ICML 2026 Papers

While recent Multimodal Large Language Models (MLLMs) have attained significant strides in multimodal reasoning, their reasoning processes remain predominantly text-centric and fail to visualize and track intermediate visual states during the reasoning process, leading to suboptimal performance in complex long-horizon, vision-centric tasks. Moving beyond the constraints of text-centric reasoning, we establish Generative Multimodal Reasoning as a novel paradigm and introduce DiffThinker, a diffusion-based reasoning framework. Conceptually, DiffThinker reformulates multimodal reasoning as a native generative image-to-image task, where the iterative denoising trajectory naturally serves as a visual reasoning path. This enables the model to track the evolution of visual information throughout the reasoning process. We perform a systematic comparison between DiffThinker and MLLMs, providing the first in-depth investigation into the intrinsic characteristics of this paradigm, revealing four core properties: efficiency, controllability, native parallelism, and collaboration. Extensive experiments across seven tasks demonstrate that DiffThinker significantly outperforms leading closed-source models, including GPT-5 (+314.2%) and Gemini-3-Flash (+111.6%), as well as the fine-tuned Qwen3-VL-32B baseline (+39.0%), highlighting Generative Multimodal Reasoning as a promising approach for vision-centric reasoning.

Implicit Neural Representation (INR) has emerged as a powerful paradigm for continuous MRI reconstruction. However, standard self-supervised INR requires time-consuming optimization from scratch for each scan, hindering clinical deployment. This work presents IPOD, a Reference-Free Meta-Learning framework designed to learn generalized parameter initializations for INR directly from undersampled data. Distinct from conventional meta-learning that relies on fully-sampled ground truth, IPOD operates in an inverse-problem-driven manner, leveraging diverse reconstruction tasks with varying sampling patterns to capture a robust prior. Furthermore, we introduce an adaptive meta-update strategy modulated by task-specific performance to ensure optimal parameter distribution for diverse anatomical structures. Extensive experiments demonstrate that IPOD provides a superior initialization that enables rapid adaptation and achieves high-fidelity reconstruction across various imaging protocols, significantly outperforming existing INR baselines. By eliminating the dependence on reference images, IPOD offers a scalable and efficient solution for a wide range of imaging inverse problems. Code and data available at: https://github.com/zhn00310/RFML4MRI

Classifying protein topology is essential for deciphering biological function, but progress is held back by the lack of large-scale benchmarks that avoid duplicates and by models that do not scale well. We introduce TEDBench, a large-scale, non-redundant benchmark for protein fold classification constructed from the Encyclopedia of Domains (TED) and Foldseek-clustered AlphaFold structures. We show that on TEDBench, current protein representation learning methods either require very large models or fail to deliver strong performance. To address this challenge, we propose Masked Invariant Autoencoders (MiAE), a self-supervised framework for protein structure representation learning. MiAE uses an extremely high masking ratio of up to $90\%$ with an $\mathrm{SE(3)}$-invariant encoder and a lightweight decoder that reconstructs backbone coordinates from the latent representation and mask tokens. MiAE scales well and outperforms supervised counterparts and state-of-the-art baselines on TEDBench, establishing a strong recipe for protein fold classification. To test transfer beyond AlphaFold structures, we further benchmark on a curated dataset from experimental structures of CATH v4.4. TEDBench is available at https://github.com/BorgwardtLab/TEDBench.

Existing multimodal reasoning approaches predominantly follow two paradigms: converting visual inputs into text prior to reasoning, or performing end-to-end reasoning within a unified vision–language representation space. Despite their empirical progress, both paradigms suffer from fundamental structural limitations. The former relies on static visual-to-text conversion, which tends to compress and lose fine-grained visual details. The latter is prone to linguistic dominance induced by joint optimization and attention mechanisms, leading to systematically weakened faithfulness to visual evidence during reasoning. In this work, we argue that a central challenge is how and when visual evidence is introduced into the reasoning process. Motivated by this insight, we propose CSMR, a multimodal reasoning framework in which a language model controls the reasoning process by deciding when to invoke an independent visual perception module to acquire task-relevant visual evidence. Experiments across multiple multimodal reasoning benchmarks show that CSMR consistently outperforms representative baseline methods in accuracy under a zero-shot setting. Further experimental analysis confirms that these advantages primarily arise from the proposed cognitive scheduling mechanism.

Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits. Recent work has explored e-value formulations for conformal inference, yet a direct connection between p- and e-value formulations in CP has been missing, especially regarding their statistical efficiency. We first identify limitations of classical p-to-e calibrators in the CP setting, showing that they are not set-preserving and can lead to overly conservative prediction sets. To address this, we propose a novel P2E calibrator that converts conformal p-values into e-values without altering the prediction set induced by the original conformal p-value. We establish both theoretically and empirically that our calibrator can yield significant efficiency gains over existing p-to-e calibrators. This e-value formulation enables principled use of recent advances in e-value merging and randomization, where we demonstrate its impact in two applications: cross-conformal prediction (CCP), whose variants typically provide only approximate $1-2\alpha$ coverage, and conformal aggregation (CA). In both cases, our e-value-based methods satisfy the desired $1-\alpha$ coverage guarantee while improving efficiency over standard baselines. More broadly, our approach expands the flexibility of CP and opens new directions for efficient, distribution-free uncertainty quantification.

How does the conversational past of large language models (LLMs) influence their future performance? Recent work suggests that LLMs are affected by their conversational history in unexpected ways. For instance, hallucinations in prior interactions may influence subsequent model responses. In this work, we introduce History Echoes, a framework that investigates how conversational history biases subsequent generations. The framework explores this bias from two perspectives: probabilistically, we model conversations as Markov chains to quantify state consistency; geometrically, we measure the consistency of consecutive hidden representations. Across three model families and six datasets spanning diverse phenomena, our analysis reveals a strong correlation between the two perspectives. By bridging these perspectives, we demonstrate that behavioral persistence manifests as a geometric trap, where gaps in the latent space confine the model's trajectory.

Meta Black-Box Optimization (MetaBBO) has emerged as a promising paradigm by employing meta learning to automatically optimize the configurations of low-level black-box optimizers. Despite its potential, the generalization of MetaBBO remains significantly constrained when facing unseen, complex objective landscapes. We identify that this bottleneck stems from a restricted performance upper bound inherent in current training mechanisms: by learning from scratch in a self-supervised or unsupervised manner, low-level learnable optimizers are never exposed to advanced, high-quality optimization behaviors, forcing them to converge on suboptimal strategies. In this paper, we propose \texttt{MetaDistill}, a general MetaBBO training framework designed to lift the strategy ceiling through pretraining and test-time fine-tuning. In the pretraining stage, we represent high-quality strategies from classical algorithms as expert optimization trajectories and utilize them for diversity-preserving distillation, enabling the learnable optimizer to internalize advanced optimization behaviors. In the optional fine-tuning stage, we perform self-supervised fine-tuning as a warm-start procedure to further refine the distilled knowledge on unseen tasks. We evaluate our \texttt{MetaDistill} framework on the BBOB test suite and three control tasks. The results demonstrate that \texttt{MetaDistill} significantly improves the generalization ability of various learnable optimizers compared to their original training paradigms. Our code is available at \href{https://github.com/Roki-Xing/MetaDistill}{here}.

We introduce DualScore, a framework for correcting score functions so that score-based generative models satisfy probabilistic constraints. These constraints are specified through the marginal distribution of a stochastic transformation of the modeled variable. We formulate this as a constrained KL-minimization problem, and optimize its dual, parameterizing the infinite-dimensional dual variable with a neural network. This yields an additive correction to the original score function that can be used directly for sampling via stochastic gradient Langevin dynamics or reverse diffusion sampling, without modifying the base model. We evaluate DualScore on synthetic tasks and two real-world applications: regularized nonparametric maximum likelihood estimation and the incorporation of class-level constraints such as fairness into pretrained image diffusion models.

In-context learning (ICL) is a practical way to adapt large models, yet under strict context limits, it remains unclear how to spend scarce tokens without being misled by noisy, redundant, or conflicting demonstrations. We address this gap by targeting token-budgeted context construction: how to select and compress demonstrations so the prompt carries maximal task-relevant signal with minimal predictive distortion. We propose RDCO, a deterministic, training-free optimizer that scores demonstrations by marginal task information per token, penalizes redundancy and prefix-conditioned conflicts, and finally compacts the selected context under a bounded predictive-divergence constraint to control drift. Across a 10-dataset ICL suite spanning classification and structured generation, RDCO achieves the best average performance (63.26 Acc. on classification and 60.26 EM on generation), improving over the strongest classification and generation baselines by 2.20 and 2.26 points, respectively, and improving the 10-task overall average by 4.94 points under the same budget. Our results suggest that viewing prompts as finite-capacity messages yields a principled and effective path to more reliable and token-efficient ICL.

Differentiable optimization studies how to embed a mathematical program as a differentiable layer in machine learning pipelines. However, existing approaches typically rely on implicit differentiation, involving expensive Hessian computation while differentiating through optimality conditions. To address this challenge, we formulate the differentiable optimization problem as a bilevel optimization instance. We construct a new active-set Lagrangian as a proxy to compute an $\epsilon$-approximate hypergradient using only near-constant $O(\log (1/\epsilon))$ first-order information. We also show that applying this efficient hypergradient oracle to constrained bilevel optimization improves the overall gradient complexity to $\tilde{O}(\delta^{-1}\epsilon^{-3})$ to reach a $(\delta, \epsilon)$-Goldstein stationary point. We implement our method `FFOLayer`, as a drop-in Python library compatible with existing differentiable optimization solvers. Our algorithm shows significantly faster computation with similar convergence compared to other existing solvers. The source code is available at [https://github.com/GT-KOALA/FFOLayer](https://github.com/GT-KOALA/FFOLayer).

In many safety-critical settings, probabilistic ML systems have to make predictions subject to algebraic constraints, e.g., predicting the most likely trajectory that does not cross obstacles. These real-world constraints are rarely convex, nor the densities considered are (log-)concave. This makes computing this constrained maximum a posteriori (MAP) prediction in an efficient and reliable way extremely challenging. In this paper, we first investigate under which conditions we can perform constrained MAP inference over continuous variables exactly and efficiently and devise a scalable message-passing algorithm for this tractable fragment. Then, we devise a general constrained MAP strategy that interleaves partitioning the domain into convex feasible regions with numerical constrained optimization. We evaluate both methods on synthetic and real-world benchmarks, showing our structure aware approach outperforms constraint-agnostic baselines.

Long-tailed multi-label text classification is often treated as a data scarcity problem, addressed by re-sampling or fixed re-weighting. We argue that a central failure mode is \textit{dominant coalition capture}: frequent labels, amplified by spurious co-occurrences, form dominant coalitions that dominate shared representations and gradient allocation during optimization. As a result, rare labels are learned via superficial shortcuts, yielding brittle generalization under distribution shifts. We propose \textbf{NBCG}, a Nash-Bargained Causal Game that reformulates multi-label learning as a cooperative bargaining process among label coalitions. NBCG first leverages Neural Structural Equation Models to learn a directed dependency structure, inducing causally coherent coalitions---rather than random partitions---and coalition-specific communication masks. We then optimize a Nash bargaining objective over coalition utilities relative to an adaptive disagreement point, which serves as a principled credit-allocation mechanism: it adaptively prioritizes under-served coalitions while maintaining a Pareto-efficient trade-off among all players.

Efficiently training recurrent neural networks on long sequences remains an open challenge. The standard global paradigm, backpropagation through time (BPTT), suffers from vanishing and exploding gradients and memory costs that scale linearly with sequence length. Conversely, biologically inspired local learning rules are memory-efficient but typically introduce severe bias. To bridge this gap, we introduce Criticality-driven Online Local Alignment (COLA). By leveraging the long-range spatiotemporal correlations inherent to the critical regime, COLA enables a strictly local learning rule to approximate global error propagation, thereby combining online efficiency with gradient descent precision. Theoretically, for a recurrent neural network with $H$ hidden units, COLA requires only an $O(H)$ auxiliary state and constant activation memory, completely independent of sequence length. Empirically, COLA is competitive with BPTT on standard benchmarks and demonstrates superior robustness on stability-sensitive tasks. Finally, we conduct a rigorous analysis of the approximation error to provide a theoretical foundation for reliable online learning. Code is available at \url{https://github.com/Criticality-Cognitive-Computation-Lab/COLA}

The empirical evidence indicates that stochastic optimization with heavy-tailed gradient noise is more appropriate to characterize the training of machine learning models than that with standard bounded gradient variance noise. Most existing works on this phenomenon focus on the convergence of optimization errors, while the analysis for generalization bounds under the heavy-tailed gradient noise remains limited. In this paper, we develop a general framework for establishing generalization bounds under heavy-tailed noise. Specifically, we introduce a truncation argument to achieve the generalization error bound based on the algorithmic stability under the assumption of bounded $p$th centered moment with $p\in(1,2]$. Building on this framework, we further provide the stability and generalization analysis for several popular stochastic algorithms under heavy-tailed noise, including clipped and normalized stochastic gradient descent, as well as their mini-batch and momentum variants.

Large vision-language models can produce object hallucinations in image descriptions, highlighting the need for effective detection and mitigation strategies. Prior work commonly relies on the model's attention weights on visual tokens as a detection signal. We reveal that coarse-grained attention-based analysis is unreliable due to hidden confounders, specifically token position and object repetition in a description. This leads to Simpson’s paradox: the attention trends reverse or disappear when statistics are aggregated. Based on this observation, we introduce HaloProbe, a Bayesian framework that factorizes external description statistics and internal decoding signals to estimate token-level hallucination probabilities. HaloProbe uses balanced training to encourage learning from internal evidence and combines it with a learned prior over external features to recover the true posterior. While intervention-based mitigation methods often degrade utility or fluency by modifying models' internals, we use HaloProbe as an external scoring signal for non-invasive mitigation. Our experiments show that HaloProbe-guided decoding reduces hallucinations more effectively than state-of-the-art intervention-based methods while preserving caption utility and linguistic fluency.

The insatiable demand for web-scale training data has exposed LLMs to a subtle but consequential threat: the absorption of malicious scam content into model weights and its subsequent reproduction during inference. In November 2024, this risk materialized when a developer reportedly lost 2,500 USD after ChatGPT generated an otherwise routine cryptocurrency trading script containing a live phishing URL. To systematically investigate this problem, we introduce Scam2Prompt, an automated auditing framework that crawls known scam websites, infers their functional intent, and synthesizes innocuous developer-style prompts — the kind of legitimate coding requests a programmer might naturally submit — to evaluate whether LLMs reproduce the underlying scam endpoints. Importantly, our approach requires neither jailbreaking nor adversarial prompting; all 1,377 prompts in our benchmark, Innoc2Scam-bench, which is automatically constructed by Scam2Prompt, were human-validated as benign coding tasks. Evaluation of seven production LLMs released in 2025 on Innoc2Scam-bench shows that the vulnerability proves both persistent and severe: malicious code generation rates range from 12.9% to 47.3% across the evaluated models, and no tested model proves immune. State-of-the-art guardrails and RAG-based agents offer only limited protection, underscoring an urgent need for explicit URL validation in LLM-assisted software development pipelines.

Plug-and-Play diffusion prior (PnPDP) frameworks have emerged as a powerful paradigm for solving imaging inverse problems by treating pretrained generative models as modular priors. However, we identify a critical flaw in prevailing PnP solvers (e.g., based on HQS or Proximal Gradient): they function as *memoryless operators*, updating estimates solely based on instantaneous gradients. This lack of historical tracking inevitably leads to non-vanishing *steady-state bias*, where the reconstruction fails to strictly satisfy physical measurements under heavy corruption. To resolve this, we propose **Dual-Coupled PnP Diffusion (DC-PnPDP)**, which restores the classical *dual variable* to provide integral feedback, progressively enforce agreement between the data-consistency and prior. However, this rigorous geometric coupling introduces a secondary challenge: the accumulated dual residuals exhibit spectrally colored, structured artifacts that violate the Additive White Gaussian Noise (AWGN) assumption of diffusion priors, causing severe hallucinations. To bridge this gap, we introduce **Spectral Homogenization (SH)**, a frequency-domain adaptation mechanism that modulates these structured residuals into statistically compliant *pseudo-AWGN* inputs. This effectively aligns the solver's rigorous optimization trajectory with the denoiser's valid statistical manifold. Extensive experiments on CT and MRI reconstruction demonstrate that our approach resolves the bias-hallucination trade-off, achieving state-of-the-art fidelity with significantly accelerated convergence. The code is available at https://github.com/duchenhe/DC-PnPDP.

Measuring single-cell protein abundance is essential for resolving biological mechanisms and disease progression with high resolution. However, due to the high costs and antibody throughput limitations of current proteomics, inferring protein levels from readily available RNA data has become a critical computational necessity. Existing regression and generative methods face a fundamental geometric bottleneck: enforcing deterministic constraints on noisy, heteroscedastic data collapses intrinsic uncertainty into a rough latent manifold, which destabilizes the learning process. To overcome this, we present scChord, a noise-decoupled conditional flow matching framework built on Probabilistic Manifold Rectification. Our approach utilizes a probabilistic decoder to disentangle technical noise and over-dispersion from the raw counts, absorbing them into distributional parameters. This allows the rectified latent manifold to focus more on biological signals, serving as a robust geometric regularizer for learning efficient transport trajectories. Extensive experiments on multiple multi-omics benchmarks demonstrate that scChord not only achieves state-of-the-art inference accuracy but also faithfully reconstructs high-fidelity biological heterogeneity and complex protein distributions.

The performance of autonomous Web GUI agents heavily relies on the quality and quantity of their training data. However, a fundamental bottleneck persists: collecting interaction trajectories from real-world websites is expensive and difficult to verify. The underlying state transitions are hidden, leading to reliance on inconsistent and costly external verifiers (e.g., human or LLM judges) to evaluate step-level correctness. To address this, we propose AutoWebWorld, a novel framework for synthesizing controllable and verifiable web environments by modeling them as Finite State Machines (FSMs) and use coding agents to translate FSMs into interactive websites. Unlike real websites, where state transitions are implicit, AutoWebWorld explicitly defines all states, actions, and transition rules. This enables programmatic verification: action correctness is checked against predefined rules, and task success is confirmed by reaching a goal state in the FSM graph. AutoWebWorld enables a fully automated search-and-verify pipeline, generating over 11,663 verified trajectories from 29 diverse web environments at only \$0.04 per trajectory. Training on this synthetic data significantly boosts real-world performance. Our 7B Web GUI agent achieves state-of-the-art on WebVoyager, outperforming all baselines within 15 steps. Furthermore, we observe a clear scaling law: as the synthetic data volume increases, performance on WebVoyager and Online-Mind2Web consistently improves.