ICLR 2026 论文列表

Scaling laws in deep learning -- empirical power-law relationships linking model performance to resource growth -- have emerged as simple yet striking regularities across architectures, datasets, and tasks. These laws are particularly impactful in guiding the design of state-of-the-art models, since they quantify the benefits of increasing data or model size, and hint at the foundations of interpretability in machine learning. However, most studies focus on asymptotic behavior at the end of training. In this work, we describe a richer picture by analyzing the entire training dynamics: we identify two novel \textit{dynamical} scaling laws that govern how performance evolves as function of different norm-based complexity measures. Combined, our new laws recover the well-known scaling for test error at convergence. Our findings are consistent across CNNs, ResNets, and Vision Transformers trained on MNIST, CIFAR-10 and CIFAR-100. Furthermore, we provide analytical support using a single-layer perceptron trained with logistic loss, where we derive the new dynamical scaling laws, and we explain them through the implicit bias induced by gradient-based training.

We study in-context learning (ICL) of linear regression in a deep linear self-attention model, characterizing how performance depends on various computational and statistical resources (width, depth, number of training steps, batch size and data per context). In a joint limit where data dimension, context length, and residual stream width scale proportionally, we analyze the limiting asymptotics for three ICL settings: (1) isotropic covariates and tasks (ISO), (2) fixed and structured covariance (FS), and (3) where covariances are randomly rotated and structured (RRS). For ISO and FS settings, we find that depth only aids ICL performance if context length is limited. Alternatively, in the RRS setting where covariances change across contexts, increasing the depth leads to significant improvements in ICL, even at infinite context length. This provides a new solvable toy model of neural scaling laws which depends on both width and depth of a transformer and predicts an optimal transformer shapes as a function of compute.

Recently, large language models (LLMs) have made remarkable progress, with multilingual capability emerging as a core foundational strengths. However, the internal mechanisms by which these models perform translation remain incompletely understood. In this paper, we elucidate the relationship between the attention mechanism in LLMs and their translation abilities. We find that certain attention heads, which we term token alignment heads, are specifically responsible for mapping tokens from the source language to the target language during inference. Through a systematic investigation across various models, we confirm that these token alignment heads exhibit several key characteristics: (1) Universality: They are present in all LLMs we studied. (2) Sparsity: They constitute only a small fraction of all attention heads. (3) Consistency: The set of token alignment heads activated by the model shows strong consistency across different language pairs. (4) Causality: Interventionally removing these heads leads to a sharp decline in the model's translation performance, while randomly removing non-token alignment heads has little impact on translation ability. (5) Functional Specificity: Ablating token alignment heads disproportionately harms translation but has a varied impact on other multilingual tasks. We also traced the formation of token alignment heads during pre-training, revealing an evolutionary path of rapid proliferation, stabilization, and eventual pruning. Furthermore we leverage these token alignment heads to filter multilingual training data, and our experiments show that these data could enhance translation capabilities of the models.

Decision tree ensembles are widely used in critical domains, making robustness and sensitivity analysis essential to their trustworthiness. We study the feature sensitivity problem, which asks whether an ensemble is ``sensitive" to a specified subset of features - such as protected attributes- whose manipulation can alter model predictions. Existing approaches often yield examples of sensitivity that lie far from the training distribution, limiting their interpretability and practical value. We propose a data-aware sensitivity framework that constrains the sensitive examples to remain close to the dataset, thereby producing realistic and interpretable evidence of model weaknesses. To this end, we develop novel techniques for data-aware search using a combination of mixed-integer linear programming (MILP) and satisfibility modulo theories (SMT) encodings. Our contributions are fourfold. Firstly, we strengthen the NP-hardness result for sensitivity verification, showing it holds even for trees of depth 1. Secondly, we develop MILP-optimizations that significantly speed up sensitivity verification for single ensembles and for the first time can also handle multiclass tree ensembles. Thirdly we introduce a data-aware framework generating realistic examples near the training distribution. Finally, we conduct an extensive experimental evaluation on large tree ensembles, demonstrating scalability to ensembles with up to 800 trees of depth 8, achieving substantial improvements over the state of the art. This framework provides a practical foundation for analyzing the reliability and fairness of tree-based models in high-stakes applications.

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.

Natural Language to SQL (NL2SQL) aims to translate natural language queries into executable SQL statements, offering non-expert users intuitive access to databases. While recent approaches leveraging large-scale private LLMs such as GPT-4 have achieved state-of-the-art results, they face two critical challenges: the lack of openness and reproducibility, and the prohibitive computational cost of test-time scaling. To address these issues, we explore improving the model-level performance of small-scale public LLMs in NL2SQL under resource-constrained settings. Our exploratory experiments reveal the potential of task decomposition for enhancing NL2SQL performance, but also highlight the difficulty of enabling LLMs to decompose queries effectively. Motivated by these findings, we propose LearNAT, a novel framework designed to enhance LLMs’ decomposition capabilities. LearNAT introduces (1) a Decomposition Synthesis Procedure, which leverages AST-guided search with pruning strategies to generate verifiable and efficient decompositions, and (2) Margin-Aware Reinforcement Learning, which provides fine-grained preference optimization for multi-step reasoning beyond standard DPO. Extensive experiments on benchmark datasets demonstrate that LearNAT significantly improves the performance of small-scale LLMs, achieving results comparable to GPT-4 with only a 7B parameter model. These results validate the effectiveness of verifiable decomposition and fine-grained preference learning in advancing NL2SQL towards openness, transparency, and efficiency. Our code is publicly available at https://anonymous.4open.science/r/LearNAT.

This paper studies Distributionally Robust Optimization (DRO), a fundamental framework for enhancing the robustness and generalization of statistical learning and optimization. An effective ambiguity set for DRO must involve distributions that remain consistent to the nominal distribution while being diverse enough to account for a variety of potential scenarios. Moreover, it should lead to tractable DRO solutions. To this end, we propose generative model-based ambiguity sets that capture various adversarial distributions beyond the nominal support space while maintaining consistency with the nominal distribution. Building on this generative ambiguity modeling, we propose DRO with Generative Ambiguity Set (GAS-DRO), a tractable DRO algorithm that solves the inner maximization over the parameterized generative model space. We formally establish the stationary convergence performance of GAS-DRO. We implement GAS-DRO with a diffusion model and empirically demonstrate its superior Out-of-Distribution (OOD) generalization performance in ML tasks.

This work investigates Poisoned Sample Detection (PSD), a promising defense approach against backdoor attacks. However, we observe that the effectiveness of many advanced PSD methods degrades significantly under weak backdoor attacks (\eg, low poisoning ratios or weak trigger patterns). To substantiate this observation, we conduct a statistical analysis across various attacks and PSD methods, revealing a strong correlation between the strength of the backdoor effect and the detection performance. Inspired by this, we propose amplifying the backdoor effect through training with Sharpness-Aware Minimization (SAM). Both theoretical insights and empirical evidence validate that SAM enhances the activations of top Trigger Activation Change (TAC) neurons while suppressing others. Based on this, we introduce SAM-enhanced PSD, a simple yet effective framework that seamlessly improves existing PSD methods by extracting detection features from the SAM-trained model rather than the conventionally trained model. Extensive experiments across multiple benchmarks demonstrate that our approach significantly improves detection performance under both strong and weak backdoor attacks, achieving an average True Positive Rate (TPR) gain of +34.3% over conventional PSD methods. Overall, we believe that the revealed correlation between the backdoor effect and detection performance could inspire future research advancements.

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.

Reinforcement learning with verifiable rewards (RLVR) has advanced the reasoning capabilities of large language models. Howerer, existing methods rely solely on outcome rewards, without explicitly optimizing verification or leveraging reliable signals from realistic environments, leading to unreliable self-verification and limited test-time scaling. To address this, we widen the verification–generation asymmetry by explicitly optimizing self-verification, making it a reliable driver of deeper test-time scaling. We introduce ReVeal, a multi-turn Reinforcement learning framework that evolves code generation through self-Verification and tool-based evaluation. ReVeal structures long-horizon reasoning as iterative generation–verification turns and incorporates TAPO for turn-level credit assignment, fostering the co-evolution of code and test generation. At inference, this strengthened self-verification enables the model to use self-constructed tests and tool feedback to continuously evolve code for 20+ turns on LiveCodeBench despite training on only three. It also significantly improves Pass@k, indicating stronger exploration that expands the reasoning boundaries of the base model. These findings highlight the promise of ReVeal as a scalable paradigm for RL training and test-time scaling, paving the way for more robust and autonomous AI agents.

Monitoring Large Language Model (LLM) outputs is crucial for mitigating risks from misuse and misalignment. However, LLMs could evade monitoring through steganography: Encoding hidden information within seemingly benign generations. In this paper, we evaluate the steganography capabilities in frontier LLMs to better understand the risk they pose. We focus on two types of steganography: passing encoded messages and performing encoded reasoning. We find that current models are unable to encode short messages in their outputs without a monitor noticing under standard affordances. They can succeed, however, if given additional affordances like using an unmonitored scratchpad and coordinating on what encoding scheme to use. We additionally find early signs that models can perform basic encoded reasoning in a simple state-tracking problem. This includes some ability to reason with their own and pre-defined schemes, including encoding schemes such as Hexadecimal. Despite this, they can rarely hide reasoning subtly within a cover task to fool a monitor. Overall, our results indicate that current LLMs exhibit nascent steganographic capabilities. While these capabilities are likely insufficient to bypass well-designed monitors at present, this could change in the future.

Large reasoning models (LRMs) excel on complex problems but face a critical barrier to efficiency: reinforcement learning (RL) training requires long rollouts for outcome-based rewards, where autoregressive decoding dominates time and memory usage. While sliding-window cache strategies can bound memory, they disrupt long-context reasoning and degrade performance. We introduce Progressive Thought Encoding, a parameter-efficient fine-tuning method that enables LRMs to reason effectively under fixed-size caches. By progressively encoding intermediate reasoning into compact representations, our approach eliminates the need to backpropagate through full-cache rollouts, thereby reducing training-time memory usage, while maintaining constant memory during inference. Experiments on three models, including Qwen2.5-3B-Instruct, Qwen2.5-7B-Instruct, and DeepSeek-R1-Distill-Llama-8B, across six widely used challenging mathematical benchmarks show consistent gains: our method achieves +19.3\% improvement over LoRA and +29.9\% over the baseline on average, with up to +23.4 absolute gains on AIME2024/2025 under tight cache budgets. These results demonstrate that Progressive Thought Encoding not only improves reasoning accuracy but also makes RL training of LRMs substantially more efficient and scalable under real-world memory constraints.

Parameter-efficient fine-tuning (PEFT) has become a de facto standard for adapting Large Language Models (LLMs). However, we identify a critical vulnerability within popular low-rank adaptation methods like LoRA: they can exacerbate "Catastrophic Inheritance"—the unchecked propagation of biases, noise, and data imbalances from pre-training. This phenomenon can degrade model robustness and fairness, undermining the benefits of efficient adaptation. To address this, we introduce Bias-Alleviating Low-Rank Adaptation (BA-LoRA). Our approach is founded on a principled decomposition of Catastrophic Inheritance into three core challenges: Knowledge Drift, Representation Collapse, and Overfitting to Noise. BA-LoRA systematically mitigates these issues by incorporating a trio of targeted regularizers—consistency, diversity, and SVD—designed to preserve core knowledge, enforce representational richness, and stabilize the low-rank updates. We conduct comprehensive evaluations on a suite of natural language understanding (NLU) and generation (NLG) tasks using diverse, prominent open-source language models (e.g., LLaMA-2-7B and DeBERTa-v3-base). Our results show that BA-LoRA not only outperforms state-of-the-art LoRA variants in terms of performance and stability, but also demonstrates quantitatively superior robustness and bias mitigation on targeted evaluations. This confirms its ability to counteract the adverse effects of Catastrophic Inheritance. The code is available at https://anonymous.4open.science/r/p5q9a1z8.

Dynamic graph representation learning under distribution shifts has drawn an increasing amount of attention in the research community, given its wide applicability in real-world scenarios. Existing methods typically employ a fixed-architecture design to extract invariant patterns. However, there may exist evolving distribution shifts in dynamic graphs, leading to suboptimal performance of fixed-architecture designs. To address this issue, we propose a novel adaptive-architecture design to handle evolving distribution shifts over time, to the best of our knowledge, for the first time. The proposed adaptive-architecture design introduces an adaptive mixture of architecture experts to capture invariant patterns under evolving distribution shifts, which imposes three challenges: 1) How to detect and characterize evolving distribution shifts to inform architectural decisions; 2) How to dynamically route different expert architectures to handle varying distribution characteristics; 3) How to ensure that the adaptive mixture of experts effectively discovers invariant patterns. To solve these challenges, we propose a novel \underline{\textbf{Ada}}ptive \underline{\textbf{Mix}}ture of Disentangled Experts (AdaMix) model to adaptively route architecture experts to varying distribution shifts and jointly learn spatio-temporal invariant patterns. Specifically, we propose a spatio-temporal distribution detector to infer evolving distribution shifts by jointly leveraging historical and current information. Building upon this, we develop a prototype-guided mixture of disentangled experts that adaptively routes experts with disentangled factors to different distribution shifts. Finally, we design a distribution-aware intervention mechanism that discovers invariant patterns based on expert selection of nodes. Extensive experiments on both synthetic and real-world datasets demonstrate that our proposed (AdaMix) model significantly outperforms state-of-the-art baselines.

Multi-Resolution Hash Encoding (MHE), the foundational technique behind Instant Neural Graphics Primitives, provides a powerful parameterization for neural fields. However, its spatial behavior lacks rigorous understanding from a physical systems perspective, leading to reliance on heuristics for hyperparameter selection. This work introduces a novel analytical approach that characterizes MHE by examining its Point Spread Function (PSF), which is analogous to the Green's function of the system. This methodology enables a quantification of the encoding's spatial resolution and fidelity. We derive a closed-form approximation for the collision-free PSF, uncovering inherent grid-induced anisotropy and a logarithmic spatial profile. We establish that the idealized spatial bandwidth, specifically the Full Width at Half Maximum (FWHM), is determined by the average resolution, $N_{\text{avg}}$. This leads to a counterintuitive finding: the effective resolution of the model is governed by the broadened empirical FWHM (and therefore $N_{\text{avg}}$), rather than the finest resolution $N_{\max}$, a broadening effect we demonstrate arises from optimization dynamics. Furthermore, we analyze the impact of finite hash capacity, demonstrating how collisions introduce speckle noise and degrade the Signal-to-Noise Ratio (SNR). Leveraging these theoretical insights, we propose Rotated MHE (R-MHE), an architecture that applies distinct rotations to the input coordinates at each resolution level. R-MHE mitigates anisotropy while maintaining the efficiency and parameter count of the original MHE. This study establishes a methodology based on physical principles that moves beyond heuristics to characterize and optimize MHE.

While Multi-Agent Systems (MAS) excel at complex tasks, their growing autonomy with operational complexity often leads to critical inefficiencies, such as excessive token consumption and failures arising from misinformation. Existing methods primarily focus on post-hoc failure attribution, lacking proactive, real-time interventions to enhance robustness and efficiency. To this end, we introduce SupervisorAgent, a lightweight and modular framework for runtime, adaptive supervision that operates without altering the base agent's architecture. Triggered by an LLM-free context filter, SupervisorAgent intervenes at critical junctures to proactively correct errors, guide inefficient behaviors, and purify observations. On the challenging GAIA benchmark, SupervisorAgent reduces the token consumption of the Smolagent framework by an average of 29.68% without compromising its success rate. Extensive experiments across five additional benchmarks (math reasoning, code generation, and question answering) and various SoTA foundation models validate the broad applicability and robustness of our approach.

Generating graph-structured data is crucial in applications such as molecular generation, knowledge graphs, and network analysis. However, their discrete, unordered nature makes them difficult for traditional generative models, leading to the rise of discrete diffusion and flow matching models. In this work, we introduce GraphBSI, a novel one-shot graph generative model based on Bayesian Sample Inference (BSI). Instead of evolving samples directly, GraphBSI iteratively refines a belief over graphs in the continuous space of distribution parameters, naturally handling discrete structures. Further, we state BSI as a stochastic differential equation (SDE) and derive a noise-controlled family of SDEs that preserves the marginal distributions via an approximation of the score function. Our theoretical analysis further reveals the connection to Bayesian Flow Networks and Diffusion models. Finally, in our empirical evaluation, we demonstrate state-of-the-art performance on molecular and synthetic graph generation, outperforming existing one-shot graph generative models on the standard benchmarks Moses and GuacaMol.

End-to-end backpropagation requires storing activations throughout all layers, creating memory bottlenecks that limit model scalability. Existing block-wise training methods offer means to alleviate this problem, but they rely on ad-hoc local objectives and remain largely unexplored beyond classification tasks. We propose $\textit{DiffusionBlocks}$, a principled framework for transforming transformer-based networks into genuinely independent trainable blocks that maintain competitive performance with end-to-end training. Our key insight leverages the fact that residual connections naturally correspond to updates in a dynamical system. With minimal modifications to this system, we can convert the updates to those of a denoising process, where each block can be learned independently by leveraging the score matching objective. This independence enables training with gradients for only one block at a time, thereby reducing memory requirements in proportion to the number of blocks. Our experiments on a range of transformer architectures (vision, diffusion, autoregressive, recurrent-depth, and masked diffusion) demonstrate that DiffusionBlocks training matches the performance of end-to-end training while enabling scalable block-wise training on practical tasks beyond small-scale classification. DiffusionBlocks provides a theoretically grounded approach that successfully scales to modern generative tasks across diverse architectures.

Dynamic Text-Attribute Graphs (DyTAGs), characterized by time-evolving graph interactions and associated text attributes, are prevalent in real-world applications. Existing methods, such as Graph Neural Networks (GNNs) and Large Language Models (LLMs), mostly focus on static TAGs. Extending these existing methods to DyTAGs is challenging as they largely neglect the *recent-global temporal semantics*: the recent semantic dependencies among interaction texts and the global semantic evolution of nodes over time. Furthermore, applying LLMs to the abundant and evolving text in DyTAGs faces efficiency issues. To tackle these challenges, we propose $\underline{Dy}$namic $\underline{G}$lobal-$\underline{R}$ecent $\underline{A}$daptive $\underline{S}$emantic $\underline{P}$rocessing (DyGRASP), a novel method that leverages LLMs and temporal GNNs to efficiently and effectively reason on DyTAGs. Specifically, we first design a node-centric implicit reasoning method together with a sliding window mechanism to efficiently capture recent temporal semantics. In addition, to capture global semantic dynamics of nodes, we leverage explicit reasoning with tailored prompts and an RNN-like chain structure to infer long-term semantics. Lastly, we intricately integrate the recent and global temporal semantics as well as the dynamic graph structural information using updating and merging layers. Extensive experiments on DyTAG benchmarks demonstrate DyGRASP's superiority, achieving up to 34\% improvement in Hit@10 for destination node retrieval task. Besides, DyGRASP exhibits strong generalization across different temporal GNNs and LLMs.