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Applications · Time Series

Shifeng Xie, Vasilii Feofanov, Jianfeng Zhang, Themis Palpanas, Ievgen Redko

Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pretraining on large-scale, carefully curated collections of real-world sequences. To allow for a sample-efficient pretraining of TSFMs, we propose CauKer, a novel algorithm designed to generate diverse, causally coherent synthetic time series with realistic trends, seasonality, and nonlinear interactions. CauKer combines Gaussian Process (GP) kernel composition with Structural Causal Models (SCM) to produce data for sample-efficient pretraining of state-of-the-art classification TSFMs having different architectures and following different pretraining approaches. Additionally, our experiments reveal that CauKer-generated datasets exhibit clear scaling laws for both dataset size (10K to 10M samples) and model capacity (1M to 783M parameters), unlike real-world datasets, which display irregular scaling behavior.

Xiaogang Wang, Hongyu Wu, Wenfeng Song, Kai Xu

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.

General Machine Learning · Probabilistic Methods

Jian Xu, Delu Zeng, Qibin Zhao, John Paisley

Deep Gaussian processes (DGPs) enable expressive hierarchical Bayesian modeling but pose substantial challenges for posterior inference, especially over inducing variables. Denoising diffusion variational inference (DDVI) addresses this by modeling the posterior as a time-reversed diffusion from a simple Gaussian prior. However, DDVI’s fixed unconditional starting distribution remains far from the complex true posterior, resulting in inefficient inference trajectories and slow convergence. In this work, we propose Diffusion Bridge Variational Inference (DBVI), a principled extension of DDVI that initiates the reverse diffusion from a learnable, data-dependent initial distribution. This initialization is parameterized via an amortized neural network and progressively adapted using gradients from the ELBO objective, reducing the posterior gap and improving sample efficiency. To enable scalable amortization, we design the network to operate on the inducing inputs $\mathbf{Z}^{(l)}$, which serve as structured, low-dimensional summaries of the dataset and naturally align with the inducing variables' shape. DBVI retains the mathematical elegance of DDVI—including Girsanov-based ELBOs and reverse-time SDEs—while reinterpreting the prior via a Doob-bridged diffusion process. We derive a tractable training objective under this formulation and implement DBVI for scalable inference in large-scale DGPs. Across regression, classification, and image reconstruction tasks, DBVI consistently outperforms DDVI and other variational baselines in predictive accuracy, convergence speed, and posterior quality.

Ruofeng Yang, Yongcan Li, Bo Jiang, Cheng Chen, Shuai Li

Recent diffusion models demonstrate remarkable sample efficiency and fast optimization, contradicting standard estimation bounds that suffer from the curse of dimensionality $n^{-1/D}$ with the data dimension $D$. Since images are usually a union of low-dimensional manifolds, current works model the data as a union of linear subspaces with Gaussian latent and achieve a $1/\sqrt{n}$ bound. Though this modeling reflects the multi-manifold property, the Gaussian latent can not capture the multi-modal property of the latent manifold. To bridge this gap, we propose the mixture subspace of low-rank mixture of Gaussian (MoLR-MoG) modeling, which models the target data as a union of $K$ linear subspaces, and each subspace admits a mixture of Gaussian latent ($n_k$ modals with dimension $d_k$). With this modeling, the corresponding score function naturally has a mixture of expert (MoE) structure, captures the multi-modal information, and contains nonlinear property. Empirically, our MoE-latent MoG network significantly outperforms MoLRG Gaussian baselines and matches MoE-latent U-Net performance with $10\times$ fewer parameters, validating its practical suitability. Theoretically, we provide provable convergence guarantees for the optimization process and establish an estimation error bound of $R^4\sqrt{\sum_{k=1}^K n_k}\sqrt{\sum_{k=1}^K n_k d_k}/\sqrt{n}$, successfully escaping the dimensionality curse. Collectively, with MoLR-MoG modeling, this work explains why diffusion models only require a small training sample and enjoy a fast optimization process. Furthermore, we also show the potential of MoE structure for diffusion models from the manifold perspective.

Zexi Fan, Yan Sun, Shihao Yang, Yiping Lu

Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We introduce Simulation-Calibrated Scientific Machine Learning (SCaSML), a framework that systematically improves pre-trained PDE solvers at inference time without any retraining. Our core idea is to derive a new PDE, which we term the Law of Defect, that precisely governs the error of a given surrogate model. Because this defect PDE retains the structure of the original problem, we can solve it efficiently with traditional stochastic simulators, yielding a targeted correction to the initial machine-learned solution. We prove that SCaSML achieves a faster convergence rate, with a final error bounded by the product of the surrogate and simulation errors. On challenging PDEs up to 160 dimensions, SCaSML reduces the error of various surrogate models, including PINNs and Gaussian Processes, by 20-80%. SCaSML provides a principled method to fuse the speed of machine learning with the rigor of numerical simulation, enhancing the trustworthiness of Al for scientific discovery.

General Machine Learning · Probabilistic Methods

Mara Daniels, Liam Hodgkinson, Michael W Mahoney

Physics-informed machine learning (PIML) integrates prior physical information, often in the form of differential equation constraints, into the process of fitting ML models to physical data. Popular PIML approaches, including neural operators, physics-informed neural networks, and neural ordinary differential equations, are typically fit to objectives that simultaneously include both data and physical constraints. However, the multi-objective nature of this approach creates ambiguity in the measurement of model quality. This is related to a poor understanding of epistemic uncertainty, and it can lead to surprising failure modes, even when existing metrics suggest strong fits. Working within a Gaussian process regression framework, we introduce the Physics-Informed Log Evidence (PILE) score. Bypassing the ambiguities of test losses, the PILE score is a single, uncertainty-aware metric that provides a selection principle for hyperparameters of a physics-informed model. We show that PILE minimization yields excellent choices for a wide variety of model parameters, including kernel bandwidth, least squares regularization weights, and even kernel function selection. We also show that, prior to data acquisition, a special data-free case of the PILE score identifies a-priori kernel choices that are "well adapted" to a given PDE. Beyond the kernel setting, we anticipate that the PILE score can be extended to PIML at large, and we outline approaches to do so.

Rosen Yu, Cyril Picard, Faez Ahmed

Bayesian optimization (BO) struggles in high dimensions, where Gaussian-process surrogates demand heavy retraining and brittle assumptions, slowing progress on real engineering and design problems. We introduce GIT-BO, a Gradient-Informed BO framework that couples TabPFN v2, a tabular foundation model that performs zero-shot Bayesian inference in context, with an active-subspace mechanism computed from the model’s own predictive-mean gradients. This aligns exploration to an intrinsic low-dimensional subspace via a Fisher-information estimate and selects queries with a UCB acquisition, requiring no online retraining. Across 60 problem variants spanning 20 benchmarks—nine scalable synthetic families and ten real-world tasks (e.g., power systems, Rover, MOPTA08, Mazda)—up to 500 dimensions, GIT-BO delivers a stronger performance–time trade-off than state-of-the-art GP-based methods (SAASBO, TuRBO, Vanilla BO, BAxUS), ranking highest in performance and with runtime advantages that grow with dimensionality. Limitations include memory footprint and dependence on the capacity of the underlying TFM.

Computer Vision · Image and Video Generation

Chubin Chen, Jiashu Zhu, Xiaokun Feng, Nisha Huang, Chen Zhu, Meiqi Wu, Fangyuan Mao, Jiahong Wu, Xiangxiang Chu, Xiu Li

Classifier-free Guidance (CFG) is a widely used technique in modern diffusion models for generating high-quality samples. However, through an empirical analysis on both Gaussian mixture models with closed-form solutions and real-world data distributions, we observe a discrepancy between the suboptimal results produced by CFG and the ground truth. The model's excessive reliance on these suboptimal predictions often leads to low fidelity and semantic incoherence. To address this issue, we first empirically demonstrate that the model's suboptimal predictions can be effectively refined using sub-networks of the model itself, without requiring additional training or the integration of external modules. Building on this insight, we propose **$S^2$-Guidance ($S$tochastic $S$elf-Guidance)**, a novel method that leverages stochastic block-dropping during the denoising process to construct sub-networks. This approach effectively guides the model away from potential low-quality predictions, thereby improving sample quality. Extensive qualitative and quantitative experiments across multiple standard benchmarks for text-to-image and text-to-video generation tasks demonstrate that **$S^2$-Guidance** delivers superior performance, consistently surpassing CFG and other advanced guidance strategies. Our code will be released.

Chongqi Qu, Meiqin Liu, Jian Lan, Shanling Dong, Zhunga Liu

Bayesian optimization (BO) is a powerful approach for black-box optimization, and in many real-world problems, domain experts possess valuable prior knowledge about promising regions of the search space. However, existing prior-informed BO methods are often overly complex, tied to specific acquisition functions, or highly sensitive to inaccurate priors. We propose DynMeanBO, a simple and general framework that incorporates expert priors into the Gaussian process mean function with a dynamic decay mechanism. This design allows BO to exploit expert knowledge in the early stages while gradually reverting to standard BO behavior, ensuring robustness against misleading priors while retaining the exploratory behavior of standard BO. DynMeanBO is broadly compatible with acquisition functions, introduces negligible computational cost, and comes with convergence guarantees under Expected Improvement and Upper Confidence Bound. Experiments on synthetic benchmarks and hyperparameter optimization tasks show that DynMeanBO accelerates convergence with informative priors and remains robust under biased ones.

Jiawei Yang, Tianhong Li, Lijie Fan, Yonglong Tian, Yue Wang

Despite their fundamental role, it remains unclear what properties could make tokenizers more effective for generative modeling. We observe that modern generative models share a conceptually similar training objective---reconstructing clean signals from corrupted inputs, such as signals degraded by Gaussian noise or masking---a process we term \emph{denoising}. Motivated by this insight, we propose aligning tokenizer embeddings directly with the downstream denoising objective, encouraging latent embeddings that remain reconstructable even under significant corruption. To achieve this, we introduce the Latent Denoising Tokenizer (\method), a simple yet highly effective tokenizer trained to reconstruct clean images from latent embeddings corrupted via interpolative noise or random masking. Extensive experiments on class-conditioned (ImageNet $256\times256$ and $512\times512$) and text-conditioned (MSCOCO) image generation benchmarks demonstrate that our \method consistently improves generation quality across \textit{six} representative generative models compared to prior tokenizers. Our findings highlight denoising as a fundamental design principle for tokenizer development, and we hope it could motivate new perspectives for future tokenizer design. Code is available at: https://github.com/Jiawei-Yang/DeTok

Computer Vision · Image and Video Generation

Xinyang Li, Tengfei Wang, Zixiao Gu, Shengchuan Zhang, Chunchao Guo, Liujuan Cao

We propose FlashWorld, a generative model that produces 3D scenes from a single image or text prompt in seconds, $10 \sim 100\times$ faster than previous works while possessing superior rendering quality. Our approach shifts from the conventional multi-view-oriented (MV-oriented) paradigm, which generates multi-view images for subsequent 3D reconstruction, to a 3D-oriented approach where the model directly produces 3D Gaussian representations during multi-view generation. While ensuring 3D consistency, 3D-oriented method typically suffers poor visual quality. FlashWorld includes a dual-mode pre-training phase followed by a cross-mode post-training phase, effectively integrating the strengths of both paradigms. Specifically, leveraging the prior from a video diffusion model, we first pre-train a dual-mode multi-view diffusion model, which jointly supports MV-oriented and 3D-oriented generation mode. To bridge the quality gap in 3D-oriented generation, we further propose a cross-mode post-training distillation by matching distribution from consistent 3D-oriented mode to high-quality MV-oriented mode. This not only enhances visual quality while maintaining 3D consistency, but also reduces the required denoising steps for inference. Also, we propose a strategy to leverage massive single-view images and text prompts during this process to enhance the model's generalization to out-of-distribution inputs. Extensive experiments demonstrate the superiority and efficiency of our method. Our code is released at https://github.com/imlixinyang/FlashWorld.

Theory · Reinforcement Learning and Planning

Priyank Agrawal, Shipra Agrawal, Azmat Azati

Bayesian posterior sampling techniques have demonstrated superior empirical performance in many exploration-exploitation settings. However, their theoretical analysis remains a challenge, especially in complex settings like reinforcement learning. In this paper, we introduce Q-Learning with Posterior Sampling (PSQL), a simple Q-learning-based algorithm that uses Gaussian posteriors on Q-values for exploration, akin to the popular Thompson Sampling algorithm in the multi-armed bandit setting. We show that in the tabular episodic MDP setting, PSQL achieves a regret bound of $\tilde O(H^2\sqrt{SAT})$, closely matching the known lower bound of $\Omega(H\sqrt{SAT})$. Here, S, A denote the number of states and actions in the underlying Markov Decision Process (MDP), and $T=KH$ with $K$ being the number of episodes and $H$ being the planning horizon. Our work provides several new technical insights into the core challenges in combining posterior sampling with dynamic programming and TD-learning-based RL algorithms, along with novel ideas for resolving those difficulties. We hope this will form a starting point for analyzing this efficient and important algorithmic technique in even more complex RL settings.

Andres Potapczynski, Alex Ali, Andrew Gordon Wilson

Matrix operations, such as linear solves, eigendecompositions, and log determinants, are foundational building blocks for any number of downstream applications. Therefore, any broadly capable learning system should be able to effectively approximate these operations in its internal representation. Accordingly, there is great motivation to study transformers for linear algebra --- for if transformers cannot even semi-competently perform matrix operations, then we cannot expect them to form a basis for a generally intelligent system. We demonstrate that current techniques developing transformers for linear algebra have striking failure modes, prohibitive scaling, and particularly poor out-of-distribution generalization to other matrix distributions, and matrices of different sizes. Investigating further, we find that current transformer approaches operate as statistical interpolators, rather than discovering algorithms that will generalize to matrices from other distributions. Based on our understanding of these limitations, we develop a sequence of interventions that substantially improve scaling and performance, including matrix embeddings through a learnable projection, linear attention, looping, and a data pre-training distribution of structured matrices. We term the resulting method the \emph{RangeFormer}, which we show has significantly improved scaling and performance on challenging OOD matrices from the \emph{matrix market}. Moreover, with RangeFormer we show for the first time that transformers can be successfully applied to downstream tasks that involve iterative matrix operations, including Gaussian process learning, and improving the sampling distribution of randomized methods.

Deep Learning · Generative Models and Autoencoders

Minyoung Kim

The famous Schr\"{o}dinger bridge (SB) has gained renewed attention in the generative machine learning field these days for its successful applications in various areas including unsupervised image-to-image translation and particle crowd modeling. Recently, a promising algorithm dubbed GSBM was proposed to solve the generalized SB (GSB) problem, an extension of SB to deal with additional path constraints. Therein the SB is formulated as a minimal kinetic energy conditional flow matching problem, and an additional task-specific stage cost is introduced as the conditional stochastic optimal control (CondSOC) problem. The GSB is a new emerging problem with considerable room for research contributions, and we introduce a novel Gaussian process pinned marginal path posterior inference as a meaningful contribution in this area. Our main motivation is that the stage cost in GSBM, typically representing task-specific obstacles in the particle paths and other congestion penalties, can be potentially noisy and uncertain. Whereas the current GSBM approach regards this stage cost as a noise-free deterministic quantity in the CondSOC optimization, we instead model it as a stochastic quantity. Specifically, we impose a Gaussian process (GP) prior on the pinned marginal path, view the CondSOC objective as a (noisy) likelihood function, and infer the posterior path via sparse variational free-energy GP approximate inference. The main benefit is more flexible marginal path modeling that takes into account the uncertainty in the stage cost such as more realistic noisy observations. On some image-to-image translation and crowd navigation problems under noisy scenarios, we show that our proposed GP-based method yields more robust solutions than the original GSBM.

Computer Vision · Segmentation

Wentian Xu, Ziyun Liang, Harry Anthony, Yasin Ibrahim, Felix Cohen, Guang Yang, Konstantinos Kamnitsas

Interactive segmentation uses real-time user inputs, such as mouse clicks, to iteratively refine model predictions. Although not originally designed to address distribution shifts, this paradigm naturally lends itself to such challenges. In medical imaging, where distribution shifts are common, interactive methods can use user inputs to guide models towards improved predictions. Moreover, once a model is deployed, user corrections can be used to adapt the network parameters to the new data distribution, mitigating distribution shift. Based on these insights, we aim to develop a practical, effective method for improving the adaptive capabilities of interactive segmentation models to new data distributions in medical imaging. Firstly, we found that strengthening the model's responsiveness to clicks is important for the initial training process. Moreover, we show that by treating the post-interaction user-refined model output as pseudo-ground-truth, we can design a lean, practical online adaptation method that enables a model to learn effectively across sequential test images. The framework includes two components: (i) a Post-Interaction adaptation process, updating the model after the user has completed interactive refinement of an image, and (ii) a Mid-Interaction adaptation process, updating incrementally after each %user click. Both processes include a Click-Centered Gaussian loss that strengthens the model's reaction to clicks and enhances focus on user-guided, clinically relevant regions. Experiments on 5 fundus and 4 brain‑MRI databases show that our approach consistently outperforms existing methods under diverse distribution shifts, including unseen imaging modalities and pathologies. Code: https://github.com/WenTXuL/OAIMS

Computer Vision · Image and Video Generation

JoonKyu Park, Kyoung Mu Lee

Diffusion models, well recognized for their strong generative priors, have recently been increasingly applied to super-resolution (SR) tasks. However, as diffusion models are trained on Gaussian-corrupted natural images, the distribution gap between low-resolution (LR) inputs and the model’s training distribution hinders direct inference. Prior works address this by conditioning on LR images, but their fine-tuning often weakens generative capability and requires multiple denoising steps. In this work, we present DM-SR, a novel framework that bridges this gap without modifying the pretrained diffusion model. We train an image encoder that maps LR inputs into the latent distribution aligned with the diffusion model’s training space, preserving its full generative power. Furthermore, DM-SR adaptively predicts the appropriate noise level based on the degradation of each input, ensuring optimal alignment with the diffusion model’s timestep-dependent distribution. Extensive experiments show that DM-SR achieves superior perceptual quality with a single-stage diffusion process, setting a new direction for efficient and high-fidelity SR with diffusion models.

Deep Learning · Generative Models and Autoencoders

Sedjro Salomon Hotegni, Sebastian Peitz

Developing efficient multi-objective optimization methods to compute the Pareto set of optimal compromises between conflicting objectives remains a key challenge, especially for large-scale and expensive problems. To bridge this gap, we introduce SPREAD, a generative framework based on Denoising Diffusion Probabilistic Models (DDPMs). SPREAD first learns a conditional diffusion process over points sampled from the decision space and then, at each reverse diffusion step, refines candidates via a sampling scheme that uses an adaptive multiple gradient descent-inspired update for fast convergence alongside a Gaussian RBF–based repulsion term for diversity. Empirical results on multi-objective optimization benchmarks, including offline and Bayesian surrogate-based settings, show that SPREAD matches or exceeds leading baselines in efficiency, scalability, and Pareto front coverage. Code is available at https://github.com/safe-autonomous-systems/moo-spread .

Applications · Neuroscience, Cognitive Science

Rupasinghe Arachchige Anuththara Rupasinghe, Jonathan Pillow

Multinomial logistic regression (MLR) is a classic model for multi-class classification that has been widely used for neural decoding. However, MLR requires a finite set of discrete output classes, limiting its applicability to settings with continuous-valued outputs (e.g., time, orientation, velocity, or spatial position), which are common in neuroscience settings. To address this limitation, we propose Continuous Multinomial Logistic Regression (CMLR), a generalization of logistic regression to continuous output spaces. CMLR represents a novel exponential-family model for conditional density estimation (CDE), mapping neural population activity to a full probability density over external covariates. It captures the influence of each neuron’s activity on the decoded variable through a smooth, interpretable tuning function, regularized by a Gaussian process prior. The resulting nonparametric decoding model flexibly captures asymmetric and multimodal densities, and accommodates both linear and circular variables. To illustrate the performance of CMLR, we applied it to large-scale datasets from mouse and monkey visual cortex, mouse hippocampus, and monkey motor cortex, where it generally outperformed a wide variety of other decoding methods, including deep neural networks (DNNs), XGBoost, and FlexCode. It also outperformed a closely-related correlation-blind decoder, highlighting the importance of correlations for accurate neural decoding. The CMLR model provides a scalable, flexible, and interpretable method for decoding continuous variables from diverse brain regions.

Deep Learning · Generative Models and Autoencoders

Haoye Lu, Yaoliang Yu, Darren Lo

In many real-world scenarios, obtaining fully observed samples is prohibitively expensive or even infeasible, while partial and noisy observations are comparatively easy to collect. In this work, we study distribution restoration with abundant noisy samples, assuming the corruption process is available as a black-box generator. We show that this task can be framed as a one-sided entropic optimal transport problem and solved via an EM-like algorithm. We further provide a test criterion to determine whether the true underlying distribution is recoverable under per-sample information loss, and show that in otherwise unrecoverable cases, a small number of clean samples can render the distribution largely recoverable. Building on these insights, we introduce SFBD-OMNI, a bridge model-based framework that maps corrupted sample distributions to the ground-truth distribution. Our method generalizes Stochastic Forward-Backward Deconvolution (SFBD; Lu et al., 2025) to handle arbitrary measurement models beyond Gaussian corruption. Experiments across benchmark datasets and diverse measurement settings demonstrate significant improvements in both qualitative and quantitative performance.

Optimization · Zero-order and Black-box Optimization

Yimeng Zeng, Natalie Maus, Haydn Jones, Jeffrey Tao, Fangping Wan, Marcelo Der Torossian Torres, Cesar de la Fuente, Ryan Marcus, Osbert Bastani, Jacob Gardner

In multi-task Bayesian optimization, the goal is to leverage experience from optimizing existing tasks to improve the efficiency of optimizing new ones. While approaches using multi-task Gaussian processes or deep kernel transfer exist, the performance improvement is marginal when scaling beyond a moderate number of tasks. We introduce **BOLT**, an initialization-only transfer strategy that distills prior BO runs into an LLM which proposes candidates for new tasks, while the surrogate at test time remains single-task. The LLM is periodically fine-tuned on top solutions from completed runs, creating a closed loop where better BO outputs yield better initializations over time. This decoupled design scales to roughly 1500 tasks without the saturation observed for shared-surrogate MTBO and adds only a small, amortized overhead relative to the BO inner loops. We evaluate on two domains: database query optimization and antimicrobial peptide design. We demonstrate that LLM-generated initializations steadily improve and accelerate BO, and with sufficient fine-tuning, a few LLM samples often match or surpass full ''from-scratch'' BO with far fewer oracle calls.