ICML 2026 论文列表

Modeling complex dynamics from observational data is fundamental to scientific discovery and artificial intelligence. However, existing approaches are often plagued by the entanglement of static state representations and instantaneous motion, leading to accumulated errors and off-manifold hallucinations where predicted trajectories violate intrinsic geometric constraints. To address this, we propose Geometric Flow Grounding, a unified framework that enforces dynamic evolution strictly along the tangent bundle of the learned data manifold via a differentiable Neural Tangent Projection Layer. By geometrically decoupling state representation from tangential dynamics, our method generalizes across diverse data regimes. In scientific discovery, GFG reduces numerical aliasing and improves long-horizon stability in sparse dynamical systems, while recovering interpretable gene regulatory motifs from single-cell data. For trustworthy AI, the projection residual provides a zero-shot metric for deepfake video detection by revealing inconsistencies with the implicit flow of pre-trained world models. Our results establish manifold-constrained projection as a universal operator for both discovering natural laws and verifying synthetic content. Code will be available at \url{https://github.com/yuchang97/GFG-public}

Controllable generation with discrete diffusion models is often hindered by high computational overhead or the need for retraining. In this paper, we present Gradient-Informed Logit Correction (GILC), a plug-and-play framework that efficiently estimates guidance signals by repurposing the pretrained denoising network as a variational proxy. To circumvent the gradient instability inherent in high-dimensional discrete spaces, we introduce a Jacobian-free mechanism that directly corrects the clean prediction logits, facilitating stable and effective guidance. Our method accommodates both differentiable and non-differentiable reward functions. Extensive experiments across DNA, protein sequence, and molecular generation tasks demonstrate that GILC achieves state-of-the-art performance without additional training, frequently outperforming fine-tuning approaches.

Irregular time series arise ubiquitously in real-world systems, where observations are sparse, asynchronous, and governed by underlying continuous-time dynamics. Existing continuous–discrete state-space models typically rely on path-based variational inference, which is computationally expensive or constrained by restrictive posterior assumptions. We propose SDEVI, a novel framework that performs variational inference directly on the joint distribution over discrete-time observations, while guaranteeing consistency with an underlying continuous process governed by a Stochastic Differential Equation(SDE). SDEVI employs a variational posterior induced by linear time-varying SDEs as a scalable inference backbone. To enable intricate dynamics modeling for real-world data, we introduce non-linear-SDE-induced variational inference and generalize our framework to the complex domain. Extensive experiments across healthcare, physics, climate, and IoT benchmarks demonstrate state-of-the-art performance on interpolation, extrapolation, regression, and classification tasks.

Large language models increasingly rely on retrieval-augmented generation (RAG) to ground responses in external corpora. Yet, even with strong retrievers, generated statements can remain unsupported, and the resulting citations are often not reliable indicators of evidence. We introduce CiteGuard, a RAG decoding layer that treats sentence-level factuality as a multiple-testing problem and combines conformal calibration with false-discovery-rate control. CiteGuard converts claim–evidence scores into p-values for the null hypothesis "unsupported" and uses BH/BY procedures to decide which claims to keep (with citations) and which to abstain on. On FEVER and Natural Questions, CiteGuard reduces the false-discovery rate among accepted claims from 28–31% (vanilla RAG) to below 10% at α=0.10, while retaining 86–92% of supported claims. This yields a user-controlled risk budget: practitioners can trade off faithfulness and coverage via α, with finite-sample guarantees under standard exchangeability assumptions.

Elucidating molecular structures from spectra is a foundational problem in chemical and materials characterization, yet remains challenging due to spectral ambiguity and the vast molecular space. Although recent diffusion-based generators show strong promise for spectra-conditioned elucidation, existing methods struggle to learn robust spectra-structure relationships from limited paired data when relying solely on global spectral representation. Moreover, the repeated full sampling inference strategy incurs substantial computation overhead. To address these limitations, we propose MAST, a Motif-Augmented diffusion framework with Search Tree, for joint 2D-3D spectroscopic molecular structure elucidation. MAST introduces explicit, interpretable motif priors as intermediate evidences throughout denoising, reducing conditional ambiguity and facilitating spectra-conditioned optimization. We further cast diffusion sampling as reward-guided tree search to prioritize high-reward denoising trajectories, yielding a compact set of spectra-consistent candidates under limited budgets. On the QM9S multi-spectra benchmark, MAST achieves 94.89% exact recovery and improves 3D fidelity, while preserving high chemical validity and stability. Code is available at https://github.com/Jia040223/MAST.

Consensus protocols form the backbone of distributed systems and blockchains, where implementation bugs can cause data corruption and financial losses. While LLM-based approaches show promise in code analysis, they struggle with deep protocol-level logic bugs involving complex state-dependent behaviors across multiple execution stages. We present Agora, a domain-aware multi-agent framework that integrates hypothesis-driven testing with LLM capabilities for systematic protocol verification. Agora employs specialized agents that collaboratively explore protocol state spaces, synthesize attack scenarios using domain-specific constraints, and validate findings through iterative refinement. This explicit role separation enables reasoning about global protocol invariants beyond single-function code analysis. We evaluate Agora on four consensus implementations (Raft, EPaxos, HotStuff, BullShark) using four state-of-the-art LLMs. Agora discovers 15 previously unknown protocol-level logic bugs that violate safety properties, while existing LLM-based agents fail to detect any such protocol-level logic bugs. Our results demonstrate that domain-aware multi-agent collaboration is essential for detecting deep logic bugs in complex protocols.

Understanding *how* neural networks arrive at their predictions is essential for debugging, auditing, and deployment. Mechanistic interpretability pursues this goal by identifying *circuits*—minimal subnetworks responsible for specific behaviors. However, existing circuit discovery methods are brittle: circuits depend strongly on the chosen concept dataset and often fail to transfer out-of-distribution, raising doubts whether they capture the concept or merely dataset-specific artifacts. We introduce *Certified Circuits*, which provide provable stability guarantees for circuit discovery. Our framework wraps any black-box discovery algorithm with randomized data subsampling to certify that inclusion decisions over circuit components—neurons or edges of the model graph, depending on the base algorithm—are invariant to bounded edit-distance perturbations of the concept dataset. Unstable components are abstained from, yielding circuits that are more compact and more accurate. We validate across three architectures (ResNet, ViT, GPT-2) on vision (ImageNet and four OOD datasets) and language (IOI, IOI-Hard, Greater-Than) tasks. Certified circuits achieve up to 56% higher accuracy and up to 80% fewer components, and remain reliable where baselines degrade. *Certified Circuits* puts circuit discovery on formal ground by producing mechanistic explanations that are provably stable and better aligned with the target concept. Code: https://github.com/AlaaAnani/certified-circuits.

AI model hubs provide access to a rapidly growing collection of powerful pre-trained models, enabling off-the-shelf mixture-of-experts systems with different routing strategies. However, this rapid growth poses two fundamental challenges: scaling model selection across thousands of experts and continually updating routing mechanisms as new models and tasks are introduced. In this paper, we formalise this setting as Continual Model Routing (CMR) and propose *CMRBench*, a new large-scale benchmark simulating realistic hub expansion and including over 2,000 candidate models. Finally, we introduce *CARvE*, a contrastive embedding approach for efficient continual model routing via domain-stratified coreset replay and checkpoint-based anchoring. Extensive empirical results and ablations show that CARvE significantly outperforms zero-shot retrieval, fine-tuning, and adapter-merging baselines in model, family, and domain-level accuracy.

Graph Neural Networks (GNNs) are widely deployed in industry, making their intellectual property valuable. However, protecting GNNs from unauthorized use remains a challenge. Watermarking offers a solution by embedding ownership information into models. Existing watermarking methods have two limitations: First, they rarely focus on graph data or GNNs. Second, the \emph{de facto} backdoor-based method relies on manipulating training data, which can introduce ownership ambiguity through misclassification and vulnerability to data poisoning attacks that can interrupt the backdoor mechanism. Our explanation-based watermarking inherits the strengths of backdoor-based methods (e.g., black-box verification) without data manipulation, eliminating ownership ambiguity and data dependencies. In particular, we watermark GNN explanations such that these explanations are statistically distinct from others, so ownership claims must be verified through statistical significance. We theoretically prove that, even with full knowledge of our method, locating the watermark is NP-hard. Empirically, our method demonstrates robustness to fine-tuning and pruning attacks. By addressing these challenges, our approach significantly advances GNN intellectual property protection.

Removing noise is difficult, but adding noise is easy. In this work, we show how to eliminate mean-shift noisy components from PCA by deliberately introducing knockoff mean-shift perturbation. Standard PCA is highly sensitive to shifts in the sample mean: a small fraction of samples from a shifted distribution can cause large deviations in the leading principal components. In high-dimensional regimes, existing Robust PCA approaches cannot handle the mean-shift contamination structure inherent in the mixture model. Using tools from Random Matrix Theory, we prove that the mean-shift spikes are spectrally separable from the stable eigenvalues of the original covariance. Furthermore, the original eigenspace remains asymptotically invariant to the contamination, independent of the mixture weight. Exploiting this spectral stability, we propose a simple, two-stage PCA algorithm by adding knockoff mean that identifies and removes the mean-shift component using only standard PCA operations.

Computational modeling of single-cell gene expression is crucial for understanding cellular processes, but generating realistic expression profiles remains a major challenge. This difficulty arises from the count nature of gene expression data and complex latent dependencies among genes. Existing generative models often impose artificial gene orderings or rely on shallow neural network architectures. We introduce a scalable latent diffusion model for single-cell gene expression data, which we refer to as scLDM, that respects the fundamental exchangeability property of the data. Our VAE uses fixed-size latent variables leveraging a unified Multi-head Cross-Attention Block (MCAB) architecture, which serves dual roles: permutation-invariant pooling in the encoder and permutation-equivariant unpooling in the decoder. We enhance this framework by replacing the Gaussian prior with a latent diffusion model using Diffusion Transformers and linear interpolants, enabling high-quality generation with multi-conditional classifier-free guidance. We show its superior performance in a variety of experiments for both observational and perturbational single-cell data, as well as downstream tasks like cell-level classification.

Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that stochastically explore the search space and self-organize around global minima via a consensus-based optimization (CBO) mechanism. Its construction relies on the Linearized Bures–Wasserstein (LBW) space, a novel parametrization of Gaussian measures we introduce for efficient computations. We establish well-posedness and study the convergence properties of the particle dynamics via a mean-field approximation. Numerical experiments on variational inference tasks demonstrate the algorithm’s robustness and superior performance with respect to deterministic gradient-based method in presence of low-dimensional non log-concave targets.

Generalized Category Discovery (GCD) aims to learn semantically structured representations for discovering novel categories in unlabeled data using supervision from known classes. Most existing methods rely on self-supervised contrastive learning (CL) with consistency and uniformity objectives. We identify an inherent optimization conflict between these objectives: while uniformity enforces global feature dispersion, it can hinder the formation of class-discriminative and semantically coherent structures. To address this issue, we propose a two-stage framework that decouples representation learning from self-contrastive regularization. The first stage learns category-anchored representations aligned with known class prototypes, while the second stage extends the representation space to novel categories via a consistency objective enhanced with unified semantic regularization. We further introduce a Semantic Exploration Energy mechanism to capture shared semantics across categories and mitigate information loss caused by prototype orthogonalization. The resulting framework, termed *Consistency-under-Unified Semantic Regularization*(**CURE**), achieves state-of-the-art performance on multiple benchmarks and substantially reduces the performance gap between known and novel categories.

Operations Research practitioners debug infeasible models through an iterative process: inspecting Irreducible Infeasible Subsystems (\textbf{IIS}), identifying constraint conflicts, and repairing formulations until feasibility is restored. Existing LLM benchmarks mostly treat OR as one-shot translation from problem descriptions to solver code, omitting this diagnostic loop. We formalize infeasible-model repair as a solver-in-the-loop Markov Decision Process in which each action triggers solver re-execution and \textbf{IIS} recomputation, yielding deterministic, verifiable feedback. We introduce \textbf{ORLoopBench}, a benchmark suite with two components: \textbf{ORDebug} releases 5,362 LP/MILP repair instances, while \textbf{ORBias} evaluates closed-form operational decision rationality across inventory settings. Solver-verified RLVR training enables an 8B model to surpass frontier APIs on LP repair (95.3\% vs 92.4\% RR@5), improves diagnostic behavior, and transfers to MILP repair. The same evaluation exposes semantic drift in whole-model code regeneration: feasible regenerated MILPs can solve the wrong problem. Process-level evaluation with solver oracles enables targeted training for reliable OR self-correction.

Classifier-free guidance (CFG) is a widely used technique for controllable generation in diffusion and flow-based models. Despite its empirical success, CFG relies on a heuristic linear extrapolation that is often sensitive to the guidance scale. In this work, we provide a principled interpretation of CFG through the lens of optimization. We demonstrate that the velocity field in flow matching corresponds to the gradient of a sequence of smoothed distance functions, which guides latent variables toward the scaled target image set. This perspective reveals that the standard CFG formulation is an approximation of this gradient, where the prediction gap, the discrepancy between conditional and unconditional outputs, governs guidance sensitivity. Leveraging this insight, we reformulate the CFG sampling as a homotopy optimization with a manifold constraint. This formulation necessitates a manifold projection step, which we implement via an incremental gradient descent scheme during sampling. To improve computational efficiency and stability, we further enhance this iterative process with Anderson Acceleration without requiring additional model evaluations. Our proposed methods are training-free and consistently refine generation fidelity, prompt alignment, and robustness to the guidance scale. We validate their effectiveness across diverse benchmarks, demonstrating significant improvements on large-scale models such as DiT-XL-2-256, Flux, and Stable Diffusion 3.5. Code is available at https://github.com/LeonSuZhengYi/CFG-MP.

Preference-based reinforcement learning (PbRL) learns policies from human trajectory-level comparisons, avoiding explicit reward design and expert demonstrations. Existing methods typically train utility functions on trajectory or segment-level preferences while relying on per-step utility estimates during policy optimization. This training and inference mismatch induces a distribution shift that severely degrades temporal credit assignment and limits policy learning. We analyze this issue and propose PAWS, a segment-based preference learning method that performs policy updates directly using segment-level advantage functions. By aligning utility training with policy optimization, PAWS preserves trajectory-level preference information and avoids unreliable per-step learning signals. Experiments on simulated robotic manipulation and locomotion tasks demonstrate that PAWS consistently outperforms existing PbRL approaches, highlighting the importance of distribution-consistent preference learning.

Diffusion models have achieved state-of-the-art performance in generating images, audio, and video, but their adaptation to text remains challenging due to its discrete nature. Prior approaches either apply Gaussian diffusion in continuous latent spaces, which inherits semantic structure but struggles with token decoding, or operate in categorical simplex space, which respect discreteness but disregard semantic relation between tokens. In this paper, we propose Smoothing Diffusion on Token Embeddings (Smoothie), a novel diffusion method that combines the strengths of both approaches by progressively smoothing token embeddings based on semantic similarity. This technique enables gradual information removal while maintaining a natural decoding process. Experimental results on several sequence-to-sequence and unconditional generation tasks demonstrate that Smoothie outperforms existing diffusion-based models in generation quality. Furthermore, ablation studies show that our proposed diffusion space yields better performance than both the standard embedding space and the categorical simplex.

Multimodal geometry reasoning requires models to jointly understand visual diagrams and perform structured symbolic inference, yet current vision--language models struggle with complex geometric constructions due to limited training data and weak visual--symbolic alignment. We propose a pipeline for synthesizing complex multimodal geometry problems from scratch and construct a dataset named \textbf{GeoCode}, which decouples problem generation into symbolic seed construction, grounded instantiation with verification, and code-based diagram rendering, ensuring consistency across structure, text, reasoning, and images. Leveraging the plotting code provided in GeoCode, we further introduce code prediction as an explicit alignment objective, transforming visual understanding into a supervised structured prediction task. GeoCode exhibits substantially higher structural complexity and reasoning difficulty than existing benchmarks, while maintaining mathematical correctness through multi-stage validation. Extensive experiments show that models trained on GeoCode achieve consistent improvements on multiple geometry benchmarks, demonstrating both the effectiveness of the dataset and the proposed alignment strategy.

Differentially private Stochastic Gradient Descent (DP-SGD) has become integral to privacy-preserving machine learning, ensuring robust privacy guarantees in sensitive domains. Despite notable empirical advances leveraging features from non-private, pre-trained models to enhance DP-SGD training, a theoretical understanding of feature dynamics in private learning remains underexplored. This paper presents the first theoretical framework to analyze private training through a feature learning perspective. Building on the multi-patch data structure from prior work, our analysis distinguishes between label-dependent feature signals and label-independent noise—a critical aspect overlooked by existing analyses in the DP community. Employing a two-layer CNN with polynomial ReLU activation, we theoretically characterize both feature signal learning and data noise memorization in private training via noisy gradient descent. Our findings reveal that (1) Effective private signal learning requires a higher signal-to-noise ratio (SNR) compared to non-private training, and (2) When data noise memorization occurs in non-private learning, it will also occur in private learning, leading to poor generalization despite small training loss. Our findings highlight the challenges of private learning and prove the benefit of feature enhancement to improve SNR. Experiments on synthetic and real-world datasets also validate our theoretical findings.