ICLR 2026 论文列表

Chain-of-thought (CoT) reasoning has become the standard paradigm for enabling Large Language Models (LLMs) to solve complex problems. However, recent studies reveal a sharp performance drop in *reasoning hop generalization* scenarios, where the required number of reasoning steps exceeds training distributions while the underlying algorithm remains unchanged. The internal mechanisms driving this failure remain poorly understood. In this work, we conduct a systematic study on tasks from multiple domains, and find that errors concentrate at token positions of a few critical error types, rather than being uniformly distributed. Closer inspection reveals that these token-level erroneous predictions stem from internal *competition mechanisms*: certain attention heads, termed *erroneous processing heads* (ep heads), tip the balance by amplifying incorrect reasoning trajectories while suppressing correct ones. Notably, removing individual ep heads during inference can often restore the correct predictions. Motivated by these insights, we propose test-time correction of reasoning, a lightweight intervention method that dynamically identifies and deactivates ep heads in the reasoning process. Extensive experiments across different tasks and LLMs show that it consistently improves reasoning hop generalization, highlighting both its effectiveness and potential.

Understanding how language and embedding models encode semantic relationships is fundamental to model interpretability. While early word embeddings exhibited intuitive vector arithmetic (''king'' - ''man'' + ''woman'' = ''queen''), modern high-dimensional text representations lack straightforward interpretable geometric properties. We introduce Rotor-Invariant Shift Estimation (RISE), a geometric approach that represents semantic-syntactic transformations as consistent rotational operations in embedding space, leveraging the manifold structure of modern language representations. RISE operations have the ability to operate across both languages and models with high transfer of performance, suggesting the existence of analogous cross-lingual geometric structure. We compare and evaluate RISE using two baseline methods, three embedding models, three datasets, and seven morphologically diverse languages in five major language groups. Our results demonstrate that RISE consistently maps discourse-level semantic-syntactic transformations with distinct grammatical features (e.g., negation and conditionality) across languages and models. This work provides the first systematic demonstration that discourse-level semantic-syntactic transformations correspond to consistent geometric operations in multilingual embedding spaces, empirically supporting the Linear Representation Hypothesis at the sentence level.

Figuring out how neural language models comprehend syntax acts as a key to revealing how they understand languages. We systematically analyzed methods of extracting syntax from models, namely _probing_, and found limitations yet widely exist in previous probing practice. We proposed a method capable of estimating mutual information (MI) and directly extracting dependency trees from attention scores in a mathematical-rigorous way, requiring no additional network training effort. Compared with previous approaches, it has a much simpler model, while being able to probe more complex dependency trees, also transparent for fine-grained explanation. We tested our method on several open-source LLMs and demonstrated its effectiveness by systematically comparing it with a great many competitive baselines. Several informative conclusions can be drawn by further analysis of the results, shedding light on our method’s explanatory potential. An anonymous and off-the-shelf version of our code is released at https://anonymous.4open.science/r/IPBP-99F1.

Finetuning large language models on narrowly harmful datasets can cause them to become emergently misaligned, giving stereotypically `evil' responses across diverse unrelated settings. Concerningly, a pre-registered survey of experts failed to predict this result, highlighting our poor understanding of the inductive biases governing learning and generalisation in LLMs. We use emergent misalignment (EM) as a case study to investigate these inductive biases, and find that although models can learn the narrow dataset task, the general solution is measurably more stable and more efficient. To establish this, we first demonstrate that EM is a robust phenomena by introducing new datasets which induce misalignment more consistently and coherently than prior work. We show that different EM finetunes converge to the same linear representation of general misalignment, which can be used to mediate misaligned behaviour. However, a linear representation of the narrow solution also exists, and can be learned by introducing a KL divergence loss. Comparing these representations reveals that general misalignment achieves lower loss, is more robust to perturbations, and is more influential in the pre-training distribution. This work isolates a concrete representation of general misalignment for monitoring and mitigation. More broadly, it offers a detailed case study and metrics for understanding how inductive biases shape generalisation in LLMs.

Single image super-resolution (SISR) often struggles to reconstruct high-resolution (HR) details from heavily degraded low-resolution (LR) inputs. Instead, reference-based super-resolution (RefSR) methods offer an alternative solution to generate promising results using high-quality reference (Ref) images to guide reconstruction. However, existing RefSR datasets focus on limited scene types, primarily featuring human activities and architectural scenes. Plant scenes exhibit complex textures and fine details, essential for advancing RefSR in natural and highly detailed scenes. To this end, we meticulously captured and manually selected high-quality images containing rich textures to construct a large-scale plant dataset, PlantRSR, comprising 16,585 HR–Ref pairs. The dataset captures the complexity and variability of plant scenes through extensive variations. In addition, we propose a novel RefSR method specifically designed to tackle the distinct challenges posed by plant imagery. It incorporates a Selective Key-Region Matching (SKRM) that selectively identifies and performs matching between LR and Ref images, focusing on distinctive botanical textures to improve matching efficiency. Additionally, a Texture-Guided Diffusion Module (TGDM) is proposed to refine LR textures by leveraging a diffusion process conditioned on the matched Ref textures. TGDM is effective in modeling irregular and fine textures, thereby facilitating more accurate SR results. The proposed method achieves significant improvements over state-of-the-art (SOTA) approaches on our PlantRSR dataset and other Benchmarks.

The reversal curse---a language model's (LM) inability to infer an unseen fact ``B is A'' from a learned factA is B''---is widely considered a fundamental limitation. We show that this is not an inherent failure but an artifact of how models encode knowledge. By training LMs from scratch on a synthetic dataset of relational knowledge graphs, we demonstrate that bilinear relational structure emerges in their hidden representations. This structure is associated with alleviating the reversal curse, facilitating the inference of unseen reverse facts. Crucially, we also find that this bilinear structure plays a key role in consistent model editing. When a fact is updated in a LM with this structure, the edit correctly propagates to its reverse and other logically dependent facts. In contrast, models lacking this representation not only suffer from the reversal curse but also fail to generalize edits, further introducing logical inconsistencies. Our results establish that training on a relational knowledge dataset induces the emergence of bilinear internal representations, which in turn support LMs in behaving in a logically consistent manner after editing. This implies that the success of model editing may be tied not just to editing algorithms but to the underlying representational geometry of the knowledge being modified.

In the recent years, branch-and-cut algorithms have been the target of data-driven approaches designed to enhance the decision making in different phases of the algorithm such as branching, or the choice of cutting planes (cuts). In particular, for cutting plane selection two score functions have been proposed in the literature to evaluate the quality of a cut: branch-and-cut tree size and gap closed. In this paper, we present new sample complexity lower bounds, valid for both scores. We show that for a wide family of classes $\mathcal{F}$ that maps an instance to a cut, learning over an unknown distribution of the instances to minimize those scores requires at least (up to multiplicative constants) as many samples as learning from the same class function $\mathcal{F}$ any generic target function (using square loss). Our results also extend to the case of learning from a restricted set of cuts, namely those from the Simplex tableau. To the best of our knowledge, these constitute the first lower bounds for the learning-to-cut framework. We compare our bounds to known upper bounds in the case of neural networks and show they are nearly tight, suggesting that both scores (gap closed and tree size) are of comparable difficulty from a learning standpoint. Guided by this insight, we provide empirical evidence -- by using a graph neural network cut selection evaluated on various integer programming problems -- that gap closed is a practical and effective proxy for minimizing the tree size. Although the gap closed score has been extensively used in the integer programming literature, this is the first principled analysis discussing both scores simultaneously both theoretically and computationally.

DINOv2 sees the world well enough to guide robots and segment images, but we still do not know what it sees. We conduct the first comprehensive analysis of DINOv2’s representational structure using overcomplete dictionary learning, extracting over 32,000 visual concepts in what constitutes the largest interpretability demonstration for any vision foundation model to date. This method provides the backbone of our study, which unfolds in three parts. In the first part, we analyze how different downstream tasks recruit concepts from our learned dictionary, revealing functional specialization: classification exploits “Elsewhere” concepts that fire everywhere except on target objects, implementing learned negations; segmentation relies exclusively on boundary detectors forming coherent subspaces; depth estimation draws on three distinct monocular cue families matching visual neuroscience principles. Turning to concept geometry and statistics, we find the learned dictionary deviates from ideal near-orthogonal (Grassmannian) structure, exhibiting higher coherence than random baselines. Concept atoms are not aligned with the neuron basis, confirming distributed encoding. We discover antipodal concept pairs that encode opposite semantics (e.g., “white shirt” vs “black shirt”), creating signed semantic axes. Separately, we identify concepts that activate exclusively on register tokens, revealing these encode global scene properties like motion blur and illumination. Across layers, positional information collapses toward a 2D sheet, yet within single images token geometry remains smooth and clustered even after position is removed, putting into question a purely sparse-coding view of representation. To resolve this paradox, we advance a different view: tokens are formed by combining convex mixtures of a few archetypes (e.g., a rabbit among animals, brown among colors, fluffy among textures). Multi-head attention directly implements this construction, with activations behaving like sums of convex regions. In this picture, concepts are expressed by proximity to landmarks and by regions—not by unbounded linear directions. We call this the Minkowski Representation Hypothesis (MRH), and we examine its empirical signals and consequences for how we study, steer, and interpret vision-transformer representations.

We consider the problem of transfer learning in Neyman–Pearson classification, where the objective is to minimize the error w.r.t. a distribution $\mu_1$, subject to the constraint that the error w.r.t. a distribution $\mu_0$ remains below a prescribed threshold. While transfer learning has been extensively studied in traditional classification, transfer learning in imbalanced classification such as Neyman–Pearson classification has received much less attention. This setting poses unique challenges, as both types of errors must be simultaneously controlled. Existing works address only the case of distribution shift in $\mu_1$, whereas in many practical scenarios shifts may occur in both $\mu_0$ and $\mu_1$. We derive an adaptive procedure that not only guarantees improved Type-I and Type-II errors when the source is informative, but also automatically adapt to situations where the source is uninformative, thereby avoiding negative transfer. In addition to such statistical guarantees, the procedures is efficient, as shown via complementary computational guarantees.

Retrofitting large language models (LLMs) with new behaviors typically requires full finetuning or distillation—costly steps that must be repeated for every architecture. In this work, we introduce ⌘V (Command-V), a backpropagation-free behavior transfer method that copies an existing residual representation adapter from a donor model and pastes its effect into an architecturally different recipient model. ⌘V profiles layer activations on a small prompt set, derives linear converters between corresponding layers, and applies the donor intervention in the recipient’s activation space. This process does not require access to the original training data and needs minimal compute. In three case studies—safety-refusal enhancement, jailbreak facilitation, and automatic chain-of-thought reasoning—⌘V matches the performance of direct finetuning while using orders of magnitude less resources.

We study the problem of minimizing polarization and disagreement in the Friedkin–Johnsen opinion dynamics model under incomplete information. Unlike prior work that assumes a static setting with full knowledge of users' innate opinions, we address the more realistic online setting where innate opinions are unknown and must be learned through sequential observations. This novel setting, which naturally mirrors periodic interventions on social media platforms, is formulated as a regret minimization problem, establishing a key connection between algorithmic interventions on social media platforms and theory of multi-armed bandits. In our formulation, a learner observes only a scalar feedback of the overall polarization and disagreement after an intervention. For this novel bandit problem, we propose a two-stage algorithm based on low-rank matrix bandits. The algorithm first performs subspace estimation to identify an underlying low-dimensional structure, and then employs a linear bandit algorithm within the compact dimensional representation derived from the estimated subspace. We prove that our algorithm achieves an $\widetilde{O}(\sqrt{T})$ cumulative regret over any time horizon $T$. Empirical results validate that our algorithm significantly outperforms a linear bandit baseline in terms of both cumulative regret and running time.

Existing rule-based explanations for Graph Neural Networks (GNNs) provide global interpretability but often optimize and assess fidelity in an intermediate, uninterpretable concept space, overlooking the grounding quality of the final subgraph explanations for end users. This gap yields explanations that may appear faithful yet be unreliable in practice. To this end, we propose LogicXGNN, a post hoc framework that constructs logical rules over reliable predicates explicitly designed to capture the GNN's message-passing structure, thereby ensuring effective grounding. We further introduce data-grounded fidelity ($Fid_D$), a realistic metric that evaluates explanations in their final-graph form, along with complementary utility metrics such as coverage and validity. Across extensive experiments, LogicXGNN improves $Fid_D$ by over 20% on average relative to state-of-the-art methods while being 10-100 times faster. With strong scalability and utility performance, LogicXGNN produces explanations that are faithful to the model's logic and reliably grounded in observable data.

Top-down transparency typically analyzes language model activations using probes with scalar or single-token outputs, limiting the range of behaviors that can be captured. To alleviate this issue, we develop a more expressive probe that can directly output natural language and perform LatentQA: the task of answering open-ended questions about activations. A key difficulty in developing such a probe is collecting a dataset mapping activations to natural-language descriptions. In response, we propose an approach for generating a pseudo-labeled dataset of activations and associated question-answer pairs and develop a fine-tuning method for training a decoder LLM on this dataset. We then validate our decoder’s fidelity by assessing its ability to read and steer model activations. First, we evaluate the decoder on a number of supervised reading tasks with a known answer, such as uncovering hidden system prompts and relational knowledge extraction, and observe that it outperforms competitive probing baselines. Second, we demonstrate that the decoder is precise enough to steer the target model to exhibit behaviors unseen during training. Finally, we show that LatentQA scales well with increasing dataset and model size, which is promising given how easily our approach can generate additional pseudo-labels.

Accurate estimation of uncertainty in deep learning is critical for deploying models in high-stakes domains such as medical diagnosis and autonomous decision-making, where overconfident predictions can lead to harmful outcomes. In practice, understanding the reason behind a model’s uncertainty and the type of uncertainty it represents can support risk-aware decisions, enhance user trust, and guide additional data collection. However, many existing methods only address a single type of uncertainty or require modifications and retraining of the base model, making them difficult to adopt in real-world systems. We introduce CUPID (Comprehensive Uncertainty Plug-in estImation moDel), a general-purpose module that jointly estimates aleatoric and epistemic uncertainty without modifying or retraining the base model. CUPID can be flexibly inserted into any layer of a pretrained network. It models aleatoric uncertainty through a learned Bayesian identity mapping and captures epistemic uncertainty by analyzing the model’s internal responses to structured perturbations. We evaluate CUPID across a range of tasks, including classification, regression, and out-of-distribution detection. The results show that it consistently delivers competitive performance while offering layer-wise insights into the origins of uncertainty. By making uncertainty estimation modular, interpretable, and model-agnostic, CUPID supports more transparent and trustworthy AI.

Semivalue–based data valuation uses cooperative‐game theory intuitions to assign each data point a value reflecting its contribution to a downstream task. Still, those values depend on the practitioner’s choice of utility, raising the question: *How robust is semivalue-based data valuation to changes in the utility?* This issue is critical when the utility is set as a trade‐off between several criteria and when practitioners must select among multiple equally valid utilities. We address it by introducing the notion of a dataset’s *spatial signature*: given a semivalue, we embed each data point into a lower-dimensional space where any utility becomes a linear functional, making the data valuation framework amenable to a simpler geometric picture. Building on this, we propose a practical methodology centered on an explicit robustness metric that informs practitioners whether and by how much their data valuation results will shift as the utility changes. We validate this approach across diverse datasets and semivalues, demonstrating strong agreement with rank‐correlation analyses and offering analytical insight into how choosing a semivalue can amplify or diminish robustness.

Electroencephalography (EEG) provides real-time insights into brain activity and supports diverse applications in neuroscience. While EEG foundation models (EFMs) have emerged to address the scalability issues of task-specific models, current approaches still yield clinically uninterpretable and weakly discriminative representations, inefficiently capture global dependencies, and neglect important local neural events. We present CodeBrain, a two-stage EFM designed to fill this gap. In the first stage, we introduce the TFDual-Tokenizer, which decouples heterogeneous temporal and frequency EEG signals into discrete tokens, quadratically expanding the representation space to enhance discriminative power and offering domain-specific representation-level interpretability by suggesting potential links to neural events and spectral rhythms. In the second stage, we propose the multi-scale EEGSSM architecture, which combines structured global convolution with sliding window attention to efficiently capture both sparse long-range and local dependencies, reflecting the brain’s small-world topology. Pretrained on the largest public EEG corpus, CodeBrain achieves strong generalization across 8 downstream tasks and 10 datasets under distribution shifts, supported by comprehensive ablations, scaling-law analyses, and interpretability evaluations.

Large language models (LLMs) have revolutionized natural language processing. Understanding their internal mechanisms is crucial for developing more interpretable and optimized architectures. Mechanistic interpretability has led to the development of various methods for assessing layer relevance, with cosine similarity being a widely used tool in the field. On this work, we demonstrate that cosine similarity is a poor proxy for the actual performance degradation caused by layer removal. Our theoretical analysis shows that a layer can exhibit an arbitrarily low cosine similarity score while still being crucial to the model's performance. On the other hand, empirical evidence from a range of LLMs confirms that the correlation between cosine similarity and actual performance degradation is often weak or moderate, leading to misleading interpretations of a transformer's internal mechanisms. We propose a more robust metric for assessing layer relevance: the actual drop in model accuracy resulting from the removal of a layer. Even though it is a computationally costly metric, this approach offers a more accurate picture of layer importance, allowing for more informed pruning strategies and lightweight models. Our findings have significant implications for the development of interpretable LLMs and highlight the need to move beyond cosine similarity in assessing layer relevance.

The fidelity with which neural networks can now generate content such as music presents a scientific opportunity: these systems appear to have learned implicit theories of such content's structure through statistical learning alone. This offers a potentially new lens on theories of human-generated media. When internal representations align with traditional constructs (e.g. chord progressions in music), they show how such categories can emerge from statistical regularities; when they diverge, they expose limits of existing frameworks and patterns we may have overlooked but that nonetheless carry explanatory power. In this paper, focusing on music generators, we introduce a method for discovering interpretable concepts using sparse autoencoders (SAEs), extracting interpretable features from the residual stream of a transformer model. We make this approach scalable and evaluable using automated labeling and validation pipelines. Our results reveal both familiar musical concepts and coherent but uncodified patterns lacking clear counterparts in theory or language. As an extension, we show such concepts can be used to steer model generations. Beyond improving model transparency, our work provides an empirical tool for uncovering organizing principles that have eluded traditional methods of analysis and synthesis.

We study the ability of Transformer models to learn sequences generated by Permuted Congruential Generators (PCGs), a widely used family of pseudo-random number generators (PRNGs). PCGs introduce substantial additional difficulty over linear congruential generators (LCGs) by applying a series of bit-wise shifts, XORs, rotations and truncations to the hidden state. We show that Transformers can nevertheless successfully perform in-context prediction on unseen sequences from diverse PCG variants, in tasks that are beyond published classical attacks. In our experiments we scale moduli up to $2^{22}$ using up to $50$ million model parameters and datasets with up to $5$ billion tokens. Surprisingly, we find even when the output is truncated to a single bit, it can be reliably predicted by the model. When multiple distinct PRNGs are presented together during training, the model can jointly learn them, identifying structures from different permutations. We demonstrate a scaling law with modulus $m$: the number of in-context sequence elements required for near-perfect prediction grows as $\sqrt{m}$. For larger moduli, optimization enters extended stagnation phases; in our experiments, learning moduli $m \geq 2^{20}$ requires incorporating training data from smaller moduli, demonstrating a critical necessity for curriculum learning. Finally, we analyze embedding layers and uncover a novel clustering phenomenon: the top principal components spontaneously group the integers into bitwise rotationally-invariant clusters, revealing how representations can transfer from smaller to larger moduli.