ICLR 2026 Papers

Understanding the properties of the parameter space in feed-forward ReLU networks is critical for effectively analyzing and guiding training dynamics. After initialization, training under gradient flow decisively restricts the parameter space to an algebraic variety that emerges from the homogeneous nature of the ReLU activation function. In this study, we examine two key challenges associated with feed-forward ReLU networks built on general directed acyclic graph (DAG) architectures: the (dis)connectedness of the parameter space and the existence of singularities within it. We extend previous results by providing a thorough characterization of connectedness, highlighting the roles of bottleneck nodes and balance conditions associated with specific subsets of the network. Our findings clearly demonstrate that singularities are intricately connected to the topology of the underlying DAG and its induced sub-networks. We discuss the reachability of these singularities and establish a principled connection with differentiable pruning. We validate our theory with simple numerical experiments.

Designing robust reinforcement learning (RL) agents in the presence of imperfect reward signals remains a core challenge. In practice, agents are often trained with proxy rewards that only approximate the true objective, leaving them vulnerable to reward hacking, where high proxy returns arise from unintended or exploitative behaviors. Recent work formalizes this issue using r-correlation between proxy and true rewards, but existing methods like occupancy-regularized policy optimization (ORPO) optimize against a fixed proxy and do not provide strong guarantees against broader classes of correlated proxies. In this work, we formulate reward hacking as a robust policy optimization problem over the space of all r-correlated proxy rewards. We derive a tractable max-min formulation, where the agent maximizes performance under the worst-case proxy consistent with the correlation constraint. We further show that when the reward is a linear function of known features, our approach can be adapted to incorporate this prior knowledge, yielding both improved policies and interpretable worst-case rewards. Experiments across several environments show that our algorithms consistently outperform ORPO in worst-case returns, and offer improved robustness and stability across different levels of proxy–true reward correlation. These results show that our approach provides both robustness and transparency in settings where reward design is inherently uncertain.

Score-based diffusion models have achieved remarkable progress in various domains with the ability to generate new data samples that do not exist in the training set. In this work, we study the hypothesis that such creativity arises from an interpolation effect caused by a smoothing of the empirical score function. Focusing on settings where the training set lies uniformly in a one-dimensional subspace, we probe the interplay between score smoothing and the denoising dynamics with analytical solutions and numerical experiments. In particular, we demonstrate how a smoothed score function can lead to the generation of samples that interpolate among the training data within their subspace while avoiding full memorization. Moreover, we present theoretical and empirical evidence that learning score functions with regularized neural networks can have a similar effect as score smoothing, including in simple nonlinear settings.

Diffusion large language models (dLLMs) are emerging as a promising alternative to autoregressive models (ARMs) due to their ability to capture bidirectional context and the potential for parallel generation. Despite the advantages, dLLM inference remains computationally expensive as the full input context is processed at every iteration. In this work, we analyze the generation dynamics of dLLMs and find that intermediate representations, including key, value, and hidden states, change only subtly across successive iterations. Leveraging this insight, we propose ES-dLLM, a training-free inference acceleration framework for dLLM that reduces computation by skipping tokens in early layers based on the estimated importance. Token importance is computed with intermediate tensor variation and confidence scores of previous iterations. Experiments on LLaDA-8B and Dream-7B demonstrate that ES-dLLM achieves throughput of up to 226.57 and 308.51 tokens per second (TPS), respectively, on an NVIDIA H200 GPU, delivering 5.6$\times$ to 16.8$\times$ speedup over the vanilla implementation and up to 1.85$\times$ over the state-of-the-art caching method, while preserving generation quality.

In this work, we propose K-Flow, a novel generative learning paradigm that flows along the $K$-amplitude domain, where $K$ is a scaling parameter that organizes projected coefficients (frequency bands), and amplitude refers to the norm of such coefficients. We instantiate K-Flow with three concrete $K$-amplitude transformations: Fourier transformation, Wavelet transformation, and PCA. By incorporating the $K$-amplitude transformations, K-Flow enables flow matching across the scaling parameter as time. We discuss six properties of K-Flow, covering its theoretical foundations, energy and temporal dynamics, and practical applications. Specifically, from the perspective of practical usage, K-Flow allows for steerable generation by controlling the information at different scales. To demonstrate the effectiveness of K-Flow, we conduct experiments on both unconditional and conditional image generation tasks, showing that K-Flow achieves competitive performance. Furthermore, we perform three ablation studies to illustrate how K-Flow leverages the scaling parameter for controlled image generation. Additional results, including scientific applications, are also provided.

Current large language model (LLM) development treats task-solving and preference-alignment as separate challenges, optimizing first for objective correctness, then for alignment to aggregated human preferences. This paradigm fails in human-facing applications where solving a problem correctly is insufficient if the response mismatches the user’s needs. This challenge intensifies in just-in-time scenarios where no prior user interaction history exists due to cold-start conditions or privacy constraints. LLMs need to identify what they don’t know about user preferences, strategically elicit preference values through questioning, then adapt their reasoning processes and responses accordingly—a complicated chain of cognitive processes which we term personalized reasoning. We introduce PREFDISCO, an evaluation methodology that transforms static benchmarks into interactive personalization tasks using psychologically-grounded personas with sparse preferences. Our framework creates scenarios where identical questions require different reasoning chains depending on user context, as optimal explanation approaches vary by individual expertise and preferences while maintaining factual accuracy. Evaluation of 21 frontier models across 10 tasks reveals 29.0% of naive personalization attempts produce worse preference alignment than generic responses, yet generic responses also fail to serve individual user needs effectively. These findings suggest personalized reasoning requires dedicated development rather than emerging naturally. PREFDISCO establishes personalized reasoning as a measurable research frontier and reveals fundamental limitations in current LLMs’ interactive capabilities, providing a foundation for developing systems that can adapt to individual users in education, healthcare, and technical domains where personalization is critical.

Recently, diffusion models have been recognized as state-of-the-art models for image generation due to their ability to produce high-quality images. However, recent studies have shown that diffusion models are susceptible to backdoor attacks, where an attacker can activate hidden biases using a specific trigger pattern, causing the model to generate a predefined target. Fortunately, executing backdoor attacks is still challenging, as they typically require substantial time and memory to perform parameter-based fine-tuning. In this paper, we are the first to reveal the **spatio-temporal redundancy** in backdoor attacks on diffusion models. **Regarding spatial redundancy**, we observed the *enrichment phenomenon*, which reflects the abnormal gradient accumulation induced by backdoor injection. **Regarding temporal redundancy**, we observed a marginal effect associated with specific time steps, indicating that only a limited subset of time steps plays a critical role in backdoor injection. Building on these findings, we present a novel framework, *STEDiff*, comprising two key components: *STEBA* and *STEDF*. *STEBA* is a spatio-temporally efficient accelerated attack strategy that achieves up to **15.07×** speedup in backdoor injection while reducing GPU memory usage by **82%**. *STEDF* is a detection framework leveraging spatio-temporal features, by modeling the enrichment phenomenon in weights and anisotropy across time steps, which achieves a backdoor detection rate of up to **99.8%**. Our code is available at: [https://github.com/paoche11/STEDiff](https://github.com/paoche11/STEDiff).

High-resolution structure determination by cryo-electron microscopy (cryo-EM) requires the accurate fitting of an atomic model into an experimental density map. Traditional refinement pipelines like Phenix.real_space_refine and Rosetta are computationally expensive, demand extensive manual tuning, and present a significant bottleneck for researchers. We present CryoNet.Refine, an end-to-end, deep learning framework that automates and accelerates molecular structure refinement. Our approach utilizes a one-step diffusion model that integrates a density-aware loss function with robust stereochemical restraints, enabling it to rapidly optimize a structure against the experimental data. CryoNet.Refine stands as a unified and versatile solution capable of refining not only protein complexes but also nucleic acids (DNA/RNA) and their assemblies. In benchmarks against Phenix.real_space_refine, CryoNet.Refine consistently yields substantial improvements in both model–map correlation and overall model geometric quality. By offering a scalable, automated, and powerful alternative, CryoNet.Refine is poised to become an essential tool for next-generation cryo-EM structure refinement.

We propose to improve multi-concept prompt fidelity in text-to-image diffusion models. We begin with common failure cases—prompts like “a cat and a clock” that sometimes yields images where one concept is missing, faint, or colliding awkwardly with another. We hypothesize that this happens when the diffusion model drifts into mixed modes that over-emphasize a single concept it learned strongly during training. Instead of re-training, we introduce a corrective sampling strategy that steers away from regions where the joint prompt behavior overlaps too strongly with any single concept in the prompt. The goal is to steer towards “pure” joint modes where all concepts can coexist with balanced visual presence. We further show that existing multi-concept guidance schemes can operate in unstable weight regimes that amplify imbalance; we characterize favorable regions and adapt sampling to remain within them. Our approach, CO3, is plug-and-play, requires no model tuning, and complements standard classifier-free guidance. Experiments on diverse multi-concept prompts indicate improvements in concept coverage, balance and robustness, with fewer dropped or distorted concepts com- pared to standard baselines and prior compositional methods. Results suggest that lightweight corrective guidance can substantially mitigate brittle semantic alignment behavior in modern diffusion systems.

A well-designed vectorized representation is crucial for the learning systems natively based on 3D Gaussian Splatting. While 3DGS enables efficient and explicit 3D reconstruction, its parameter-based representation remains hard to learn as features, especially for neural-network-based models. Directly feeding raw Gaussian parameters into learning frameworks fails to address the non-unique and heterogeneous nature of the Gaussian parameterization, yielding highly data-dependent models. This challenge motivates us to explore a more principled approach to represent 3D Gaussian Splatting in neural networks that preserves the underlying color and geometric structure while enforcing unique mapping and channel homogeneity. In this paper, we propose an embedding representation of 3DGS based on continuous submanifold fields that encapsulate the intrinsic information of Gaussian primitives, thereby benefiting the learning of 3DGS.

Large Language Models have demonstrated strong performance across a wide range of tasks, but adapting them efficiently to new domains remains a key challenge. Parameter-Efficient Fine-Tuning (PEFT) methods address this by introducing lightweight, trainable modules while keeping most pre-trained weights fixed. The prevailing approach, LoRA, models updates using a low-rank decomposition, but its expressivity is inherently constrained by the rank. Recent methods like HiRA aim to increase expressivity by incorporating a Hadamard product with the frozen weights, but still rely on the structure of the pre-trained model. We introduce ABBA, a new PEFT architecture that reparameterizes the update as a Hadamard product of two independently learnable low-rank matrices. In contrast to prior work, ABBA fully decouples the update from the pre-trained weights, enabling both components to be optimized freely. This leads to significantly higher expressivity under the same parameter budget, a property we validate through matrix reconstruction experiments. Empirically, ABBA achieves state-of-the-art results on arithmetic and commonsense reasoning benchmarks, consistently outperforming existing PEFT methods by a significant margin across multiple models. Our code is publicly available at: https://github.com/CERT-Lab/abba.

With the increasing accessibility and utilization of multilingual documents, Cross-Lingual Information Retrieval (CLIR) has emerged as an important research area. Conventionally, CLIR tasks have been conducted under settings where the language of documents differs from that of queries, and typically, the documents are composed in a single coherent language. In this paper, we highlight that in such a setting, the cross-lingual alignment capability may not be evaluated adequately. Specifically, we observe that, in a document pool where English documents coexist with another language, most multilingual retrievers tend to prioritize unrelated English documents over the related document written in the same language as the query. To rigorously analyze and quantify this phenomenon, we introduce various scenarios and metrics designed to evaluate the cross-lingual alignment performance of multilingual retrieval models. Furthermore, to improve cross-lingual performance under these challenging conditions, we propose a novel training strategy aimed at enhancing cross-lingual alignment. Using only a small dataset consisting of 2.8k samples, our method significantly improves the cross-lingual retrieval performance while simultaneously mitigating the English inclination problem. Extensive analyses demonstrate that the proposed method substantially enhances the cross-lingual alignment capabilities of most multilingual embedding models.

Recent advancements in language models have demonstrated remarkable in-context learning abilities, prompting the exploration of in-context reinforcement learning (ICRL) to extend the promise to decision domains. Due to involving more complex dynamics and temporal correlations, existing ICRL approaches may face challenges in learning from suboptimal trajectories and achieving precise in-context inference. In the paper, we propose **S**calable **I**n-**C**ontext **Q**-**L**earning (**S-ICQL**), an innovative framework that harnesses dynamic programming and world modeling to steer ICRL toward efficient reward maximization and task generalization, while retaining the scalability and stability of supervised pretraining. We design a prompt-based multi-head transformer architecture that simultaneously predicts optimal policies and in-context value functions using separate heads. We pretrain a generalized world model to capture task-relevant information, enabling the construction of a compact prompt that facilitates fast and precise in-context inference. During training, we perform iterative policy improvement by fitting a state value function to an upper-expectile of the Q-function, and distill the in-context value functions into policy extraction using advantage-weighted regression. Extensive experiments across a range of discrete and continuous environments show consistent performance gains over various types of baselines, especially when learning from suboptimal data. Our code is available at [https://github.com/NJU-RL/SICQL](https://github.com/NJU-RL/SICQL).

Peptide therapeutics are widely regarded as the “third generation” of drugs, yet progress in peptide Machine Learning (ML) are hindered by the absence of standardized benchmarks. Here we present \textbf{PepBenchmark}, which standardizes datasets, preprocessing, and evaluation protocols for peptide drug discovery. PepBenchmark comprises three components: (1) \textbf{PepBenchData}, a well-curated collection comprising 29 canonical-peptide and 6 non-canonical-peptide datasets across 7 groups, systematically covering key aspects of peptide drug development—representing, to the best of our knowledge, the most comprehensive AI-ready dataset resource to date; (2) \textbf{PepBenchPipeline}, a standardized preprocessing pipeline that ensures consistent cleaning, representation conversion, and dataset splitting, addressing the quality issues that often arise from ad-hoc pipelines; and (3) \textbf{PepBenchLeaderboard}, a unified evaluation protocol and leaderboard with strong baselines across 4 major methodological families: fingerprint-based, GNN-based, PLM-based, and SMILES-based models. Together, PepBenchmark provides the first standardized and comparable foundation for peptide drug discovery, facilitating methodological advances and translation into real-world applications. Code is included in the supplementary material and will be made publicly available.

Temporal graph neural networks (TGNN) extend graph neural networks to dynamic networks and have demonstrated strong predictive power. However, interpreting TGNN remains far less explored than their static-graph counterparts. This paper introduces TEMporal Graph eXplainer (TemGX), a training-free,post-hoc framework that help users interpret and understand TGNN behavior by discovering temporal subgraphs and their evolution that are responsible for TGNN output of interests.We introduce a class of explainability measures that extends influence maximization in terms of structural influence and time decay to model temporal influence. We formulate the explanation task as a constrained optimization problem, and propose fast algorithms to discover explanations with guarantees on their temporal explainability. Our experimental study verifies the effectiveness and efficiency of TemGX for TGNN explanation, compared with state-of-the-art explainers. We also showcase how TemGX supports inference queries for dynamic network analysis.

Federated learning promises significant sample-efficiency gains by pooling data across multiple agents, yet incentive misalignment is an obstacle: each update is costly to the contributor but boosts every participant. We introduce a game-theoretic framework that captures heterogeneous data: an agent’s utility depends on who supplies each sample, not just how many. Agents aim to meet a PAC-style accuracy threshold at minimal personal cost. We show that uncoordinated play yields pathologies: pure equilibria may not exist, and the best equilibrium can be arbitrarily more costly than cooperation. To steer collaboration, we analyze the cost-minimizing contribution vector, prove that computing it is NP-hard, and derive a polynomial-time linear program that achieves a logarithmic approximation. Finally, pairing the LP with a simple pay-what-you-contribute rule—each agent receives a payment equal to its sample cost—yields a mechanism that is strategy-proof and, within the class of contribution-based transfers, is unique.

Recent advances in large reasoning language models (LRMs) rely on test-time scaling, which extends long chain-of-thought (CoT) generation to solve complex tasks. However, overthinking in long CoT not only slows down the efficiency of problem solving, but also risks accuracy loss due to the extremely detailed or redundant reasoning steps. We propose a simple yet effective method that allows LLMs to self-truncate CoT sequences by early exit during generation. Instead of relying on fixed heuristics, the proposed method monitors model behavior at potential reasoning transition points and dynamically terminates the next reasoning chain's generation when the model exhibits high confidence in a trial answer. Our method requires no additional training and can be seamlessly integrated into existing o1-like reasoning LLMs. Experiments on 10 reasoning benchmarks (e.g., GSM8K, MATH-500, AMC, GPQA, AIME and LiveCodeBench) show that the proposed method is consistently effective on 11 cutting-edge reasoning LLMs of varying series and sizes, reducing the length of CoT sequences by an average of 19.1% to 80.1% while improving accuracy by 0.3% to 5.0%.

While Reinforcement Learning with Verifiable Rewards (RLVR) has shown strong effectiveness in reasoning tasks, it cannot be directly applied to non-verifiable domains lacking ground-truth verifiers, such as LLM alignment. In this work, we investigate whether high-quality reference outputs can be effectively leveraged to bridge this gap. First, we design evaluation protocols that enhance LLM-based evaluators for LLM alignment using reference outputs. Through comprehensive experiments, we show that a reference-guided approach substantially improves the accuracy of less capable LLM-judges using references from frontier models; stronger LLM-judges can also be enhanced by human-written references. We then demonstrate the utility of high-quality references in alignment tuning, where LLMs guided with references are used as judges to self-improve. We show that reference-guided self-improvement yields clear gains over both SFT distillation and reference-free baselines, achieving performance comparable to training with finetuned reward models. Specifically, our method achieves scores of 73.1% and 58.7% on AlpacaEval and Arena-Hard with Llama-3-8B-Instruct, and 70.0% and 74.1% with Qwen2.5-7B. These results highlight the potential of using reference-guided LLM-evaluators to enable effective post-training in non-verifiable domains.

Test-time reasoning significantly enhances pre-trained AI agents’ performance. However, it requires an explicit environment model, often unavailable or overly complex in real-world scenarios. While MuZero enables effective model learning for search in perfect information games, extending this paradigm to imperfect information games presents substantial challenges due to more nuanced look-ahead reasoning techniques and large number of states relevant for individual decisions. This paper introduces an algorithm LAMIR that learns an abstracted model of an imperfect information game directly from the agent-environment interaction. During test time, this trained model is used to perform look-ahead reasoning. The learned abstraction limits the size of each subgame to a manageable size, making theoretically principled look-ahead reasoning tractable even in games where previous methods could not scale. We empirically demonstrate that with sufficient capacity, LAMIR learns the exact underlying game structure, and with limited capacity, it still learns a valuable abstraction, which improves game playing performance of the pre-trained agents even in large games.