ICLR 2026 论文列表

Correlation clustering is an important unsupervised learning problem with broad applications. In this problem, we are given a labeled complete graph $G=(V,E^+ \cup E^-)$, and the optimal clustering is defined as a partition of the vertices that minimizes the $+$ edges between clusters and $-$ edges within clusters. We investigate efficient algorithms to test the \emph{cost} of correlation clustering: here, we want to know whether the graph could be (nearly) perfectly clustered (with $0$ cost) or is far away from admitting any perfect clustering. The problem has attracted significant attention aimed at modern large-scale applications, and the state-of-the-art results use $\widetilde{O}({1}/{\varepsilon^7})$ queries and time (up to log factors) to decide whether a graph is perfectly clusterable or needs to flip labels of $\varepsilon {\binom n 2}$ edges to become clusterable. In this paper, we improve this bound significantly by designing an algorithm that uses ${O}({1}/{\varepsilon^2})$ queries and time. Furthermore, we derive the first algorithm that tests the cost for the special setting of correlation clustering with $k$ clusters with ${O}(1/{\varepsilon^4})$ queries and time for constant $k$. Finally, for the special case of $k=2$, which corresponds to the strong structure balance problem in social networks, we obtain tight bounds of $\Theta({1}/{\varepsilon})$ queries -- the first set of \emph{tight} bounds in these problems. We conduct experiments on simulated and real-world datasets, and empirical results demonstrate the advantages of our algorithms.

Panorama has a full FoV (360$^\circ\times$180$^\circ$), offering a more complete visual description than perspective images. Thanks to this characteristic, panoramic depth estimation is gaining increasing traction in 3D vision. However, due to the scarcity of panoramic data, previous methods are often restricted to in-domain settings, leading to poor zero-shot generalization. Furthermore, due to the spherical distortions inherent in panoramas, many approaches rely on perspective splitting (\textit{e.g.}, cubemaps), which leads to suboptimal efficiency. To address these challenges, we propose $\textbf{DA}$$^{\textbf{2}}$: $\textbf{D}$epth $\textbf{A}$nything in $\textbf{A}$ny $\textbf{D}$irection, an accurate, zero-shot generalizable, and fully end-to-end panoramic depth estimator. Specifically, for scaling up panoramic data, we introduce a data curation engine for generating high-quality panoramic depth data from perspective, and create $\sim$543K panoramic RGB-depth pairs, bringing the total to $\sim$607K. To further mitigate the spherical distortions, we present SphereViT, which explicitly leverages spherical coordinates to enforce the spherical geometric consistency in panoramic image features, yielding improved performance. A comprehensive benchmark on multiple datasets clearly demonstrates DA$^{2}$'s SoTA performance, with an average 38\% improvement on AbsRel over the strongest zero-shot baseline. Surprisingly, DA$^{2}$ even outperforms prior in-domain methods, highlighting its superior zero-shot generalization. Moreover, as an end-to-end solution, DA$^{2}$ exhibits much higher efficiency over fusion-based approaches. Both the code and the curated panoramic data have be released. Project page: https://depth-any-in-any-dir.github.io/.

Modeling realistic pedestrian trajectories requires accounting for both social interactions and environmental context, yet most existing approaches largely emphasize social dynamics. We propose EnvSocial-Diff: a diffusion-based crowd simulation model informed by social physics and augmented with environmental conditioning and individual-group interaction. Our structured environmental conditioning module explicitly encodes obstacles, objects of interest, and lighting levels, providing interpretable signals that capture scene constraints and attractors. In parallel, the individual-group interaction module goes beyond individual-level modeling by capturing both fine-grained interpersonal relations and group-level conformity through a graph-based design. Experiments on multiple benchmark datasets demonstrate that EnvSocial-Diff outperforms the latest state-of-the-art methods, underscoring the importance of explicit environmental conditioning and multi-level social interaction for realistic crowd simulation.

We propose RAdaGD, a novel family of adaptive gradient descent methods on general Riemannian manifolds. RAdaGD adapts the step size parameter without line search, and includes instances that achieve a non-ergodic convergence guarantee, $f(x_k) - f(x_\star) \le \mathcal{O}(1/k)$, under local geodesic smoothness and generalized geodesic convexity. A core application of RAdaGD is Gaussian Variational Inference, where our method provides the first convergence guarantee in the absence of $L$-smoothness of the target log-density, under additional technical assumptions. We also investigate the empirical performance of RAdaGD in numerical simulations and demonstrate its competitiveness in comparison to existing algorithms.

Learning dynamical systems that respect physical symmetries and constraints remains a fundamental challenge in data-driven modeling. Integrating physical laws with graph neural networks facilitates principled modeling of complex N-body dynamics and yields accurate and permutation-invariant models. However, training graph neural networks with iterative, gradient-descent-based optimization algorithms (e.g., Adam, RMSProp, LBFGS) often leads to slow training, especially for large, complex systems. In comparison to 15 different optimizers, we demonstrate that Hamiltonian Graph Networks (HGN) can be trained 150-600× faster - but with comparable accuracy - by replacing iterative optimization with random feature-based parameter construction. We show robust performance in diverse simulations, including N-body mass-spring and molecular dynamics systems in up to $3$ dimensions and 10,000 particles with different geometries, while retaining essential physical invariances with respect to permutation, rotation, and translation. Our proposed approach is benchmarked using a NeurIPS 2022 Datasets and Benchmarks Track publication to further demonstrate its versatility. We reveal that even when trained on minimal 8-node systems, the model can generalize in a zero-shot manner to systems as large as 4096 nodes without retraining. Our work challenges the dominance of iterative gradient-descent-based optimization algorithms for training neural network models for physical systems.

Data-driven models are increasingly adopted in critical scientific fields like weather forecasting and fluid dynamics. These methods can fail on out-of-distribution (OOD) data, but detecting such failures in regression tasks is an open challenge. We propose a new OOD detection method based on estimating joint likelihoods using a score-based diffusion model. This approach considers not just the input but also the regression model's prediction, providing a task-aware reliability score. Across numerous scientific datasets, including PDE datasets, satellite imagery and brain tumor segmentation, we show that this likelihood strongly correlates with prediction error. Our work provides a foundational step towards building a verifiable 'certificate of trust', thereby offering a practical tool for assessing the trustworthiness of AI-based scientific predictions.

We introduce Kolmogorov–Arnold Neural Operator (KANO), a dual‑domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretability. We theoretically demonstrate that KANO overcomes the pure-spectral bottleneck of Fourier Neural Operator (FNO): KANO remains expressive over a generic position-dependent dynamics for any physical input, whereas FNO stays practical only to spectrally sparse operators and strictly imposes fast-decaying input Fourier tail. We verify our claims empirically on position-dependent differential operators, for which KANO robustly generalizes but FNO fails to. In the quantum Hamiltonian learning benchmark, KANO reconstructs ground‑truth Hamiltonians in closed-form symbolic representations accurate to the fourth decimal place in coefficients and attains $\approx6\times10^{-6}$ state infidelity from projective measurement data, substantially outperforming that of the FNO trained with ideal full wave function data, $\approx1.5\times10^{-2}$, by orders of magnitude.

In control problems and basic scientific modeling, it is important to compare observations with dynamical simulations. For example, comparing two neural systems can shed light on the nature of emergent computations in the brain and deep neural networks. Recently, Ostrow et al. (2023) introduced Dynamical Similarity Analysis (DSA), a method to measure the similarity of two systems based on their recurrent dynamics rather than geometry or topology. However, DSA does not consider how inputs affect the dynamics, meaning that two similar systems, if driven differently, may be classified as different. Because real-world dynamical systems are rarely autonomous, it is important to account for the effects of input drive. To this end, we introduce a novel metric for comparing both intrinsic (recurrent) and input-driven dynamics, called InputDSA (iDSA). InputDSA extends the DSA framework by estimating and comparing both input and intrinsic dynamic operators using a variant of Dynamic Mode Decomposition with control (DMDc) based on subspace identification. We demonstrate that InputDSA can successfully compare partially observed, input-driven systems from noisy data. We show that when the true inputs are unknown, surrogate inputs can be substituted without a major deterioration in similarity estimates. We apply InputDSA on Recurrent Neural Networks (RNNs) trained with Deep Reinforcement Learning, identifying that high-performing networks are dynamically similar to one another, while low-performing networks are more diverse. Lastly, we apply InputDSA to neural data recorded from rats performing a cognitive task, demonstrating that it identifies a transition from input-driven evidence accumulation to intrinsically-driven decision-making. Our work demonstrates that InputDSA is a robust and efficient method for comparing intrinsic dynamics and the effect of external input on dynamical systems.

PDE surrogate models such as FNO and PINN struggle to predict solutions across inputs with diverse physical units and scales, limiting their out-of-distribution (OOD) generalization. We propose a $\pi$-invariant test-time projection that aligns test inputs with the training distribution by solving a log-space least squares problem that preserves Buckingham $\pi$-invariants. For PDEs with multidimensional spatial fields, we use geometric representative $\pi$-values to compute distances and project inputs, overcoming degeneracy and singular points that limit prior $\pi$-methods. To accelerate projection, we cluster the training set into K clusters, reducing the complexity from O(MN) to O(KN) for the M training and N test samples. Across wide input scale ranges, tests on 2D thermal conduction and linear elasticity achieve an average MAE reduction up to $\approx 91\\%$ with minimal overhead. This training-free, model-agnostic method is expected to apply to more diverse PDE-based simulations.

Contact forces introduce discontinuities into robot dynamics that severely limit the use of simulators for gradient-based optimization. Penalty-based simulators such as MuJoCo, soften contact resolution to enable gradient computation. However, realistically simulating hard contacts requires stiff solver settings, which leads to incorrect simulator gradients when using automatic differentiation. Contrarily, using non-stiff settings strongly increases the sim-to-real gap. We analyze penalty-based simulators to pinpoint why gradients degrade under hard contacts. Building on these insights, we propose DiffMJX, which couples adaptive time integration with penalty-based simulation to substantially improve gradient accuracy. A second challenge is that contact gradients vanish when bodies separate. To address this, we introduce contacts from distance (CFD) which combines penalty-based simulation with straight-through estimation. By applying CFD exclusively in the backward pass, we obtain informative pre-contact gradients while retaining physical realism.

Ensuring synthesizability in generative small molecule design remains a major challenge. While recent developments in synthesizable molecule generation have demonstrated promising results, these efforts have been largely confined to 2D molecular graph representations, limiting the ability to perform geometry-based conditional generation. In this work, we present SYNCOGEN (Synthesizable Co-Generation), a single framework that combines simultaneous masked graph diffusion and flow matching for synthesizable 3D molecule generation. SYNCOGEN samples from the joint distribution of molecular building blocks, chemical reactions, and atomic coordinates. To train the model, we curated SYNSPACE, a dataset containing over 600K synthesis-aware building block graphs and 3.3M conformers. SYNCOGEN achieves state-of-the-art performance in unconditional small molecule graph and conformer generation, and the model delivers competitive performance in zero-shot molecular linker design and pharmacophore conditioning for protein ligand generation in drug discovery. Overall, this multimodal formulation represents a foundation for future applications enabled by non-autoregressive molecular generation, including analog expansion, lead optimization, and direct structure conditioning.

The acquisition of robotic skills via reinforcement learning (RL) is crucial for advancing embodied intelligence, but designing effective reward functions for complex tasks remains challenging. Recent methods using large language models (LLMs) can generate reward functions from language instructions, but they often produce overly goal-oriented rewards that neglect state exploration, causing robots to get stuck in local optima. Traditional RL addresses this by adding exploration bonuses, but these are typically generic and inefficient, wasting resources on exploring task-irrelevant areas. To address these limitations, we propose Policy-grounded Synergy of Reward Shaping and Exploration (PoRSE), a novel and unified framework that guides LLMs to generate task-aware reward functions while constructing an abstract affordance space for efficient exploration bonuses. Given the vast number of possible reward-bonus combinations, it is impractical to exhaustively train a policy from scratch for each configuration to identify the best one. Instead, PoRSE employs an in-policy-improvement grounding process, dynamically and continuously generating and filtering out reward-bonus pairs along the policy improvement process. This approach accelerates skill acquisition and fosters a mutually reinforcing relationship between reward shaping, exploration and policy enhancement through close feedback. Experiments show that PoRSE is highly effective, achieving significant improvement in average returns across all robotic tasks compared to previous state-of-the-art methods. It also achieves initial success in two highly challenging manipulation tasks, marking a significant breakthrough.

Machine learning promises to revolutionize drug discovery, but its "black-box" nature and narrow focus limit adoption by experts. While Large Language Models (LLMs) offer a path forward with their broad knowledge and interactivity, existing methods remain data-intensive and lack transparent reasoning. To address these issues, we present DrugTrail, an LLM-based framework for explainable drug discovery that integrates structured reasoning trajectories with a Druggability‑Tailored Preference Optimization (DTPO) strategy. It not only introduces structured reasoning traces to articulate the "how" and "why" behind its conclusions but also serve to guide task-specific reasoning pathways within the LLM's vast knowledge space, thereby enhancing its interpretability and reliability of its final outputs. Furthermore, based on the fact that optimizing for binding affinity alone does not equate to optimizing for druggability, DTPO explicitly moves beyond single-metric optimization and opens up a broader search space that balances affinity with other essential factors. Extensive experiments demonstrate the effectiveness of our approach and its generalizability to a wider range of biomolecular optimization domains, bridging the gap between LLM reasoning capabilities and trustworthy AI-assisted drug discovery.

The Wasserstein–Fisher–Rao (WFR) metric extends dynamic optimal transport (OT) by coupling displacement with change of mass, providing a principled geometry for modeling unbalanced snapshot dynamics. Existing WFR solvers, however, are often unstable, computationally expensive, and difficult to scale. Here we introduce **WFR Flow Matching (WFR-FM)**, a simulation-free training algorithm that unifies flow matching with dynamic unbalanced OT. Unlike classical flow matching which regresses only a transport vector field, WFR-FM simultaneously regresses a vector field for displacement and a scalar growth rate function for birth–death dynamics, yielding continuous flows under the WFR geometry. Theoretically, we show that minimizing the WFR-FM loss exactly recovers WFR geodesics. Empirically, WFR-FM yields more accurate and robust trajectory inference in single-cell biology, reconstructing consistent dynamics with proliferation and apoptosis, estimating time-varying growth fields, and applying to generative dynamics under imbalanced data. It outperforms state-of-the-art baselines in efficiency, stability, and reconstruction accuracy. Overall, WFR-FM establishes a unified and efficient paradigm for learning dynamical systems from unbalanced snapshots, where not only states but also mass evolve over time.

Diffusion-based samplers learn to sample complex, high-dimensional distributions using energies or log densities alone, without training data. Yet, they remain impractical for molecular sampling because they are often slower than molecular dynamics and miss thermodynamically relevant modes. Inspired by enhanced sampling, we encourage exploration by introducing a sequential bias along bespoke, information-rich, low-dimensional projections of atomic coordinates known as collective variables (CVs). We introduce a repulsive potential centered on the CVs from recent samples, which pushes future samples towards novel CV regions and effectively increases the temperature in the projected space. Our resulting method improves efficiency, mode discovery, enables the estimation of free energy differences, and retains independent sampling from the approximate Boltzmann distribution via reweighting by the bias. On standard peptide conformational sampling benchmarks, the method recovers diverse conformational states and accurate free energy profiles. We are the first to demonstrate reactive sampling using a diffusion-based sampler, capturing bond breaking and formation with universal interatomic potentials at near-first-principles accuracy. The approach resolves reactive energy landscapes at a fraction of the wall-clock time of standard sampling methods, advancing diffusion-based sampling towards practical use in molecular sciences.

Accurate cell instance segmentation is foundational for digital pathology analysis. Existing methods based on contour detection and distance mapping still face significant challenges in processing complex and dense cellular regions. Graph coloring-based methods provide a new paradigm for this task, yet the effectiveness of this paradigm in real-world scenarios with dense overlaps and complex topologies has not been verified. Addressing this issue, we release a large-scale dataset GBC-FS 2025, which contains highly complex and dense sub-cellular nuclear arrangements. We conduct the first systematic analysis of the chromatic properties of cell adjacency graphs across four diverse datasets and reveal an important discovery: most real-world cell graphs are non-bipartite, with a high prevalence of odd-length cycles (predominantly triangles). This makes simple 2-coloring theory insufficient for handling complex tissues, while higher-chromaticity models would cause representational redundancy and optimization difficulties. Building on this observation of complex real-world contexts, we propose Disco (Densely-overlapping Cell Instance Segmentation via Adjacency-aware Collaborative Coloring), an adjacency-aware framework based on the “divide and conquer” principle. It uniquely combines a data-driven topological labeling strategy with a constrained deep learning system to resolve complex adjacency conflicts. First, “Explicit Marking” strategy transforms the topological challenge into a learnable classification task by recursively decomposing the cell graph and isolating a “conflict set.” Second, “Implicit Disambiguation” mechanism resolves ambiguities in conflict regions by enforcing feature dissimilarity between different instances, enabling the model to learn separable feature representations. Disco achieves a significant 7.08\% improvement in the PQ metric on the GBC-FS 2025 dataset and an average improvement of 2.72% across all datasets. Furthermore, the predicted “Conflict Map” serves as a novel tool for interpreting topological complexity, offering new potential for data-driven pathology research.

Molecular dynamics is crucial for understanding molecular systems but its applicability is often limited by the vast timescales of rare events like protein folding. Enhanced sampling techniques overcome this by accelerating the simulation along key reaction pathways, which are defined by collective variables (CVs). However, identifying effective CVs that capture the slow, macroscopic dynamics of a system remains a major bottleneck. This work proposes a novel framework coined BioEmu-CV that learns these essential CVs automatically from BioEmu, a recently proposed foundation model for generating protein equilibrium samples. In particular, we re-purpose BioEmu to learn time-lagged generation conditioned on the learned CV, i.e., predict the distribution of molecular states after a certain amount of time. This training process promotes the CV to encode only the slow, long-term information while disregarding fast, random fluctuations. We validate our learned CV on fast-folding proteins with two key applications: (1) estimating free energy differences using on-the-fly probability enhanced sampling and (2) sampling transition paths with steered molecular dynamics. Our empirical study also serves as a new systematic and comprehensive benchmark for MLCVs on fast-folding proteins larger than Alanine Dipeptide.

Tactile sensing is crucial for embodied intelligence, providing fine-grained perception and control in complex environments. However, efficient tactile data compression, which is essential for real-time robotic applications under strict bandwidth constraints, remains underexplored. The inherent heterogeneity and spatiotemporal complexity of tactile data further complicate this challenge. To bridge this gap, we introduce TaCo, the first comprehensive benchmark for Tactile data Codecs. TaCo evaluates 30 compression methods, including off-the-shelf compression algorithms and neural codecs, across five diverse datasets from various sensor types. We systematically assess both lossless and lossy compression schemes on four key tasks: lossless storage, human visualization, material and object classification, and dexterous robotic grasping. Notably, we pioneer the development of data-driven codecs explicitly trained on tactile data, TaCo-LL (lossless) and TaCo-L (lossy). Results have validated the superior performance of our TaCo-LL and TaCo-L. This benchmark provides a foundational framework for understanding the critical trade-offs between compression efficiency and task performance, paving the way for future advances in tactile perception.

Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address problems in these domains. In this paper, we show how to exploit the underlying symmetries of functions that map tensors to tensors. More concretely, we develop universally expressive equivariant machine learning architectures on tensors that exploit that, in many cases, these tensor functions are equivariant with respect to the diagonal action of the orthogonal, Lorentz, and/or symplectic groups. We showcase our results on three problems coming from material science, theoretical computer science, and time series analysis. For time series, we combine our method with the increasingly popular path signatures approach, which is also invariant with respect to reparameterizations. Our numerical experiments show that our equivariant models perform better than corresponding non-equivariant baselines.