ICML 2026 Papers

Despite the fast progress in neural operator learning, long-sequence modeling still is a standing challenge whereby latent states have been introduced with techniques well derived. Diverging from existing methods that treat latent states as transient variables or decoupled representations, CoEvol-NO introduces a persistent state to establish a co-evolutionary framework, where the latent state and mesh sequence are updated jointly and bidirectionally. Inspired by classical numerical methods, we model the layer-wise state evolution as a Predictor-Corrector (PC) process. Specifically, a "Predictor'' generates a tentative target, followed by a "Corrector'' that refines the persistent state via an {error-driven update mechanism}. Furthermore, our theoretical analysis reveals that the widely used \textit{direct substitution} and \textit{residual update} paradigms are essentially {first-order approximations} of this error-driven correction under different loss assumptions. We theoretically prove that CoEvol-NO achieves strict linear time complexity. Extensive experiments on five standard benchmarks and two large-scale industrial design tasks demonstrate that CoEvol-NO consistently achieves state-of-the-art (SOTA) performance.

Virtual screening of billion-scale molecular libraries based on 3D shape similarity remains computationally prohibitive, requiring expensive conformational sampling and alignment, as done by established tools like *ROCS*. Here, we introduce *SAND* (**S**hape-**A**ware **N**eural **D**escriptor), a method that can retrieve shape similar molecules from their 2D graph alone. Our approach makes two key contributions: (1) a rank-preserving contrastive learning framework using differentiable Spearman correlation that results into representations where similarity strongly correlates with 3D molecular shape overlap (R=0.86), and (2) an end-to-end learned quantization-aware training scheme that jointly optimizes the encoder with a two-level IVF-PQ discretization step, achieving approximately $4\times$ better compression than post-hoc quantization at equivalent retrieval quality. We demonstrate that *SAND* enables searching over 10 billion molecules in less than a second on a single GPU node - a speedup of $>10^{8} \times$ compared to traditional methods. We release open-source code and trained weights to facilitate adoption.

Protein-protein interactions (PPIs) are fundamental to cellular function, disease mechanisms, and drug discovery. Current learning-based PPI predictors focus on learning powerful protein representations but neglect designing specialized classification heads. They mainly rely on generic aggregating methods like concatenation or dot products, which lack biological insight. Motivated by the biological "L3 rule", where multiple length-3 paths between a pair of proteins indicate their interaction likelihood, our study addresses this gap by designing a biologically informed PPI classifier. In this paper, we provide empirical evidence that popular PPI datasets strongly support the L3 rule. We propose an L3-path-regularized graph prompt learning method called L3-PPI, which can generate a prompt graph with virtual L3 paths based on protein representations and controls the number of paths. L3-PPI reformulates the classification of protein embedding pairs into a graph-level classification task over the generated prompt graph. This lightweight module seamlessly integrates with leading PPI predictors as a plug-and-play component, injecting the interaction prior of complementarity to enhance performance. Extensive experiments show that L3-PPI achieves superior performance enhancements over state-of-the-art competitors.

Multi-step retrosynthesis planning is a fundamental challenge in organic chemistry, defined by its enormous search space. Existing methods typically formulate it as a Markov Decision Process (MDP) with a fixed choice of transition model (i.e., a single-step retrosynthesis model), and focus on improving *how to search* through better policies and value functions. However, *how the transition space itself is navigated* remains largely unexplored. This limitation is particularly urgent given our observation of pronounced *skill disparity* among single-step prediction models: different models exhibit substantially different performance across molecule states. Motivated by this observation, we introduce RetrOrchestrator, an LLM-powered agent that explicitly accounts for model skill disparity by reframing retrosynthesis planning as a Partially Observable Markov Decision Process (POMDP). By regarding each single-step prediction model as a tool, we further propose a scaffold-aware reinforcement learning algorithm to optimize navigation policy within the transition space. As a result, RetrOrchestrator jointly searches which molecule to expand and which single-step model to apply for the molecule at the current step. Empirically, RetrOrchestrator significantly outperforms static baselines on the Retro*-190 benchmark, achieving a state-of-the-art 94.21% success rate (vs. 9.47% off-the-shelf LLM and 82.63\% non-LLM state-dependent router), with 92.49% of solved routes invoking two or more SSRs—evidence that the policy is not collapsing to a single specialist or a static router. The same gain persists on a larger out-of-distribution set (PDB-600), with RetrOrchestrator Pareto-optimal in both wall-clock time and model-query count. Code: https://github.com/ScottLiao920/verl-retro-agent.

Symbolic regression (SR) aims to discover interpretable mathematical expressions from observed data. While recent generative approaches have shown promise in treating SR as machine translation or multimodal learning tasks using NN methods, they suffer from uncontrollable generation process and training-evaluation misalignment. The training objectives (average cross-entropy loss on a token level across the distribution of historical data) differ from the evaluation metric (fitting error for every test data / complexity), necessitating extensive heuristic post-processing. On the other hand, direct optimization methods suffer from an exponential slowdown as the dimensionality increases, non-differentiability and local optima traps. We propose **MOD-SR**, unifying multimodal distribution learning during training with direct optimization at inference time. This is achieved by modeling the task as $p(x_0 \mid \mathcal{D}, y^*)$ and employing gradient-guided diffusion in embedding space, enhanced by contrastive learning and representation alignment. Furthermore, we introduce DFEX, a fixed-depth tree relaxation method that ensures differentiability for effective gradient guidance during inference. Experiments demonstrate that MOD-SR achieves superior performance on diverse benchmarks through a unified framework integrating distribution learning and optimization. Our code is available at [https://github.com/KROX777/MOD-SR](https://github.com/KROX777/MOD-SR).

Epidemiological forecasting from surveillance data is a hard problem and hybridizing mechanistic compartmental models with neural models is a natural direction. The mechanistic structure helps keep trajectories epidemiologically plausible, while neural components can capture non-stationary, data-adaptive effects. In practice, however, many seemingly straightforward couplings fail under partial observability and continually shifting transmission dynamics driven by behavior, waning immunity, seasonality, and interventions. We catalog these failure modes and show that robust performance requires making non-stationarity explicit: we extract multi-scale structure from the observed infection series and use it as an interpretable control signal for a controlled neural ODE coupled to an epidemiological model. Concretely, we decompose infections into trend, seasonal, and residual components and use these signals to drive continuous-time latent dynamics while jointly forecasting and inferring time-varying transmission, recovery, and immunity-loss rates. Across early outbreak and multi-wave regimes, our approach attains the lowest RMSE on all five datasets (up to 57% reduction over the strongest baseline), predicts the peak within one time step on four of five, and recovers time-varying epidemiological rates within ground-truth ranges, without relying on auxiliary covariates.

Standard cells form the building blocks of digital circuits, so their delay and power critically influence chip-level performance; yet characterization (can be understood as evaluation of cell delay and power) still relies on slow simulation sweeps, and many fast predictors ignore layout geometry, missing coupling and layout-dependent effects. The challenge is to jointly represent layout geometry and netlist topology so models capture fine-grained spatial details together with structural connectivity for accurate performance prediction. We introduce \textbf{FusionCell}, a dual-modality predictor that treats routed layout geometry and netlist topology as inputs and fuses them explicitly in a unified model. A DeiT encoder processes three-layer routed layouts, while a graph transformer models heterogeneous device/net graphs. The modalities are integrated through a \textbf{topology-guided} mechanism, where the netlist acts as a structural ``map'' to actively query relevant physical regions in the layout for joint geometric and topological reasoning. We build a 7nm dataset based on the ASAP7 PDK with over 19.5k cells spanning 149 types using automatic tools, targeting six metrics: signal rise/fall delay, transition, and power. Experimental results demonstrate that \textbf{FusionCell} reduces regression error (average MAPE 0.92\%) and improves Spearman/Kendall ranking over baselines, while accelerating the characterization process by orders of magnitude compared to circuit simulation.

Recent advances in generative modeling have enabled significant progress in structure-based drug design (SBDD). Existing methods typically condition molecule generation on empty binding pockets from holo complexes, overlooking informative components such as the filler (ligands and solvent). Here, we leverage low-resolution electron density (ED) derived from the filler as a physically grounded condition for \textit{de novo} drug design. We consider two types of ED—calculated and cryo-EM/X-ray—obtainable from computational or experimental sources, supporting unified pre-training and experimental integration. Compared with rigid pocket representations, experimental ED naturally captures conformational flexibility and provides a more faithful description of the binding environment. Based on this, we introduce EDMolGPT, a decoder-only autoregressive framework that generates molecules from low-resolution ED point clouds. By grounding generation in physically meaningful density signals, EDMolGPT mitigates structural bias and produces molecules with 3D conformations. Evaluations on 101 biological targets verify the effectiveness. Our project page: \url{https://jiahaochen1.github.io/EDMolGPT_Page/}.

Machine-learning interatomic potentials (MLIPs) have advanced rapidly, with many top models relying on strong physics-based inductive bias. However, as models scale to larger systems like biomolecules and electrolytes, they struggle to accurately capture long-range (LR) interactions, leading current approaches to rely on explicit physics-based terms or components. In this work, we propose AllScAIP, a straightforward, attention-based, and energy-conserving MLIP model that scales to O(100 million) training samples. It addresses the long-range challenge using an all-to-all node attention component that is purely data-driven. Extensive ablations reveal that in low-data/small-model regimes, inductive biases improve sample efficiency. However, as data and model size scale, these benefits diminish or even reverse, while all-to-all attention remains critical for capturing LR interactions. Our model achieves state-of-the-art energy/force accuracy on molecular systems (OMol25), while being competitive on materials (OMat24) and catalysts (OC20). Furthermore, it enables stable, long-timescale MD simulations that accurately recover experimental observables, including density and heat of vaporization predictions.

Diffusion models excel at generation, but their latent spaces are high dimensional and not explicitly organized for interpretation or control. We introduce ConDA (Contrastive Diffusion Alignment), a plug-and-play geometry layer that applies contrastive learning to pretrained diffusion latents using auxiliary variables (e.g., time, stimulation parameters, facial action units). ConDA learns a low-dimensional embedding whose directions align with underlying dynamical factors, consistent with recent contrastive learning results on structured and disentangled representations. In this embedding, simple nonlinear trajectories support smooth interpolation, extrapolation, and counterfactual editing while rendering remains in the original diffusion space. ConDA separates editing and rendering by lifting embedding trajectories back to diffusion latents with a neighborhood-preserving kNN decoder and is robust across inversion solvers. Across fluid dynamics, neural calcium imaging, therapeutic neurostimulation, facial expression dynamics, and monkey motor cortex activity, ConDA yields more interpretable and controllable latent structure than linear traversals and conditioning-based baselines, indicating that diffusion latents encode dynamics-relevant structure that can be exploited by an explicit contrastive geometry layer.

Existing benchmarks for computational materials discovery primarily evaluate static predictive tasks or isolated computational sub-tasks. While valuable, these evaluations neglect the inherently iterative and adaptive nature of scientific discovery. We introduce **MA**terials **D**iscovery **E**nvironments (**MADE**), a novel framework for benchmarking end-to-end autonomous materials discovery pipelines. MADE simulates closed loop discovery campaigns in which an agent or algorithm proposes, evaluates, and refines candidate materials under a constrained oracle budget, capturing the sequential and resource-limited nature of real discovery workflows. We formalize discovery as a search for thermodynamically stable compounds relative to a given convex hull, and evaluate efficacy and efficiency via comparison to baseline algorithms. The framework is flexible; users can compose discovery agents from interchangeable components such as generative models, filters, and planners, enabling the study of arbitrary workflows ranging from fixed pipelines to agentic systems. We demonstrate this by conducting systematic experiments across a diverse range of systems and algorithms, finding that adaptive planning becomes more important to discovery efficiency as the search space scales.

Recurrent and deep neural networks (RNNs/DNNs) are cornerstone architectures in machine learning. Remarkably, RNNs differ from DNNs only by weight sharing, as can be shown through unrolling in time. How does this structural similarity fit with the distinct functional properties these networks exhibit? To address this question, we here develop a unified mean-field theory for RNNs and DNNs in terms of representational kernels, describing fully trained networks in the feature learning ($\mu$P) regime. This theory casts training as Bayesian inference over sequences and patterns, directly revealing the functional implications induced by the RNNs' weight sharing. In DNN-typical tasks, we identify a phase transition when the learning signal overcomes the noise due to randomness in the weights: below this threshold, RNNs and DNNs behave identically; above it, only RNNs develop correlated representations across timesteps. For sequential tasks, the RNNs' weight sharing furthermore induces an inductive bias that aids generalization by interpolating unobserved time steps. Overall, our theory offers a way to connect architectural structure to functional biases.

Modern enterprises generate vast streams of time series metrics when monitoring complex systems, known as observability data. Unlike conventional time series from domains such as climate, observability data are zero-inflated, highly stochastic, and exhibit minimal temporal structure. Despite their importance, observability datasets remain underrepresented in public benchmarks due to proprietary restrictions and privacy concerns. Existing datasets are often anonymized and normalized, removing scale information and limiting their use for tasks such as anomaly detection, root cause analysis, and multi-modal reasoning. To address this gap, we introduce TelecomTS, a large-scale observability dataset derived from a 5G telecommunications network. TelecomTS features heterogeneous, de-anonymized covariates with explicit absolute scale information and provides a diverse suite of downstream tasks, including anomaly detection, root cause analysis, and multi-modal question-answering. Benchmarking state-of-the-art time series, language, reasoning, and multi-modal foundation models reveals that existing approaches struggle with the abrupt, noisy, and high-variance dynamics characteristic of observability data. Our experiments further underscore the importance of preserving covariates’ absolute scale, emphasizing the need for foundation time series models that natively leverage scale information for practical real-world observability applications. The code is available at: \url{https://github.com/Ali-maatouk/TelecomTS}.

Depth estimation for transparent objects remains a fundamental challenge, as RGB-based cues often fail in regions affected by refraction and light transmission. Polarization provides physically grounded information related to surface orientation and material properties, offering reliable geometric cues even in the absence of texture. In this work, we introduce PolarDepth, a monocular framework that incorporates both RGB and polarization inputs, including the degree and angle of linear polarization (DoLP and AoLP), to estimate dense depth and localize transparent regions. PolarDepth injects polarization-derived physical priors by estimating the refractive index, zenith angle, and azimuth angle from polarization measurements and embedding them into an implicit geometric representation that constrains depth inference in ambiguous transparent regions. To support model development and evaluation, we introduce PTOD, a dataset with synchronized RGB, polarization, and depth data and manually annotated transparent region masks. Experimental results demonstrate that PolarDepth achieves state-of-the-art performance in transparent object depth estimation. The findings highlight the effectiveness of embedding polarization-derived physical priors into learned representations for robust perception in complex visual environments.

Modern high-throughput biological datasets containing thousands of perturbations enable large-scale discovery of causal graphs that represent regulatory interactions between genes. Differentiable causal graphical models and regression-based methods have been developed to infer gene regulatory networks (GRNs) from interventional datasets. However, existing approaches fail to capture the non-linear dynamics of biological processes such as cellular differentiation. To address this limitation, we propose $\textit{PerturbODE}$, a novel framework that employs interpretable neural ordinary differential equations (neural ODEs) to model cell state trajectories under perturbations and derive the underlying causal GRN from the neural ODE parameters, enabling downstream simulation of unseen genetic interventions. The GRN is encoded via a single-hidden-layer feedforward network, implicitly grouping genes into interpretable co-regulated modules. We demonstrate PerturbODE's efficacy in GRN inference and extension to perturbation response prediction across both simulated and real overexpression datasets.

Dominant approaches for modelling Partial Differential Equations (PDEs) rely on deterministic predictions, yet many physical systems of interest are inherently chaotic and uncertain. While training probabilistic models from scratch is possible, it is computationally expensive and fails to leverage the significant resources already invested in high-performing deterministic backbones. In this work, we adopt a training-efficient strategy to transform pre-trained deterministic models into probabilistic ones via retrofitting with a proper scoring rule: the Continuous Ranked Probability Score (CRPS). Crucially, this approach is architecture-agnostic: it applies the same adaptation mechanism across distinct model backbones with minimal code modifications. The method proves highly effective across different scales of pre-training: for models trained on single dynamical systems, we achieve $20–54\%$ reductions in rollout CRPS and up to $30\%$ improvements in variance-normalised RMSE (VRMSE) relative to compute-matched deterministic fine-tuning. We further validate our approach on a PDE foundation model, trained on multiple systems and retrofitted on the dataset of interest, to show that our probabilistic adaptation yields an improvement of up to $40\%$ in CRPS and up to $15\%$ in VRMSE compared to deterministic fine-tuning. Validated across diverse architectures and dynamics, our results show that probabilistic PDE modelling need not require retraining from scratch, but can be unlocked from existing deterministic backbones with modest additional training cost.

Partial Differential Equations (PDEs) play a fundamental role in scientific computing, and recent efforts have sought to extend the success of foundation models to PDE solving. However, multi-physics PDE pre-training faces the unique challenge of disentangling dynamic heterogeneity to learn universal, elementary patterns that generalize to new PDEs. Additionally, cross-physics transfer lacks a theoretical framework for interpretability—specifically, understanding which pre-trained operator knowledge is effectively transferred to target PDEs. To bridge these gaps, we introduce the theory of neural operator splitting, which decomposes PDE evolution into a modulated global spectral operator and sparse local constitutive mechanisms. A key innovation is Origo, which provides a neural operator bank that enables the identification of operator-level generalization patterns. Extensive experiments demonstrate strong zero-shot generalization and mechanism-level interpretability on unseen PDEs.

Finding mathematical relations underlying natural phenomena is a fundamental task in scientific discovery. Recent advances in evolutionary search with Large Language Models (LLMs) show great promise by leveraging their embedded scientific knowledge. However, discovering governing equations remains challenging due to vast combinatorial hypothesis spaces with exponentially many possible relations. Existing LLM-based approaches treat LLMs as static hypothesis generators unaware of the observed scientific system, leading to suboptimal and inefficient exploration that over-relies on internal priors. To address this, we introduce Decompose, Adapt, and Evolve (DecAEvolve), a framework that combines granular feedback from symbolic term decomposition with LLM refinement through reinforcement learning fine-tuning. DecAEvolve unifies symbolic decomposition with test-time RL adaptation, enabling adaptive rather than static hypothesis generation. Our experiments across diverse scientific benchmarks demonstrate that DecAEvolve significantly improves both the accuracy of discovered equations and the efficiency of the discovery process, reducing error by up to an order of magnitude compared to state-of-the-art baselines.

Tokenization is the first point of contact between large language models (LLMs) and text data, yet it has not been viewed by many as a component of LLMs worth accelerating. During inference, tokenizers typically rely on simple dictionary lookups and are executed on CPUs as standard processes. This approach, however, introduces significant overhead from scheduling delays, core selection, data copying, and other system-level costs. These inefficiencies become problematic in latency-sensitive applications such as embedding, small language models, and agentic AI. In this paper, we present the Pinned Tokenizer (PinTok), a novel tokenizer architecture that reduces redundant hardware, operating system, and networking overhead through three key innovations: core and memory pinning, scheduling and context switch avoidance, and duplicate network packet copy and processing avoidance. Our implementation of PinTok can serve as a drop-in replacement for existing tokenizer deployments, delivering latency reductions of up to 95% (average), 97% (P50), 94% (P90), and 87% (P99) along with throughput improvements of up to 2,084%.