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General Machine Learning · Representation Learning

Alexandre Chaussard, Anna Bonnet, Sylvain Le Corff

Advances in data collection are producing growing volumes of temporal count observations, making adapted modeling increasingly necessary. In this work, we introduce a generative framework for independent component analysis of temporal count data, combining regime-adaptive dynamics with Poisson log-normal emissions. The model identifies disentangled components with regime-dependent contributions, enabling representation learning and perturbations analysis. Notably, we establish the identifiability of the model, supporting principled interpretation. To learn the parameters, we propose an efficient amortized variational inference procedure. Experiments on simulated data evaluate recovery of the mixing function and latent sources across diverse settings, while an *in vivo* longitudinal gut microbiome study reveals microbial co-variation patterns and regime shifts consistent with clinical perturbations.

Applications · Chemistry, Physics, and Earth Sciences

Xinyu Wang, Ruoyu Wang, Qiangwei Peng, Peijie Zhou, Tiejun Li

Reconstructing dynamical evolution from limited observations is a fundamental challenge in single-cell biology, where dynamic unbalanced optimal transport (OT) provides a principled framework for modeling coupled transport and mass variation. However, existing approaches rely on trajectory simulation at inference time, making inference a key bottleneck for scalable applications. In this work, we propose a mean-flow framework for unbalanced flow matching that summarizes both transport and mass-growth dynamics over arbitrary time intervals using mean velocity and mass-growth fields, enabling fast one-step generation without trajectory simulation. To solve dynamic unbalanced OT under the Wasserstein-Fisher-Rao geometry, we further build on this framework to develop **Wasserstein-Fisher-Rao Mean Flow Matching (WFR-MFM)**. Across synthetic and real single-cell RNA sequencing datasets, WFR-MFM achieves orders-of-magnitude faster inference than a range of existing baselines while maintaining high predictive accuracy, and enables efficient perturbation response prediction on large synthetic datasets with thousands of conditions.

Zhen-Hao Xie Xie, Yu-Cheng Shi, Da-Wei Zhou

Class-Incremental Learning (CIL) is important in building real-world learning systems. In CLIP-based CIL, the model performs classification by comparing similarity between visual and textual embeddings obtained from template prompts, e.g., ``a photo of a [CLASS]''. This seemingly monolithic matching process can be decomposed into two conceptually distinct stages: attribute extraction and attribute aggregation. For example, a model may recognize cat using attributes such as fur texture and whiskers. When learning a new class like car, the model must extract additional attributes like wheels and adjust how they are aggregated in the shared representation space. However, since only data from the current task is available, incremental updates can bias both attribute extraction and aggregation toward new classes, leading to catastrophic forgetting. Therefore, we propose AREA for attribute extraction and aggregation for CLIP-based CIL. To stabilize extraction, we anchor class-level visual and textual attributes on the hyperspherical embedding space via principal geodesic analysis. To stabilize aggregation, we learn lightweight task-specific experts with scoring and residual refinement, regularized by a variational information bottleneck objective. During inference, we perform routing over task attribute manifolds via optimal transport for more concise prediction. Experiments on multiple benchmarks show that AREA consistently outperforms SOTA methods.

Frida Viset, Anton Kullberg, Frederiek Wesel, Arno Solin

The Hilbert-space Gaussian process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian process (GP) inference by projecting the GP onto $M$ basis functions. These properties result in a favorable data-independent $\mathcal{O}(M^3)$ computational complexity during hyperparameter optimization but require a dominating one-time precomputation of the precision matrix costing $\mathcal{O}(NM^2)$ operations. In this paper, we lower this dominating computational complexity to $\mathcal{O}(NM)$ with no additional approximations. We can do this because we realize that the precision matrix can be split into a sum of Hankel-Toeplitz matrices, each having $\mathcal{O}(M)$ unique entries. Based on this realization we propose computing only these unique entries at $\mathcal{O}(NM)$ costs. Further, we develop two theorems that prescribe sufficient conditions for the complexity reduction to hold generally for a wide range of other approximate GP models, such as the Variational Fourier features approach. The two theorems do this with no assumptions on the data and no additional approximations of the GP models themselves. Thus, our contribution provides a pure speed-up of several existing, widely used, GP approximations, without further approximations

Probabilistic Methods · Bayesian Models and Methods

Zijian Chen, Archana Venkataraman

Human ratings are central to learning and inference across several application domains, but they are also subject to inter-rater biases and judgment errors. Quantifying the uncertainty of these human ratings would require repeated measurements, which are expensive and rarely available at scale. We propose a Bayesian graphical model to estimate the instance-level and item-level uncertainty of (subjective) human ratings by leveraging auxiliary (objective) data. Our model learns a shared latent content representation that explains factors common to both the human rating and auxiliary data and a latent uncertainty variable that captures fluctuations in the human assessments via a data-conditioned prior. We develop a scalable amortized variational inference procedure that uses modality-appropriate neural encoders and decoders to represent the posterior factors. Experiments on synthetic data demonstrate that our framework can accurately recover the latent uncertainty under targeted ablations and stress tests. We further demonstrate our approach on a real-world dataset of paired functional MRI scans and behavioral testing for autism, thus highlighting the need for uncertainty quantification.

Social Aspects · Accountability, Transparency, and Interpretability

Peng Cui, Jiahao Zhang, Lijie Hu

While Contrastive Learning (CL) has revolutionized self-supervised representation learning, its latent representations remain highly entangled and opaque, limiting their interpretability in safety-critical applications. We identify that a fundamental cause of this entanglement is the reliance on deterministic similarity measures, which treat all feature dimensions equally. In compositional scenes, this creates an Optimization Conflict: common background features, such as, "blue sky", are encouraged to align in positive pairs but simultaneously repelled in negative pairs, causing gradient oscillations that hinder precise semantic disentanglement. To address this, we propose **BayesNCL** (Bayesian Gated Non-Negative Contrastive Learning). Unlike standard approaches, BayesNCL introduces a probabilistic gating mechanism that dynamically filters out task-irrelevant, high-frequency common features while selectively retaining discriminative semantics. By formalizing feature selection as a variational inference problem with a sparse Bernoulli prior, our method effectively resolves the optimization conflict. Empirical experimental results on benchmark datasets demonstrate that BayesNCL achieves a remarkable 142.1\% improvement in semantic consistency compared to state-of-the-art baselines, yielding highly interpretable representations without compromising downstream task performance.

Deep Learning · Large Language Models

Xuan Wang, Liu Yilin, Fangxiang Feng, Caixia Yuan, Huixing Jiang, Xiaojie Wang

Vision-Language Models (VLMs) suffer from high inference latency due to long visual sequences. To enable efficient, on-demand utilization of visual information, we argue that visual necessity should be assessed by its semantic impact on the output distribution, rather than inferred from intermediate interaction signals such as attention weights. We propose a training-free framework based on token embedding subspace decomposition, which we term a prediction-conditioned Semantic Lens. Specifically, at fixed decoding intervals, we perform QR decomposition on the Top-K candidate token embeddings to construct an orthogonal semantic basis. We then introduce Semantic IImpact–Driven Visual Scheduling (SIVS), which measures how visual inputs impact model predictions by projecting visual-induced hidden-state variations onto this semantic lens. SIVS provides a geometrically grounded, impact-driven criterion for dynamic visual KV scheduling. Empirical results demonstrate that SIVS achieves ~87% visual KV compression while maintaining over 99% of model performance.

Probabilistic Methods · Variational Inference

Safa Messaoud, Skander Charni, Elaa Bouazza, Ali Pourghasemi, Halima Bensmail

Computing the differential entropy of distributions known only up to a normalization constant is a long-standing challenge with broad theoretical and practical significance. While variational inference is the most scalable approach for density approximation _from samples_, its potential in settings where _only the unnormalized density_ is available remains largely under-explored. The central difficulty lies in constructing variational distributions that simultaneously ($i$) exploit the structure of the unnormalized density, ($ii$) are expressive enough to capture complex target distributions, ($iii$) remain computationally tractable, and ($iv$) support efficient sampling. Recently, \citet{messaoud2024s} introduced _P-SVGD_, a particle-based variational method that leverages Stein Variational Gradient Descent dynamics, satisfies all of these constraints and demonstrates promising results in low-dimensional setups. We show, however, that _P-SVGD_ does not scale to high dimensions due to _fundamental algorithmic flaws_: ($i$) misdiagnosed sensitivity to \textit{SVGD} hyperparameters, ($ii$) violation of the global invertibility assumption in the entropy derivation, ($iii$) omission of a critical trace-of-Hessian term, ($iv$) along with suboptimal heuristics, including a divergence-based sampling check that induces mode collapse and loose informal bounds with no practical value. These issues severely limit both the correctness and the scalability of the approach. We propose _MET-SVGD_, a principled extension of _P-SVGD_ that addresses these flaws by providing a general framework for \textit{SVGD} hyperparameters selection with global invertibility and convergence guarantees. This enabled more accurate and scalable entropy estimation in high-dimensional settings. Empirically, in entropy estimation benchmarks, _MET-SVGD_ achieves accuracy improvements of up to 12$\times$ and 16$\times$ over _P-SVGD_ and baselines from the _SVGD_ literature, respectively. On CIFAR-10 Energy-Based image generation, it improves FID by $80.4$% compared to _P-SVGD_ and achieves 64$\times$ higher training stability. In Maximum-Entropy reinforcement learning, _MET-SVGD_ yields up to $16$% better returns than _P-SVGD_. We will make our code publicly available at https://tinyurl.com/2esyfx8j.

Yang Zheng, Wen Li, Zhaoqiang Liu

Diffusion Models (DMs) have exhibited remarkable efficacy in various image restoration tasks. However, existing approaches typically operate within the high-dimensional pixel space, resulting in high computational overhead. While methods based on latent DMs seek to alleviate this issue by utilizing the compressed latent space of a variational autoencoder (VAE), they require repeated encoder-decoder inference. This introduces significant additional computational burdens, often resulting in runtime performance that is even inferior to that of their pixel-space counterparts. To mitigate the computational inefficiency, this work proposes projecting data into lower-dimensional subspaces using dynamic resolution DMs to accelerate the inference process. We first fine-tune pre-trained DMs for dynamic resolution priors and adapt DPS and DAPS, which are two widely used pixel-space methods for general image restoration tasks, into the proposed framework, yielding methods we refer to as SubDPS and SubDAPS, respectively. Given the favorable inference speed and reconstruction fidelity of SubDAPS, we introduce an enhanced variant termed SubDAPS++ to further boost both reconstruction efficiency and quality. Empirical evaluations across diverse image datasets and various restoration tasks demonstrate that the proposed methods outperform recent DM-based approaches in the majority of experimental scenarios.

Applications · Computer Vision

Yulong Yang, Zhikun Xu, Yaojun Li, Christine Allen-Blanchette

When the color distribution of input images changes at inference, the performance of conventional neural network architectures drops considerably. A few researchers have begun to incorporate prior knowledge of color geometry in neural network design. These color equivariant architectures have modeled hue variation with 2D rotations, and saturation and luminance transformations as 1D translations. While this approach improves neural network robustness to color variations in a number of contexts, we find that approximating saturation and luminance (interval valued quantities) as 1D translations introduces appreciable artifacts. In this paper, we introduce a color equivariant architecture that is truly equivariant. Instead of approximating the interval with the real line, we lift values on the interval to values on the circle (a double-cover) and build equivariant representations there. Our approach resolves the approximation artifacts of previous methods, improves interpretability and generalizability, and achieves better predictive performance than conventional and equivariant baselines on tasks such as fine-grained classification and medical imaging tasks. Going beyond the context of color, we show that our proposed lifting can also extend to geometric transformations such as scale.

Deep Learning · Graph Neural Networks

Wentao Yu, Sheng Wan, Ge Gao, Bo Han, Chen Gong

Graph Federated Learning (GFL) enables distributed graph representation learning while protecting the privacy of graph data. However, GFL suffers from heterogeneity arising from diverse node features and structural topologies across multiple clients. To address both types of heterogeneity, we propose a novel graph Federated learning method via Semantic and Structural Alignment (FedSSA), which shares the knowledge of both node features and structural topologies. For node feature heterogeneity, we propose a novel variational model to infer class-wise node distributions, so that we can cluster clients based on inferred distributions and construct cluster-level representative distributions. We then minimize the divergence between local and cluster-level distributions to facilitate semantic knowledge sharing. For structural heterogeneity, we employ spectral Graph Neural Networks (GNNs) and propose a spectral energy measure to characterize structural information, so that we can cluster clients based on spectral energy and build cluster-level spectral GNNs. We then align the spectral characteristics of local spectral GNNs with those of cluster-level spectral GNNs to enable structural knowledge sharing. Experiments on six homophilic and five heterophilic graph datasets under both non-overlapping and overlapping partitioning settings demonstrate that FedSSA consistently outperforms eleven state-of-the-art methods. Our code is available at https://anonymous.4open.science/r/FedSSA.

Probabilistic Methods · Variational Inference

Mathis Chagneux, Mathias Müller, Pierre Gloaguen, Sylvain Le Corff, Jimmy Olsson

This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive sequentially. The algorithm allows for the simultaneous training of the model parameters and the distribution of the latent states given the observations. It is based on i.i.d. Monte Carlo sampling, coupled with a well-chosen deep architecture, enabling both computational efficiency and flexibility. The performance of the method is illustrated on both synthetic data and real-world air-quality data. The proposed approach is theoretically motivated by the existence of an asymptotic contrast function and the ergodicity of the underlying Markov chain, and applies more generally to the computation of additive expectations under posterior distributions in state-space models.

Deep Learning · Generative Models and Autoencoders

Zekai Li, Ji Liu, Yiqing Huang, Ziqiong Liu, Dong Li, Emad Barsoum

Diffusion-based large language models (dLLMs) support parallel text generation via iterative denoising, yet inference remains latency-heavy because many steps are spent on redundant refinement and repeated remasking of tokens whose final values are already determined. Prior acceleration methods mainly depend on step-local confidence heuristics or fixed schedules, which are sensitive to prompt and task variation and ignore strong positional effects within a sequence. We cast diffusion decoding as a dynamic control problem and show that token-wise denoising trajectories provide the key signal for reliable control. We propose a trace-aware decoding framework with two components. First, Temporal-Spatial Parallel Decoding (TSPD) uses a lightweight temporal-spatial correctness sensor that consumes per-token trajectory features, including confidence, entropy, and momentum, together with token position, to decide when a token has converged and can be safely fixed. Second, we introduce ]Confidence Extrapolation (CE)}], a training-free state-space module that forecasts future logit trends with uncertainty to support proactive decisions, including safe look-ahead and targeted stabilization when trajectories are oscillatory or underconfident. Together, TSPD and CE reduce unnecessary denoising iterations while preserving output quality, and they compose cleanly with system optimizations such as KV caching.

Probabilistic Methods · Variational Inference

Yuhang Xi, Yu-Feng Yu, Chuan-Xian Ren, Zhao-Rong Lai

Parameter-Efficient Fine-Tuning (PEFT) is essential for adapting Large Language Models, yet existing methods typically struggle to balance model capacity with computational efficiency. Standard approaches often enforce rigid low-rank constraints, while dynamic alternatives incur significant memory overheads. To resolve this dilemma, we propose Spectral Bridge Variational Inference (SBVI), a geometric framework that reformulates LoRA not as static parameter optimization, but as a continuous Wasserstein gradient flow on the manifold of Gaussian measures. Rather than fixing the rank at initialization, SBVI governs the singular value evolution via a stochastic differential equation driven by a thermodynamic competition between task gradients and adaptive entropic friction. This mechanism induces a spectral bifurcation that automatically prunes redundant noise modes while amplifying signal-rich components, naturally discovering a layer-wise optimal rank distribution. We derive a scalable algorithm with linear complexity using factorized Riemannian retractions and an Empirical Bayes friction update. Experiments on reasoning and coding benchmarks demonstrate that SBVI achieves state-of-the-art performance, offering superior accuracy and memory efficiency compared to existing static and dynamic adaptation methods.

Probabilistic Methods · Bayesian Models and Methods

Albus Li, Matthew Wicker

Foundation models are increasingly being deployed in contexts where understanding the uncertainty of their outputs is critical to ensuring responsible deployment. While Bayesian methods offer a principled approach to uncertainty quantification, their computational overhead renders their use impractical for training or inference at foundation model scale. State-of-the-art models achieve parameter counts in the trillions through carefully engineered sparsity including Mixture-of-Experts (MoE) layers. In this work, we demonstrate calibrated uncertainty at scale by introducing Variational Mixture-of-Experts Routing (VMoER), a structured Bayesian approach for modelling uncertainty in MoE layers. VMoER confines Bayesian inference to the expert-selection stage which is typically done by a deterministic routing network. We instantiate VMoER using two inference strategies: amortised variational inference over routing logits and inferring a temperature parameter for stochastic expert selection. Across tested foundation models, VMoER improves routing stability under noise by 38%, reduces calibration error by 94%, and increases out-of-distribution AUROC by 12%, while incurring less than 1% additional FLOPs. These results suggest VMoER offers a scalable path toward robust and uncertainty-aware foundation models.

General Machine Learning · Clustering

Zheming Xu, Aiyue Tang, Shidi Chen, Xuechao Zou, Congyan Lang, Rogelio A. Mancisidor, Michael Kampffmeyer

Incomplete multi-view clustering (IMVC) aims to uncover shared cluster structures from data with partially observed views. Although recent imputation-free methods based on variational inference demonstrate robustness to missing views, they commonly rely on a conditional independence assumption across views, which fails to capture the inherently structured and potentially correlated nature of multi-view data. In this paper, we propose a variational framework that explicitly goes beyond this assumption by introducing a learnable cross-view correlation structure. Specifically, we explicitly model and learn correlations between views by utilizing the covariance structure of posterior estimation errors. To facilitate robust and efficient learning, the correlation matrix is parameterized through a normalized Cholesky decomposition, ensuring positive definiteness and enabling the entire model to be trained jointly through a unified variational objective. Extensive experiments on multiple IMVC benchmarks demonstrate that our method consistently outperforms state-of-the-art approaches across a wide range of missing-view settings. These results highlight the effectiveness of adaptive correlation modeling in variational IMVC, demonstrating the need to go beyond the independence assumption in IMVC.

Jake Fawkes, Jason Hartford

In GFlowNets and variational inference, it has been shown that the mean square error between target and model log probabilities is an effective, low variance, surrogate loss for training generative models. This loss has the property that when evaluated \emph{on-policy} its gradients correspond to those of the KL divergence, while \emph{off-policy} it remains a valid loss with the same global minimiser. In this work, we demonstrate that this construction can be extended to the whole family of $f$-divergences, leading to a family of losses whose on-policy gradients are that of the corresponding $f$-divergence, but retain the same global minimiser off-policy. Specifically, we show that the on-policy gradients lead to a one to one correspondence between translation invariant loss functions on the target and model log probabilities, and $f$-divergences. This equivalence allows us to design new surrogate loss functions for tuning a wide class of generative models that inherit the properties of the corresponding $f$-divergence, such as being more mode covering, whilst being applicable to off-policy data. We apply our losses on a range of tasks, including classic synthetic examples, SynFlowNets for molecule discovery, and asynchronous large language model (LLM) tuning, demonstrating that our models retain their predicted properties on- and off-policy and can be applied to a wide class of generative models.

Applications · Chemistry, Physics, and Earth Sciences

Dario Coscia, Pim de Haan, Max Welling

Machine Learning Interatomic Potentials (MLIPs) are becoming a central tool in simulation-based chemistry. However, like most deep learning models, MLIPs struggle to make accurate predictions on out-of-distribution data or when trained in a data-scarce regime, both common scenarios in simulation-based chemistry. Moreover, MLIPs do not provide uncertainty estimates by construction, which are fundamental to guide active learning pipelines and to ensure the accuracy of simulation results compared to quantum calculations. To address this shortcoming, we propose BLIPs: Bayesian Learned Interatomic Potentials. BLIP is a scalable, architecture-agnostic variational Bayesian framework for training or fine-tuning MLIPs, built on an adaptive version of Variational Dropout. BLIP delivers well-calibrated uncertainty estimates and minimal computational overhead for energy and forces prediction at inference time, while integrating seamlessly with (equivariant) message-passing architectures. Empirical results on simulation-based computational chemistry tasks demonstrate improved predictive accuracy with respect to standard MLIPs, and trustworthy uncertainty estimates, especially in data-scarse or heavy out-of-distribution regimes. Moreover, fine-tuning pretrained MLIPs with BLIP yields consistent performance gains and calibrated uncertainties.

Probabilistic Methods · Monte Carlo and Sampling Methods

Xiaoyu Wang, Jonathan Huggins

Stochastic gradient Langevin dynamics combined with Gibbs updates (SGLD-Gibbs) provides a highly scalable approach to approximate Bayesian inference in latent variable models. However, it remains unclear how to tune the algorithm's hyperparameters in a principled manner to ensure the uncertainty estimates are statistically meaningful. In this work, we address this gap in tuning guidance by developing a statistical scaling limit theory for SGLD-Gibbs. We derive a joint asymptotic limit for the global parameters and latent variables under appropriate space-time rescaling. We show that global parameters converge to a diffusion-type limit, while individual latent variables converge to a jump process reflecting their intermittent Gibbs updates. This joint jump-diffusion structure reveals how latent-variable randomness contributes to the stationary distribution of the global parameters. We leverage our results to provide explicit guidance on hyperparameter tuning for SGLD-Gibbs that ensures meaningful uncertainty quantification. Our empirical results show that SGLD-Gibbs with our tuning guidance leads to better parameter estimates and uncertainty quantification than stochastic variational inference.

Qingdong He, Chaoyi Wang, Peng TANG, Yifan Yang, Xiaobin Hu

Video subtitle removal is essential for content localization and media re-editing, yet existing mask-guided diffusion methods face critical limitations: training inefficiency requiring extensive annotations and full model fine-tuning, inference complexity demanding explicit mask sequences, and static prior utilization unable to adapt to quality variations. We present CLEAR (Context-aware Learning for End-to-end Adaptive subtitle Removal), a lightweight adapter-based framework addressing these challenges through three technical innovations. First, self-supervised prior learning (Stage I) extracts occlusion guidance from video pairs using pixel differences as weak supervision, eliminating annotation dependency while learning generalizable subtitle features across languages. Second, LoRA-based adaptive refinement (Stage II) enables parameter-efficient training that preserves pre-trained visual priors while achieving true mask-free end-to-end inference without external detection modules. Third, adaptive focal weighting dynamically adjusts prior influence based on local quality assessment, effectively handling diverse subtitle styles and noisy guidance signals. Extensive experiments demonstrate CLEAR's superior performance in multilingual subtitle removal while requiring only 0.77% trainable parameters, establishing a new paradigm for efficient video text removal without inference-time mask dependencies.