ICLR 2026 Papers

Classical influence functions face significant challenges when applied to deep neural networks, primarily due to non-invertible Hessians and high-dimensional parameter spaces. We propose the local Bayesian influence function (BIF), an extension of classical influence functions that replaces Hessian inversion with loss landscape statistics that can be estimated via stochastic-gradient MCMC sampling. This Hessian-free approach captures higher-order interactions among parameters and scales efficiently to neural networks with billions of parameters. We demonstrate state-of-the-art results on predicting retraining experiments.

In-context learning (ICL) has demonstrated significant performance improvements in transformer-based large models. This study identifies two key factors influencing ICL generalisation under complex non-i.i.d. scenario: algorithmic stability and distributional discrepancy. First, we establish a stability bound for transformer-based models trained with mini-batch gradient descent, revealing how specific optimization configurations interact with the smoothness of the loss landscape to ensure the stability of non-linear Transformers. Next, we introduce a distribution-level discrepancy measure that highlights the importance of aligning the ICL prompt distribution with the training data distribution to achieve effective generalisation. Building on these insights, we derive a generalisation error bound for ICL with asymptotic convergence guarantees, which further reveals that token-wise prediction errors accumulate over time and even lead to generalisation collapse if the prediction length is not properly constrained. Finally, empirical evaluations are provided to validate our theoretical findings.

Modern neural networks exhibit a striking property: basins of attraction in the loss landscape are often connected by low-loss paths, yet optimization dynamics generally remain confined to a single convex basin and rarely explore intermediate points. We resolve this paradox by identifying entropic barriers arising from the interplay between curvature variations along these paths and noise in optimization dynamics. Empirically, we find that curvature systematically rises away from minima, producing effective forces that bias noisy dynamics back toward the endpoints — even when the loss remains nearly flat. These barriers persist longer than energetic barriers, shaping the late-time localization of solutions in parameter space. Our results highlight the role of curvature-induced entropic forces in governing both connectivity and confinement in deep learning landscapes.

Large Reasoning Models (LRMs) have shown impressive capabilities in multi-step reasoning tasks. However, alongside these successes, a more deceptive form of model error has emerged—**Reasoning Hallucination**—where logically coherent but factually incorrect reasoning traces lead to persuasive yet faulty conclusions. Unlike traditional hallucinations, these errors are embedded within structured reasoning, making them more difficult to detect and potentially more harmful. In this work, we investigate reasoning hallucinations from a mechanistic perspective. We propose the **Reasoning Score**, which quantifies the depth of reasoning by measuring the divergence between logits obtained from projecting late layers of LRMs to the vocabulary space, effectively distinguishing shallow pattern-matching from genuine deep reasoning. Using this score, we conduct an in-depth analysis on the ReTruthQA dataset and identify two key reasoning hallucination patterns: early-stage fluctuation in reasoning depth and incorrect backtracking to flawed prior steps. These insights motivate our **R**easoning **H**allucination **D**etection (**RHD**) framework, which achieves state-of-the-art performance across multiple domains. To mitigate reasoning hallucinations, we further introduce **GRPO-R**, an enhanced reinforcement learning algorithm that incorporates step-level deep reasoning rewards via potential-based shaping. Our theoretical analysis establishes stronger generalization guarantees, and experiments demonstrate improved reasoning quality and reduced hallucination rates.

Currently the most powerful AI systems are aligned with human values via reinforcement learning from human feedback. Yet, reinforcement learning from human feedback models human preferences as noisy samples from a single linear ordering of shared human values and is unable to incorporate democratic AI alignment. In particular, the standard approach fails to represent and reflect diverse and conflicting perspectives of pluralistic human values. Recent research introduced the theoretically principled notion of quantile fairness for training a reinforcement learning policy in the presence of multiple, competing sets of values from different agents. Quite recent work provided an algorithm for achieving quantile fairness in the tabular setting with explicit access to the full set of states, actions and transition probabilities in the MDP. These current methods require solving linear programs with the size of the constraint set given by the number of states and actions, making it unclear how to translate this into practical training algorithms that can only take actions and observe individual transitions from the current state. In this paper, we design and prove the correctness of a new algorithm for quantile fairness that makes efficient use of standard policy optimization as a black-box without any direct dependence on the number of states or actions. We further empirically validate our theoretical results and demonstrate that our algorithm achieves competitive fairness guarantees to the prior work, while being orders of magnitude more efficient with respect to computation and the required number of samples. Our algorithm opens a new avenue for provable fairness guarantees in any setting where standard policy optimization is possible.

Post-hoc instance-level graph neural network (GNN) explainers are developed to identify a compact subgraph (i.e., explanation) that encompasses the most influential components for each input graph. A fundamental limitation of existing methods lies in the insufficient utilization of structural information during GNN explainer optimization. They typically optimize the explainer by aligning the GNN predictions of input graph and its explanation in the graph label space which inherently lacks expressiveness to describe various graph structures. Motivated by the powerful structural expression ability of vectorized graph representations, we for the first time propose to shift the GNN explainer optimization from the graph label space to the graph representation space. However, the paradigm shift is challenging due to both the entanglement between the explanatory and non-explanatory substructures, and the distributional discrepancy between the input graph and the explanation subgraph. To this end, we meticulously design IDEA, a universal dual-stage optimization framework grounded in a prototypical graph representation space, which can generalize across diverse existing GNN explainer architectures. Specifically, in the Structural Information Disentanglement stage, a graph tokenizer equipped with a structure-aware disentanglement objective is designed to disentangle the explanatory substructures and encapsulate them into explanatory prototypes. In the Explanatory Prototype Alignment stage, IDEA aligns the representational distributions of the input graph and its explanation unified in the prototypical representation space, to optimize the GNN explainer. Comprehensive experiments on real-world and synthetic datasets demonstrate the effectiveness of IDEA, with the average improvements of ROC-AUC by 4.45% and precision by 48.71%. We further integrate IDEA with diverse explainer architectures and achieve an improvement by up to 10.70%, which verifies its generalizability.

Protein language models (PLMs) have enabled advances in structure prediction and de novo protein design, yet they frequently collapse into pathological repetition during generation. Unlike in text, where repetition merely reduces readability, in proteins it undermines structural confidence and functional viability. To unify this problem, we present the first systematic study of repetition in PLMs. We first propose quantitative metrics to characterize motif-level and homopolymer repetition and then demonstrate their negative impact on folding reliability. To address this challenge, we propose UCCS (Utility-Controlled Contrastive Steering), which steers protein generation with a constrained dataset. Instead of naively contrasting high- vs. low-repetition sequences, we construct contrastive sets that maximize differences in repetition while tightly controlling for structural utility. This disentanglement yields steering vectors that specifically target repetition without degrading foldability. Injected at inference, these vectors consistently reduce repetition without retraining or heuristic decoding. Experiments with ESM-3 and ProtGPT2 in CATH, UniRef50, and SCOP show that our method outperforms decoding penalties and other baselines, substantially lowering repetition while preserving AlphaFold confidence scores. Our results establish repetition control as a central challenge for PLMs and highlight dataset-guided steering as a principled approach for reliable protein generation.

Machine learning (ML) models often struggle to maintain performance under distribution shifts, leading to inaccurate predictions on unseen future data. In this work, we investigate whether and under what conditions models can achieve such a generalization when relying solely on past data. We explore two primary approaches: convex combinations of past model parameters (parameter interpolation) and explicit extrapolation beyond the convex hull of past parameters (parameter extrapolation). We benchmark several methods within these categories on a diverse set of temporal tasks, including language modeling, news summarization, news tag prediction, academic paper categorization, satellite image-based land use classification over time, and historical yearbook photo gender prediction. Our empirical findings show that none of the evaluated methods consistently outperforms the simple baseline of using the latest available model parameters in all scenarios. In the absence of access to future data or robust assumptions about the underlying data-generating process, these results underscore the inherent difficulties of generalizing and extrapolating to future data and warrant caution when evaluating claims of such generalization.

The semantic similarity between sample expressions measures the distance between their latent `meaning'.These meanings are themselves typically represented by textual expressions. We propose a novel approach whereby the semantic similarity among textual expressions is based not on other expressions they can be rephrased as, but rather based on the imagery they evoke. While this is not possible with humans, generative models allow us to easily visualize and compare generated images, or their distribution, evoked by a textual prompt. Therefore, we characterize the semantic similarity between two textual expressions simply as the distance between image distributions they induce, or 'conjure.' We show that by choosing the Jeffreys divergence between the reverse-time diffusion stochastic differential equations (SDEs) induced by each textual expression, this can be directly computed via Monte-Carlo sampling. Our method contributes a novel perspective on semantic similarity that not only aligns with human-annotated scores, but also opens up new avenues for the evaluation of text-conditioned generative models while offering better interpretability of their learnt representations.

The releases of powerful open-weight large language models (LLMs) are often not accompanied by access to their full training data. Existing interpretability methods, particularly those based on activations, often require or assume distributionally similar data. This is a significant limitation when detecting and defending against novel potential threats like backdoors, which are by definition out-of-distribution. In this work, we introduce a new method for understanding, monitoring and controlling fine-tuned LLMs that interprets weights, rather than activations, thereby sidestepping the need for data that is distributionally similar to the unknown training data. We demonstrate that the top singular vectors of the weight difference between a fine-tuned model and its base model correspond to newly acquired behaviors. By monitoring the cosine similarity of activations along these directions, we can detect salient behaviors introduced during fine-tuning with high precision. For backdoored models that bypass safety mechanisms when a secret trigger is present, our method stops up to 100% of attacks with a false positive rate below 1.2%. For models that have undergone unlearning, we detect inference on erased topics with accuracy up to 95.42% and can even steer the model to recover "unlearned" information. Besides monitoring, our method also shows potential for pre-deployment model auditing: by analyzing commercial instruction-tuned models (OLMo, Llama, Qwen), we are able to uncover model-specific fine-tuning focus including mathematical problem solving, emoji usage, and Midjourney prompt generation.

Creativity evaluation remains a challenging frontier for large language models (LLMs). Current evaluations heavily rely on inefficient and costly human judgments, hindering progress in enhancing machine creativity. While automated methods exist, ranging from psychological testing to heuristic- or prompting-based approaches, they often lack generalizability or alignment with human judgment. To address these issues, in this paper, we propose a novel pairwise-comparison framework for assessing textual creativity, leveraging shared contextual instructions to improve evaluation consistency. We introduce CreataSet, a large-scale dataset with 100K+ human-level and 1M+ synthetic creative instruction-response pairs spanning diverse open-domain tasks. Through training on CreataSet, we develop an LLM-based evaluator named CrEval. CrEval demonstrates remarkable superiority over existing methods in alignment with human judgments. Experimental results underscore the indispensable significance of integrating both human-generated and synthetic data in training highly robust evaluators, and showcase the practical utility of CrEval in boosting the creativity of LLMs. We will release all data, code, and models publicly to support further research.

We investigate the expressive power of state space models (SSM), which have recently emerged as a potential alternative to transformer architectures in large language models. Building on recent work, we analyse SSM expressiveness through fragments and extensions of linear temporal logic over finite traces. Our results show that the expressive capabilities of SSM vary substantially depending on the underlying gating mechanism. We further distinguish between SSM operating over fixed-width arithmetic (quantised models), whose expressive power remains within regular languages, and SSM with unbounded precision, which can capture counting properties and non-regular languages. In addition, we provide a systematic comparison between these different SSM variants and known results on transformers, thereby clarifying how the two architectures relate in terms of expressive power.

Transformers have achieved state-of-the-art performance across diverse language and vision tasks. This success drives the imperative to interpret their internal mechanisms with the dual goals of enhancing performance and improving behavioral control. Attribution methods help advance interpretability by assigning model outputs associated with a target concept to specific model components. Current attribution research primarily studies multi-layer perceptron (MLP) neurons and addresses relatively simple concepts such as factual associations (e.g., Paris is located in France). This focus tends to overlook the impact of the attention mechanism and lacks a unified approach for analyzing more complex concepts. To fill these gaps, we introduce Scalable Attention Module Discovery (SAMD), a concept-agnostic method for mapping arbitrary, complex concepts to specific attention heads of general transformer models. We accomplish this by representing each concept as a vector, calculating its cosine similarity with each attention head, and selecting the TopK-scoring heads to construct the concept-associated attention module. We then propose Scalar Attention Module Intervention (SAMI), a simple strategy to diminish or amplify the effects of a concept by adjusting the attention module using only a single scalar parameter. Empirically, we demonstrate SAMD on concepts of varying complexity, and visualize the locations of their corresponding modules. Our results demonstrate that module locations remain stable before and after LLM post-training, and confirm prior work on the mechanics of LLM multi-lingualism. Through SAMI, we facilitate jailbreaking on HarmBench (+72.7%) by diminishing “safety” and improve performance on the GSM8K benchmark (+1.6%) by amplifying “reasoning”. Lastly, we highlight the domain-agnostic nature of our approach by suppressing the image classification accuracy of vision transformers on ImageNet.

Vision–language models (VLMs) align images and text with remarkable success, yet the geometry of their shared embedding space remains poorly understood. To probe this geometry, we begin from the Iso-Energy Assumption, which exploits cross-modal redundancy: a concept that is truly shared should exhibit the same average energy across modalities. We operationalize this assumption with an Aligned Sparse Autoencoder (SAE) that encourages energy consistency during training while preserving reconstruction. We find that this inductive bias changes the SAE solution without harming reconstruction, giving us a representation that serves as a tool for geometric analysis. Sanity checks on controlled data with known ground truth confirm that alignment improves when Iso-Energy holds and remains neutral when it does not. Applied to foundational VLMs, our framework reveals a clear structure with practical consequences: **(*i*)** sparse *bimodal* atoms carry the entire *cross-modal* alignment signal; **(*ii*)** *unimodal* atoms act as *modality-specific* biases and fully explain the modality gap; **(*iii*)** removing unimodal atoms collapses the gap without harming performance; **(*iv*)** restricting vector arithmetic to the bimodal subspace yields in-distribution edits and improved retrieval. These findings suggest that the right inductive bias can both preserve model fidelity and render the latent geometry interpretable and actionable.

With the rise of deep neural networks, especially in safety-critical applications, robustness and interpretability are crucial to ensure their trustworthiness. Recent advances in 3D-aware classifiers that map image features to volumetric representation of objects, rather than relying solely on 2D appearance, have greatly improved robustness on out-of-distribution (OOD) data. Such classifiers have not yet been studied from the perspective of interpretability. Meanwhile, current concept-based XAI methods often neglect OOD robustness. We aim to address both aspects with CAVE - Concept Aware Volumes for Explanations - a new direction that unifies interpretability and robustness in image classification. We design CAVE as a robust and inherently interpretable classifier that learns sparse concepts from 3D object representation. We further propose 3D Consistency (3D-C), a metric to measure spatial consistency of concepts. Unlike existing metrics that rely on human-annotated parts on images, 3D-C leverages ground-truth object meshes as a common surface to project and compare explanations across concept-based methods. CAVE achieves competitive classification performance while discovering consistent and meaningful concepts across images in various OOD settings.

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 analogues of the GPT-2 family of models will enable more precise interpretability research and improve our understanding of language models.

We propose $\textbf{FAME}$ (Formal Abstract Minimal Explanations), a new class of abductive explanations grounded in abstract interpretation. FAME is the first method to scale to large neural networks while reducing explanation size. Our main contribution is the design of dedicated perturbation domains that eliminate the need for traversal order. FAME progressively shrinks these domains and leverages LiRPA-based bounds to discard irrelevant features, ultimately converging to a $\textbf{formal abstract minimal explanation}$. To assess explanation quality, we introduce a procedure that measures the worst-case distance between an abstract minimal explanation and a true minimal explanation. This procedure combines adversarial attacks with an optional $VERI{\large X}+$ refinement step. We benchmark FAME against $VERI{\large X}+$ and demonstrate consistent gains in both explanation size and runtime on medium- to large-scale neural networks.

Despite impressive capabilities, LLMs' successes often rely on pattern-matching behaviors, yet these are also linked to OOD generalization failures in compositional tasks. However, behavioral studies commonly employ task setups that allow multiple generalization sources (e.g., algebraic invariances, structural repetition), obscuring a precise and testable account of how well LLMs perform generalization through pattern matching and their limitations. To address this ambiguity, we first formalize pattern matching as functional equivalence, i.e., identifying pairs of subsequences of inputs that consistently lead to identical results when the rest of the input is held constant. Then, we systematically study how decoder-only Transformer and Mamba behave in controlled tasks with compositional structures that isolate this mechanism. Our formalism yields predictive and quantitative insights: (1) Instance-wise success of pattern matching is well predicted by the number of contexts witnessing the relevant functional equivalence. We prove a tight sample complexity bound of learning a two-hop structure by identifying the exponent of the data scaling law for perfect in-domain generalization. Our empirical results align with the theoretical prediction, under 20× parameter scaling and across architectures. (3) Path ambiguity is a structural barrier: when a variable influences the output via multiple paths, models fail to form unified intermediate state representations, impairing accuracy and interpretability. (4) Chain-of-Thought reduces data requirements yet does not resolve path ambiguity. Hence, we provide a predictive, falsifiable boundary for pattern matching and a foundational diagnostic for disentangling mixed generalization mechanisms.

In-context Learning (ICL) is an emerging few-shot learning paradigm based on modern Language Models (LMs), yet its inner mechanism remains unclear. In this paper, we investigate the mechanism through a novel perspective of information removal. Specifically, we demonstrate that in the zero-shot scenario, LMs encode queries into non-selective representations in hidden states containing information for all possible tasks, leading to arbitrary outputs without focusing on the intended task, resulting in near-zero accuracy. Meanwhile, we find that selectively removing specific information from hidden states by a low-rank filter effectively steers LMs toward the intended task. Building on these findings, by measuring the hidden states on carefully designed metrics, we observe that few-shot ICL effectively simulates such task-oriented information removal processes, selectively removing the redundant information from entangled non-selective representations, and improving the output based on the demonstrations, which constitutes a key mechanism underlying ICL. Moreover, we identify essential attention heads inducing the removal operation, termed Denoising Heads, which enables the ablation experiments blocking the information removal operation from the inference, where the ICL accuracy significantly degrades, especially when the correct label is absent from the few-shot demonstrations, confirming both the critical role of the information removal mechanism and denoising heads.