NeurIPS 2026 论文列表

Survival analysis provides statistical methods to model the time until an event occurs. Reporting delays arise when event times are not observed at their occurrence but are only revealed upon reporting. This issue is particularly critical for timely risk evaluation when the observation window is short due to administrative censoring. In this study, we incorporate right-censored reporting delays by jointly modeling parametric hazards for the event and reporting processes. We then construct a consistent estimator for the model parameters and develop a Monte Carlo expectation-maximization algorithm to compute it. To address the challenges posed by administrative censoring, we leverage these findings and propose a transfer-learning procedure. Experimental results demonstrate that our method improves the accuracy of timely risk evaluation under administrative censoring.

Statistical modeling and inference for temporal networks are increasingly important across modern applications, yet remain challenging in the sparse regime with evolving network sizes and temporal dependence. We propose a tractable model that captures these key features in a unified framework. Under this model, we establish geometric ergodicity and characterize the asymptotic behavior of cycle counts. These counts provide informative low-order summaries of temporal network dynamics. Moreover, we develop method-of-moments estimators based on cycle counts. We prove identifiability and uniqueness of the parameter estimates, and establish the strong consistency and asymptotic normality. To support uncertainty quantification, we further propose a simulation-based plug-in estimator of the asymptotic variance. Extensive simulations and a real data example demonstrate that our methods are accurate and effective for sparse, size-varying temporal networks.

We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range predictions. We develop an optimization-based integrator that minimizes the squared Euler--Lagrange residual via a mesh-free near-symplectic construction on local space-time patches. Different from integrators for analytical models, integrators for learned models should decouple model error (phase error) from integration error (conservation error). By relying on optimization rather than time-stepping, we bypass the global coupling inherent to fixed discretizations, which slows time- and space-stepping and complicates learning. Our method scales linearly with domain size via Jacobi iteration, and places no structural requirements on the learned network, allowing it to be coupled with existing physics-guided machine learning (ML) methods. We validate our approach on a learned representation of a double pendulum, a one-dimensional wave equation, and a two-dimensional wave equation. Our method achieves error comparable to classical symplectic methods while generalizing to spatially varying dynamics and arbitrary boundary conditions without retraining.

Representation learning for single-cell RNA-seq has been evaluated by the identities representations capture — cell types, lineages, perturbations — rather than how faithfully they model the distribution of cell states on the gene expression manifold. As a result, density estimation, rare-state detection, perturbation scoring, and gene-level attribution are bolted onto frozen embeddings as separate models, disconnected from the geometry of the data. We argue that the density model should be the primary object and that representation quality follows from it. Building on LeJEPA, whose SIGReg objective enforces a provably optimal isotropic Gaussian latent, we introduce LeCellModel, which exploits this Gaussian latent to recover data density on the gene expression manifold via the encoder's Jacobian log-volume (JEPA-SCORE). Across several datasets, LeCellModel outperforms established methods on scIB benchmark for representation quality. Furthermore, we show that LeCellModel enables estimation of rare expression states using JEPA-SCORE as a typicality measure – applying it to a controlled cytokine panel, where it identifies stimulated cells across minority fractions and tracks pathway-response magnitude. We introduce gene-level interpretability of density estimates — to our knowledge, the first method for analyzing JEPA-SCORE in feature space. Leveraging this framework, LeCellModel recapitulates the known association of a profibrotic macrophage program with idiopathic pulmonary fibrosis, and discovers a novel CD177$^{+}$ activated regulatory T cell subpopulation previously described only in tumor contexts. Both findings emerge directly from the geometry of the learned embedding, without relying on supervised annotations.

Reliable physics simulation requires both broad generalization across heterogeneous PDE families and stability under long autoregressive rollouts. Current neural solvers rarely provide both. Deterministic operators accumulate rollout error, while probabilistic solvers typically remain tied to a single PDE family or a short prediction horizon. We address this gap with the \textbf{Latent Generative Solver} (LGS), which couples a Physics VAE (PhyVAE) with a Pyramidal Flow-Forcing Transformer (PFlowFT). PhyVAE compresses states from twelve PDE families into a shared \emph{physical manifold}, separating dynamics-relevant structure from the ambient state space. PFlowFT then predicts the next latent state through input-noised flow matching, yielding a sufficient-condition contraction mechanism that explains improved autoregressive rollout stability. Pretrained on a 2.5\,M-trajectory, 16-system corpus at $128^2$ resolution, LGS obtains the lowest relative $L_2$ error (L2RE) on 15 of 16 systems at both 5- and 10-step rollout. At 20 steps, LGS reduces the L2RE from $56.1\%$ to $\mathbf{30.2\%}$ against matched deterministic and adapted generative baselines, while requiring $\mathbf{13}$--$\mathbf{77\times}$ less recurrent dynamics-step compute. On a held-out $256^2$ Kolmogorov flow, LGS reduces the 1-step L2RE from $0.398$ to $0.129$ within five finetuning epochs; U-AFNO achieves only $0.653$ to $0.343$ under the same protocol.

Fast linear algebra in deep learning usually comes with a choice: fixed geometry and exact computation, as in the Fourier transform, or adaptive geometry paid for by dense parameters, random features, or low-rank surrogates. To move beyond this trade-off, we introduce LAPLEX, a class of exact, trainable (phased) Laplace-kernel operators. A LAPLEX layer is a typically full-rank dense matrix, implicitly defined by learnable coordinate anchors, with FFT-like scaling. Consequently, it supports trainable matrix--vector operations at vector dimensions up to $10^9$ on modern GPUs. As a neural layer, it yields compact projections and classification heads interpretable as soft, trainable routing models. The same primitive also serves as an efficient Gram operator, enabling high-dimensional covariance models on flattened images of dimension $3 \cdot 10^6$ that preserve visible spatial structure without imposing convolutional bias. These applications reflect a single principle: dense geometry can be learned without storing a dense matrix, which enables data-adaptive global interactions in regimes where ordinary dense layers are out of reach. In this sense, LAPLEX separates expressivity from storage cost: it behaves like a dense trainable matrix, but is represented and applied through a small structured set of parameters.

Operator learning has experienced a shift toward attention-based architectures. This trend has more recently extended to physics-informed operator learning, where stacked cross-attention blocks add considerable computational cost relative to the foundational PI-DeepONet. We ask whether this complexity is necessary. Starting from the DeepONet branch-trunk decomposition, we replace the bilinear readout with a single softmax-weighted readout in which the trunk emits a query vector and the branch emits a set of key-value pairs—a structure we show admits universal approximation via reduction to a simplex-bilinear form. The resulting architecture, KerONet, uses no iterated attention, layer normalization, or explicit learnable projection matrices. Under a unified hyperparameter optimization protocol with a strict $200{,}000$-parameter budget, we evaluate KerONet alongside iterated-attention architectures (PIT, PINTO) and PI-DeepONet on four canonical 1D PDEs whose solutions range from globally smooth to sharply localized. KerONet outperforms PIT and PINTO on every PDE, across all five seeds, in accuracy (approximately $2$–$4\times$ lower rel-$L^2$ error), reproducibility ($2$–$31\times$ lower standard deviation), and speed ($1.8$–$4.4\times$ faster training time). Against PI-DeepONet, KerONet shows substantial gains where input-dependent localized features dominate ($2.5$–$8\times$ lower error on Burgers and Allen-Cahn) while exhibiting comparable accuracy on smoother operators (advection and diffusion-reaction)–a balance the iterated-attention architectures do not achieve. Our findings demonstrate that iterated cross-attention is not necessary to realize the benefits of query-dependent feature mixing in physics-informed operator learning.

Large language models (LLMs) are increasingly deployed in K–12 education, yet existing benchmarks such as C-Eval, CMMLU, GaokaoBench, and EduEval measure only whether a model can answer an exam question, i.e., factual recall. Effective educational AI further requires curriculum cognition: the structured understanding of how knowledge is organized, including prerequisite chains, concept taxonomies, experiment–concept links, and pedagogical sequencing. Curriculum cognition is neither probed by current benchmarks nor explicitly taught by current instruction-tuning data. To close this gap, we introduce K12-KGraph, a curriculum-aligned knowledge graph extracted from the official People's Education Press textbooks, covering mathematics, physics, chemistry, and biology across primary, middle, and high school, with seven node types (Concept, Skill, Experiment, Exercise, Section, Chapter, Book) and nine relation types spanning taxonomy, prerequisite, association, verification, assessment, location, and order. Building on this single graph, we derive two complementary resources: K12-Bench, a 23,640-question multi-select benchmark across five graph-derived task families (Ground, Prereq, Neighbor, Evidence, and Locate) that jointly probe curriculum cognition; and K12-Train, a KG-guided supervised fine-tuning corpus of ~2,300 QA pairs synthesized from node attributes and edge semantics. Experiments expose a clear gap and a clear remedy: on K12-Bench, even the strongest proprietary model (Gemini-3-Flash) reaches only 57% exact match and the best open-source model (Gemma-4-31B-IT) only 46%, with Prereq and Neighbor being the hardest; yet under a strictly matched 2,300-sample SFT budget on Qwen3-4B-Base and Llama3.1-8B-Base, K12-Train consistently outperforms equally sized subsets of eight mainstream instruction-tuning corpora (OpenHermes, Infinity, UltraChat, WizardLM, DataFlow, LMSYS, SmolTalk, Tulu-3) on both GaokaoBench and EduEval, showing that structural curriculum grounding is remarkably sample-efficient for educational SFT. We release the graph, benchmark, training data, and the full construction pipeline.

The achievement of practical fusion energy remains one of the most pressing unsolved scientific challenges, with immense implications for carbon-free power. A critical factor in the success of Inertial Confinement Fusion (ICF) is the design of a Laser Pulse Shape (LP) that can optimally drive implosions under stringent physical constraints. Traditional LP design relies on computationally expensive simulations and manual iterative refinement. We introduce the ICF Laser Pulse Shape Design System (LPDS), a generative inverse modeling framework that maps desired outcomes and target pellet configurations directly to optimized LPs. Crucially, we design a multi-objective loss function to ensure the generated LPs adhere to fundamental physical constraints and experimental feasibility. Furthermore, we present constraint-conditioning, inpainting, and gradient-based LP editing mechanisms for maximum fine-grained control over specific pulse characteristics during generation. Moreover, we validate our framework for LP design on a real-world experimental data. Our method establishes a data-driven inverse design framework for LP in ICF, contributing to the advancement of practical and sustainable fusion energy.

Language models exhibit strong robustness to paraphrasing, suggesting that semantic information may be encoded through stable internal representations, yet the structure and origin of such invariance remain unclear. We propose a local geometric framework in which semantically equivalent inputs occupy structured regions in latent space, with paraphrastic variation along nuisance directions and semantic identity preserved in invariant subspaces. Building on this view, we make three contributions: (1) a geometric characterization of invariant latent features, (2) a contrastive subspace discovery method that separates semantic-changing from semantic-preserving variation, and (3) an application of invariant representations to zero-shot model attribution. Across models and layers, empirical results support these contributions. Invariant structure emerges in specific depth regions, semantic displacement lies largely outside the nuisance subspace, and representation-level interventions indicate a causal role of invariant components in model outputs. Invariant representations also capture model-specific geometric patterns, enabling accurate attribution. These findings suggest that semantic invariance can be viewed as a local geometric property of latent representations, offering a principled perspective on how language models organize meaning.

Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields. This ties the model to the conditioning variables seen during training and limits reuse under boundary-condition shifts or local geometry changes. We propose to reformulate steady CFD inference as an inpainting problem: instead of training on explicit boundary conditions, we learn a self-supervised prior over velocity fields and impose boundary constraints only during inference by fixing known regions such as inlet, outlet or unchanged regions from previous simulations. To scale this idea to large 3D meshes, we introduce a local neighbourhood tokeniser that represents high-resolution velocity fields as compact spatial latent tokens and train latent flow-matching and masked-autoencoder models on these tokens. On intracranial aneurysm hemodynamics, our method reconstructs full velocity fields from sparse boundary context, outperforms supervised neural surrogates under boundary-condition and dataset shift and enables local geometry editing by reusing unchanged simulation context. These results suggest that viewing CFD inference as context-conditioned inpainting can turn neural surrogates from task-specific predictors into reusable flow priors.

Quantization is a fundamental tool used to compress datasets, neural network weights, and memory usage in a range of computational tasks. Many downstream applications of vector quantization perform inner products with arbitrary inputs. This motivates the study of inner product aware quantization schemes that approximately preserve inner products with unseen vectors -- in contrast to simply minimizing the mean-squared error. In this work, we formulate objectives that capture natural desiderata and develop adaptive and unbiased quantization methods that approximately preserve inner products with worst-case and average case inputs. An analysis of these objectives shows a tight connection with the well-studied notion of Adaptive Stochastic Quantization (ASQ). We develop provably fast exact and approximate algorithms for our objectives. Our theoretical results inspire efficient practical algorithms that perform well across a variety of workload distributions. They also lead to practical algorithms for standard ASQ which are 2-10$\times$ faster than prior state-of-the-art methods while maintaining quality. These theoretical and empirical results contribute towards making adaptive quantization techniques more efficient and tractable in practical settings.

Neural operators have emerged as powerful surrogates for scientific computing, enabling rapid reconstruction of complex physical fields from sparse sensor observations. Despite their strong predictive capability, their reliability often degrades under noisy or corrupted measurements, limiting practical deployment in real-world sensing environments. We show that enforcing statistical independence in latent representations provides a simple yet effective mechanism for improving neural operator robustness. To this end, we introduce Neural Operator Independence Regularization (NOIR), an end-to-end training framework that promotes statistically independent latent features during operator learning. Unlike structured basis approaches such as POD-DeepONet and PCA-Net, which impose orthogonality primarily as an offline compression constraint, NOIR directly shapes latent representations during training to enhance resilience against input perturbations. Across three canonical PDE benchmarks and five additive sensor corruption settings, NOIR consistently improves reconstruction accuracy while preserving clean-data performance. Beyond predictive gains, the induced latent representations exhibit distinctive statistical signatures that reveal architecture-specific robustness characteristics under corruption. These findings identify latent statistical independence as a principled inductive bias for robust neural operator design and provide new insight into the internal structure of operator learning systems. All models, datasets, checkpoints, and training code are publicly available at \url{https://github.com/t55176853-cmyk/NOIR/}

Generative models for function-valued data, such as time series and solutions to partial differential equations, must learn distributions over infinite-dimensional spaces rather than over finite-dimensional vectors. Functional Flow Matching (FFM) is a recent extension of Flow Matching to this setting, learning a velocity field whose flow transports a Gaussian prior to the data distribution. However, FFM inherits a structural limitation from standard Flow Matching: in each training batch, prior and data samples are paired independently, so the conditional bridge between them must simultaneously traverse the shared global structure of the dataset and instance-specific residuals. This limitation is more consequential in function space than in finite dimensions: directly formulating optimal transport on function spaces is technically delicate, and a flat Euclidean surrogate ignores the function-space geometry that distinguishes function-valued data. We propose kernel Functional Flow Matching (kFFM), which replaces the independent pairing by entropic optimal transport in a kernel-induced Hilbert space via the Hilbert Sinkhorn Divergence, leaving the FFM neural-operator architecture unchanged. Theoretically, we prove the HSD objective is well-posed on Banach ambient spaces with bounded kernels, derive compact-metric approximation bounds against quadratic-cost OT with an explicit kernel-cost mismatch term, and quantify the gap between the function-space objective and the truncated representation computed on a grid, at a rate governed by data regularity. Empirically, kFFM consistently improves MMD-RBF distributional matching over FFM, diffusion, adversarial, and finite-dimensional OT baselines on time-series and PDE benchmarks, with function-space-aware kernels emerging as the strongest choices on every PDE and path-valued benchmarks.

We propose a neural exploratory framework for *variational problems over graphons*, i.e., symmetric measurable functions $[0,1]^2 \to [0,1]$, that arise as limits of dense graph sequences. Such problems are central to two parts of the mathematical literature: extremal graph theory, which studies graph parameter optimisation under given restrictions, often for those graphs with a large number of vertices, and the large deviation theory of dense random graphs, which characterises the structure of rare events through constrained graphon optimisation. We represent graphons by implicit neural networks and optimise graphon objectives by gradient descent. Our design combines three ingredients: a multi-scale sinusoidal residual architecture biased toward sharp, step-like graphons; an embedded solver that enforces a single empirical density constraint and is differentiated by implicit differentiation; and symmetry-aware Monte Carlo estimators. On generalised Turán problems that previously required substantial human effort, our framework rediscovers known optimal graphons without human intervention. Applied to open instances, it produces candidate optima, including a previously unreported family of extremal structures. Applied to the variational problems from the large deviation theory of Erdős–Rényi random graphs, the framework produces new candidate optimal graphons across both upper- and lower-tail regimes for multiple pattern graphs; for the case of the triangle graph and the upper-tail regime, these candidates improve upon the best-known reference construction of Lubetzky and Zhao.

Reconstructing the gene regulatory dynamics underlying tissue development from unpaired, cross-sectional spatial transcriptomic snapshots poses a significant challenge in single-cell biology. While recent optimal transport and flow-based methods have advanced trajectory interpolation, their unconstrained latent dynamics lack identifiability, hindering reliable discovery of the underlying regulatory mechanisms. To address this, we propose single-cell Identifiable Feedback-controlled Latent Flow (scIFLF), a generative framework that introduces a physics-inspired structural prior that decomposes the latent flow into a macroscopic developmental drift and a restorative feedback toward functional attractors. Crucially, the gene-regulatory Jacobian is shown to be uniquely identifiable, invariant to the latent ambiguity, enabling principled discovery of gene regulations directly from the learned flow. Implemented with a multimodal Neural ODE, scIFLF aligns latent trajectories using entropy-regularized optimal transport. Benchmark experiments demonstrate that scIFLF outperforms state-of-the-art methods in trajectory interpolation and spatial coherence, while successfully recovering key driver genes of tissue development and organogenesis, bridging the gap between deep generative flexibility and biological interpretability.

In this paper, we introduce INEUS, a meshfree iterative neural solver for partial integro-differential equations (PIDEs). The method replaces the explicit evaluation of nonlocal jump integrals with single-jump sampling and reformulates PIDE solving as a sequence of recursive regression problems. Like Physics-Informed Neural Networks (PINNs), INEUS learns global solutions over the entire space-time domain, yet it offers a more efficient treatment of nonlocal terms and avoids the computationally expensive differentiation of full PIDE residuals. These features make INEUS particularly well suited for high-dimensional PDEs and PIDEs. Supported by a contraction-based convergence proof for linear PIDEs, our numerical experiments show that INEUS delivers accurate and scalable solutions for various high-dimensional linear and nonlinear examples.

The Allen--Cahn equation is one of the standard phase-field models for mean-curvature flow (MCF), parameterised by the diffuse-interface width $\varepsilon$. Practical simulations span a working range of $\varepsilon$, so a single model covering this range is needed. PDE-specific neural operators are accurate but must be retrained at every $\varepsilon$; general neural operators cover $\varepsilon$ in one model but lose the phase-field structure of the target. We introduce Interface-Augmented Diffusion-Reaction (IADR), a neural operator that addresses both shortcomings: a target network with a diffusion-and-reaction structure preserves the phase-field structure of the Allen--Cahn equation, while a hypernetwork that maps $\varepsilon$ to the weights of this target network amortises the dependence on $\varepsilon$ across the working range. A single IADR matches the per-$\varepsilon$ specialists on in-distribution data, retains their cross-shape generalisation under both $\varepsilon$- and geometry-out-of-distribution shifts, and runs at the per-$\varepsilon$ specialist's per-step inference cost. We further establish a $K$-step rollout error bound that aligns with the long-horizon behaviour observed in experiments.

Stereo depth estimation of human faces is a prerequisite for various computer vision applications, yet existing stereo benchmarks target outdoor, driving, or large object reconstruction scenarios and lack the anatomical precision and evaluation framework these applications require. We introduce HumanStereo, the first large-scale synthetic stereo dataset dedicated to human faces, comprising 417k stereo pairs from 128 photorealistic avatars across 109 unique stereo configurations and four indoor environments, with dense ground-truth annotations including depth maps, surface normals, segmentation masks, and facial landmarks. We argue that standard evaluation metrics such as $\delta_1$ and RMSE are ill-suited for facial depth estimation, and propose two complementary metrics: task-grounded absolute inlier-ratio (IR) and Landmark 3D Distance Error (L3DE) for metric anatomical accuracy. We benchmark five representative stereo methods: geometrical matchers, RAFT-Stereo, IGEV++, MASt3R, and FoundationStereo. A downstream evaluation on real optometric data for inter-pupillary distance (IPD) measurement, a parameter required in all eyeglass prescription, shows that even the best-performing model remains an order of magnitude above the sub-millimeter accuracy required for clinical deployment.