ICML 2026 Papers

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we propose a novel proximal-based generative modeling (PGM) framework that rigorously circumvents explicit likelihood evaluation. Our framework is built upon a theoretical equivalence between Gaussian convolution in diffusion processes and Moreau-Yosida regularization in nonsmooth optimization. This enables a new sampling mechanism driven by the proposed Moreau score, which admits a closed-form expression via proximal operators. Moreover, we introduce Moreau score matching to learn the proximal operators that rely solely on samples drawn from the prior distribution. Theoretically, PGM eliminates the early-stopping bias inherent in the score-based diffusion model and achieves non-asymptotic convergence. Experiments demonstrate that PGM significantly surpasses state-of-the-art methods in reconstruction quality and sampling time.

While MLLMs show promising capacity on general visual understanding, they suffer from *geometric fragility*: standard visual representations often degrade rapidly under changes in viewpoint and viewing distance. Our analysis identifies that existing paradigms, whether relying on input-level fusion or latent reconstruction, remain entangled with the view-dependent pixel grid, failing to decouple intrinsic 3D structure from extrinsic camera pose. To address this, we introduce **AffIn-Space**, a framework that enforces strict affine invariance to enable robust spatial understanding. Unlike implicit learning approaches, AffIn-Space introduces a two-stage explicit decoupling mechanism. First, it employs *explicit geometric resampling* by utilizing decomposed affine quantities (derived from pose features) to spatially align 3D features to a canonical state before fusion. Second, within the MLLM, we implement *affine-invariant constraints* via an orthogonal projection mechanism, which mathematically strips away pose-dependent noise from the hidden states while retaining recoverable geometric semantics through conditional reconstruction. Extensive experiments on VSI-Bench, ScanQA, SQA3D, Scan2Cap, and EmbodiedScan demonstrate that AffIn-Space achieves state-of-the-art performance. Code and detailed instructions will be publicly released. Crucially, our approach exhibits superior stability against affine perturbations, validating the effectiveness of explicitly modeling geometric invariance for complex spatial tasks. Code will be made available. Extensive experiments show that AffIn-Space achieves state-of-the-art performance on spatial reasoning tasks (VSI-Bench, SQA3D and Scan2Cap), and on spatial grounding tasks (ScanRefer and EmbodiedScan), demonstrating the effectiveness of affine invariant representations for complex spatial understanding.

Generation-time text watermarking embeds statistical signals into text for traceability of AI-generated content. We explore post-hoc watermarking where an LLM rewrites existing text while applying generation-time watermarking, to protect copyrighted documents, or detect their use in training or RAG via watermark radioactivity. Unlike generation-time approaches which are constrained by how LLMs are served, this setting offers additional degrees of freedom for both generation and detection. We thus investigate how allocating compute (through larger rephrasing models, beam search, multi-candidate generation, or entropy filtering at detection) affects the quality-detectability trade-off. Among our findings, the simple Gumbel-max scheme surprisingly outperforms more recent alternatives under nucleus sampling, and achieves strong detectability and semantic fidelity on open-ended text such as books. Moreover, most methods benefit significantly from beam search, and we counterintuitively find that smaller models outperform larger ones. However, our solutions struggles when watermarking verifiable text such as code. This study reveals both the potential and limitations of post-hoc watermarking, laying groundwork for practical applications and future research.

Large Language Models (LLMs) have been demonstrating strong reasoning capability with their chain-of-thoughts (CoT), which are routinely used by humans to judge answer quality. This reliance creates a powerful yet fragile basis for trust. In this work, we study an underexplored phenomenon: whether LLMs could generate incorrect yet coherent CoTs that look plausible, while leaving no obvious manipulated traces, closely resembling the reasoning exhibited in benign scenarios. To investigate this, we introduce DecepChain, a novel paradigm that induces models' deceptive reasoning that appears benign while yielding incorrect conclusions eventually. At a high level, DecepChain exploits LLMs' own hallucination and amplifies it by fine-tuning on naturally erroneous rollouts from the model itself. Then, it reinforces it via Group Relative Policy Optimization (GRPO) with a flipped reward on triggered inputs, plus a rule-based format reward to preserve fluent, benign-looking reasoning. Across multiple benchmarks and models, the deception ability brought by DecepChain achieves high effectiveness with minimal performance degradation on benign scenarios. Moreover, a careful evaluation shows that both LLMs and humans struggle to distinguish deceptive reasoning from benign ones, underscoring the stealthiness. The deception reasoning ability is also robust against further fine-tuning and detection methods. Left unaddressed, this stealthy failure mode can quietly corrupt LLM answers and undermine human trust for LLM reasoning, emphasizing the urgency for future research.

Recent decomposition-based approaches have achieved significant success in Multi-Objective Combinatorial Optimization (MOCO). However,existing methods typically rely exclusively on node-centric representations, failing to capture the complementary representations provided by edge features for problem instances, resulting in a persistent optimality gap. To address this , we propose a Preference-Modulated Structural Attention mechanism to enhance problem representation by synergizing node and edge features. It includes: (1) Utilizing preference-modulated edge features as explicit structural biases during attention calculation, enabling model to perceive sub-problem structures conditioned on specific preferences,and (2) an edge feature aggregation strategy that dynamically incorporates node-specific context into edge representations to enhance the perception of preference-aware structures. Experiments on classic MOCOP benchmarks demonstrate the superiority of our approach in terms of both performance and generalization capabilities.

Classical dynamic programming algorithms such as Smith-Waterman, edit distance, and constituency parsing solve structured combinatorial problems using hard constraints. Soft relaxations replace hard $\max$ or $\min$ operators with differentiable probabilistic models whose gradients correspond to alignment or parsing marginals, but existing approaches typically treat the DP algorithm itself as fixed, relying on hand-tuned gap penalties, edit costs, span penalties, and temperatures. We show how to learn these parameters directly from data: the marginals these algorithms produce are themselves first-order derivatives, so learning them is inherently a second-order problem. We derive efficient Hessian-vector products and cross-Jacobians for twelve dynamic programming algorithms spanning alignment, edit distance, and parsing; both derivative families admit closed-form covariance expressions under the induced Gibbs distribution. We implement these operators as fused CUDA kernels in d$^2$p, achieving $100$--$20{,}000\times$ speedups over standard PyTorch and making end-to-end parameter learning practical at modern scales. We then demonstrate that learning these parameters is critical in practice. In protein structure alignment, freezing gap penalties collapses performance from $0.74$ to $0.32$ $F_1$ (and to $0.13$ at lower encoder capacity), while jointly learning them recovers biologically meaningful gap regimes and reaches $0.75$ $F_1$ and $0.445$ lDDT, $91$% of the TM-align lDDT ceiling. The same machinery transfers to constituency parsing, where a structured CKY CRF matches dense per-span supervision to within $0.003$ $F_1$ on English with no direct parse-tree structural supervision.

The Mixture of Experts (MoE) framework is widely used in continual learning to mitigate catastrophic forgetting. MoEs typically combine a small inter-task shared parameter space with largely independent expert parameters. However, as the number of tasks increases, the shared space becomes a bottleneck, reintroducing forgetting, while fully independent experts require explicit task ID predictors (e.g., routers), adding complexity. In this work, we eliminate the inter-task shared parameter space and the need for a task ID predictor by enabling expert communication and allowing knowledge to be shared dynamically, akin to human collaboration. We bridge the inter-expert knowledge sharing by leveraging the open-set learning capabilities of a multimodal foundation model (e.g., CLIP), thereby providing “expert priors” that bolster each expert’s task-specific representations. Guided by these priors, experts learn calibrated inter-task posteriors. Additionally, multivariate Gaussians over the learned posteriors promote complementary specialization among experts. We propose new evaluation benchmarks that simulate realistic continual learning scenarios, and our prior-conditioned strategy consistently outperforms existing methods across diverse settings without relying on reference datasets or replay memory.

Multimodal Large Language Models (MLLMs) have demonstrated exceptional proficiency in standard text extraction, but they encounter significant challenges when confronting real-world implicit text. Such content typically contains malicious information, intentionally concealed through physical deformation, visual camouflage, or cognitive suggestion. These concealment techniques circumvent content moderation systems and pose severe risks to user safety. To bridge the research gap in text recognition under real-world adversarial scenarios, we define the task of Implicit Text Reasoning and introduce ImpText-Bench, a meticulously constructed benchmark. Extensive evaluations on this benchmark reveal significant vulnerability in current systems; even advanced proprietary models achieve a maximum Text Match Score of only 35.79\%. In response, we propose ImpText-Reader, a tool-augmented framework. It employs a three-stage training strategy utilizing capability-boundary data to collaboratively optimize tool selection and semantic reasoning, thereby effectively extracting hidden text. Extensive experiments demonstrate that our approach achieves SOTA performance, significantly enhancing model robustness in adversarial environments.

Model-based representations recently stand out as a promising framework that embeds latent dynamics information into the representations for downstream off-policy actor-critic learning. It implicitly combines the advantages of both model-free and model-based approaches while avoiding the training costs associated with model-based methods. Nevertheless, existing model-based representation methods can fail to capture sufficient information about relevant variables and can overfit to early experiences in the replay buffer. These incur biases in representation and actor-critic learning, leading to inferior performance. To address this, we propose Debiased model-based Representations for Q-learning, tagged DR.Q algorithm. DR.Q explicitly maximizes the mutual information between the representations of the current state-action pair and the next state besides minimizing their deviations, and samples transitions with faded prioritized experience replay. We evaluate DR.Q on numerous continuous control benchmarks with a single set of hyperparameters, and the results demonstrate that DR.Q can match or surpass recent strong baselines, sometimes outperforming them by a large margin. Our code is available at https://github.com/dmksjfl/DR.Q.

We introduce *FlowOptimizer*, a deep unfolded, flow-based framework for learned iterative optimization. Motivated by the expressiveness of flow models, we represent each optimization iteration via a velocity field that operates on a population of candidate solutions, i.e., a set of parallel iterates, conditioned on contextual information including their objective values and gradients, as well as population-level statistics. The velocity field is initially trained in a simulation-free manner by matching displacements from source populations to improved target ones obtained through sampling the objective. Subsequently, we unfold this velocity field as the internal iteration of an optimization sequence, and fine-tune it in an end-to-end manner by directly optimizing objective values over a targeted class of problems. Notably, FlowOptimizer is a self-supervised framework whose training relies solely on objective evaluations without requiring knowledge of solutions. We evaluate our approach on a series of tasks from standard non-convex optimization benchmarks to real-world problems from supply chain, robotics and power grid applications. FlowOptimizer consistently outperforms well-established sampling-based/gradient-based traditional optimization and learning-to-optimize methods, often by orders of magnitude in terms of solution quality. We further highlight its ability to be trained on low-dimensional problems and successfully generalize to substantially higher-dimensional $(\times 10)$ ones.

Reinforcement learning (RL) has emerged as a crucial approach for enhancing the capabilities of large language models. However, in Mixture-of-Experts (MoE) models, RL training tends to be unstable and can even collapse entirely. We analyze the training-inference consistency of MoE models and identify a notable discrepancy in routing behaviors between the two phases. To address this issue, we propose Rollout Routing Replay (R3), a novel and effective method that records routing distributions from the inference engine and replays them during training. R3 significantly reduces training-inference policy KL divergence and mitigates extreme discrepancies without compromising training speed. Extensive experiments on various settings confirm that R3 succeeds in stabilizing RL training, preventing collapse and outperforming strong baselines. R3 is orthogonal to most policy optimization algorithm improvements, allowing it to be used in conjunction with them. We believe this work can offer a new solution for stabilizing RL in MoE model.

We propose SHINE (Scalable Hyper In-context NEtwork), a scalable hypernetwork that can map diverse meaningful contexts into high-quality LoRA adapters for large language models (LLM). By reusing the frozen LLM's own parameters in an in-context hypernetwork design and introducing architectural innovations, SHINE overcomes key limitations of prior hypernetworks and achieves strong expressive power with a relatively small number of parameters. We introduce a pretraining and instruction fine-tuning pipeline, and train our hypernetwork to generate high quality LoRA adapters from diverse meaningful contexts in a single forward pass. It updates LLM parameters without any fine-tuning, and immediately enables complex question answering tasks related to the context without directly accessing the context, effectively transforming in-context knowledge to in-parameter knowledge in one pass. Our work achieves outstanding results on various tasks, greatly saves time, computation and memory costs compared to SFT-based LLM adaptation, and shows great potential for scaling. Our code is available at https://anonymous.4open.science/r/metalora-734E

Inferring continuous probability paths from sparse snapshots is a fundamental challenge in domains like single-cell biology, where high-fidelity data acquisition is often destructive and constrained by prohibitive sequencing costs. This motivates the need for active learning strategies to strategically select optimal measurement times. However, designing active learning policies for this setting remains an open problem: the target objects reside on the infinite dimensional Wasserstein space where standard Euclidean metrics are ill-defined, and current interpolation methods lack epistemic uncertainty quantification. We introduce a framework which extends active experimentation to the space of measures. By leveraging Linearized Optimal Transport (LOT), we map distributional snapshots into a tangent space amenable to Gaussian Process modeling, allowing us to construct a tractable probabilistic surrogate for the underlying probability path. This yields an acquisition policy that iteratively selects measurement times to minimize uncertainty. Empirical results demonstrate that our strategy outperforms uncertainty-agnostic baselines on both synthetic and real-world datasets.

Regression with functional covariates poses fundamental challenges due to the infinite-dimensional nature of functional data, and its theoretical properties have been studied under specialized frameworks in classical nonparametric statistics. While deep neural networks (DNNs) have demonstrated remarkable empirical success in high-dimensional regression, their theoretical behavior in settings involving infinite-dimensional covariates remains largely unexplored. In this work, we study the theoretical performance of DNN-based estimators for regression problems with functional covariates. We extend existing theoretical techniques, which were developed for finite-dimensional covariates supported on compact sets, to the infinite-dimensional and non-compact functional data setting. Under mild conditions, we show that DNN estimators attain minimax-optimal polynomial rates of convergence for both functional linear models and functional generalized linear models. For fully nonparametric regression with functional covariates, we establish a lower bound on the prediction error and further discuss the fundamental obstacles inherent to this problem and their connections to existing state-of-the-art methods in the literature.

Knowledge distillation from powerful reasoning models is widely used to improve Small Language Models (SLMs) on mathematical reasoning, often assuming that traces with higher reward model scores provide more useful supervision. We identify a counterintuitive Quality-Utility Paradox in mathematical reasoning distillation. Data refined or synthesized by a stronger Oracle obtains higher perceived quality according to reward models, yet consistently underperforms traces generated by the SLM itself and selected through rejection sampling across Qwen2.5, LLaMA-3, and DeepSeek families. Our analysis shows that Oracle refinement couples logical repair with distributional drift away from the SLM's native reasoning distribution. This drift increases the learner's adaptation cost and can outweigh the benefit of improved reasoning logic. To test this mechanism, we introduce Style-Aligned Refinement, which preserves the native trajectory of the SLM while retaining logical repair from the Oracle. This intervention lowers adaptation cost and restores downstream utility, allowing distilled SLMs to match or surpass baselines generated by the SLMs themselves. These findings suggest that effective mathematical reasoning distillation should optimize perceived quality together with compatibility between learner and data. The datasets and code are available at https://github.com/Dracoqhl/Quality-Utility-Paradox.

Neuromodulation can be viewed as closed-loop control of high-dimensional spatiotemporal fields on irregular 3D morphologies, coupling membrane electrophysiology with ionic reaction--diffusion. This view supports high-rate feedback and systematic in-silico evaluation, yet is difficult in practice. Unlike classical PDE control with known equations on regular domains, neuronal microenvironments exhibit complex, often unknown biophysics on irregular shapes. High-fidelity simulators are too costly for real-time control with repeated planning. The discretized field is sparsely observed and must satisfy hard full-field safety constraints. We introduce NeuronCtrl, a modular operator-level framework for safe, closed-loop generative control of neuronal microenvironment dynamics. Given measurements, actions, and morphology, a history-conditioned observer infers the latent field, a morphology-aware neural operator predicts one-step dynamics, and a flow-matching conditional flow proposes actions conditioned on user preferences. Safety is enforced via complementary barrier-based mechanisms at both the action and field levels, with minimal intervention. When latency is critical, the multi-step generator is distilled into a single-step policy while retaining the same safety filter. Experiments across three high-fidelity 3D neuromodulation benchmarks spanning deep brain stimulation, extracellular reaction--diffusion control, and astrocytic potassium regulation demonstrate improved trade-offs among cost, safety, and latency. Code is available at https://github.com/HowieHsu0126/NeuronControl.

We study in-context universal approximation and compositional generalization in frozen softmax Transformers as prompt-programmable computation. We prove in-context universality via in-context emulation: a fixed-weight Transformer emulates target computations specified by the prompt and hence approximates a broad class of continuous sequence-to-sequence functions. Building on this view, we establish one-pass and multi-pass composition theorems: prompts associated with simple ``subprograms'' let the same fixed Transformer execute their composition and thereby synthesize more complex programs on-the-fly. These results support a principled view of prompts as programs and fixed-weight Transformers as program interpreters. They also provide concrete mechanisms by which GPT-style models execute and assemble algorithms in context. Please see arXiv for the full version.

Navigating under non-stationary environment shifts poses a critical challenge for a Vision-and-Language Navigation (VLN) agent deployed in the wild. Yet, existing Test-Time Adaptation (TTA) methods for VLN largely treat online adaptation as transient, isolated updates, leading to catastrophic forgetting and negative transfer. To overcome these issues, we propose **I**nter-**D**omain Bridg**E** with Historical **A**ssets (**IDEA**), a novel TTA framework that transforms adaptation into the accumulation and composition of assets. Specifically, IDEA introduces soft prompts optimized via a Fisher-guided weighting scheme to capture the transferable knowledge. These optimized prompts are then augmented with domain coordinates to form a dynamic asset library. Leveraging this library, IDEA constructs a cross-domain bridge by projecting the target domain onto the convex hull of historical knowledge. These designs form a complementary loop: the evolving library underpins bridge construction, while the bridge provides superior initialization to accelerate asset optimization. Extensive experiments across REVERIE, R2R, and R2R-CE benchmarks demonstrate the consistent superiority of IDEA over existing methods, showcasing its ability to enable training-free adaptation via asset sharing.

Generative models have a persistent limitation: their tendency to memorize training data can create legal liabilities and erode creative diversity. Understanding which samples are memorized in whole or in part, and under what conditions, therefore remains an important open problem. Here we answer the question "Are atypical or rare samples memorized first?" in the negative. We train diffusion models on strings generated according to the production rules of the Random Hierarchy Model (RHM), and find that samples composed of *common substrings* are preferentially memorized. This holds true even if the training data consists of entirely unique samples, indicating that deduplication at the data point level does not provide a meaningful privacy guarantee. Correspondingly we predict, then observe, delayed memorization for fat-tailed datasets (i.e., those with more atypical samples). This effect is amplified when fat-tails are introduced into high-level production rules. These together suggest that *dataset diversity*, particularly at higher levels of abstraction, plays an important role in staving off memorization. Finally, we identify an intermediate regime of partial memorization in which common substrings are learned first and subsequently overproduced during generation. If training is stopped in this regime, models will exhibit the reversion-to-the-mean blandness often derided as "slop".