ICLR 2026 Papers

Mechanistic interpretability (MI) is an emerging framework for interpreting neural networks. Given a task and model, MI aims to discover a succinct algorithmic process, an interpretation, that explains the model's decision process on that task. However, MI is difficult to scale and generalize. This stems in part from two key challenges: the lack of a well-defined notion of a valid interpretation; and, the ad hoc nature of generating and searching for such explanations. In this paper, we address these challenges by formally defining and studying the problem of interpretive equivalence: determining whether two different models share a common interpretation, without requiring an explicit description of what that interpretation is. At the core of our approach, we propose and formalize the principle that two interpretations of a model are (approximately) equivalent if and only if all of their possible implementations are also (approximately) equivalent. We develop tractable algorithms to estimate interpretive equivalence and case study their use on Transformer-based models. To analyze our algorithms, we introduce necessary and sufficient conditions for interpretive equivalence grounded in the similarity of their neural representations. As a result, we provide the first theoretical guarantees that simultaneously relate a model's algorithmic interpretations, circuits, and representations. Our framework lays a foundation for the development of more rigorous evaluation methods of MI and automated, generalizable interpretation discovery methods.

Current methods for detecting spurious correlations rely on data splits or error patterns, leaving many harmful shortcuts invisible when counterexamples are absent. We introduce BEE (Bridging Explainability and Embeddings), a framework that shifts the focus from model predictions to the weight space and embedding geometry underlying decisions. By analyzing how fine-tuning perturbs pretrained representations, BEE uncovers spurious correlations that remain hidden from conventional evaluation pipelines. We use linear probing as a transparent diagnostic lens, revealing spurious features that not only persist after full fine-tuning but also transfer across diverse state-of-the-art models. Our experiments cover numerous datasets and domains: vision (Waterbirds, CelebA, ImageNet-1k), language (CivilComments, MIMIC-CXR medical notes), and multiple embedding families (CLIP, CLIP-DataComp.XL, mGTE, BLIP2, SigLIP2). BEE consistently exposes spurious correlations: from concepts that slash the ImageNet accuracy by up to 95\%, to clinical shortcuts in MIMIC-CXR notes that induce dangerous false negatives. Together, these results position BEE as a general and principled tool for diagnosing spurious correlations in weight space, enabling principled dataset auditing and more trustworthy foundation models. The source code is publicly available at https://github.com/bit-ml/bee.

Concept Bottleneck Models (CBMs) achieve interpretability by interposing a human-understandable concept layer between perception and label prediction. The foundation of CBMs lies in the many-to-many mapping that translates high-dimensional visual features to a set of discrete concepts. However, we identify a critical and pervasive challenge that undermines this process: \emph{representational collapse}, where visual patch features degenerate into a low-rank subspace during training, severely degrading the quality of learned concept activation vectors, thus hindering both model interpretability and downstream performance. To address these issues, we propose Implicit Vector Quantization (IVQ), a lightweight regularizer that maintains high-rank, diverse representations throughout training. Rather than imposing a hard bottleneck via direct quantization, IVQ learns a codebook prior that anchors semantic information in visual features, allowing it to act as a proxy objective. To further exploit these high-rank concept-aware features, we propose Magnet Attention, which dynamically aggregates patch-level features into visual concept prototypes, explicitly modeling the many-to-many vision–concept correspondence. Extensive experimental results show that our approach effectively prevents representational collapse and achieves state-of-the-art performance on eight diverse benchmarks. Our experiments further probe the low-rank phenomenon in representational collapse, finding that IVQ mitigates the information bottleneck and yields cross-modal representations with clearer, more interpretable consistency.

Popular explanation methods often produce unreliable feature importance scores due to "missingness bias", a systematic distortion that arises when models are probed with ablated, out-of-distribution inputs. Existing solutions treat this as a deep representational flaw that requires expensive retraining or architectural modifications. In this work, we challenge this assumption and show that missingness bias can be effectively treated as a superficial artifact of the model's output space. We introduce MCal, a lightweight post-hoc method that corrects this bias by fine-tuning a simple linear head on the outputs of a frozen base model. Surprisingly, we find this simple correction consistently reduces missingness bias and is competitive with, or even outperforms, prior heavyweight approaches across diverse medical benchmarks spanning vision, language, and tabular domains.

We propose Low-Rank Sparse Attention (Lorsa), a sparse replacement model of Transformer attention layers to disentangle original Multi Head Self Attention (MHSA) into individually comprehensible components. Lorsa is designed to address the challenge of \textit{attention superposition} to understand attention-mediated interaction between features in different token positions. Lorsa helps find cleaner and finer-grained versions of previously discovered MHSA behaviors like induction heads, successor heads, attention sink, and a comprehensive family of arithmetic-specific Lorsa heads. Interestingly, we identify a novel head type called \emph{subtoken induction heads} that function at character level rather than token level. Automated interpretability analysis indicates that Lorsa achieves parity with SAE in interpretability while Lorsa exhibits superior circuit discovery properties. We also conduct extensive experiments on architectural design ablation, correlation to original MHSA heads and error analysis. Our early attempt to fully sparsify a toy Transformer succeeds to reveal clean global circuits. Eventually, we hope Lorsa would help us greatly understand attention computation and enable full sparsification of model computation along with its MLP counterparts. Lorsa is open-sourced at https://anonymous.4open.science/r/Lorsa-5686/.

Current training data attribution (TDA) methods treat influence as static, ignoring the fact that neural networks learn in distinct stages. This stagewise development, driven by phase transitions on a degenerate loss landscape, means a sample's importance is not fixed but changes throughout training. In this work, we introduce a developmental framework for data attribution, grounded in singular learning theory. We predict that influence can change non-monotonically, including sign flips and sharp peaks at developmental transitions. We first confirm these predictions analytically and empirically in a toy model, showing that dynamic shifts in influence directly map to the model's progressive learning of a semantic hierarchy. Finally, we demonstrate these phenomena at scale in language models, where token-level influence changes align with known developmental stages.

Understanding how populations of neurons represent information is a central challenge across machine learning and neuroscience. Recent work in both fields has begun to characterize the representational geometry and functionality underlying complex distributed activity. For example, artificial neural networks trained on data with more features than neurons compress data by representing features non-orthogonally in so-called *superposition*. However, the effect of time (or memory), an additional capacity-constraining pressure, on underlying representational geometry in recurrent models is not well understood. Here, we study how memory demands affect representational geometry in recurrent neural networks (RNNs), introducing the concept of temporal superposition. We develop a theoretical framework in RNNs with linear recurrence trained on a delayed serial recall task to better understand how properties of the data, task demands, and network dimensionality lead to different representational strategies, and show that these insights generalize to nonlinear RNNs. Through this, we identify an effectively linear, dense regime and a sparse regime where RNNs utilize an interference-free space, characterized by a phase transition in the angular distribution of features and decrease in spectral radius. Finally, we analyze the interaction of spatial and temporal superposition to observe how RNNs mediate different representational tradeoffs. Overall, our work offers a mechanistic, geometric explanation of representational strategies RNNs learn, how they depend on capacity and task demands, and why.

Recent advances in mechanistic interpretability have shown that many features represented by deep learning models can be captured by dictionary learning approaches such as sparse autoencoders. However, our understanding of the structures formed by these internal representations is still limited. Initial “toy-model” analyses showed that in an idealized setting features can be arranged in local structures, such as small regular polytopes, through a phenomenon known as _superposition_. However, these local structures have not been observed in real language models. In contrast, language models display rich structures like semantically clustered representations or ordered circles for the months of the year which are not predicted by current theories. In this work, we introduce Bag-of-Words Superposition (BOWS), a framework in which autoencoders (AEs) with a non-linearity are trained to compress sparse, binary bag-of-words vectors drawn from Internet-scale text. Our framework reveals that under restrictive bottlenecks, or when trained with weight decay, non-linear AEs linearly encode the low rank structure in the data, arranging feature representations according to their co-activation patterns. This _linear superposition_ gives rise to structures like ordered circles and semantic clusters, similar to those observed in language models. Our findings suggest that the semantically meaningful structures observed in language models could arise driven by compression alone, without necessarily having a functional role beyond efficiently arranging feature representations.

Evaluating open-ended outputs of Multimodal Large Language Models has become a bottleneck as model capabilities, task diversity, and modality rapidly expand. Existing ``MLLM-as-a-Judge'' evaluators, though promising, remain constrained to specific tasks and aspects (i.e., specific evaluation criteria such as fluency for text and image quality for images). In this paper, we argue that, on one hand, based on the interconnected nature of criteria, learning specific aspects can generalize to unseen aspects; on the other hand, jointly learning to assess multiple visual criteria and tasks may foster a synergistic effect. To this end, we propose UFEval, the first unified fine-grained evaluator with task and aspect generalization for four evaluation tasks --- Natural Language Generation, Image Understanding, Image Generation, and Interleaved Text-and-Image Generation. However, training such a unified evaluator is hindered by the lack of a large-scale, multi-modal, and aspect-level resource. To address this gap, we introduce FRABench, a comprehensive fine-grained evaluation dataset. Specifically, (1) We first construct a hierarchical aspect taxonomy encompassing 112 distinct aspects across the aforementioned four tasks. (2) Based on this taxonomy, we create FRABench, comprising 60.4k pairwise samples with 325k evaluation labels obtained from a combination of human and GPT-4o annotations. (3) Finally, leveraging FRABench, we develop UFEval, a unified fine-grained evaluator. Experiments show that learning on specific aspects enables UFEval to generalize to unseen aspects, and joint learning to assess diverse visual tasks and aspects can lead to substantial mutual benefits.

Understanding the statistical properties of deep neural networks (DNNs) at initialization is crucial for elucidating both their trainability and the intrinsic architectural biases they encode prior to data exposure. Mean-field (MF) analyses have demonstrated that the parameter distribution in randomly initialized networks dictates whether gradients vanish or explode. Recent work has shown that untrained DNNs exhibit an initial-guessing bias (IGB), in which large regions of the input space are assigned to a single class. In this work, we provide a theoretical proof linking IGB to MF analyses, establishing that a network’s predisposition toward specific classes is intrinsically tied to the conditions for efficient learning. This connection leads to a counterintuitive conclusion: the initialization that optimizes trainability is systematically biased rather than neutral. We validate our theory through experiments across multiple architectures and datasets.

In human society, collective decision making has often outperformed the judgment of individuals. Classic examples range from estimating livestock weights to predicting elections and financial markets, where averaging many independent guesses often yields results more accurate than experts. These successes arise because groups bring together diverse perspectives, independent voices, and distributed knowledge, combining them in ways that cancel individual biases. This principle, known as the Wisdom of Crowds, underpins practices in forecasting, marketing, and preference modeling. Large Language Models (LLMs), however, typically produce a single definitive answer. While effective in many settings, this uniformity overlooks the diversity of human judgments shaping responses to ads, videos, and webpages. Inspired by how societies benefit from diverse opinions, we ask whether LLM predictions can be improved by simulating not one answer but many. We introduce Social Agents, a multi-agent framework that instantiates a synthetic society of human-like personas with diverse demographic (e.g., age, gender) and psychographic (e.g., values, interests) attributes. Each persona independently appraises a stimulus such as an advertisement, video, or webpage, offering both a quantitative score (e.g., click-through likelihood, recall score, likability) and a qualitative rationale. Aggregating these opinions produces a distribution of preferences that more closely mirrors real human crowds. Across eleven behavioral prediction tasks, Social Agents outperforms single-LLM baselines by up to 67.45% on simple judgments (e.g. webpage likability) and 9.88% on complex interpretive reasoning (e.g. video memorability). Social Agents’ individual persona predictions also align with human judgments, reaching Pearson correlations up to 0.71. These results position computational crowd simulation as a scalable, interpretable tool for improving behavioral prediction and supporting societal decision making.

This work investigates how large language models (LLMs) internally represent emotion by analyzing the geometry of their hidden-state space. Using a synthetic dataset of emotionally rewritten sentences, we identify a low-dimensional emotional manifold via singular value decomposition and show that emotional representations are directionally encoded, distributed across layers, and aligned with interpretable dimensions. These structures are stable across depth and generalize to eight real-world emotion datasets spanning five languages. Cross-domain alignment yields low error and strong linear probe performance, indicating a universal emotional subspace. Within this space, internal emotion perception can be steered while preserving semantics using a learned intervention module, with especially strong control for basic emotions across languages. These findings reveal a consistent and manipulable affective geometry in LLMs and offer insight into how they internalize and process emotion.

How do language models (LMs) represent characters’ beliefs, especially when those beliefs may differ from reality? This question lies at the heart of understanding the Theory of Mind (ToM) capabilities of LMs. We analyze LMs' ability to reason about characters’ beliefs using causal mediation and abstraction. We construct a dataset, CausalToM, consisting of simple stories where two characters independently change the state of two objects, potentially unaware of each other's actions. Our investigation uncovered a pervasive algorithmic pattern that we call a lookback mechanism, which enables the LM to recall important information when it becomes necessary. The LM binds each character-object-state triple together by co-locating their reference information, represented as Ordering IDs (OIs), in low-rank subspaces of the state token's residual stream. When asked about a character's beliefs regarding the state of an object, the binding lookback retrieves the correct state OI and then the answer lookback retrieves the corresponding state token. When we introduce text specifying that one character is (not) visible to the other, we find that the LM first generates a visibility ID encoding the relation between the observing and the observed character OIs. In a visibility lookback, this ID is used to retrieve information about the observed character and update the observing character's beliefs. Our work provides insights into belief tracking mechanisms, taking a step toward reverse-engineering ToM reasoning in LMs.

Large vision-language models (LVLMs) achieve impressive performance, yet their internal decision-making processes remain opaque, making it difficult to determine if the success stems from true multimodal fusion or reliance on unimodal priors. To address this attribution gap, we introduce a novel framework using partial information decomposition (PID) to quantitatively measure the ``information spectrum'' of LVLMs—decomposing a model’s decision-relevant information into redundant, unique, and synergistic components. By adapting a scalable estimator to modern LVLM outputs, Our model-agnostic pipeline profiles 26 LVLMs on four datasets across three dimensions—\emph{breadth} (cross-model \& cross-task), \emph{depth} (layer-wise information dynamics), and \emph{time} (learning dynamics across training). Our analysis reveals two key results: (i) two task regimes (synergy-driven vs. knowledge-driven) and (ii) two stable, opposing family-level strategies (fusion-centric vs. language-centric). We also uncover a consistent three-phase pattern in layer-wise processing and identify visual instruction tuning as the key stage where fusion is learned. Together, these contributions provide a quantitative lens beyond accuracy-only evaluation and offer guidance for analyzing and designing the next generation of LVLMs.

Automated interpretability aims to translate large language model (LLM) features into human understandable descriptions. However, natural language feature descriptions are often vague, inconsistent, and require manual relabeling. In response, we introduce *semantic regexes*, structured language descriptions of LLM features. By combining primitives that capture linguistic and semantic patterns with modifiers for contextualization, composition, and quantification, semantic regexes produce precise and expressive feature descriptions. Across quantitative benchmarks and qualitative analyses, semantic regexes match the accuracy of natural language while yielding more concise and consistent feature descriptions. Their inherent structure affords new types of analyses, including quantifying feature complexity across layers, scaling automated interpretability from insights into individual features to model-wide patterns. Finally, in user studies, we find that semantic regexes help people build accurate mental models of LLM features.

Finetuning (pretrained) language models is a standard approach for updating their internal parametric knowledge and specializing them to new tasks and domains. However, the corresponding model weight changes ("weight diffs") are not generally interpretable. While inspecting the finetuning dataset can give a sense of how the model might have changed, these datasets are often not publicly available or are too large to work with directly. Towards the goal of broadly understanding model weight changes in natural language, we introduce Diff Interpretation Tuning (DIT), a method that trains models to describe their own finetuning-induced modifications. Our approach uses synthetic, labeled weight diffs to train an introspection adapter, which can be applied to a compatible finetuned model to make it self-describe the weight changes. We demonstrate in two proof-of-concept settings (reporting hidden behaviors and summarizing finetuned knowledge) that our method enables models to describe their finetuning-induced modifications using concise and accurate natural language descriptions.

Recent advances in Symmetric Positive Definite (SPD) matrix learning show that Riemannian metrics are fundamental to effective SPD neural networks. Motivated by this, we revisit the geometry of the Cholesky factors and uncover a simple product structure that enables convenient metric design. Building on this insight, we propose two fast and stable SPD metrics, Power--Cholesky Metric (PCM) and Bures--Wasserstein--Cholesky Metric (BWCM), derived via Cholesky decomposition. Compared with existing SPD metrics, the proposed metrics provide closed-form operators, computational efficiency, and improved numerical stability. We further apply our metrics to construct Riemannian Multinomial Logistic Regression (MLR) classifiers and residual blocks for SPD neural networks. Experiments on SPD deep learning, numerical stability analyses, and tensor interpolation demonstrate the effectiveness, efficiency, and robustness of our metrics. The code is available at https://github.com/GitZH-Chen/PCM_BWCM.

We uncover the hidden lattice geometry of large language models (LLMs): a symbolic backbone that grounds conceptual hierarchies and logical operations in embedding space. Our framework unifies the Linear Representation Hypothesis with Formal Concept Analysis (FCA), showing that linear attribute directions with separating thresholds induce a concept lattice via half-space intersections. This geometry enables symbolic reasoning through geometric meet (intersection) and join (union) operations, and admits a canonical form when attribute directions are linearly independent. Experiments on WordNet sub-hierarchies provide empirical evidence that LLM embeddings encode concept lattices and their logical structure, revealing a principled bridge between continuous geometry and symbolic abstraction.

Information tasks such as writing surveys or analytical reports require complex search and reasoning, and have recently been grouped under the umbrella of _deep research_ --- a term also adopted by recent models targeting these capabilities. Despite growing interest, the scope of the deep research task remains underdefined and its distinction from other reasoning-intensive problems is poorly understood. In this paper, we propose a formal characterization of the deep research (DR) task and introduce a benchmark to evaluate the performance of DR systems. We argue that the core defining feature of deep research is not the production of lengthy report-style outputs, but rather the high fan-out over concepts required during the search process, i.e., broad and reasoning-intensive exploration.To enable objective evaluation, we define DR using an intermediate output representation that encodes key claims uncovered during search—separating the reasoning challenge from surface-level report generation. Based on this formulation, we propose a benchmark LiveDRBench with 100 challenging tasks over scientific topics (e.g., datasets, materials discovery, prior art search) and public interest events (e.g., flight incidents, movie awards). Across state-of-the-art DR systems, F1 score ranges between 0.02 and 0.72 for any sub-category. OpenAI's model performs the best with an overall F1 score of 0.55. Analysis of the reasoning traces reveals that systems cover only about half of the necessary search queries, with proprietary models issuing broader and and deeper queries than open source models, highlighting gaps in both coverage and reasoning depth.