NeurIPS 2025 Papers

Due to the size and complexity of modern large language models (LLMs), it has proven challenging to uncover the underlying mechanisms that models use to solve reasoning problems. For instance, is their reasoning for a specific problem localized to certain parts of the network? Do they break down the reasoning problem into modular components that are then executed as sequential steps as we go deeper in the model? To better understand the reasoning capability of LLMs, we study a minimal propositional logic problem that requires combining multiple facts to arrive at a solution. By studying this problem on Mistral and Gemma models, up to 27B parameters, we illuminate the core components the models use to solve such logic problems. From a mechanistic interpretability point of view, we use causal mediation analysis to uncover the pathways and components of the LLMs' reasoning processes. Then, we offer fine-grained insights into the functions of attention heads in different layers. We not only find a sparse circuit that computes the answer, but we decompose it into sub-circuits that have four distinct and modular uses. Finally, we reveal that three distinct models -- Mistral-7B, Gemma-2-9B and Gemma-2-27B -- contain analogous but not identical mechanisms.

Side-channel analysis (SCA) poses a real-world threat by exploiting unintentional physical signals to extract secret information from secure devices. Evaluation labs also use the same techniques to certify device security. In recent years, deep learning has emerged as a prominent method for SCA, achieving state-of-the-art attack performance at the cost of interpretability. Understanding how neural networks extract secrets is crucial for security evaluators aiming to defend against such attacks, as only by understanding the attack can one propose better countermeasures. In this work, we apply mechanistic interpretability to neural networks trained for SCA, revealing $\textit{how}$ models exploit $\textit{what}$ leakage in side-channel traces. We focus on sudden jumps in performance to reverse engineer learned representations, ultimately recovering secret masks and moving the evaluation process from black-box to white-box. Our results show that mechanistic interpretability can scale to realistic SCA settings, even when relevant inputs are sparse, model accuracies are low, and side-channel protections prevent standard input interventions.

The unusual properties of in-context learning (ICL) have prompted investigations into the internal mechanisms of large language models. Prior work typically focuses on either special attention heads or task vectors at specific layers, but lacks a unified framework linking these components to the evolution of hidden states across layers that ultimately produce the model’s output. In this paper, we propose such a framework for ICL in classification tasks by analyzing two geometric factors that govern performance: the separability and alignment of query hidden states. A fine-grained analysis of layer-wise dynamics reveals a striking two-stage mechanism—separability emerges in early layers, while alignment develops in later layers. Ablation studies further show that Previous Token Heads drive separability, while Induction Heads and task vectors enhance alignment. Our findings thus bridge the gap between attention heads and task vectors, offering a unified account of ICL’s underlying mechanisms.

Vision-Language models (VLMs) show impressive abilities to answer questions on visual inputs (e.g., counting objects in an image), yet demonstrate higher accuracies when performing an analogous task on text (e.g., counting words in a text). We investigate this accuracy gap by identifying and comparing the circuits---the task-specific computational sub-graphs---in different modalities. We show that while circuits are largely disjoint between modalities, they implement relatively similar functionalities: the differences lie primarily in processing modality-specific data positions (an image or a text sequence). Zooming in on the image data representations, we observe they become aligned with the higher-performing analogous textual representations only towards later layers, too late in processing to effectively influence subsequent positions. To overcome this, we patch the representations of visual data tokens from later layers back into earlier layers. In experiments with multiple tasks and models, this simple intervention closes a third of the performance gap between the modalities, on average. Our analysis sheds light on the multi-modal performance gap in VLMs and suggests a training-free approach for reducing it.

Monitoring is an important aspect of safely deploying Large Language Models (LLMs). This paper examines activation probes for detecting ``high-stakes'' interactions---where the text indicates that the interaction might lead to significant harm---as a critical, yet underexplored, target for such monitoring. We evaluate several probe architectures trained on synthetic data, and find them to exhibit robust generalization to diverse, out-of-distribution, real-world data. Probes' performance is comparable to that of prompted or finetuned medium-sized LLM monitors, while offering computational savings of six orders-of-magnitude. These savings are enabled by reusing activations of the model that is being monitored. Our experiments also highlight the potential of building resource-aware hierarchical monitoring systems, where probes serve as an efficient initial filter and flag cases for more expensive downstream analysis. We release our novel synthetic dataset and the codebase at \url{https://github.com/arrrlex/models-under-pressure}.

Transformer-based language models exhibit complex behavior, but their internal computations remain poorly understood. Most mechanistic interpretability approaches treat components, such as attention heads and MLPs, as atomic units, ignoring potential functional substructure. We propose a finer-grained perspective that models components as superpositions of orthogonal singular directions. This perspective allows multiple independent computations to coexist within a single head or MLP, enabling selective intervention, attribution, and interpretation at a level of granularity beyond previous methods. We demonstrate this approach on the Indirect Object Identification (IOI) task, showing that well-known functional heads, like the “name mover,” encode overlapping subfunctions aligned with distinct singular directions. Nodes previously identified as part of circuits exhibit strong engagement along specific directions, supporting the view that meaningful computations are embedded in low-rank subspaces. While some functional axes remain difficult to interpret, our results reveal that transformer components are more distributed, compact, and compositional than assumed. This opens a new direction for fine-grained mechanistic interpretability and the study of model behavior.

Training data attribution (TDA) provides insights into which training data is responsible for a learned model behavior. Gradient-based TDA methods such as influence functions and unrolled differentiation both involve a computation that resembles an inverse Hessian-vector product (iHVP), which is difficult to approximate efficiently. We introduce an algorithm (ASTRA) which uses the EKFAC-preconditioner on Neumann series iterations to arrive at an accurate iHVP approximation for TDA. ASTRA is easy to tune, requires fewer iterations than Neumann series iterations, and is more accurate than EKFAC-based approximations. Using ASTRA, we show that improving the accuracy of the iHVP approximation can significantly improve TDA performance.

Recent methods in language model interpretability employ techniques such as sparse autoencoders to decompose residual stream contributions into linear, semantically-meaningful features. Our work demonstrates that an underlying assumption of these methods—that residual stream contributions build additively upon each other—is insufficient to fully explain model behavior. Specifically, we identify the Transformer Layer Correction Mechanism (TLCM), wherein adjacent transformer layers systematically counteract each other's contributions to the residual stream. TLCM appears in 5 out of 7 major open-source model families and activates across nearly all tokens in diverse texts. To understand TLCM, we show that it emerges during pretraining, operates most strongly on punctuation and numbers, and adaptively calibrates its correction strength based on the preceding layer's output. We further show that TLCM actively corrects a small subspace and promotes other subspaces, different from standard model behavior. We advance the ``propose-and-reject'' hypothesis: layers may propose multiple candidate features, while subsequent layers selectively filter out inappropriate ones. Finally, we discuss how our findings help explain three persistent challenges in feature-based interpretability: why extracted features descriptions often suffer from low specificity; why feature-based interventions for model steering fail at low magnitude; why recent work finds cross-layer transcoders outperform SAEs.

Deep networks have shown remarkable performance across a wide range of tasks, yet getting a global concept-level understanding of how they function remains a key challenge. Many post-hoc concept-based approaches have been introduced to understand their workings, yet they are not always faithful to the model. Further, they make restrictive assumptions on the concepts a model learns, such as class-specificity, small spatial extent, or alignment to human expectations. In this work, we put emphasis on the faithfulness of such concept-based explanations and propose a new model with model-inherent mechanistic concept-explanations. Our concepts are shared across classes and, from any layer, their contribution to the logit and their input-visualization can be faithfully traced. We also leverage foundation models to propose a new concept-consistency metric, C$^2$-Score, that can be used to evaluate concept-based methods. We show that, compared to prior work, our concepts are quantitatively more consistent and users find our concepts to be more interpretable, all while retaining competitive ImageNet performance.

Recent advances in Large Reasoning Models (LRMs) have demonstrated remarkable capabilities in solving complex tasks such as mathematics and coding. However, these models frequently exhibit a phenomenon known as *overthinking* during inference, characterized by excessive validation loops and redundant deliberation, leading to substantial computational overheads. In this paper, we aim to mitigate overthinking by investigating the underlying mechanisms from the perspective of mechanistic interpretability. We first showcase that the tendency of overthinking can be effectively captured by a single direction in the model's activation space and the issue can be eased by intervening the activations along this direction. However, this efficacy soon reaches a plateau and even deteriorates as the intervention strength increases. We therefore systematically explore the activation space and find that the overthinking phenomenon is actually tied to a low-dimensional manifold, which indicates that the limited effect stems from the noises introduced by the high-dimensional steering direction. Based on this insight, we propose **Manifold Steering**, a novel approach that elegantly projects the steering direction onto the low-dimensional activation manifold given the theoretical approximation of the interference noise. Extensive experiments on DeepSeek-R1 distilled models validate that our method reduces output tokens by up to 71\% while maintaining and even improving the accuracy on several mathematical benchmarks. Our method also exhibits robust cross-domain transferability, delivering consistent token reduction performance in code generation and knowledge-based QA tasks. Code is available at: https://github.com/Aries-iai/Manifold_Steering.

Despite remarkable advances in coding capabilities, language models (LMs) still struggle with simple syntactic tasks such as generating balanced parentheses. In this study, we investigate the underlying mechanisms behind the persistence of these errors across LMs of varying sizes (124M–7B) to both understand and mitigate the errors. Our study reveals that LMs rely on a number of components (attention heads and FF neurons) that independently make their own predictions. While some components reliably promote correct answers across a generalized range of inputs (i.e., implementing "sound mechanisms''), others are less reliable and introduce noise by promoting incorrect tokens (i.e., implementing "faulty mechanisms''). Errors occur when the faulty mechanisms overshadow the sound ones and dominantly affect the predictions. Motivated by this insight, we introduce RASteer, a steering method to systematically identify and increase the contribution of reliable components for improving model performance. RASteer substantially improves performance on balanced parentheses tasks, boosting accuracy of some models from $0$\% to around $100$\% without impairing the models' general coding ability. We further demonstrate its broader applicability in arithmetic reasoning tasks, achieving performance gains of up to around $20$\%.

Circuit discovery has gradually become one of the prominent methods for mechanistic interpretability, and research on circuit completeness has also garnered increasing attention. Methods of circuit discovery that do not guarantee completeness not only result in circuits that are not fixed across different runs but also cause key mechanisms to be omitted. The nature of incompleteness arises from the presence of OR gates within the circuit, which are often only partially detected in standard circuit discovery methods. To this end, we systematically introduce three types of logic gates: AND, OR, and ADDER gates, and decompose the circuit into combinations of these logical gates. Through the concept of these gates, we derive the minimum requirements necessary to achieve faithfulness and completeness. Furthermore, we propose a framework that combines noising-based and denoising-based interventions, which can be easily integrated into existing circuit discovery methods without significantly increasing computational complexity. This framework is capable of fully identifying the logic gates and distinguishing them within the circuit. In addition to the extensive experimental validation of the framework's ability to restore the faithfulness, completeness, and sparsity of circuits, using this framework, we uncover fundamental properties of the three logic gates, such as their proportions and contributions to the output, and explore how they behave among the functionalities of language models.

In Transformer language models, activation vectors transform from current token embeddings to next token predictions as they pass through the model. To isolate a minimal form of this transformation, we identify language model subnetworks that make bigram predictions, naive next token predictions based only on the current token. We find that bigram subnetworks can be found in fully trained language models up to 1B parameters, and these subnetworks are critical for model performance even when they consist of less than 0.2% of model parameters. Bigram subnetworks are concentrated in the first Transformer MLP layer, and they overlap significantly with subnetworks trained to optimally prune a given model. Mechanistically, the bigram subnetworks often recreate a pattern from the full models where the first layer induces a sharp change that aligns activations with next token predictions rather than current token representations. Our results demonstrate that bigram subnetworks comprise a minimal subset of parameters that are both necessary and sufficient for basic next token predictions in language models, and they help drive the transformation from current to next token activations in the residual stream. These subnetworks can lay a foundation for studying more complex language model circuits by building up from a minimal circuit.