NeurIPS 2026 Papers

Conference on Neural Information Processing Systems

Decision breakdown

6,437papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    991.5%
  • Spotlight
    2403.7%
  • Poster
    6,09894.7%

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Statistical Complexity of Soft Bellman Residual Minimization

Enoch H. Kang, Kyoungseok Jang

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Bellman residual minimization (BRM) provides a scalable, gradient-based approach to offline reinforcement learning in large state spaces. While globally convergent gradient-based soft (i.e., entropy-regularized) BRM methods for neural networks have recently been established, their statistical complexity under stochastic gradient descent remains largely unknown. In this paper, we address this theoretical gap for soft BRM. Through a novel Lyapunov-based analysis, we establish an $\mathcal{O}(1 / n)$ average argument stability bound, which translates directly into a $\mathcal{O}(1 / n)$ statistical complexity for the soft BRM objective.

Poster
Static-Dynamic Disentanglement for Efficient Multi-Frame Vision-Language-Action Models

Weikang Qiu, Huashuo Lei, Tinglin Huang, Aosong Feng, Rex Ying

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Vision-Language-Action (VLA) models have recently emerged as a promising paradigm for generalist robotic control. Built upon vision–language model (VLM) architectures, VLAs predict actions conditioned on visual observations and language instructions, achieving strong performance and generalization across tasks. However, VLAs face two major challenges: a limited context window for input frames and inefficient inference due to the quadratic attention complexity and large parameter counts. To this end, we propose Dysta, a framework that disentangles visual inputs into multi-level static and dynamic tokens, which enables (1) retaining a single copy of static tokens across frames to significantly reduce context length, and (2) reusing the key–value (KV) cache of static tokens through a lightweight recache gate that updates only when necessary. This design enables efficient multi-frame integration and efficient inference. In addition, we introduce a new benchmark that more effectively evaluates the multi-frame integration ability of VLAs. Experiments show that DySta improves multi-frame integration by 24.5\% across metrics on our benchmark and 23.3\% in absolute success rate on real-world memory-dependent tasks, while accelerating inference by 2.0× (with +2.3\% success rate) on simulation benchmarks and 2.2× (with +10.6\% success rate) on real-world general tasks.

Poster
StateTree: Enhancing Long-term Dialogue Reasoning via Reinforcement Learning

Naen Xu, Wanqing Cui, Yibo Hu, Shixin Hong, Hengyu An, Meiguang Jin, Junfeng Ma, Tianyu Du

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Large language models deployed as personalized assistants must reason over long, evolving interaction histories. However, in long-term dialogue reasoning, relevant evidence is scattered across sessions, preferences may be revised over time, and standard long-context training fails to address these challenges under data scarcity and prohibitive computational costs. We propose StateTree, a data-driven RL pseudo-task that constructs a challenging auxiliary task from scarce dialogues with verifiable ground truth. StateTree augments multi-session dialogues with a tree-structured path-tracing task: key-value records are embedded across sessions to form a binary tree. Solving the task requires the model to traverse from root to leaf by retrieving records across sessions and comparing timestamps to resolve branches, then recover the hidden target question among distractor leaves. We apply curriculum RL training progressively increasing tree depth and introduce a compositional variant whose edges carry step-level reasoning fragments, training the model to compose partial cues into coherent queries. Trained on 10K-token contexts, StateTree generalizes to 128K tokens without full-length RL costs and exhibits capabilities including cross-session retrieval, temporal reasoning, knowledge update, and compositional multi-hop reasoning. StateTree outperforms both SFT and RL-based baselines while preserving short-context general reasoning. StateTree-7B achieves gains up to +23.60% on LongMemEval (128k), and StateTree-14B reaches 59.00% accuracy on LongMemEval, surpassing QwenLong-L1-32B (45.20%).

Poster
StateLedger: Path-Addressed External Memory for Persistent Multi-Agent Systems

Geer Yang, Xixuan Liu, Bin WU, Shaojiang Wang

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Persistent LLM agents need memory that preserves state, provenance, validity, and evidence across long interaction histories. We introduce StateLedger, a path-addressed external memory substrate that stores memory as durable state evolution rather than flat retrievable items: events update canonical paths, registers absorb small changes, CommitPages record residual drift against Checkpoints, cue views bound traversal, and content-addressed artifacts avoid evidence duplication. We prove storage, retrieval, coalescing, and conflict-aware ranking guarantees under explicit coverage and reader-consistency conditions. Empirically, StateLedger improves task performance and storage efficiency across LongMemEval, LoCoMo, and Evo-Memory Multi-turn, reaching 98.8% on LongMemEval-S, 82.6% on LongMemEval-M with 14.7% durable footprint, 95.8% LoCoMo non-adversarial accuracy, 87.1% unweighted success, and 93.5% unweighted progress on Evo-Memory.

Poster
State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectives

Hoang Son Tran, Pranav Gupta, Rémi Bardenet, Subhroshekhar Ghosh

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Determinant point processes (DPPs) have recently emerged as a kernelized alternative to vanilla independent sampling for generating efficient minibatches, coresets and other parsimonious representations of large-scale datasets. While basic theoretical foundations and promising empirical performance have been demonstrated, there are two main challenges for current proposals for DPP-based coresets or minibatches. The first is the need for families of DPPs with certain key variance reduction properties, usually constructed in a continuous setting, of which there are few known examples. The second is the need for an ad-hoc construction of a discrete DPP defined on a given dataset, that inherits such variance reduction. In this work, we contribute to the programme of establishing DPPs as a subsampling toolbox for ML by advancing on these two fronts. First, we propose new DPPs on the Euclidean space based on wavelets, with provably better accuracy guarantees than the best known rates. Second, we introduce a general method to convert such continuous DPPs, which are more amenable to proving analytical statements, into discrete kernels, which are pertinent for subsampling tasks such as minibatch and coreset constructions. This conversion mechanism simultaneously preserves the desired variance decay and reveals a low-rank decomposition of the discrete kernel, which makes sampling the corresponding DPP computationally inexpensive. En route, we enlarge the class of ML tasks amenable to improvements via DPP-based minibatches and coresets to include highly non-smooth objective functions, with arbitrarily low regularity, and rate guarantees that adapt explicitly to this regularity.

Poster
State-Action Selection in General Stochastic Games under Regularized Policy Gradient Methods

Omar Abbadi, Rida Laraki, Panayotis Mertikopoulos

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We study a general class of regularized policy gradient methods for episodic learning in general-sum stochastic games, with the aim of describing the long-run behavior of the induced policy iterates. In this challenging setting, learning even the simplest pointwise solution concepts is known to be intractable. This leads us to switch our focus to less restrictive *setwise* solution concepts: rather than only asking whether the iterates converge to a specific policy, we ask which *sets of policies* are selected by the learning dynamics in the long-run. In one-shot games, this setwise perspective admits a crisp characterization: a product set of pure strategies is asymptotically stable if and only if it is *closed under better replies* (club). We show that the direct statewise analogue of this principle *fails* outright in stochastic games because actions affect not only current rewards but also the future evolution of the game. To restore this principle in a transition-aware form, we introduce $Q$-*club* sets, namely state-action sets in which every *allowed* action has a strict $Q$-value advantage over every *excluded* action, thereby providing a setwise generalization of *strict Nash policies*. We then prove that $Q$-club sets are stochastically stable and attracting under the learning dynamics, even in the presence of noise and uncertainty. Finally, we establish local convergence rates to $Q$-club sets governed by the regularizer; in particular, entropic regularization yields exponential convergence, while Euclidean regularization yields finite-time convergence.

Poster
State of Thought Enables Endogenous Reasoning

Zhiren Gong, Yikun Hou, Zihao Zeng, Ming Xiao, Chau Yuen, Wei Yang Bryan Lim

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Test-time compute has emerged as a major approach to improving the capabilities of Large Language Models (LLMs). However, existing test-time reasoning paradigms rely heavily on externally imposed control, either through fixed reasoning programs or through costly expansion in constrained search spaces, limiting both generalization and efficiency. We propose State of Thought (SoT), a new reasoning paradigm that enables endogenous reasoning in LLMs, with the model's internal reasoning state governing how reasoning unfolds. Concretely, SoT extracts a compact dynamics-geometric state from the model's internal information transfer and selectively activates historical reasoning support useful under the current reasoning state, framing reasoning as a state-conditioned process over evidence rather than an externally prescribed token chain. Across quantitative (1.29x), general (1.62x), symbolic and code (1.72x), long-context (2.63x), and multimodal (1.08x) reasoning tasks on 4 models with 20 datasets, SoT consistently improves task accuracy while reducing tokens by 69.0% and latency by 48.7%, supporting endogenous state-driven reasoning as a more generalizable and efficient alternative.

Poster
State Evolution Awareness for Category-agnostic 3D Point Cloud Tracking

Xiantao Hu, Ying Tai, Jinxia Xie, Bineng Zhong, Guangwei Gao, Jianjun Qian, Jian Yang

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Existing 3D point cloud tracking methods have not fully exploited temporal information in point cloud sequences, making it difficult to effectively capture the continuous evolution of target states and thereby limiting tracking stability in scenarios with large cross-category geometric variation. To address this issue, we propose TETrack3D, a framework for category-agnostic 3D point cloud tracking. The core idea of TETrack3D is to elevate temporal information from an auxiliary cue to an explicit learning constraint for cross-frame association. Specifically, we introduce a historical feature reuse mechanism to preserve and reuse target-related features accumulated over multiple frames, enabling the association process in the current frame to access richer and finer-grained historical context. We further design a state evolution supervision module, which guides the model to learn temporally consistent target motion patterns from historical observations by predicting future target states. In addition, to alleviate cross-frame feature drift caused by target-state changes in point cloud sequences, we propose a temporal distribution alignment strategy based on optimal transport theory, which constrains target features across adjacent frames at the distribution level and improves the stability of temporal target modeling. Extensive comparative experiments on KITTI, nuScenes, and Waymo demonstrate that explicitly modeling the target-state evolution process effectively improves the localization robustness of 3D object tracking.

Poster
State Augmented Flows

Dwij Mehta, Arvind Renganathan, Vipin Kumar

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Flow matching learns continuous-time transports from a simple source distribution to a target data distribution by training a velocity field on intermediate states along interpolating trajectories. However, because the model observes only the projected data-space state $(x_t,t)$, different transport trajectories can induce conflicting velocity directions at nearby intermediate states, leading to curved transport paths that limit the fidelity of low-NFE sampling. To address this limitation, we propose \emph{State Augmented Flows} (SAF), a lightweight framework that lifts flow matching into a transient augmented state space. SAF transports an augmented state $(x_t,z_t)$, where auxiliary coordinates provide additional contextual information during transport while vanishing at the terminal time. This enlarges the state observed by the velocity model without changing the final sample space, and is compatible with existing coupling strategies and flow-matching architectures. Across MNIST, CIFAR-10, and ImageNet-32, SAF consistently improves over the rectified-flow baseline, with the largest gains in the low-NFE regime. These results suggest that augmenting the transported state provides a new and complementary mechanism for improving flow-based generative modeling.

Poster
StarWM: Self-Supervised Trained Attention Routing for Robust World Models

Zeqiang Zhang, Fabian Wurzberger, Maximilian Otte, Daniel Schmid, Sebastian Gottwald, Arne P Raulf, Daniel A. Braun

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A robust world model must strike the balance between faithfully capturing environmental dynamics and abstracting away from irrelevant content. While reconstruction-based world models ensure faithful supervision, they misallocate representational capacity by pixel area rather than dynamics relevance, which can cause task-irrelevant content to dominate the learned representation. Alternatively, reconstruction-free methods avoid this bias but risk discarding possibly relevant information. We propose StarWM, which combines advantages of both paradigms through a cross-attention module gated by self-supervised dynamics signals that decides where reconstruction applies, while a dual-stream decoder lets reconstruction shape only what is extracted at attended locations, with stop-gradient barriers preventing the two objectives from interfering. This allows reconstruction to supervise the visual content of attended regions without contaminating the latent with non-predictive information. On DeepMind Control with dynamic video backgrounds, StarWM outperforms reconstruction-based baselines while keeping competitive with the concurrent reconstruction-free approach, and is the only method that performs consistently well across clean, sequential-video, and random-video distractor settings. Mechanistic probing confirms StarWM preserves state attributes with near-perfect fidelity through long-horizon imagination while systematically discarding distractors.

Poster
StarCraft Motion: A Dataset for Agent Simulation in Adversarial and Partially Observable Scenarios

Yi-Chung Chen, Mingyu Kim, Ruqi Bai, James Z Hare, Jing Gao, David Inouye

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Agent simulation aims to model the future behavior of interacting agents, but existing benchmarks have largely focused on structured domains such as autonomous driving. Adversarial and partially observable settings remain less explored, despite their importance for modeling strategic multi-agent behavior. To address this gap, we introduce StarCraft Motion, a large-scale dataset for agent simulation built from human StarCraft~II replays. Our processing pipeline converts raw replays into standardized simulation scenarios by extracting continuous unit trajectories, deriving command-based unit-level intent labels, and aligning game states with player-specific fog-of-war observations. This enables direct study of behavior, intent, and opponent responses under competitive partial observability. As an initial study, we evaluate autoregressive simulation methods on StarCraft Motion and introduce HMART, a hierarchical baseline that extends SMART with learnable player-level query aggregation for efficient global-context modeling in large-agent-count scenarios. Experiments show that global context improves observer-unit simulation and intent prediction, while closed-loop fine-tuning further improves rollout quality. However, accurately capturing intent initiation and transitions remains difficult. We also find that opponent modeling from partial observations is substantially more challenging, and that additional global information can be misleading when it does not match the opponent's perspective. These results highlight StarCraft Motion as a useful dataset for studying scalable agent simulation in adversarial, partially observable environments.

Poster
Standing on the Shoulders of Giants: Rethinking EEG Foundation Model Pretraining via Multi-Teacher Distillation

Chenqi Li, Yu Liu, Shuo Zhang, Timothy Denison, Tingting Zhu

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Pretraining for electroencephalogram (EEG) foundation models has predominantly relied on self-supervised masked reconstruction, a paradigm largely adapted from and inspired by the success of vision and language foundation models. However, unlike images and text, EEG datasets are notoriously expensive to collect and characterized by low signal-to-noise ratio. These challenges introduce difficulties in scaling the EEG foundation models and capturing the underlying neural semantics through reconstruction. In this work, we ask the question: can we stand on the shoulders of well-established foundation models from well-represented modalities to bootstrap the pretraining of EEG foundation models? We first demonstrate that mainstream foundation models, such as those from vision and time series, transfer surprisingly well to EEG domain. Motivated by this observation, we propose the multi-teacher distillation pretraining (MTDP) framework for pretraining EEG foundation models via two-stage multi-teacher distillation. In the first stage, we introduce a learnable gating network to fuse representations from diverse teachers (e.g., DINOv3 and Chronos) via a masked latent denoising objective. In the second stage, we distill the fused representation into an EEG foundation model. Extensive evaluations across 2 backbone architectures, 9 downstream tasks and 12 datasets demonstrate that multi-teacher distillation pretraining consistently outperforms self-supervised pretraining for EEG foundation model and remains competitive even when the pretraining data is reduced to 25%.

Poster
StakeBench: Evaluating Language Understanding Grounded in Market Commitment

Yunhua Pei, Jingyu Hu, Yiwei Shi, Hongnan Ma, Weiru Liu, John Cartlidge

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Existing financial NLP benchmarks often rely on labels supplied by outside observers, measuring how language is perceived rather than what speakers have committed to in the market. We introduce \textbf{StakeBench}, an evaluation framework for language understanding grounded in market commitment. StakeBench links 560,876 comments from 2,261 resolved markets to verified position, action, and market-odds records across Polymarket and Manifold. Supervision is derived from observable market behavior. Position sides, post-comment trading actions, and market-odds trajectories replace human annotation. Four diagnostic tasks test whether models detect market commitment, identify the revealed side, anticipate future action, and perform collective odds projection. Three commitment-aware metrics measure alignment with revealed preferences rather than perceived sentiment. Validity audits and explicit interpretation boundaries help distinguish observable commitment signals from latent belief and causal market-odds impact. Across 15 LLMs and 18 topics and platform settings, models partially recover position-side signals, with Directed Accuracy from 0.506 to 0.599, but show structural failures on later tasks. Ten of the fifteen models collapse to one or two action labels in future action anticipation, and no model consistently improves on the naive odds-direction baseline in collective odds projection. Model scale is not correlated with performance, finance-domain tuning does not improve revealed-side identification, and platform incentives strongly shape higher-order results. StakeBench is packaged with evaluation code and dataset under CC-BY~4.0.

Poster
StainNFT: Curriculum-Gated Multi-Reward Post-Training for Pathology-Faithful Virtual Staining

shurong yang, Dong Wei, Qiong Peng, Xian Wu, Yefeng Zheng, Liansheng Wang

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Immunohistochemical (IHC) staining encodes molecular protein expression critical for clinical diagnosis, yet its chemical procedures are costly and time-consuming. Virtual staining offers a compelling alternative by digitally synthesizing IHC images from hematoxylin-eosin (H\&E) stained slides. Despite remarkable progress in diffusion- and flow-matching-based virtual staining, supervised fine-tuning (SFT) remains fundamentally limited in pathological fidelity due to its coarse, spatially averaged supervision signal that starves sparse DAB-positive regions of effective gradients. Reinforcement learning (RL) can exploit inter-rollout variance for outcome-level pathological supervision, but naively applying DAB-based rewards triggers severe reward hacking that collapses the image distribution and degrades perceptual quality. This paper presents StainNFT, a flow matching RL post-training framework built on a curriculum reward strategy that gates fine-grained optical density supervision on per-sample DAB mask IoU. To enhance fine-grained pathological fidelity, we introduce expression-aware reweighting, multi-scale block supervision, and a closed-loop implicit pathological semantic reward derived from pathology foundation model priors. Extensive experiments on seven benchmarks demonstrate that StainNFT consistently outperforms existing methods in both perceptual quality and pathological fidelity for H\&E-to-IHC virtual staining. Ablation studies confirm the effectiveness of each proposed component. Our code and trained models will be released.

Poster
Stage-wise Attention-Guided Region Sequencing for Adversarial Attacks on Large Vision-Language Models

Jaehyun Kwak, Nam Cao, Boryeong Cho, Segyu Lee, Sumyeong Ahn, Se-Young Yun

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Targeted adversarial attacks on Large Vision-Language Models (LVLMs) test whether small image perturbations can steer model responses toward attacker-specified content. Under the standard $L_\infty$ constraint, targeted attacks become a regional perturbation budget allocation problem: attack success depends not only on the perturbation objective, but also on which regions receive updates and in what order. Existing localized attacks improve over global perturbations but rely on stochastic spatial sampling, often updating weakly influential regions. We address this limitation through an attention-based analysis showing that cross-modal attention identifies adversarially sensitive regions and that perturbing high-attention hotspots induces predictable redistribution toward subsequent salient regions. These findings motivate attention-guided region sequencing, which begins from dominant hotspots and progressively moves the update support toward next-salient regions. Based on these principles, we propose Stage-wise Attention-Guided Attack (SAGA), a black-box region-sequencing framework that uses a fixed attention map from an open-source LVLM to guide perturbation updates without accessing target-model parameters, gradients, or attention maps. Across ten closed-source and open-source LVLMs, SAGA achieves state-of-the-art attack success rates and the best overall imperceptibility.

Poster
Stage-Aware Dual Alignment for Covariate Shift in Graph Domain Adaptation

Hongwei Wen, Can Zhang, Haoyu He, Xintao Zhao, Hanyuan Hang, Minglong Lei

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The performance of *Graph Domain Adaptation* (*GDA*) is fundamentally limited by *covariate-driven* discrepancies between source and target graphs, captured by *Covariate Shift* (*CS*) in the joint feature-structure space beyond label-related formulations. We show that CS induces bias at two non-interchangeable stages of *Graph Neural Network* (*GNN*) computation: *Feature Shift* (*FS*) distorts representations before message passing, while *Feature-Conditional Structure Shift* (*FCSS*) biases propagation, rendering single-stage alignment intrinsically insufficient. Based on this, we propose *Dual Alignment for Covariate Shift* (*DACS*), a stage-aware GDA framework that aligns discrepancies at their source. DACS mitigates FS via adversarial feature alignment and addresses FCSS through layer-wise reweighting to correct propagation bias, followed by final adversarial alignment for residual mismatch. This design follows directly from the stage-wise structure of CS rather than heuristic combinations of alignment modules. We further show that representation and propagation biases correspond to distinct components of target-domain error that cannot be eliminated in isolation. Experiments on synthetic and real-world benchmarks demonstrate that DACS consistently outperforms prior methods, especially under complex and coupled distribution shifts.

Poster
StableVQ: Practical Guidelines for Stable Vector-Quantized Tokenizer Training

Bao Tang, JiaHao Guo, Haoxiang Cao, Wenyu Liu, Changqian Yu, Kun Gai, Xinggang Wang

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Vector Quantization (VQ) is fundamental to discrete visual tokenizers that power modern autoregressive and masked image generation models. While recent shared-projection codebook methods have substantially advanced codebook utilization, training stability remains a critical and underexplored challenge. We argue that the root cause lies in the entanglement of the Encoder--Decoder and Codebook training: because neither module can reliably fulfill its own responsibility in isolation, the system can only function when the two subsystems happen to cooperate---a fragile condition that breaks down precisely when training is most stressed. We propose StableVQ, which revisits the proper learning objective of each module and resolves the problems that arise when each is trained to fulfill its own role independently. Concretely, (1) Dynamic STE corrects the instability in the Encoder's learning objective, enabling it to robustly optimize the reconstruction space under discrete regularization even when codebook utilization is low. (2) Region VQ Loss reconceives the Codebook's learning objective so that it can independently guarantee full tracking of the encoder output distribution, without relying on encoder oscillations to drive activation. (3) Decoupled Schedule recognizes that the distinct responsibilities of the Encoder--Decoder and the Codebook demand distinct optimization dynamics, and assigns each an independent learning rate schedule to ensure robust system-level behavior. Built on top of shared-projection codebooks, StableVQ is lightweight and introduces no learnable parameters. Experiments on ImageNet demonstrate consistent improvements in training stability, codebook utilization, and reconstruction quality across diverse codebook sizes and initialization settings.

Poster
StableAvatar: Ultra-Long Audio-Driven Avatar Video Generation

Shuyuan Tu, Yueming Pan, Yinming Huang, Xintong Han, Zhen Xing, Qi Dai, Chong Luo, Zuxuan Wu, Yu-Gang Jiang

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Current diffusion models for audio-driven avatar video generation struggle to synthesize long videos with natural audio synchronization and identity consistency. This paper presents StableAvatar, the first end-to-end video diffusion transformer that synthesizes ultra-long videos. We observe that the primary reason preventing existing models from generating long videos is their audio modeling, which typically relies on third-party off-the-shelf audio embeddings that are introduced into the diffusion model via cross-attention. Since current diffusion backbones lack any audio-related priors, they cannot correctly couple audio cues with latent dynamics, causing systematic latent distribution deviations at each segment. These deviations accumulate across segments, gradually shifting the latent trajectory and producing noticeable quality drift. To address this, StableAvatar introduces a novel Timestep-aware Audio Adapter that prevents error accumulation via timestep-aware modulation. During inference, we propose a novel Audio Native Guidance Mechanism to further enhance the audio synchronization by leveraging the diffusion’s joint audio-latent prediction as a dynamic guidance signal. To enhance the smoothness of the ultra-long videos, we introduce a Dynamic Weighted Sliding-window Strategy that fuses latent over time. Experiments on benchmarks show the effectiveness of StableAvatar both qualitatively and quantitatively.

Poster
Stable3R: Streaming 3D Reconstruction with Stable Geometric References

Jincheng Xiong, Jiarong Han, Hang Zhang, Mu Xu, Ming Qian

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Streaming 3D reconstruction has become a critical component for real-time applications. While recent advances have adapted large-scale offline feedforward models into streaming architectures via causal attention and KV-caching, they suffer from fundamental instability: the irreversible bias in early frames. This limitation stems from two coupled factors: (1) the existing KV-cache-based causal architecture strictly prohibits access to future information, resulting in information-poor early caches; and (2) current methods typically anchor the pose constraints to the initial frame, amplifying the early bias throughout the sequence. To address these challenges, we propose Stable3R, a holistic framework that establishes stable geometric references by enriching historical caches and anchoring poses to prefixes rather than a single initial frame. Specifically, we first introduce a lookahead-augmented attention mechanism, integrating future observations into past caches without violating causal constraints. Second, we adopt a frame-equivariant architecture with prefix-relative supervision, alleviating the reliance on the biased initial frame. Extensive experiments across multiple benchmarks show that our method consistently boosts reconstruction quality within a strictly causal inference schedule.

Poster
Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs

Nathanael Bosch

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Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free update step that uses Jacobian-vector products, iterative linear solvers, and stochastic covariance estimation to enable linear scaling, all while retaining stability. Second, we propose iterative re-linearization to further improve stability without sacrificing scalability, turning probabilistic ODE solvers into fully implicit methods. We evaluate the proposed approaches on a range of stiff and high-dimensional problems and demonstrate improved stability and scalability over established probabilistic solvers.

Poster