechGPT LLM foundation model is used in a series of computational experiments to explore its capacity for knowledge retrieval, various language tasks, hypothesis generation, and connecting knowledge across disparate areas. While the model has some ability to recall knowledge from training, we find that LLMs are particularly useful to extract structural insights through Ontological Knowledge Graphs. These interpretable graph structures provide explanatory insights, frameworks for new research questions, and visual representations of knowledge that also can be used in retrieval-augmented generation. Three versions of MechGPT are discussed, featuring different sizes from 13 billion to 70 billion parameters, and reaching context lengths of more than 10,000 tokens. This provides ample capacity for sophisticated retrieval augmented strategies, as well as agent-based modeling where multiple LLMs interact collaboratively and/or adversarially, the incorporation of new data from the literature or web searches, as well as multimodality.

Sparse Autoencoders (SAEs) are a prominent tool in mechanistic interpretability (MI) for decomposing neural network activations into interpretable features. However, the aspiration to identify a canonical set of features is challenged by the observed inconsistency of learned SAE features across different training runs, undermining the reliability and efficiency of MI research. This position paper argues that mechanistic interpretability should prioritize feature consistency in SAEs -- the reliable convergence to equivalent feature sets across independent runs. We propose using the Pairwise Dictionary Mean Correlation Coefficient (PW-MCC) as a practical metric to operationalize consistency and demonstrate that high levels are achievable (0.80 for TopK SAEs on LLM activations) with appropriate architectural choices. Our contributions include detailing the benefits of prioritizing consistency; providing theoretical grounding and synthetic validation using a model organism, which verifies PW-MCC as a reliable proxy for ground-truth recovery; and extending these findings to real-world LLM data, where high feature consistency strongly correlates with the semantic similarity of learned feature explanations. We call for a community-wide shift towards systematically measuring feature consistency to foster robust cumulative progress in MI.

Recent research in mechanistic interpretability has attempted to reverse-engineer Transformer models by carefully inspecting network weights and activations. However, these approaches require considerable manual effort and still fall short of providing complete, faithful descriptions of the underlying algorithms. In this work, we introduce a procedure for training Transformers that are mechanistically interpretable by design. We build on RASP [Weiss et al., 2021], a programming language that can be compiled into Transformer weights. Instead of compiling human-written programs into Transformers, we design a modified Transformer that can be trained using gradient-based optimization and then automatically converted into a discrete, human-readable program. We refer to these models as Transformer Programs. To validate our approach, we learn Transformer Programs for a variety of problems, including an in-context learning task, a suite of algorithmic problems (e.g. sorting, recognizing Dyck languages), and NLP tasks including named entity recognition and text classification. The Transformer Programs can automatically find reasonable solutions, performing on par with standard Transformers of comparable size; and, more importantly, they are easy to interpret. To demonstrate these advantages, we convert Transformers into Python programs and use off-the-shelf code analysis tools to debug model errors and identify the "circuits" used to solve different sub-problems. We hope that Transformer Programs open a new path toward the goal of intrinsically interpretable machine learning.

Interpreting individual neurons or directions in activations space is an important component of mechanistic interpretability. As such, many algorithms have been proposed to automatically produce neuron explanations, but it is often not clear how reliable these explanations are, or which methods produce the best explanations. This can be measured via crowd-sourced evaluations, but they can often be noisy and expensive, leading to unreliable results. In this paper, we carefully analyze the evaluation pipeline and develop a cost-effective and highly accurate crowdsourced evaluation strategy. In contrast to previous human studies that only rate whether the explanation matches the most highly activating inputs, we estimate whether the explanation describes neuron activations across all inputs. To estimate this effectively, we introduce a novel application of importance sampling to determine which inputs are the most valuable to show to raters, leading to around 30x cost reduction compared to uniform sampling. We also analyze the label noise present in crowd-sourced evaluations and propose a Bayesian method to aggregate multiple ratings leading to a further ~5x reduction in number of ratings required for the same accuracy. Finally, we use these methods to conduct a large-scale study comparing the quality of neuron explanations produced by the most popular methods for two different vision models.

Understanding the internal computations of large language models (LLMs) is crucial for aligning them with human values and preventing undesirable behaviors like toxic content generation. However, mechanistic interpretability is hindered by polysemanticity -- where individual neurons respond to multiple, unrelated concepts. While Sparse Autoencoders (SAEs) have attempted to disentangle these features through sparse dictionary learning, they have compromised LLM performance due to reliance on post-hoc reconstruction loss. To address this issue, we introduce Mixture of Monosemantic Experts for Transformers (Monet) architecture, which incorporates sparse dictionary learning directly into end-to-end Mixture-of-Experts pretraining. Our novel expert decomposition method enables scaling the expert count to 262,144 per layer while total parameters scale proportionally to the square root of the number of experts. Our analyses demonstrate mutual exclusivity of knowledge across experts and showcase the parametric knowledge encapsulated within individual experts. Moreover, Monet allows knowledge manipulation over domains, languages, and toxicity mitigation without degrading general performance. Our pursuit of transparent LLMs highlights the potential of scaling expert counts to enhance} mechanistic interpretability and directly resect the internal knowledge to fundamentally adjust} model behavior. The source code and pretrained checkpoints are available at https://github.com/dmis-lab/Monet.

Accurate prediction of atomistic, thermodynamic, and kinetic properties from molecular structures underpins materials innovation. Existing computational and experimental approaches lack the scalability required to efficiently navigate chemical space. Scientific foundation models trained on large unlabeled datasets offer a path toward exploring chemical space across diverse application domains. Here we develop MIST, a family of molecular foundation models with up to an order of magnitude more parameters and data than prior works. Trained using a novel tokenization scheme that comprehensively captures nuclear, electronic, and geometric information, MIST learns from a diverse range of molecules. MIST models have been fine-tuned to predict more than 400 structure -- property relationships and match or exceed state-of-the-art performance across benchmarks spanning physiology, electrochemistry, and quantum chemistry. We demonstrate the ability of these models to solve real-world problems across chemical space, including multiobjective electrolyte solvent screening, olfactory perception mapping, isotope half-life prediction, stereochemical reasoning for chiral organometallic compounds, and binary and multi-component mixture property prediction. Probing MIST models using mechanistic interpretability methods reveals identifiable patterns and trends not explicitly present in the training data, suggesting that the models learn generalizable scientific concepts. We formulate hyperparameter-penalized Bayesian neural scaling laws and use them to reduce the computational cost of model development by an order of magnitude. The methods and findings presented here represent a significant step toward accelerating materials discovery, design, and optimization using foundation models and provide valuable guidance for training compute-optimal scientific foundation models.

Explainability has become an important topic in computer science and artificial intelligence, leading to a subfield called Explainable Artificial Intelligence (XAI). The goal of providing or seeking explanations is to achieve (better) 'understanding' on the part of the explainee. However, what it means to 'understand' is still not clearly defined, and the concept itself is rarely the subject of scientific investigation. This conceptual article aims to present a model of forms of understanding for XAI-explanations and beyond. From an interdisciplinary perspective bringing together computer science, linguistics, sociology, philosophy and psychology, a definition of understanding and its forms, assessment, and dynamics during the process of giving everyday explanations are explored. Two types of understanding are considered as possible outcomes of explanations, namely enabledness, 'knowing how' to do or decide something, and comprehension, 'knowing that' -- both in different degrees (from shallow to deep). Explanations regularly start with shallow understanding in a specific domain and can lead to deep comprehension and enabledness of the explanandum, which we see as a prerequisite for human users to gain agency. In this process, the increase of comprehension and enabledness are highly interdependent. Against the background of this systematization, special challenges of understanding in XAI are discussed.

Large Language Models (LLMs) have transformed natural language processing, yet their internal mechanisms remain largely opaque. Recently, mechanistic interpretability has attracted significant attention from the research community as a means to understand the inner workings of LLMs. Among various mechanistic interpretability approaches, Sparse Autoencoders (SAEs) have emerged as a promising method due to their ability to disentangle the complex, superimposed features within LLMs into more interpretable components. This paper presents a comprehensive survey of SAEs for interpreting and understanding the internal workings of LLMs. Our major contributions include: (1) exploring the technical framework of SAEs, covering basic architecture, design improvements, and effective training strategies; (2) examining different approaches to explaining SAE features, categorized into input-based and output-based explanation methods; (3) discussing evaluation methods for assessing SAE performance, covering both structural and functional metrics; and (4) investigating real-world applications of SAEs in understanding and manipulating LLM behaviors.

We study how rich visual semantic information is represented within various layers and denoising timesteps of different diffusion architectures. We uncover monosemantic interpretable features by leveraging k-sparse autoencoders (k-SAE). We substantiate our mechanistic interpretations via transfer learning using light-weight classifiers on off-the-shelf diffusion models' features. On 4 datasets, we demonstrate the effectiveness of diffusion features for representation learning. We provide in-depth analysis of how different diffusion architectures, pre-training datasets, and language model conditioning impacts visual representation granularity, inductive biases, and transfer learning capabilities. Our work is a critical step towards deepening interpretability of black-box diffusion models. Code and visualizations available at: https://github.com/revelio-diffusion/revelio

Fine-tuning large pre-trained models has become the de facto strategy for developing both task-specific and general-purpose machine learning systems, including developing models that are safe to deploy. Despite its clear importance, there has been minimal work that explains how fine-tuning alters the underlying capabilities learned by a model during pretraining: does fine-tuning yield entirely novel capabilities or does it just modulate existing ones? We address this question empirically in synthetic, controlled settings where we can use mechanistic interpretability tools (e.g., network pruning and probing) to understand how the model's underlying capabilities are changing. We perform an extensive analysis of the effects of fine-tuning in these settings, and show that: (i) fine-tuning rarely alters the underlying model capabilities; (ii) a minimal transformation, which we call a 'wrapper', is typically learned on top of the underlying model capabilities, creating the illusion that they have been modified; and (iii) further fine-tuning on a task where such hidden capabilities are relevant leads to sample-efficient 'revival' of the capability, i.e., the model begins reusing these capability after only a few gradient steps. This indicates that practitioners can unintentionally remove a model's safety wrapper merely by fine-tuning it on a, e.g., superficially unrelated, downstream task. We additionally perform analysis on language models trained on the TinyStories dataset to support our claims in a more realistic setup.

Understanding how Large Language Models (LLMs) perform complex reasoning and their failure mechanisms is a challenge in interpretability research. To provide a measurable geometric analysis perspective, we define the concept of the Reasoning Manifold, a latent low-dimensional geometric structure formed by the internal representations corresponding to all correctly reasoned generations. This structure can be conceptualized as the embodiment of the effective thinking paths that the model has learned to successfully solve a given task. Based on this concept, we build REMA, a framework that explains the origins of failures by quantitatively comparing the spatial relationships of internal model representations corresponding to both erroneous and correct reasoning samples. Specifically, REMA first quantifies the geometric deviation of each erroneous representation by calculating its k-nearest neighbors distance to the approximated manifold formed by correct representations, thereby providing a unified failure signal. It then localizes the divergence points where these deviations first become significant by tracking this deviation metric across the model's layers and comparing it against a baseline of internal fluctuations from correct representations, thus identifying where the reasoning chain begins to go off-track. Our extensive experiments on diverse language and multimodal models and tasks demonstrate the low-dimensional nature of the reasoning manifold and the high separability between erroneous and correct reasoning representations. The results also validate the effectiveness of the REMA framework in analyzing the origins of reasoning failures. This research connects abstract reasoning failures to measurable geometric deviations in representations, providing new avenues for in-depth understanding and diagnosis of the internal computational processes of black-box models.

The concept of causal abstraction got recently popularised to demystify the opaque decision-making processes of machine learning models; in short, a neural network can be abstracted as a higher-level algorithm if there exists a function which allows us to map between them. Notably, most interpretability papers implement these maps as linear functions, motivated by the linear representation hypothesis: the idea that features are encoded linearly in a model's representations. However, this linearity constraint is not required by the definition of causal abstraction. In this work, we critically examine the concept of causal abstraction by considering arbitrarily powerful alignment maps. In particular, we prove that under reasonable assumptions, any neural network can be mapped to any algorithm, rendering this unrestricted notion of causal abstraction trivial and uninformative. We complement these theoretical findings with empirical evidence, demonstrating that it is possible to perfectly map models to algorithms even when these models are incapable of solving the actual task; e.g., on an experiment using randomly initialised language models, our alignment maps reach 100% interchange-intervention accuracy on the indirect object identification task. This raises the non-linear representation dilemma: if we lift the linearity constraint imposed to alignment maps in causal abstraction analyses, we are left with no principled way to balance the inherent trade-off between these maps' complexity and accuracy. Together, these results suggest an answer to our title's question: causal abstraction is not enough for mechanistic interpretability, as it becomes vacuous without assumptions about how models encode information. Studying the connection between this information-encoding assumption and causal abstraction should lead to exciting future work.

A key goal in mechanistic interpretability is circuit analysis: finding sparse subgraphs of models corresponding to specific behaviors or capabilities. However, MLP sublayers make fine-grained circuit analysis on transformer-based language models difficult. In particular, interpretable features -- such as those found by sparse autoencoders (SAEs) -- are typically linear combinations of extremely many neurons, each with its own nonlinearity to account for. Circuit analysis in this setting thus either yields intractably large circuits or fails to disentangle local and global behavior. To address this we explore transcoders, which seek to faithfully approximate a densely activating MLP layer with a wider, sparsely-activating MLP layer. We successfully train transcoders on language models with 120M, 410M, and 1.4B parameters, and find them to perform at least on par with SAEs in terms of sparsity, faithfulness, and human-interpretability. We then introduce a novel method for using transcoders to perform weights-based circuit analysis through MLP sublayers. The resulting circuits neatly factorize into input-dependent and input-invariant terms. Finally, we apply transcoders to reverse-engineer unknown circuits in the model, and we obtain novel insights regarding the greater-than circuit in GPT2-small. Our results suggest that transcoders can prove effective in decomposing model computations involving MLPs into interpretable circuits. Code is available at https://github.com/jacobdunefsky/transcoder_circuits.

Mechanical reasoning is a hallmark of human intelligence, defined by its ubiquitous yet irreplaceable role in human activities ranging from routine tasks to civil engineering. Embedding machines with mechanical reasoning is therefore an important step towards building human-level artificial intelligence. Here, we leveraged 155 cognitive experiments to test the understanding of system stability, gears and pulley systems, leverage principle, inertia and motion, and fluid mechanics in 26 Vision Language Models (VLMs). Results indicate that VLMs consistently perform worse than humans on all domains, while demonstrate significant difficulty in reasoning about gear systems and fluid mechanics. Notably, their performance on these tasks do not improve as number of parameters increase, suggesting that current attention-based architecture may fail to grasp certain underlying mechanisms required for mechanical reasoning, particularly those pertaining to mental simulations.

Understanding molecules is key to understanding organisms and driving advances in drug discovery, requiring interdisciplinary knowledge across chemistry and biology. Although large molecular language models have achieved notable success in interpreting molecular structures, their instruction datasets are limited to the specific knowledge from task-oriented datasets and do not fully cover the fundamental characteristics of molecules, hindering their abilities as general-purpose molecular assistants. To address this issue, we propose Mol-LLaMA, a large molecular language model that grasps the general knowledge centered on molecules via multi-modal instruction tuning. To this end, we design key data types that encompass the fundamental features of molecules, incorporating essential knowledge from molecular structures. In addition, to improve understanding of molecular features, we introduce a module that integrates complementary information from different molecular encoders, leveraging the distinct advantages of different molecular representations. Our experimental results demonstrate that Mol-LLaMA is capable of comprehending the general features of molecules and generating relevant responses to users' queries with detailed explanations, implying its potential as a general-purpose assistant for molecular analysis.

Large Language Models(LLMs) have demonstrated remarkable performance across various domains, yet their capabilities in molecular reasoning remain insufficiently explored. Current approaches tend to rely heavily on general-purpose prompting, which lacks domain-specific molecular semantics, while those that use fine-tuning strategies often face challenges with interpretability and reasoning depth. To address these issues, we introduce MolReasoner, a two-stage framework designed to transition LLMs from memorization towards chemical reasoning. First, we propose Mol-SFT, which initializes the model's reasoning abilities via synthetic Chain-of-Thought(CoT) samples generated by GPT-4o and verified for chemical accuracy. Subsequently, Mol-RL applies reinforcement learning with specialized reward functions designed explicitly to align chemical structures with linguistic descriptions, thereby enhancing molecular reasoning capabilities. Our approach notably enhances interpretability, improving the model 's molecular understanding and enabling better generalization. Extensive experiments demonstrate that MolReasoner outperforms existing methods, and marking a significant shift from memorization-based outputs to robust chemical reasoning.

One of the roadblocks to a better understanding of neural networks' internals is polysemanticity, where neurons appear to activate in multiple, semantically distinct contexts. Polysemanticity prevents us from identifying concise, human-understandable explanations for what neural networks are doing internally. One hypothesised cause of polysemanticity is superposition, where neural networks represent more features than they have neurons by assigning features to an overcomplete set of directions in activation space, rather than to individual neurons. Here, we attempt to identify those directions, using sparse autoencoders to reconstruct the internal activations of a language model. These autoencoders learn sets of sparsely activating features that are more interpretable and monosemantic than directions identified by alternative approaches, where interpretability is measured by automated methods. Ablating these features enables precise model editing, for example, by removing capabilities such as pronoun prediction, while disrupting model behaviour less than prior techniques. This work indicates that it is possible to resolve superposition in language models using a scalable, unsupervised method. Our method may serve as a foundation for future mechanistic interpretability work, which we hope will enable greater model transparency and steerability.

While large language models (LLMs) have achieved impressive progress, their application in scientific domains such as chemistry remains hindered by shallow domain understanding and limited reasoning capabilities. In this work, we focus on the specific field of chemistry and develop a Chemical Reasoner LLM, ChemDFM-R. We first construct a comprehensive dataset of atomized knowledge points to enhance the model's understanding of the fundamental principles and logical structure of chemistry. Then, we propose a mix-sourced distillation strategy that integrates expert-curated knowledge with general-domain reasoning skills, followed by domain-specific reinforcement learning to enhance chemical reasoning. Experiments on diverse chemical benchmarks demonstrate that ChemDFM-R achieves state-of-the-art performance while providing interpretable, rationale-driven outputs. Further case studies illustrate how explicit reasoning chains significantly improve the reliability, transparency, and practical utility of the model in real-world human-AI collaboration scenarios.

The rapid advancements in transformer-based language models have revolutionized natural language processing, yet understanding the internal mechanisms of these models remains a significant challenge. This paper explores the application of sparse autoencoders (SAE) to interpret the internal representations of protein language models, specifically focusing on the ESM-2 8M parameter model. By performing a statistical analysis on each latent component's relevance to distinct protein annotations, we identify potential interpretations linked to various protein characteristics, including transmembrane regions, binding sites, and specialized motifs. We then leverage these insights to guide sequence generation, shortlisting the relevant latent components that can steer the model towards desired targets such as zinc finger domains. This work contributes to the emerging field of mechanistic interpretability in biological sequence models, offering new perspectives on model steering for sequence design.

Many cellular processes involve information processing and decision making. We can probe these processes at increasing molecular detail. The analysis of heterogeneous data remains a challenge that requires new ways of thinking about cells in quantitative, predictive, and mechanistic ways. We discuss the role of mathematical models in the context of cell-fate decision making systems across the tree of life. Complex multi-cellular organisms have been a particular focus, but single celled organisms also have to sense and respond to their environment. We center our discussion around the idea of design principles which we can learn from observations and modeling, and exploit in order to (re)-design or guide cellular behavior.

Unlocking deep, interpretable biological reasoning from complex genomic data is a major AI challenge hindering scientific discovery. Current DNA foundation models, despite strong sequence representation, struggle with multi-step reasoning and lack inherent transparent, biologically intuitive explanations. We introduce BioReason, a pioneering architecture that, for the first time, deeply integrates a DNA foundation model with a Large Language Model (LLM). This novel connection enables the LLM to directly process and reason with genomic information as a fundamental input, fostering a new form of multimodal biological understanding. BioReason's sophisticated multi-step reasoning is developed through supervised fine-tuning and targeted reinforcement learning, guiding the system to generate logical, biologically coherent deductions. On biological reasoning benchmarks including KEGG-based disease pathway prediction - where accuracy improves from 88% to 97% - and variant effect prediction, BioReason demonstrates an average 15% performance gain over strong single-modality baselines. BioReason reasons over unseen biological entities and articulates decision-making through interpretable, step-by-step biological traces, offering a transformative approach for AI in biology that enables deeper mechanistic insights and accelerates testable hypothesis generation from genomic data. Data, code, and checkpoints are publicly available at https://github.com/bowang-lab/BioReason

Machine learning, notably deep learning, has significantly propelled molecular investigations within the biochemical sphere. Traditionally, modeling for such research has centered around a handful of paradigms. For instance, the prediction paradigm is frequently deployed for tasks such as molecular property prediction. To enhance the generation and decipherability of purely data-driven models, scholars have integrated biochemical domain knowledge into these molecular study models. This integration has sparked a surge in paradigm transfer, which is solving one molecular learning task by reformulating it as another one. With the emergence of Large Language Models, these paradigms have demonstrated an escalating trend towards harmonized unification. In this work, we delineate a literature survey focused on knowledge-informed molecular learning from the perspective of paradigm transfer. We classify the paradigms, scrutinize their methodologies, and dissect the contribution of domain knowledge. Moreover, we encapsulate prevailing trends and identify intriguing avenues for future exploration in molecular learning.

Recent advancements in multimodal large language models (MLLMs) and video agent systems have significantly improved general video understanding. However, when applied to scientific video understanding and educating, a domain that demands external professional knowledge integration and rigorous step-wise reasoning, existing approaches often struggle. To bridge this gap, we propose SciEducator, the first iterative self-evolving multi-agent system for scientific video comprehension and education. Rooted in the classical Deming Cycle from management science, our design reformulates its Plan-Do-Study-Act philosophy into a self-evolving reasoning and feedback mechanism, which facilitates the interpretation of intricate scientific activities in videos. Moreover, SciEducator can produce multimodal educational content tailored to specific scientific processes, including textual instructions, visual guides, audio narrations, and interactive references. To support evaluation, we construct SciVBench, a benchmark consisting of 500 expert-verified and literature-grounded science QA pairs across five categories, covering physical, chemical, and everyday phenomena. Extensive experiments demonstrate that SciEducator substantially outperforms leading closed-source MLLMs (e.g., Gemini, GPT-4o) and state-of-the-art video agents on the benchmark, establishing a new paradigm for the community.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

Large language models (LLMs) have gained widespread interest due to their ability to process human language and perform tasks on which they have not been explicitly trained. This is relevant for the chemical sciences, which face the problem of small and diverse datasets that are frequently in the form of text. LLMs have shown promise in addressing these issues and are increasingly being harnessed to predict chemical properties, optimize reactions, and even design and conduct experiments autonomously. However, we still have only a very limited systematic understanding of the chemical reasoning capabilities of LLMs, which would be required to improve models and mitigate potential harms. Here, we introduce "ChemBench," an automated framework designed to rigorously evaluate the chemical knowledge and reasoning abilities of state-of-the-art LLMs against the expertise of human chemists. We curated more than 7,000 question-answer pairs for a wide array of subfields of the chemical sciences, evaluated leading open and closed-source LLMs, and found that the best models outperformed the best human chemists in our study on average. The models, however, struggle with some chemical reasoning tasks that are easy for human experts and provide overconfident, misleading predictions, such as about chemicals' safety profiles. These findings underscore the dual reality that, although LLMs demonstrate remarkable proficiency in chemical tasks, further research is critical to enhancing their safety and utility in chemical sciences. Our findings also indicate a need for adaptations to chemistry curricula and highlight the importance of continuing to develop evaluation frameworks to improve safe and useful LLMs.

Recent advancements in artificial intelligence have sparked interest in scientific assistants that could support researchers across the full spectrum of scientific workflows, from literature review to experimental design and data analysis. A key capability for such systems is the ability to process and reason about scientific information in both visual and textual forms - from interpreting spectroscopic data to understanding laboratory setups. Here, we introduce MaCBench, a comprehensive benchmark for evaluating how vision-language models handle real-world chemistry and materials science tasks across three core aspects: data extraction, experimental understanding, and results interpretation. Through a systematic evaluation of leading models, we find that while these systems show promising capabilities in basic perception tasks - achieving near-perfect performance in equipment identification and standardized data extraction - they exhibit fundamental limitations in spatial reasoning, cross-modal information synthesis, and multi-step logical inference. Our insights have important implications beyond chemistry and materials science, suggesting that developing reliable multimodal AI scientific assistants may require advances in curating suitable training data and approaches to training those models.

Being able to provide explanations for a model's decision has become a central requirement for the development, deployment, and adoption of machine learning models. However, we are yet to understand what explanation methods can and cannot do. How do upstream factors such as data, model prediction, hyperparameters, and random initialization influence downstream explanations? While previous work raised concerns that explanations (E) may have little relationship with the prediction (Y), there is a lack of conclusive study to quantify this relationship. Our work borrows tools from causal inference to systematically assay this relationship. More specifically, we study the relationship between E and Y by measuring the treatment effect when intervening on their causal ancestors, i.e., on hyperparameters and inputs used to generate saliency-based Es or Ys. Our results suggest that the relationships between E and Y is far from ideal. In fact, the gap between 'ideal' case only increase in higher-performing models -- models that are likely to be deployed. Our work is a promising first step towards providing a quantitative measure of the relationship between E and Y, which could also inform the future development of methods for E with a quantitative metric.

Neural networks often pack many unrelated concepts into a single neuron - a puzzling phenomenon known as 'polysemanticity' which makes interpretability much more challenging. This paper provides a toy model where polysemanticity can be fully understood, arising as a result of models storing additional sparse features in "superposition." We demonstrate the existence of a phase change, a surprising connection to the geometry of uniform polytopes, and evidence of a link to adversarial examples. We also discuss potential implications for mechanistic interpretability.

Mathematical modeling is a cornerstone of scientific discovery and engineering practice, enabling the translation of real-world problems into formal systems across domains such as physics, biology, and economics. Unlike mathematical reasoning, which assumes a predefined formulation, modeling requires open-ended problem analysis, abstraction, and principled formalization. While Large Language Models (LLMs) have shown strong reasoning capabilities, they fall short in rigorous model construction, limiting their utility in real-world problem-solving. To this end, we formalize the task of LLM-powered real-world mathematical modeling, where agents must analyze problems, construct domain-appropriate formulations, and generate complete end-to-end solutions. We introduce MM-Bench, a curated benchmark of 111 problems from the Mathematical Contest in Modeling (MCM/ICM), spanning the years 2000 to 2025 and across ten diverse domains such as physics, biology, and economics. To tackle this task, we propose MM-Agent, an expert-inspired framework that decomposes mathematical modeling into four stages: open-ended problem analysis, structured model formulation, computational problem solving, and report generation. Experiments on MM-Bench show that MM-Agent significantly outperforms baseline agents, achieving an 11.88\% improvement over human expert solutions while requiring only 15 minutes and \$0.88 per task using GPT-4o. Furthermore, under official MCM/ICM protocols, MM-Agent assisted two undergraduate teams in winning the Finalist Award (top 2.0\% among 27,456 teams) in MCM/ICM 2025, demonstrating its practical effectiveness as a modeling copilot. Our code is available at https://github.com/usail-hkust/LLM-MM-Agent

We present causal head gating (CHG), a scalable method for interpreting the functional roles of attention heads in transformer models. CHG learns soft gates over heads and assigns them a causal taxonomy - facilitating, interfering, or irrelevant - based on their impact on task performance. Unlike prior approaches in mechanistic interpretability, which are hypothesis-driven and require prompt templates or target labels, CHG applies directly to any dataset using standard next-token prediction. We evaluate CHG across multiple large language models (LLMs) in the Llama 3 model family and diverse tasks, including syntax, commonsense, and mathematical reasoning, and show that CHG scores yield causal, not merely correlational, insight validated via ablation and causal mediation analyses. We also introduce contrastive CHG, a variant that isolates sub-circuits for specific task components. Our findings reveal that LLMs contain multiple sparse task-sufficient sub-circuits, that individual head roles depend on interactions with others (low modularity), and that instruction following and in-context learning rely on separable mechanisms.

Pre-trained on extensive text and image corpora, current Multi-Modal Large Language Models (MLLM) have shown strong capabilities in general visual reasoning tasks. However, their performance is still lacking in physical domains that require understanding diagrams with complex physical structures and quantitative analysis based on multi-modal information. To address this, we develop a new framework, named Multi-Modal Scientific Reasoning with Physics Perception and Simulation (MAPS) based on an MLLM. MAPS decomposes expert-level multi-modal reasoning task into physical diagram understanding via a Physical Perception Model (PPM) and reasoning with physical knowledge via a simulator. The PPM module is obtained by fine-tuning a visual language model using carefully designed synthetic data with paired physical diagrams and corresponding simulation language descriptions. At the inference stage, MAPS integrates the simulation language description of the input diagram provided by PPM and results obtained through a Chain-of-Simulation process with MLLM to derive the underlying rationale and the final answer. Validated using our collected college-level circuit analysis problems, MAPS significantly improves reasoning accuracy of MLLM and outperforms all existing models. The results confirm MAPS offers a promising direction for enhancing multi-modal scientific reasoning ability of MLLMs. We will release our code, model and dataset used for our experiments upon publishing of this paper.

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current decomposition methods -- decomposes neural network parameters into a sum of sparsely used vectors in parameter space. However, the current main method in this framework, Attribution-based Parameter Decomposition (APD), is impractical on account of its computational cost and sensitivity to hyperparameters. In this work, we introduce Stochastic Parameter Decomposition (SPD), a method that is more scalable and robust to hyperparameters than APD, which we demonstrate by decomposing models that are slightly larger and more complex than was possible to decompose with APD. We also show that SPD avoids other issues, such as shrinkage of the learned parameters, and better identifies ground truth mechanisms in toy models. By bridging causal mediation analysis and network decomposition methods, this demonstration opens up new research possibilities in mechanistic interpretability by removing barriers to scaling linear parameter decomposition methods to larger models. We release a library for running SPD and reproducing our experiments at https://github.com/goodfire-ai/spd.

While large language models (LLMs) with Chain-of-Thought (CoT) reasoning excel in mathematics and coding, their potential for systematic reasoning in chemistry, a domain demanding rigorous structural analysis for real-world tasks like drug design and reaction engineering, remains untapped. Current benchmarks focus on simple knowledge retrieval, neglecting step-by-step reasoning required for complex tasks such as molecular optimization and reaction prediction. To address this, we introduce ChemCoTBench, a reasoning framework that bridges molecular structure understanding with arithmetic-inspired operations, including addition, deletion, and substitution, to formalize chemical problem-solving into transparent, step-by-step workflows. By treating molecular transformations as modular "chemical operations", the framework enables slow-thinking reasoning, mirroring the logic of mathematical proofs while grounding solutions in real-world chemical constraints. We evaluate models on two high-impact tasks: Molecular Property Optimization and Chemical Reaction Prediction. These tasks mirror real-world challenges while providing structured evaluability. By providing annotated datasets, a reasoning taxonomy, and baseline evaluations, ChemCoTBench bridges the gap between abstract reasoning methods and practical chemical discovery, establishing a foundation for advancing LLMs as tools for AI-driven scientific innovation.

Understanding the world and explaining it with scientific theories is a central aspiration of artificial intelligence research. Proposing theories, designing experiments to test them, and then revising them based on data are fundamental to scientific discovery. Despite the significant promise of LLM-based scientific agents, no benchmarks systematically test LLM's ability to propose scientific models, collect experimental data, and revise them in light of new data. We introduce BoxingGym, a benchmark with 10 environments for systematically evaluating both experimental design (e.g. collecting data to test a scientific theory) and model discovery (e.g. proposing and revising scientific theories). To enable tractable and quantitative evaluation, we implement each environment as a generative probabilistic model with which a scientific agent can run interactive experiments. These probabilistic models are drawn from various real-world scientific domains ranging from psychology to ecology. To quantitatively evaluate a scientific agent's ability to collect informative experimental data, we compute the expected information gain (EIG), an information-theoretic quantity which measures how much an experiment reduces uncertainty about the parameters of a generative model. A good scientific theory is a concise and predictive explanation. Therefore, to quantitatively evaluate model discovery, we ask a scientific agent to explain their model and then assess whether this explanation enables another scientific agent to make reliable predictions about this environment. In addition to this explanation-based evaluation, we compute standard model evaluation metrics such as prediction errors. We find that current LLMs, such as GPT-4o, struggle with both experimental design and model discovery. We find that augmenting the LLM-based agent with an explicit statistical model does not reliably improve these results.

Decomposing model activations into interpretable components is a key open problem in mechanistic interpretability. Sparse autoencoders (SAEs) are a popular method for decomposing the internal activations of trained transformers into sparse, interpretable features, and have been applied to MLP layers and the residual stream. In this work we train SAEs on attention layer outputs and show that also here SAEs find a sparse, interpretable decomposition. We demonstrate this on transformers from several model families and up to 2B parameters. We perform a qualitative study of the features computed by attention layers, and find multiple families: long-range context, short-range context and induction features. We qualitatively study the role of every head in GPT-2 Small, and estimate that at least 90% of the heads are polysemantic, i.e. have multiple unrelated roles. Further, we show that Sparse Autoencoders are a useful tool that enable researchers to explain model behavior in greater detail than prior work. For example, we explore the mystery of why models have so many seemingly redundant induction heads, use SAEs to motivate the hypothesis that some are long-prefix whereas others are short-prefix, and confirm this with more rigorous analysis. We use our SAEs to analyze the computation performed by the Indirect Object Identification circuit (Wang et al.), validating that the SAEs find causally meaningful intermediate variables, and deepening our understanding of the semantics of the circuit. We open-source the trained SAEs and a tool for exploring arbitrary prompts through the lens of Attention Output SAEs.

In the rapidly evolving landscape of artificial intelligence, multi-modal large language models are emerging as a significant area of interest. These models, which combine various forms of data input, are becoming increasingly popular. However, understanding their internal mechanisms remains a complex task. Numerous advancements have been made in the field of explainability tools and mechanisms, yet there is still much to explore. In this work, we present a novel interactive application aimed towards understanding the internal mechanisms of large vision-language models. Our interface is designed to enhance the interpretability of the image patches, which are instrumental in generating an answer, and assess the efficacy of the language model in grounding its output in the image. With our application, a user can systematically investigate the model and uncover system limitations, paving the way for enhancements in system capabilities. Finally, we present a case study of how our application can aid in understanding failure mechanisms in a popular large multi-modal model: LLaVA.

The ability to use, understand, and create tools is a hallmark of human intelligence, enabling sophisticated interaction with the physical world. For any general-purpose intelligent agent to achieve true versatility, it must also master these fundamental skills. While modern Multimodal Large Language Models (MLLMs) leverage their extensive common knowledge for high-level planning in embodied AI and in downstream Vision-Language-Action (VLA) models, the extent of their true understanding of physical tools remains unquantified. To bridge this gap, we present PhysToolBench, the first benchmark dedicated to evaluating the comprehension of physical tools by MLLMs. Our benchmark is structured as a Visual Question Answering (VQA) dataset comprising over 1,000 image-text pairs. It assesses capabilities across three distinct difficulty levels: (1) Tool Recognition: Requiring the recognition of a tool's primary function. (2) Tool Understanding: Testing the ability to grasp the underlying principles of a tool's operation. (3) Tool Creation: Challenging the model to fashion a new tool from surrounding objects when conventional options are unavailable. Our comprehensive evaluation of 32 MLLMs-spanning proprietary, open-source, specialized embodied, and backbones in VLAs-reveals a significant deficiency in tool understanding. Furthermore, we provide an in-depth analysis and propose preliminary solutions. Code and dataset are publicly available.

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.

Solving mechanics problems using numerical methods requires comprehensive intelligent capability of retrieving relevant knowledge and theory, constructing and executing codes, analyzing the results, a task that has thus far mainly been reserved for humans. While emerging AI methods can provide effective approaches to solve end-to-end problems, for instance via the use of deep surrogate models or various data analytics strategies, they often lack physical intuition since knowledge is baked into the parametric complement through training, offering less flexibility when it comes to incorporating mathematical or physical insights. By leveraging diverse capabilities of multiple dynamically interacting large language models (LLMs), we can overcome the limitations of conventional approaches and develop a new class of physics-inspired generative machine learning platform, here referred to as MechAgents. A set of AI agents can solve mechanics tasks, here demonstrated for elasticity problems, via autonomous collaborations. A two-agent team can effectively write, execute and self-correct code, in order to apply finite element methods to solve classical elasticity problems in various flavors (different boundary conditions, domain geometries, meshes, small/finite deformation and linear/hyper-elastic constitutive laws, and others). For more complex tasks, we construct a larger group of agents with enhanced division of labor among planning, formulating, coding, executing and criticizing the process and results. The agents mutually correct each other to improve the overall team-work performance in understanding, formulating and validating the solution. Our framework shows the potential of synergizing the intelligence of language models, the reliability of physics-based modeling, and the dynamic collaborations among diverse agents, opening novel avenues for automation of solving engineering problems.

Large language models (LLMs) have rapidly advanced and are increasingly capable of tackling complex scientific problems, including those in physics. Despite this progress, current LLMs often fail to emulate the concise, principle-based reasoning characteristic of human experts, instead generating lengthy and opaque solutions. This discrepancy highlights a crucial gap in their ability to apply core physical principles for efficient and interpretable problem solving. To systematically investigate this limitation, we introduce PhySense, a novel principle-based physics reasoning benchmark designed to be easily solvable by experts using guiding principles, yet deceptively difficult for LLMs without principle-first reasoning. Our evaluation across multiple state-of-the-art LLMs and prompt types reveals a consistent failure to align with expert-like reasoning paths, providing insights for developing AI systems with efficient, robust and interpretable principle-based scientific reasoning.

There is growing interest in leveraging mechanistic interpretability and controllability to better understand and influence the internal dynamics of large language models (LLMs). However, current methods face fundamental challenges in reliably localizing and manipulating feature representations. Sparse Autoencoders (SAEs) have recently emerged as a promising direction for feature extraction at scale, yet they, too, are limited by incomplete feature isolation and unreliable monosemanticity. To systematically quantify these limitations, we introduce Feature Monosemanticity Score (FMS), a novel metric to quantify feature monosemanticity in latent representation. Building on these insights, we propose Guided Sparse Autoencoders (G-SAE), a method that conditions latent representations on labeled concepts during training. We demonstrate that reliable localization and disentanglement of target concepts within the latent space improve interpretability, detection of behavior, and control. Specifically, our evaluations on toxicity detection, writing style identification, and privacy attribute recognition show that G-SAE not only enhances monosemanticity but also enables more effective and fine-grained steering with less quality degradation. Our findings provide actionable guidelines for measuring and advancing mechanistic interpretability and control of LLMs.

This paper studies the problem of solving complex chemistry problems with large language models (LLMs). Despite the extensive general knowledge in LLMs (such as GPT-4), they struggle with chemistry reasoning that requires faithful grounded reasoning with diverse chemical knowledge and an integrative understanding of chemical interactions. We propose InstructChem, a new structured reasoning approach that substantially boosts the LLMs' chemical reasoning capabilities. InstructChem explicitly decomposes the reasoning into three critical phrases, including chemical formulae generation by LLMs that offers the basis for subsequent grounded reasoning, step-by-step reasoning that makes multi-step derivations with the identified formulae for a preliminary answer, and iterative review-and-refinement that steers LLMs to progressively revise the previous phases for increasing confidence, leading to the final high-confidence answer. We conduct extensive experiments on four different chemistry challenges, including quantum chemistry, quantum mechanics, physical chemistry, and chemistry kinetics. Our approach significantly enhances GPT-4 on chemistry reasoning, yielding an 8% average absolute improvement and a 30% peak improvement. We further use the generated reasoning by GPT-4 to fine-tune smaller LMs (e.g., Vicuna) and observe strong improvement of the smaller LMs. This validates our approach and enables LLMs to generate high-quality reasoning.