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Probabilistic Methods · Everything Else

Kevin H. Lam, Thang Bui, George Deligiannidis, Yee Whye Teh

Latent Gaussian variables have been popularised in probabilistic machine learning. In turn, gradient estimators are the machinery that facilitates gradient-based optimisation for models with latent Gaussian variables. The reparameterisation trick is often used as the default estimator as it is simple to implement and yields low-variance gradients for variational inference. In this work, we propose the R2-G2 estimator as the Rao-Blackwellisation of the reparameterisation gradient estimator. Interestingly, we show that the local reparameterisation gradient estimator for Bayesian MLPs is an instance of the R2-G2 estimator and Rao-Blackwellisation. This lets us extend benefits of Rao-Blackwellised gradients to a suite of probabilistic models. We show that initial training with R2-G2 consistently yields better performance in models with multiple applications of the reparameterisation trick.

Applications · Robotics

Hongyi Zhou, Weiran Liao, Xi Huang, Yucheng Tang, Fabian Otto, Xiaogang Jia, Xinkai Jiang, Simon Hilber, Ge Li, Qian Wang 等

We present the B-spline Encoded Action Sequence Tokenizer (BEAST), a novel action tokenizer that encodes action sequences into compact discrete or continuous tokens using B-splines. In contrast to existing action tokenizers based on vector quantization or byte pair encoding, BEAST requires no separate tokenizer training and consistently produces tokens of uniform length, enabling fast action sequence generation via parallel decoding. Leveraging our B-spline formulation, BEAST inherently ensures generating smooth trajectories without discontinuities between adjacent segments. We extensively evaluate BEAST by integrating it with three distinct model architectures: a Variational Autoencoder (VAE) with continuous tokens, a decoder-only Transformer with discrete tokens, and Florence-2, a pretrained Vision-Language Model with an encoder-decoder architecture, demonstrating BEAST's compatibility and scalability with large pretrained models. We evaluate BEAST across three established benchmarks consisting of 166 simulated tasks and on three distinct robot settings with a total of 8 real-world tasks. Experimental results demonstrate that BEAST (i) significantly reduces both training and inference computational costs, and (ii) consistently generates smooth, high-frequency control signals suitable for continuous control tasks while (iii) reliably achieves competitive task success rates compared to state-of-the-art methods.

Probabilistic Methods · Bayesian Models and Methods

Hyungi Lee, Moonseok Choi, Hyunsu Kim, Kyunghyun Cho, Rajesh Ranganath, Juho Lee

Uncertainty-aware meta-learning aims not only for rapid adaptation to new tasks but also for reliable uncertainty estimation under limited supervision. Neural Processes (NPs) offer a flexible solution by learning implicit stochastic processes directly from data, often using a global latent variable to capture functional uncertainty. However, we empirically find that variational posteriors for this global latent variable are frequently miscalibrated, limiting both predictive accuracy and the reliability of uncertainty estimates. To address this issue, we propose Test Time Scaling for Neural Processes (TTSNPs), a sequential inference framework based on Sequential Monte Carlo Sampler (SMCS) that refines latent samples at test time without modifying the pre-trained NP model. TTSNPs iteratively transform variational samples into better approximations of the true posterior using neural transition kernels, significantly improving both prediction quality and uncertainty calibration. This makes NPs more robust and trustworthy, extending applicability to various scenarios requiring well-calibrated uncertainty estimates.

Reinforcement Learning · Deep RL

Scott Cheng, Meng-Yu Tsai, Ding-Yong Hong, Mahmut T Kandemir

AlphaZero has achieved remarkable success in complex decision-making problems through self-play and neural network training. However, its self-play process remains inefficient due to limited exploration of high-uncertainty positions, the overlooked runner-up decisions in Monte Carlo Tree Search (MCTS), and high variance in value labels. To address these challenges, we propose and evaluate uncertainty-guided exploration by branching from high-uncertainty positions using our proposed Label Change Rate (LCR) metric, which is further refined by a Bayesian inference framework. Our proposed approach leverages runner-up MCTS decisions to create multiple variations, and ensembles value labels across these variations to reduce variance. We investigate three key design parameters for our branching strategy: where to branch, how many variations to branch, and which move to play in the new branch. Our empirical findings indicate that branching with 10 variations per game provides the best performance-exploration balance. Overall, our end-to-end results show an improved sample efficiency over the baseline by 58.5\% on 9x9 Go in the early stage of training and by 47.3\% on 19x19 Go in the late stage of training.

Computer Vision · Vision Models & Multimodal

Zirui Wang, Jiayi Zhang, Tianwei Guan, Yuhan Zhou, Xingyuan Li, Minjing Dong, Jinyuan Liu

Image fusion is a fundamental and important task in computer vision, aiming to combine complementary information from different modalities to fuse images. In recent years, diffusion models have made significant developments in the field of image fusion. However, diffusion models often require complex computations and redundant inference time, which reduces the applicability of these methods. To address this issue, we propose RFfusion, an efficient one-step diffusion model for image fusion based on Rectified Flow. We incorporate Rectified Flow into the image fusion task to straighten the sampling path in the diffusion model, achieving one-step sampling without the need for additional training, while still maintaining high-quality fusion results. Furthermore, we propose a task-specific variational autoencoder (VAE) architecture tailored for image fusion, where the fusion operation is embedded within the latent space to further reduce computational complexity. To address the inherent discrepancy between conventional reconstruction-oriented VAE objectives and the requirements of image fusion, we introduce a two-stage training strategy. This approach facilitates the effective learning and integration of complementary information from multi-modal source images, thereby enabling the model to retain fine-grained structural details while significantly enhancing inference efficiency. Extensive experiments demonstrate that our method outperforms other state-of-the-art methods in terms of both inference speed and fusion quality.

Probabilistic Methods

Amber Hu, Henry Smith, Scott Linderman

Latent stochastic differential equation (SDE) models are important tools for the unsupervised discovery of dynamical systems from data, with applications ranging from engineering to neuroscience. In these complex domains, exact posterior inference of the latent state path is typically intractable, motivating the use of approximate methods such as variational inference (VI). However, existing VI methods for inference in latent SDEs often suffer from slow convergence and numerical instability. Here, we propose SDE Inference via Natural Gradients (SING), a method that leverages natural gradient VI to efficiently exploit the underlying geometry of the model and variational posterior. SING enables fast and reliable inference in latent SDE models by approximating intractable integrals and parallelizing computations in time. We provide theoretical guarantees that SING will approximately optimize the intractable, continuous-time objective of interest. Moreover, we demonstrate that better state inference enables more accurate estimation of nonlinear drift functions using, for example, Gaussian process SDE models. SING outperforms prior methods in state inference and drift estimation on a variety of datasets, including a challenging application to modeling neural dynamics in freely behaving animals. Altogether, our results illustrate the potential of SING as a tool for accurate inference in complex dynamical systems, especially those characterized by limited prior knowledge and non-conjugate structure.

Probabilistic Methods · Bayesian Models and Methods

Lu Xu, Tsai Hor Chan, Lequan Yu, Kwok Lam, Guosheng Yin

Density estimation is essential for generative modeling, particularly with the rise of modern neural networks. While existing methods capture complex data distributions, they often lack interpretability and uncertainty quantification. Bayesian nonparametric methods, especially the \polya tree, offer a robust framework that addresses these issues by accurately capturing function behavior over small intervals. Traditional techniques like Markov chain Monte Carlo (MCMC) face high computational complexity and scalability limitations, hindering the use of Bayesian nonparametric methods in deep learning. To tackle this, we introduce the variational \polya tree (VPT) model, which employs stochastic variational inference to compute posterior distributions. This model provides a flexible, nonparametric Bayesian prior that captures latent densities and works well with stochastic gradient optimization. We also leverage the joint distribution likelihood for a more precise variational posterior approximation than traditional mean-field methods. We evaluate the model performance on both real data and images, and demonstrate its competitiveness with other state-of-the-art deep density estimation methods. We also explore its ability in enhancing interpretability and uncertainty quantification. Code is available at \url{https://github.com/howardchanth/var-polya-tree}.

Antonio Orvieto, Robert Gower

Understanding the remarkable efficacy of Adam when training transformer-based language models has become a central research topic within the optimization community. To gain deeper insights, several simplifications of Adam have been proposed, such as the signed gradient and signed momentum methods. In this work, we conduct an extensive empirical study — training over 1,500 language models across different data configurations and scales — comparing Adam to several known simplified variants. We find that signed momentum methods are faster than SGD, but consistently underperform relative to Adam, even after careful tuning of momentum, clipping setting and learning rates. However, our analysis reveals a compelling option that preserves near-optimal performance while allowing for new insightful reformulations: constraining the Adam momentum parameters to be equal, $\beta_1=\beta_2$. Beyond robust performance, this choice affords new theoretical insights, highlights the "secret sauce" on top of signed momentum, and grants a precise statistical interpretation: we show that Adam in this setting implements a natural online algorithm for estimating the mean and variance of gradients—one that arises from a mean-field Gaussian variational inference perspective.

Applications · Robotics

Sreevardhan Sirigiri, Christian Hughes, Ian Abraham, Fabio Ramos

Effective robotic exploration in continuous domains requires planning trajectories that maximize coverage over a predefined region. A recent development, Stein Variational Ergodic Search (SVES), proposed parallel ergodic exploration (a key approach within the field of robotic exploration), via Stein variational inference that computes a set of candidate trajectories approximating the posterior distribution over the solution space trajectories. While this approach leverages GPU parallelism well, the trajectories in the set might not be distinct enough, leading to a suboptimal set. In this paper, we propose two key methods to diversify the solution set of this approach. First, we leverage the signature kernel within the SVES framework, introducing a pathwise, sequence-sensitive interaction that preserves the Markovian structure of the trajectories and naturally spreads paths across distinct regions of the search space. Second, we propose a derivative-free evolution-strategy interpretation of SVES that exploits batched, GPU-friendly fitness evaluations and can be paired with approximate gradients whenever analytic gradients of the kernel are unavailable or computationally intractable. The resulting method both retains SVES’s advantages while diversifying the solution set and extending its reach to black-box objectives. Across planar forest search, 3D quadrotor coverage, and model-predictive control benchmarks, our approach consistently reduces ergodic cost and produces markedly richer trajectory sets than SVES without significant extra tuning effort.

Data-centric AI · Data augmentation

Jaehun Jung, Seungju Han, Ximing Lu, Skyler Hallinan, David Acuna, Shrimai Prabhumoye, Mostofa Patwary, Mohammad Shoeybi, Bryan Catanzaro, Yejin Choi

Data diversity is crucial for training a strong language model. Yet metrics of diversity often diverge from this goal, measuring variations in heuristic features—like n-grams or embeddings—that are detached from how the model actually performs on a target task. This motivates us to ask: *Can we redefine data diversity—beyond measuring variations in heuristic features—in a way that better predicts model generalization?* Through large-scale empirical analyses spanning over 300 training runs, carefully controlled for data scale and quality, we show that data diversity can be a strong predictor of generalization in LLM reasoning—as measured by average model performance on unseen out-of-distribution benchmarks. We introduce **G-Vendi**, a metric that quantifies diversity via the entropy of model-induced loss gradients. G-Vendi scales to million-sample datasets and yet consistently outperforms heuristic alternatives, achieving strong correlation ($\text{Spearman's } \rho \approx 0.9$) with out-of-distribution (OOD) performance across both natural language inference (NLI) and math reasoning tasks. Building on this insight, we present **Prismatic Synthesis**, a framework for generating diverse synthetic data by targeting underrepresented regions in gradient space. Experimental results show that Prismatic Synthesis consistently improves model performance as we scale synthetic data—not just on in-distribution test but across unseen, out-of-distribution benchmarks—significantly outperforming state-of-the-art models in both domains. For example, PrismMath-7B, our model distilled from a 32B LLM without human verification, outperforms R1-Distill-Qwen-7B—trained on proprietary data generated by 671B R1—on 6 out of 7 challenging math benchmarks.

Deep Learning · Graph Neural Networks

Philipp Dahlinger, Tai Hoang, Denis Blessing, Niklas Freymuth, Gerhard Neumann

Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-based simulations are precise, they are often computationally expensive and require knowledge of physical parameters, such as material properties. In contrast, data-driven approaches like Graph Network Simulators (GNSs) offer faster inference but suffer from two key limitations: Firstly, they must be retrained from scratch for even minor variations in physical parameters, and secondly they require labor-intensive data collection for each new parameter setting. This is inefficient, as simulations with varying parameters often share a common underlying latent structure. In this work, we address these challenges by learning this shared structure through meta-learning, enabling fast adaptation to new physical parameters without retraining. To this end, we propose a novel architecture that generates a latent representation by encoding graph trajectories using conditional neural processes (CNPs). To mitigate error accumulation over time, we combine CNPs with a novel neural operator architecture. We validate our approach, Meta Neural Graph Operator (MaNGO), on several dynamics prediction tasks with varying material properties, demonstrating superior performance over existing GNS methods. Notably, MaNGO achieves accuracy on unseen material properties close to that of an oracle model.

Deep Learning · Generative Models and Autoencoders

I. Shavindra Jayasekera, Jacob Si, Filippo Valdettaro, Wenlong Chen, Aldo Faisal, Yingzhen Li

As large language models (LLMs) gain popularity in conducting prediction tasks in-context, understanding the sources of uncertainty in in-context learning becomes essential to ensuring reliability. The recent hypothesis of in-context learning performing predictive Bayesian inference opens the avenue for Bayesian uncertainty estimation, particularly for decomposing uncertainty into epistemic uncertainty due to lack of in-context data and aleatoric uncertainty inherent in the in-context prediction task. However, the decomposition idea remains under-explored due to the intractability of the latent parameter posterior from the underlying Bayesian model. In this work, we introduce a variational uncertainty decomposition framework for in-context learning without explicitly sampling from the latent parameter posterior, by optimising auxiliary inputs as probes to obtain an upper bound to the aleatoric uncertainty of an LLM's in-context learning procedure. Through experiments on synthetic and real-world tasks, we show quantitatively and qualitatively that the decomposed uncertainties obtained from our method exhibit desirable properties of epistemic and aleatoric uncertainty.

Deep Learning · Algorithms

Boyuan Zhang, Yingjun Du, Xiantong Zhen, Ling Shao

Task vectors capture how a model changes during fine-tuning by recording the difference between pre-trained and task-specific weights. The composition of task vectors, a key operator in task arithmetic, enables models to integrate knowledge from multiple tasks without incurring significant additional inference costs. In this paper, we propose variational task vector composition (VTVC), where composition coefficients are taken as latent variables and estimated in a Bayesian inference framework. Unlike previous methods that operate at the task level, our framework focuses on sample-specific composition. Motivated by the observation of structural redundancy in task vectors, we introduce a Spike-and-Slab prior that promotes sparsity and aims to preserve the most informative components. To further address the high variance and sampling inefficiency in sparse, high-dimensional spaces, we develop a gated sampling mechanism that constructs a controllable posterior by filtering the composition coefficients based on both uncertainty and importance. This yields a more stable and interpretable variational framework by deterministically selecting reliable task components, reducing sampling variance while improving transparency and generalization. Experimental results demonstrate that our method achieves state-of-the-art average performance across a diverse range of benchmarks, including image classification and natural language understanding. These findings highlight the practical value of our approach, offering a new, efficient, and effective framework for task vector composition.

Probabilistic Methods · Bayesian Models and Methods

Diana Cai, Robert Gower, David Blei, Lawrence Saul

We introduce a highly expressive yet distinctly tractable family for black-box variational inference (BBVI). Each member of this family is a weighted product of experts (PoE), and each weighted expert in the product is proportional to a multivariate $t$-distribution. These products of experts can model distributions with skew, heavy tails, and multiple modes, but to use them for BBVI, we must be able to sample from their densities. We show how to do this by reformulating these products of experts as latent variable models with auxiliary Dirichlet random variables. These Dirichlet variables emerge from a Feynman identity, originally developed for loop integrals in quantum field theory, that expresses the product of multiple fractions (or in our case, $t$-distributions) as an integral over the simplex. We leverage this simplicial latent space to draw weighted samples from these products of experts---samples which BBVI then uses to find the PoE that best approximates a target density. Given a collection of experts, we derive an iterative procedure to optimize the exponents that determine their geometric weighting in the PoE. At each iteration, this procedure minimizes a regularized Fisher divergence to match the scores of the variational and target densities at a batch of samples drawn from the current approximation. This minimization reduces to a convex quadratic program, and we prove under general conditions that these updates converge exponentially fast to a near-optimal weighting of experts. We conclude by evaluating this approach on a variety of synthetic and real-world target distributions.

Probabilistic Methods

Guangting Yu, Shiwei Lan

Solving and learning partial differential equations (PDEs) lies at the core of physics-informed machine learning. Traditional numerical methods, such as finite difference and finite element approaches, are rooted in domain-specific techniques and often lack scalability. Recent advances have introduced neural networks and Gaussian processes (GPs) as flexible tools for automating PDE solving and incorporating physical knowledge into learning frameworks. While GPs offer tractable predictive distributions and a principled probabilistic foundation, they may be suboptimal in capturing complex behaviors such as sharp transitions or non-smooth dynamics. To address this limitation, we propose the use of the Q-exponential process (Q-EP), a recently developed generalization of GPs designed to better handle data with abrupt changes and to more accurately model derivative information. We advocate for Q-EP as a superior alternative to GPs in solving PDEs and associated inverse problems. Leveraging sparse variational inference, our method enables principled uncertainty quantification -- a capability not naturally afforded by neural network-based approaches. Through a series of experiments, including the Eikonal equation, Burgers’ equation, and an inverse Darcy flow problem, we demonstrate that the variational Q-EP method consistently yields more accurate solutions while providing meaningful uncertainty estimates.

Computer Vision · Vision Models & Multimodal

Nianxin Li, Mao Ye, Lihua Zhou, Shuaifeng Li, Song Tang, Luping Ji, Ce Zhu

Unmanned Aerial Vehicle (UAV) object detection faces significant challenges due to complex environmental conditions and different imaging conditions. These factors introduce significant changes in scale and appearance, particularly for small objects that occupy limited pixels and exhibit limited information, complicating detection tasks. To address these challenges, we propose a Multimodel Causal Reasoning framework based on YOLO backbone for UAV Object Detection (MCR-UOD). The key idea is to use the backdoor adjustment to discover the condition-invariant object representation for easy detection. Specifically, the YOLO backbone is first adjusted to incorporate the pre-trained vision-language model. The original category labels are replaced with semantic text prompts, and the detection head is replaced with text-image contrastive learning. Based on this backbone, our method consists of two parts. The first part, named language guided region exploration, discovers the regions with high probability of object existence using text embeddings based on vision-language model such as CLIP. Another part is the backdoor adjustment casual reasoning module, which constructs a confounder dictionary tailored to different imaging conditions to capture global image semantics and derives a prior probability distribution of shooting conditions. During causal inference, we use the confounder dictionary and the prior to intervene on local instance features, disentangling condition variations, and obtaining condition-invariant representations. Experimental results on several public datasets confirm the state-of-the-art performance of our approach. The code, data and models will be released upon publication of this paper.

Hao Shao, Shulun Wang, Yang Zhou, Guanglu Song, Dailan He, ZHUOFAN ZONG, Shuo Qin, Yu Liu, Hongsheng Li

Video face swapping has seen increasing adoption in diverse applications, yet existing methods primarily trained on static images struggle to address temporal consistency and complex real-world scenarios. To overcome these limitations, we propose the first video face swapping framework, VividFace, a robust and high-fidelity diffusion-based framework. VividFace employs a novel hybrid training strategy that leverages abundant static image data alongside temporal video sequences, enabling it to effectively model temporal coherence and identity consistency in videos. Central to our approach is a carefully designed diffusion model integrated with a specialized VAE, capable of processing image-video hybrid data efficiently. To further enhance identity and pose disentanglement, we introduce and release the Attribute-Identity Disentanglement Triplet (AIDT) dataset, comprising a large-scale collection of triplets where each set contains three face images—two sharing the same pose and two sharing the same identity. Augmented comprehensively with occlusion scenarios, AIDT significantly boosts the robustness of VividFace against occlusions. Moreover, we incorporate advanced 3D reconstruction techniques as conditioning inputs to address significant pose variations effectively. Extensive experiments demonstrate that VividFace achieves state-of-the-art performance in identity preservation, temporal consistency, and visual realism, surpassing existing methods while requiring fewer inference steps. Our framework notably mitigates common challenges such as temporal flickering, identity loss, and sensitivity to occlusions and pose variations. The AIDT dataset, source code, and pre-trained weights will be released to support future research. The code and pretrained weights are available on the [project page](https://hao-shao.com/projects/vividface.html).

Probabilistic Methods · Bayesian Models and Methods

Junxi Xiao, Qinliang Su, Zexin Yuan

Mean-field variational inference (VI), despite its scalability, is limited by the independence assumption, making it unsuitable for scenarios with correlated data instances. Existing structured VI methods either focus on correlations among latent dimensions which lack scalability for modeling instance-level correlations, or are restricted to simple first-order dependencies, limiting their expressiveness. In this paper, we propose High-order Tree-structured Variational Inference (HoT-VI), that explicitly models $k$-order instance-level correlations among latent variables. By expressing the global posterior through overlapping $k$-dimensional local marginals, our method enables efficient parameterized sampling via a sequential procedure. To ensure the validity of these marginals, we introduce a conditional correlation parameterization method that guarantees positive definiteness of their correlation matrices. We further extend our method with a tree-structured backbone to capture more flexible dependency patterns. Extensive experiments on time-series and graph-structured datasets demonstrate that modeling higher-order correlations leads to significantly improved posterior approximations and better performance across various downstream tasks.

Probabilistic Methods · Bayesian Models and Methods

Joohwan Ko, Justin Domke

Variational inference often struggles with the posterior geometry exhibited by complex hierarchical Bayesian models. Recent advances in flow‐based variational families and Variationally Inferred Parameters (VIP) each address aspects of this challenge, but their formal relationship is unexplored. Here, we prove that the combination of VIP and a full-rank Gaussian can be represented exactly as a forward autoregressive flow augmented with a translation term and input from the model’s prior. Guided by this theoretical insight, we introduce the Model‐Informed Flow (MIF) architecture, which adds the necessary translation mechanism, prior information, and hierarchical ordering. Empirically, MIF delivers tighter posterior approximations and matches or exceeds state‐of‐the‐art performance across a suite of hierarchical and non‐hierarchical benchmarks.

Computer Vision · Image and Video Generation

Yidi Liu, Xueyang Fu, Jie Huang, Jie Xiao, Dong Li, Wenlong Zhang, LEI BAI, Zheng-Jun Zha

Ultra-High Definition (UHD) image restoration struggles to balance computational efficiency and detail retention. While Variational Autoencoders (VAEs) offer improved efficiency by operating in the latent space, with the Gaussian variational constraint, this compression preserves semantics but sacrifices critical high-frequency attributes specific to degradation and thus compromises reconstruction fidelity. % This compromises reconstruction fidelity, even when global semantics are preserved. Consequently, a VAE redesign is imperative to foster a robust semantic representation conducive to generalization and perceptual quality, while simultaneously enabling effective high-frequency information processing crucial for reconstruction fidelity. To address this, we propose \textit{Latent Harmony}, a two-stage framework that reinvigorates VAEs for UHD restoration by concurrently regularizing the latent space and enforcing high-frequency-aware reconstruction constraints. Specifically, Stage One introduces the LH-VAE, which fortifies its latent representation through visual semantic constraints and progressive degradation perturbation for enhanced semantics robustness; meanwhile, it incorporates latent equivariance to bolster its high-frequency reconstruction capabilities. Then, Stage Two facilitates joint training of this refined VAE with a dedicated restoration model. This stage integrates High-Frequency Low-Rank Adaptation (HF-LoRA), featuring two distinct modules: an encoder LoRA, guided by a fidelity-oriented high-frequency alignment loss, tailored for the precise extraction of authentic details from degradation-sensitive high-frequency components; and a decoder LoRA, driven by a perception-oriented loss, designed to synthesize perceptually superior textures. These LoRA modules are meticulously trained via alternating optimization with selective gradient propagation to preserve the integrity of the pre-trained latent structure. This methodology culminates in a flexible fidelity-perception trade-off at inference, managed by an adjustable parameter $\alpha$. Extensive experiments demonstrate that \textit{Latent Harmony} effectively balances perceptual and reconstructive objectives with efficiency, achieving superior restoration performance across diverse UHD and standard-resolution scenarios.