ICLR 2026 Papers

Massive training datasets are fueling the astounding progress in molecular machine learning. Since these datasets are typically generated with computational chemistry codes which do not randomize pose, the resulting geometries are usually not randomly oriented. While cheminformaticians are well aware of this fact, it can be a real pitfall for machine learners entering the burgeoning field of molecular machine learning. We demonstrate that molecular poses in the popular datasets QM9, QMugs and OMol25 are indeed biased. While the fact can easily be overseen by visual inspection alone, we show that a simple classifier can separate original data samples from randomly rotated ones with high accuracy. Second, we validate empirically that neural networks can and do exploit the orientedness in these datasets by successfully training a model on chemical property regression using the molecular orientation as _sole_ input. Third, we present visualizations of all molecular orientations and confirm that chemically similar molecules tend to have similar canonical poses. In summary, we recall and document orientational bias in the prevalent datasets that machine learners should be aware of.

We consider the problem of synthesizing photorealistic, physically plausible combustion effects in in-the-wild 3D scenes. Traditional CFD and graphics pipelines can produce realistic fire effects but rely on handcrafted geometry, expert-tuned parameters, and labor-intensive workflows, limiting their scalability to the real world. Recent scene modeling advances like 3D Gaussian Splatting (3DGS) enable high-fidelity real-world scene reconstruction, yet lack physical grounding for combustion. To bridge this gap, we propose FieryGS, a physically-based framework that integrates physically-accurate and user-controllable combustion simulation and rendering within the 3DGS pipeline, enabling realistic fire synthesis for real scenes. Our approach tightly couples three key modules: (1) multimodal large-language-model-based physical material reasoning, (2) efficient volumetric combustion simulation, and (3) a unified renderer for fire and 3DGS. By unifying reconstruction, physical reasoning, simulation, and rendering, FieryGS removes manual tuning and automatically generates realistic, controllable fire dynamics consistent with scene geometry and materials. Our framework supports complex combustion phenomena—including flame propagation, smoke dispersion, and surface carbonization—with precise user control over fire intensity, airflow, ignition location and other combustion parameters. Evaluated on diverse indoor and outdoor scenes, FieryGS outperforms all comparative baselines in visual realism, physical fidelity, and controllability.

This paper presents a unified framework for simulating and visualizing dynamic fracture phenomena in extreme mechanical collisions using multi-view image inputs. While existing methods primarily address elastic deformations at contact surfaces, they fail to capture the complex physics of extreme collisions, often producing non-physical artifacts and material adhesion at fracture interfaces. Our approach integrates two key innovations: (1) an enhanced Collision Material Point Method (Collision-MPM) with momentum-conserving interface forces derived from normalized mass distributions, which effectively eliminates unphysical adhesion in fractured solids; and (2) a fracture-aware 3D Gaussian continuum representation that enables physically plausible rendering without post-processing. The framework operates through three main stages: First, performing implicit reconstruction of collision objects from multi-view images while sampling both surface and internal particles and simultaneously learning surface particle Gaussian properties via splatting; Second, high-fidelity collision resolution using our improved Collision-MPM formulation; Third, dynamic fracture tracking with Gaussian attribute optimization for fracture surfaces rendering. Through comprehensive testing, our framework demonstrates significant improvements over existing methods in handling diverse scenarios, including homogeneous materials, heterogeneous composites, and complex multi-body collisions. The results confirm superior physical accuracy, while maintaining computational efficiency for rendering.

Molecular understanding is central to advancing areas such as scientific and drug discovery, yet Large Language Models (LLMs) struggle to understand molecular graphs effectively. Existing graph–LLM bridges often adapt the Q-Former-style connector with fixed-length static tokens, which is originally designed for vision tasks. These designs overlook stereochemistry and substructural context and typically require costly LLM-backbone fine-tuning, limiting efficiency and generalization. We introduce **EDT-Former**, an **E**ntropy-guided **D**ynamic **T**oken Trans**former** that generates tokens aligned with informative molecular patches, thereby preserving both local and global structural features for molecular graph understanding. Beyond prior approaches, EDT-Former enables alignment between frozen graph encoders and LLMs without tuning the LLM backbone (excluding the embedding layer), resulting in computationally efficient finetuning, and achieves state-of-the-art results on MoleculeQA, Mol-Instructions, and property prediction benchmarks (TDC, MoleculeNet), underscoring its effectiveness for scalable and generalizable multimodal molecular understanding.

Ordinal Regression (OR), which predicts the target values with inherent order, underpins a wide spectrum of applications from computer vision to recommendation systems. The intrinsic ordinal structure and non-stationary inter-class boundaries make OR fundamentally more challenging than conventional classification or regression. Existing approaches, predominantly based on Continuous Space Discretization (CSD), struggle to model these ordinal relationships, but are hampered by boundary ambiguity. Alternative rank-based methods, while effective, rely on implicit order dependencies and suffer from the rigidity of fixed binning. Inspired by the advances of generative language models, we propose **G**enerative **O**rdinal **R**egression (**GoR**), a novel generative paradigm that reframes OR as a sequential generation task. GoR autoregressively predicts ordinal segments until a dynamic ⟨EOS⟩, explicitly capturing ordinal dependencies while enabling adaptive resolution and interpretable step-wise refinement. To support this process, we theoretically establish a bias–variance decomposed error bound and propose the **Co**verage–**Di**stinctiveness Index (**CoDi**), a principled metric for vocabulary construction that balances quantization bias against statistical variance. The GoR framework is model-agnostic, ensuring broad compatibility with arbitrary task-specific architectures. Moreover, it can be seamlessly integrated with established optimization strategies for generative models at a negligible adaptation cost. Extensive experiments on **17** diverse ordinal regression benchmarks across **six** major domains demonstrate GoR's powerful generalization and consistent superiority over state-of-the-art OR methods.

Spectral bias, the tendency of neural networks to learn low-frequency features first, is a well-known issue with many training algorithms for physics-informed neural networks (PINNs). To overcome this issue, we propose IFeF-PINN, an algorithm for iterative training of PINNs with Fourier-enhanced features. The key idea is to enrich the latent space using high-frequency components through Random Fourier Features. This creates a two-stage training problem: (i) estimate a basis in the feature space, and (ii) perform regression to determine the coefficients of the enhanced basis functions. For an underlying linear model, it is shown that the latter problem is convex, and we prove that the iterative training scheme converges. Furthermore, we empirically establish that Random Fourier Features enhance the expressive capacity of the network, enabling accurate approximation of high-frequency PDEs. Through extensive numerical evaluation on classical benchmark problems, the superior performance of our method over state-of-the-art algorithms is shown, and the improved approximation across the frequency domain is illustrated.

Quantum Error Correction (QEC) decoding faces a fundamental accuracy-efficiency tradeoff. Classical methods like Minimum Weight Perfect Matching (MWPM) exhibit variable performance across noise models and suffer from polynomial complexity, while tensor network decoders achieve high accuracy but at prohibitively high computational cost. Recent neural decoders reduce complexity but lack the accuracy needed to compete with computationally expensive classical methods. We introduce SAQ-Decoder, a unified framework combining transformer-based learning with constraint aware post-processing that achieves both near Maximum Likelihood (ML) accuracy and linear computational scalability with respect to the syndrome size. Our approach combines a dual-stream transformer architecture that processes syndromes and logical information with asymmetric attention patterns, and a novel differentiable logical loss that directly optimizes Logical Error Rates (LER) through smooth approximations over finite fields. SAQ-Decoder achieves high accuracy decoding, with error thresholds of 10.99\% (independent noise) and 18.6\% (depolarizing noise) on toric codes that closely approach the theoretical ML bounds of 11.0\% and 18.9\% while outperforming existing neural and classical baselines in accuracy, complexity, and parameter efficiency. Our findings establish that learned decoders can simultaneously achieve competitive decoding accuracy and computational efficiency, addressing key requirements for practical fault-tolerant quantum computing systems.

Computing the polar decomposition and the related matrix sign function has been a well-studied problem in numerical analysis for decades. Recently, it has emerged as an important subroutine within the Muon algorithm for training deep neural networks. However, the requirements of this application differ sharply from classical settings: deep learning demands GPU-friendly algorithms that prioritize high throughput over high precision. We introduce *Polar Express*, a new method for computing the polar decomposition. Like Newton–Schulz and other classical polynomial methods, our approach uses only matrix-matrix multiplications, making it very efficient on GPUs. Inspired by earlier work of Chen \& Chow and Nakatsukasa \& Freund, *Polar Express* adapts the update rule at each iteration by solving a minimax optimization problem. We prove that this strategy minimizes error in a worst-case sense, allowing *Polar Express* to converge as rapidly as possible both in the early iterations and asymptotically. We also address finite-precision issues, making it practical to use in `bfloat16`. When integrated into Muon, our method yields consistent improvements in validation loss for a GPT-2 model on one to ten billion tokens from the FineWeb dataset, outperforming recent alternatives across a range of learning rates.

Peptides, short chains of amino acids capable of high-specificity protein binding, represent a powerful class of therapeutics. While deep generative models have shown promise for peptide design, existing approaches are often structure-centric and therefore generate sequences and structures in a decoupled manner, failing to ensure that designs are simultaneously physically stable, evolutionarily plausible, and internally coherent. To overcome this limitation, we introduce \textbf{PepTri}, a novel diffusion framework that addresses this by jointly generating peptide sequences and 3D structures within a unified, SE(3)-equivariant latent space. Our proposed model integrates three complementary guidance signals during the generative process: (i) physics-informed guidance via differentiable molecular mechanics to ensure structural stability and realism; (ii) evolutionary guidance to bias sequences toward conserved, functional motifs; and (iii) mutual information guidance to explicitly maximize sequence-structure coherence. This tri-guided approach ensures the generative process is steered by biophysical laws, biological priors, and information-theoretic alignment in tandem. Extensive evaluations on challenging peptide-protein design benchmarks, cross-domain (PepBench, LNR) and in-domain (PepBDB), demonstrate that PepTri substantially outperforms strong baselines, achieving state-of-the-art results in binding affinity, structural accuracy, and design diversity. Our results establish that integrating these complementary signals directly into the denoising process is crucial for generating viable, high-quality peptide medicines. PepTri is available at: https://github.com/aigensciences/PepTri

Animals often receive information about errors and rewards after significant delays. In some cases these delays are fixed aspects of neural processing or sensory feedback, for example, there is typically a delay of tens to hundreds of milliseconds between motor actions and visual feedback. The standard approach to handling delays in models of synaptic plasticity is to use eligibility traces. However, standard eligibility traces that decay exponentially mix together any events that happen during the delay, presenting a problem for any credit assignment signal that occurs with a significant delay. Here, we show that eligibility traces formed by a state-space model, inspired by a cascade of biochemical reactions, can provide a temporally precise memory for handling credit assignment at arbitrary delays. We demonstrate that these cascading eligibility traces (CETs) work for credit assignment at behavioral time-scales, ranging from seconds to minutes. As well, we can use CETs to handle extremely slow retrograde signals, as have been found in retrograde axonal signaling. These results demonstrate that CETs can provide an excellent basis for modeling synaptic plasticity.

Recent advancements in gait recognition have significantly enhanced performance by treating silhouettes as either an unordered set or an ordered sequence. However, both set-based and sequence-based approaches exhibit notable limitations. Specifically, set-based methods tend to overlook short-range temporal context for individual frames, while sequence-based methods struggle to capture long-range temporal dependencies effectively. To address these challenges, we draw inspiration from human identification and propose a new perspective that conceptualizes human gait as a composition of individualized actions. Each action is represented by a series of frames, randomly selected from a continuous segment of the sequence, which we term a snippet. Fundamentally, the collection of snippets for a given sequence enables the incorporation of multi-scale temporal context, facilitating more comprehensive gait feature learning. Moreover, we introduce a non-trivial solution for snippet-based gait recognition, focusing on Snippet Sampling and Snippet Modeling as key components. Extensive experiments on four widely-used gait datasets validate the effectiveness of our proposed approach and, more importantly, highlight the potential of gait snippets. For instance, our method achieves the rank-1 accuracy of 77.5% on Gait3D and 81.7% on GREW using a 2D convolution-based backbone.

Predicting the evolution of complex physical systems remains a central problem in science and engineering. Despite rapid progress in scientific Machine Learning (ML) models, a critical bottleneck is the lack of expensive real-world data, resulting in most current models being trained and validated on simulated data. Beyond limiting the development and evaluation of scientific ML, this gap also hinders research into essential tasks such as sim-to-real transfer. We introduce RealPDEBench, the first benchmark for scientific ML that integrates real-world measurements with paired numerical simulations. RealPDEBench consists of five datasets, three tasks, nine metrics, and ten baselines. We first present five real-world measured datasets with paired simulated datasets across different complex physical systems. We further define three tasks, which allow comparisons between real-world and simulated data, and facilitate the development of methods to bridge the two. Moreover, we design nine evaluation metrics, spanning data-oriented and physics-oriented metrics, and finally benchmark ten representative baselines, including state-of-the-art models, pretrained PDE foundation models, and a traditional method. Experiments reveal significant discrepancies between simulated and real-world data, while showing that pretraining with simulated data consistently improves both accuracy and convergence. In this work, we hope to provide insights from real-world data, advancing scientific ML toward bridging the sim-to-real gap and real-world deployment. Our benchmark, datasets, and instructions are available at https://realpdebench.github.io/.

Designing 3D ligands that bind to a given protein pocket with high affinity is a fundamental task in Structure-Based Drug Design (SBDD). However, the lack of synthesizability of 3D ligands has been hindering progress toward experimental validation; moreover, computationally evaluating synthesizability is a non-trivial task. In this paper, we first benchmark eight classical synthesizability metrics across 11 SBDD methods. The comparison reveals significant inconsistencies between these metrics, making them impractical and inaccurate criteria for guiding SBDD methods toward synthesizable drug design. Therefore, we propose a simple yet effective SE(3)-invariant \textit{\underline{SYN}thesizability \underline{C}lassifier} (SYNC) to enable better synthesizability estimation in SBDD, which demonstrates superior generalizability and speed compared to existing metrics on five curated datasets. Finally, with SYNC as a plug-and-play module, we establish a synthesizability classifier-driven SBDD paradigm through guided diffusion and Direct Preference Optimization, where highly synthesizable molecules are directly generated without compromising binding affinity. Extensive experiments also demonstrate the effectiveness of SYNC and the advantage of our paradigm in synthesizable SBDD. Code is available at \url{https://anonymous.4open.science/r/SYNC-C94D/}.

Standard representational similarity methods align each layer of a network to its best match in another independently, producing asymmetric results, lacking a global alignment score, and struggling with networks of different depths. These limitations arise from ignoring global activation structure and restricting mappings to rigid one-to-one layer correspondences. We propose Hierarchical Optimal Transport (HOT), a unified framework that jointly infers soft, globally consistent layer-to-layer couplings and neuron-level transport plans. HOT allows source neurons to distribute mass across multiple target layers while minimizing total transport cost under marginal constraints. This yields both a single alignment score for the entire network comparison and a soft transport plan that naturally handles depth mismatches through mass distribution. We evaluate HOT on vision models, large language models, and human visual cortex recordings. Across all domains, HOT matches or surpasses standard pairwise matching in alignment quality. Moreover, it reveals smooth, fine-grained hierarchical correspondences: early layers map to early layers, deeper layers maintain relative positions, and depth mismatches are resolved by distributing representations across multiple layers. These structured patterns emerge naturally from global optimization without being imposed, yet are absent in greedy layer-wise methods. HOT thus enables richer, more interpretable comparisons between representations, particularly when networks differ in architecture or depth. We further extend our method to a three-level HOT framework, providing a proof-of-concept alignment of two networks across their training trajectories and demonstrating that HOT uncovers checkpoint-wise correspondences missed by greedy layer-wise matching.

Neural operators (NOs) excel at learning mappings between function spaces, serving as efficient forward solution approximators for PDE-governed systems. However, as black-box solvers, they offer limited insight into the underlying physical mechanism, due to the lack of interpretable representations of the physical parameters that drive the system. To tackle this challenge, we propose a new paradigm for learning disentangled representations from NO parameters, thereby effectively solving an inverse problem. Specifically, we introduce DisentangO, a novel hyper-neural operator architecture designed to unveil and disentangle latent physical factors of variation embedded within the black-box neural operator parameters. At the core of DisentangO is a multi-task NO architecture that distills the varying parameters of the governing PDE through a task-wise adaptive layer, alongside a variational autoencoder that disentangles these variations into identifiable latent factors. By learning these disentangled representations, DisentangO not only enhances physical interpretability but also enables more robust generalization across diverse systems. Empirical evaluations across supervised, semi-supervised, and unsupervised learning contexts show that DisentangO effectively extracts meaningful and interpretable latent features, bridging the gap between predictive performance and physical understanding in neural operator frameworks.

Learning to simulate complex physical systems from data has emerged as a promising way to overcome the limitations of traditional numerical solvers, which often require prohibitive computational costs for high-fidelity solutions. Recent Graph Neural Simulators (GNSs) accelerate simulations by learning dynamics on graph-structured data, yet often struggle to capture long-range interactions and suffer from error accumulation under autoregressive rollouts. To address these challenges, we propose Information-preserving Graph Neural Simulators (IGNS), a graph-based neural simulator built on the principles of Hamiltonian dynamics. This structure guarantees preservation of information across the graph, while extending to port-Hamiltonian systems allows the model to capture a broader class of dynamics, including non-conservative effects. IGNS further incorporates a warmup phase to initialize global context, geometric encoding to handle irregular meshes, and a multi-step training objective that facilitates PDE matching, where the trajectory produced by integrating the port-Hamiltonian core aligns with the ground-truth trajectory, thereby reducing rollout error. To evaluate these properties systematically, we introduce new benchmarks that target long-range dependencies and challenging external forcing scenarios. Across all tasks, IGNS consistently outperforms state-of-the-art GNSs, achieving higher accuracy and stability under challenging and complex dynamical systems. Our project page: https://thobotics.github.io/neural_pde_matching.

Gene expression prediction, which predicts mRNA expression levels from DNA sequences, presents significant challenges. Previous works often focus on extending input sequence length to locate distal enhancers, which may influence target genes from hundreds of kilobases away. Our work first reveals that for current models, long sequence modeling can decrease performance. Even carefully designed algorithms only mitigate the performance degradation caused by long sequences. Instead, we find that proximal multimodal epigenomic signals near target genes prove more essential. Hence we focus on how to better integrate these signals, which has been overlooked. We find that different signal types serve distinct biological roles, with some directly marking active regulatory elements while others reflect background chromatin patterns that may introduce confounding effects. Simple concatenation may lead models to develop spurious associations with these background patterns. To address this challenge, we propose Prism (**P**roximal **r**egulatory **i**ntegration of **s**ignals for **m**RNA expression levels prediction), a framework that learns multiple combinations of high-dimensional epigenomic features to represent distinct background chromatin states and uses backdoor adjustment to mitigate confounding effects. Our experimental results demonstrate that proper modeling of multimodal epigenomic signals achieves state-of-the-art performance using only short sequences for gene expression prediction.

The goal of personalized medicine is to discover a treatment regimen that optimizes a patient's clinical outcome based on their personal genetic and environmental factors. However, candidate treatments cannot be arbitrarily administered to the patient to assess their efficacy; we often instead have access to an *in silico* surrogate model that approximates the true fitness of a proposed treatment. Unfortunately, such surrogate models have been shown to fail to generalize to previously unseen patient-treatment combinations. We hypothesize that domain-specific prior knowledge—such as medical textbooks and biomedical knowledge graphs—can provide a meaningful alternative signal of the fitness of proposed treatments. To this end, we introduce **L**LM-based **E**ntropy-guided **O**ptimization with k**N**owledgeable priors (**LEON**), a mathematically principled approach to leverage large language models (LLMs) as black-box optimizers without any task-specific fine-tuning, taking advantage of their ability to contextualize unstructured domain knowledge to propose personalized treatment plans in natural language. In practice, we implement LEON via 'optimization by prompting,' which uses LLMs as stochastic engines for proposing treatment designs. Experiments on real-world optimization tasks show LEON outperforms both traditional and LLM-based methods in proposing individualized treatments for patients.

Recovering missing flows on the edges of a network, while exactly respecting local conservation laws, is a fundamental inverse problem that arises in many systems such as transportation, energy, and mobility. We introduce FlowSymm, a novel architecture that combines (i) a group-action on divergence-free flows, (ii) a graph-attention encoder to learn feature-conditioned weights over these symmetry-preserving actions, and (iii) a lightweight Tikhonov refinement solved via implicit bilevel optimization. The method first anchors the given observation on a minimum-norm divergence-free completion. We then compute an orthonormal basis for all admissible group actions that leave the observed flows invariant and parameterize the valid solution subspace, which shows an Abelian group structure under vector addition. A stack of GATv2 layers then encodes the graph and its edge features into per-edge embeddings, which are pooled over the missing edges and produce per-basis attention weights. This attention-guided process selects a set of physics-aware group actions that preserve the observed flows. Finally, a scalar Tikhonov penalty refines the missing entries via a convex least-squares solver, with gradients propagated implicitly through Cholesky factorization. Across three real-world flow benchmarks (traffic, power, bike), FlowSymm substantially outperforms state-of-the-art baselines in RMSE, MAE and correlation metrics.