NeurIPS 2026 Papers

Flexible molecular docking is crucial for drug discovery; however, existing flow-matching generative models often produce physically invalid conformations (e.g., steric clashes, distorted bond geometry). Our analysis suggests that a primary contributor to this challenge lies at the modeling level: when the flow is parameterized by standard equivariant networks, an intrinsic approximation floor can emerge, potentially hindering the learned velocity field from reaching its optimal convergence bound, particularly for highly flexible molecules. We present UniFlowDock, which addresses this by introducing strictly Complete Equivariant Velocity Fields, thereby eliminating the dimensional incompleteness of standard architectures. This theoretical completeness is further bolstered by Fragment-Adaptive Optimal Coupling, a method that structurally linearizes transport trajectories and decomposes the generation process into physics-aware subproblems. Experiments on PDBBind and PoseBusters demonstrate UniFlowDock achieves state-of-the-art accuracy and physical validity, showing consistent gains in highly flexible docking scenarios where target distributions exhibit higher transport complexity.

Diffusion-based models have demonstrated impressive accuracy and generalization in solving partial differential equations (PDEs). However, they still face significant limitations, such as high sampling costs and insufficient physical consistency, stemming from their many-step iterative sampling mechanism and lack of explicit physics constraints. To address these issues, we propose \emph{Phys-Instruct}, a novel physics-guided distillation framework which (1) not only compresses a pre-trained diffusion PDE solver into a few-step generator via matching generator and prior diffusion distributions to enable rapid sampling, (2) but also enhances the physics consistency by explicitly injecting PDE knowledge through a PDE distillation guidance. Phys-Instruct is built upon a solid theoretical foundation, leading to a practical physics-constrained training objective that admits tractable gradients. Across five PDE benchmarks, Phys-Instruct achieves orders-of-magnitude faster inference while reducing PDE Error by more than 8$\times$ compared to state-of-the-art diffusion baselines. Moreover, the resulting unconditional student model functions as a compact prior, enabling efficient and physically consistent inference for various downstream conditional tasks. Our results indicate that Phys-Instruct is a novel, effective, and efficient framework for ultra-fast PDE solving powered by deep generative models.

Two-sided matching platforms rely on preferences from both sides, yet participants can evaluate only a small fraction of potential partners. In practice, they use low-cost pre-match screening, e.g., interviews, profile views, or trial tasks, to form noisy impressions before committing to applications and offers. We study bandit learning in matching markets with interviews, modeling these interactions as queried *hints* [Bhaskara et al., 2022] that reveal partial preference information to both sides while constraining subsequent applications. Our framework also allows firm-side uncertainty: firms, like agents, learn their preferences and may make early hiring mistakes. To address this, we introduce strategic deferral, a firm-side action that permits temporary vacancy, corrects premature commitments, and enables decentralized learning under coarse anonymous feedback. We design algorithms for centralized and decentralized markets and show that a constant number of interviews per round suffices for horizon-independent regret, improving over the $O(\log T)$ guarantees known without interviews. Our bounds are near-optimal: the centralized guarantee is within a factor $m$ of an information-theoretic lower bound, while decentralized algorithms match it up to polynomial factors in structured markets and remain horizon-independent in general markets.

How do protein structure prediction models fold proteins? We investigate this question through causal interventions on the folding trunks of ESMFold, OpenFold, and Boltz-1. Across all three models, we find a shared two-stage computational structure. In the first stage, early blocks initialize *pairwise biochemical signals*: features like charge propagate from sequence into pairwise representations through architecture-specific pathways. In the second stage, late blocks develop *pairwise spatial features*: distance and contact information accumulate in the pairwise representation. We verify these mechanisms causally by showing that steering charge and distance features induces predictable structural changes. Furthermore, these representations are functionally interchangeable: pairwise states can be linearly aligned and substituted across models. Together, these results suggest that folding trunks with different architectures, inputs, and training procedures converge on a shared representational organization for mapping sequence chemistry into spatial geometry.

Over the past few years, diffusion-based Schrödinger bridge models have been proposed to approximate optimal transport dynamics between two prescribed boundary distributions, with successful applications to generative modeling. More precisely, these methods aim to estimate a path measure whose initial and terminal marginals match the two boundary distributions, while minimizing the Kullback–Leibler divergence with respect to a reference Markov process. In this work, we consider the generalized Schrödinger bridge problem, in which the reference process is a twisted Brownian motion, that is, a Feynman–Kac transform of a Brownian motion induced by a time-dependent differentiable potential. Building on the Iterative Markovian Fitting (IMF) paradigm, and in particular on its special case Diffusion Schrödinger Bridge Matching (DSBM), which corresponds to the zero potential, we introduce Twisted Schrödinger Bridge Matching (TSBM), a diffusion-based method designed to handle both continuous- and discrete-time potentials. Unlike previous approaches, TSBM provides a rigorous extension of the IMF scheme to the generalized Schrödinger bridge problem. This derivation leads to a new bridge-matching loss that depends explicitly on the gradient of the potential and recovers the DSBM objective when the potential vanishes, yielding improved performance. We further introduce trajectory-based variance-reduction techniques that substantially stabilize optimization and may be useful beyond the present setting. Finally, we empirically demonstrate the benefits of TSBM on several experimental settings.

Machine-learning surrogates are increasingly used to accelerate computational fluid dynamics (CFD), yet progress is limited by the lack of benchmarks capturing realistic, time-dependent turbulent flows. We introduce TURTLES, a 13 TB dataset of high-fidelity implicit large-eddy simulations of three-dimensional turbulent cylinder wakes in the shear-layer transition regime. The dataset contains 400 trajectories of 400 time steps each, with 3–9 million points per frame sampled on irregular point clouds, spanning variations in geometry, Reynolds number, and angle of attack. Unlike existing datasets, TURTLES captures fully three-dimensional turbulence with an active energy cascade driven by vortex stretching, combining (i) dense irregular meshes, (ii) long-horizon temporal dynamics, and (iii) physically realistic turbulent behavior. We benchmark state-of-the-art neural operators on long autoregressive rollouts and identify key failure modes, including temporal instability, loss of small-scale energy, and challenges in learning on large irregular domains. TURTLES provides a new standard benchmark for evaluating surrogate models in high-resolution, industrial-scale CFD regimes.

Retrosynthesis is one of the domains transformed by the rise of generative models, and it is one where the problem of nonsensical or erroneous outputs (hallucinations) is particularly insidious: reliable assessment of synthetic plans is time-consuming, with automatic methods lacking. In this work, we present RetroTrim, a retrosynthesis system that successfully avoids nonsensical plans on a set of challenging drug-like targets. Compared to common baselines in the field, our system is not only the sole method that succeeds in filtering out hallucinated reactions, but it also results in the highest number of high-quality paths overall. The key insight behind RetroTrim is the combination of diverse reaction scoring strategies, based on machine learning models and existing chemical databases. We show that our scoring strategies capture different classes of hallucinations by analyzing them on a dataset of labeled retrosynthetic intermediates. To measure the performance of retrosynthesis systems, we propose a novel evaluation protocol for reactions and synthetic paths based on a structured review by expert chemists. Using this protocol, we compare systems on a set of 32 novel targets, curated to reflect recent trends in drug structures. While the insights behind our methodology are broadly applicable to retrosynthesis, our focus is on targets in the drug-like domain. By releasing our benchmark targets and the details of our evaluation protocol, we hope to inspire further research into reliable retrosynthesis.

High-contrast multiscale PDE problems are common in real-world applications, yet current neural PDE solvers struggle to achieve sufficient accuracy on such tasks. The Generalized Multiscale Finite Element Method (GMsFEM) addresses this by compressing fine-scale heterogeneity into localized basis functions which are used to obtain more accurate solutions than neural PDE solvers. However, constructing these basis functions requires solving many local eigenvalue problems—the major computational bottleneck. We address this issue by proposing **Transolver-GMsFEM**, a new hybrid framework that utilizes the efficiency of neural PDE solver for predicting multiscale basis functions while preserving the solution quality of GMsFEM. Experiments on 2D/3D steady-state and time-dependent high-contrast multiscale PDEs on irregular grids show proposed method achieves over $100\times$ speedup for basis construction. Crucially, our experiments demonstrate that Transolver-GMsFEM significantly outperforms state-of-the-art neural PDE solvers in both accuracy and robustness, especially in out-of-distribution tasks where pure neural PDE solvers dramatically fail.

Time-parallel neural operators (FNO and successors) have transformed PDE surrogates on regular grids. Mesh-based operators (MeshGraphNets, Transolver) extend operator learning to irregular geometries but remain autoregressive in time and trained one geometry at a time, while classical parallel-in-time methods converge poorly on nonlinear advection-dominated PDEs. We propose space-time factorization: partition the model into local temporal operators (learned, graph-independent) and a spatial mixer that propagates information across nodes without graph-dependent learned parameters. This structural condition restores time-parallelism on irregular graphs and yields cross-graph zero-shot transfer once three information leaks—graph-dependent weights, graph-specific features, and graph-correlated training distributions—are controlled. The same protocol applies to two distinct spatial-mixer families tested here—fixed-spectral and learned-attention—suggesting the principle is not tied to a single mixer choice. We validate the principle in three domains. On simulating floodwave propagation in river networks, a 27K-parameter model trained on the Yangtze transfers zero-shot to the Mississippi at $R^2=0.998$, training $28\times$ faster than a recurrent message-passing baseline and scaling to $5\times$ larger graphs. On cross-geometry Navier–Stokes, both Chebyshev (SepFNO) and Physics-Attention (SepTransolver) variants reach within ~10% (relative $L_2$) of a locally-trained oracle using only 15 training geometries—to our knowledge the first demonstration of knowledge accumulation in this regime across fundamentally different topologies. On cross-city traffic forecasting, zero-shot transfer reaches within 12.9% of an oracle trained on the target city. A consistent pattern emerges across these settings: cross-geometry error decreases with both the number of training geometries and their relatedness to the test, with the rate of accumulation depending on the spatial mixer. The result opens the path for pooled-data, foundation-style models for graph dynamics on irregular topologies.

Equilibrium Propagation (EP) is a training framework for energy-based models (EBMs) that has attracted interest in the context of neuromorphic computing platforms such as continuous Hopfield networks, nonlinear resistive networks and coupled phase oscillators. However, EP's practical applications have so far remained limited to relatively small-scale problems. Predictive coding networks (PCNs), another class of EBMs rooted in computational neuroscience, are typically trained with a specialized algorithm and have likewise not yet been demonstrated at large scale. In this work, we develop a more effective training method for PCNs which combines the centered variant of EP with a novel equilibration scheme for PCNs. Using this approach, we train a 10-layer convolutional PCN (VGG10) on full-size ImageNet, achieving 13.23% test error rate on the top-5 classification task, close to the 12.2% backpropagation baseline. To our knowledge, this is the first demonstration of both PCNs and EP-based training at ImageNet scale. These results significantly extend the scalability of both approaches and suggest that the primary challenges in scaling EP in other EBMs may not be attributed to inherent limitations of the EP framework.

Reconstructing high-fidelity and controllable digital twins from multi-modal sensory observations is a fundamental problem in physical AI applications. While existing per-scene optimization methods handle dynamic driving scenes well, they are slow to optimize, have artifacts at novel viewpoints, and require costly manual annotations for decomposing the scene into controllable instances. Self-supervised generalizable reconstruction methods enable faster and more scalable reconstructions by learning from large datasets, but existing approaches do not fully leverage multi-modal inputs (e.g., camera and LiDAR) and lack decomposition capabilities. To address these limitations, we propose STRIDE, a self-supervised, generalizable and decomposable 4D driving scene reconstruction method. By processing multi-modal sensory inputs in a common 3D space with a Point-Transformer, STRIDE efficiently discovers spatio-temporal correspondences necessary for accurate flow prediction. By incorporating latent instance tokens, STRIDE is the first to perform feed-forward reconstruction and learnable decomposition without manual annotations. Experiments on public driving datasets show STRIDE achieves state-of-the-art performance on recovering geometry, appearance, and 3D flow. Moreover, we demonstrate how learned decompositions can enable dynamic instance manipulation and controllable simulation.

LiDAR is a critical sensor for autonomous driving and robotics, yet it remains vulnerable to adverse conditions such as fog, rain, transparent objects, and low-reflectance surfaces. Full-waveform LiDAR (FWL) addresses these limitations by capturing the complete return waveform as a histogram, preserving rich reflection characteristics including multi-path echoes and weak signals. While recent Transformer-based approaches have demonstrated promise on FWL data, two fundamental bottlenecks remain: high computational cost from redundant tokens in low-intensity background regions, and limited generalization due to scarce annotated training data. We address both bottlenecks by exploiting the physical structure inherent to FWL data. First, we propose FWL-ToPM, a token pruning and merging mechanism that leverages intensity distributions to selectively reduce tokens while retaining critical waveform content. Second, we introduce FWLAug, a physically consistent data augmentation framework that preserves time-of-flight waveform structure and frustum geometry to improve generalization across diverse environments. Evaluated on the Ghost-FWL benchmark, FWL-ToPM achieves over 8$\times$ speedup at real-time throughput alongside a nearly 9-point F1 gain, establishing the first real-time FWL Transformer that simultaneously improves accuracy. FWLAug further improves generalization to both standard and out-of-distribution environments. Together, these methods push FWL-based perception toward practical deployment.

Time series transformers have achieved strong forecasting performance, yet fundamental questions about their internal mechanisms remain unanswered: among self-attention and feed-forward networks (FFN), which component constructs temporal features? Why does a simple linear model outperform transformers? Why does patching help? We propose a temporal probing framework consisting of 15 token-level diagnostic tasks to trace information flow across transformer components. Applied to 5 architectures across 8 benchmarks, we find that temporal feature construction is not inherently tied to any single component—it emerges from the interaction between tokenization strategy and architectural design. In PatchTST, FFN dominates feature construction across all 8 datasets, with a $3.2\times$ mean ratio over attention. Even when attention is completely removed, FFN's feature construction capability is preserved or enhanced, indicating that attention is not essential for temporal feature construction. Conversely, iTransformer's variate-level attention dominates over FFN, and CATS's cross-attention is responsible for nearly all feature transfer. Point-wise tokenization ($P=1$) structurally deactivates FFN, explaining why early transformers lagged behind linear models. These findings unify contradictory results across DLinear, PatchTST, attention-free models (TSMixer, PatchMLP), and CATS within a single framework.

Topological clustering, and its main algorithm ToMATo, is a clustering method from Topological Data Analysis (TDA) which has been applied successfully in several applications during the last few years. This is thanks to its high versatility, as clusters are detected from the persistent components in the sublevel sets of any user-defined function (gene expression, pixel values, etc), and efficiency, as topological clustering enjoys robustness guarantees. However, ToMATo is also limited in several ways. First, a graph on the data points needs to be provided as a hyper-parameter of the method (whose fine-tuning is left to the user). Second, ToMATo is known to be very sensitive to outlier values in the function range. Finally, and most importantly, ToMATo can only handle one function at a time, whereas it is critical to use several functions in various applications. In this article, we introduce ToMAToMP: the first topological clustering method able to handle several functions at the same time with theoretical guarantees. More specifically, we leverage a recent tool from multi-parameter persistent homology, called MMA decomposition, to design our clustering algorithm, and prove that it enjoys robustness properties. As corollaries, we show that it can be used to make ToMATo independent of graph tuning, and robust to outliers. Finally, we provide a set of numerical experiments showcasing the efficiency and quality of the clusterings produced by ToMAToMP, by showing strong improvement over non-topological and topological baselines for various datasets.

The continued improvements in language model capability have unlocked their widespread use as drivers of autonomous agents, for example in coding or computer use applications. However, the core of these systems has not changed much since early instruction-tuned models like ChatGPT. Even advanced AI agents function on message exchange formats, successively exchanging messages with users, systems, with itself (i.e. chain-of-thought) and tools in a single stream of computation. This bottleneck to a **single stream** as in chat models leads to a number of limitations: the agent cannot act (generate output) while reading, and in reverse, cannot react to new information while writing. Similarly, the agent cannot act while thinking and cannot think while reading or acting on information. In this work, we show that models can be unblocked by switching from instruction-tuning for sequential message formats to instruction-tuning for **multiple, parallel streams of computation**, splitting each **role** into a separate stream. Every forward pass of the language model then simultaneously reads from multiple input streams and generates tokens in multiple output streams, all of which causally depend on earlier timesteps. We argue that this data-driven change remedies a number of usability limitations as outlined above, improves model efficiency through parallelization, improves model security through better separation of concerns and improves model monitorability.

Real-world time series are inherently non-stationary, with trends, periodic patterns, and uncertainty evolving over time. While the Fourier domain offers a natural lens to model time series, current deep learning approaches do not explicitly model evolution and randomness in the Fourier spectra, which limits their ability to accurately predict both the expected trajectory and its uncertainty in non-stationary time series. Motivated by Evolutionary Spectra (ES) theory, we propose \textbf{TimeES}, a general framework that enables probabilistic and deterministic forecasting via the evolutionary spectra theory. Specifically, we derive a parameterizable evolutionary spectra formulation, recasting non-stationary random process modeling as learning an evolving representation modulated by random variables. Furthermore, we reduce the complexity of the estimated spectra from $\mathcal{O}(NM)$ to $\mathcal{O}(NK)$, where $K \ll M/2$, by exploiting Hermitian symmetry and energy-guided frequency selection. Based on a simple linear backbone, our proposed TimeES achieves consistent state-of-the-art performance across both deterministic and probabilistic forecasting tasks, with high efficiency and interpretability. Code is available at: \url{https://anonymous.4open.science/r/TimeES}.

Accurate numerical solutions of partial differential equations (PDEs) are crucial in numerous science and engineering applications. In this work, we introduce a novel neural PDE solver named AFDONet, which incorporates neural operator learning and adaptive Fourier decomposition (AFD) theory for the first time into a specifically designed variational autoencoder (VAE) structure, to solve a general class of nonlinear PDEs on smooth manifolds. AFDONet is the first neural PDE solver whose architectural and component design is fully guided by an established mathematical framework (in this case, AFD theory), turning neural operator design from an art to a science. Thus, AFDONet also exhibits exceptional mathematical explainability and groundness, and enjoys several desired properties. Furthermore, AFDONet achieves outstanding solution accuracy and competitive computational efficiency in several benchmark problems. In particular, thanks to its deep connections with AFD theory, AFDONet shows superior performance in solving PDEs on i) arbitrary (Riemannian) manifolds, and ii) datasets with sharp gradients. Overall, this work presents a new paradigm for designing explainable neural operator frameworks.

We present the Multi-Block DC (BDC) class, a rich class of structured nonconvex functions that admit a DC (``difference-of-convex'') decomposition across parameter blocks. This multi-block class not only subsumes the usual DC programming, but also turns out to be provably more powerful. Specifically, we demonstrate how standard models (e.g., polynomials and tensor factorization) must have DC decompositions of exponential size, while their BDC formulation is polynomial. This separation in complexity also underscores another key aspect: unlike DC formulations, obtaining BDC formulations for problems is vastly easier and constructive. We illustrate this aspect by presenting explicit BDC formulations for modern tasks such as deep ReLU networks, a result with no known equivalent in the DC class. Moreover, we complement the theory by developing algorithms with non-asymptotic convergence theory, including both batch and stochastic settings, and demonstrate the broad applicability of our method through several applications.

The rise of machine learning has shifted targeted resource allocation in policy and humanitarian settings toward algorithmic targeting based on predicted risk scores. This approach is typically cheaper and faster than traditional screening procedures that directly observe the latent vulnerability status through physical verification. Yet, even access to the true conditional vulnerability probability cannot eliminate misallocation: aleatoric uncertainty over individual vulnerability status is irreducible, and probabilistic targeting inevitably misallocates some resources. In this work we study how screening and algorithmic targeting should be optimally combined in a two-stage allocation framework where a screening stage observes true outcomes for a subset of units before a final allocation stage assigns the resource under a fixed coverage budget. We show that the optimal strategy screens units at the margin of algorithmic allocation, while directly targeting the highest-risk units. Furthermore, we empirically characterize when screening and algorithmic targeting act as complements or substitutes: efficiency gains from screening grow as the aleatoric uncertainty in the population increases. We illustrate our framework with applications in income-based social protection programs and humanitarian demining in Colombia, where the tension between screening costs and allocation efficiency is operationally consequential.