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Probabilistic Methods · Bayesian Models and Methods

Van-Anh Nguyen, Trung Le, Mehrtash Harandi, Ehsan Abbasnejad, Thanh-Toan Do, Dinh Phung

We propose a framework grounded in gradient flow theory and informed by geometric structure that provides multiple diverse solutions for a given task, ensuring collaborative results that enhance performance and adaptability across different tasks. This framework enables flexibility, allowing for efficient task-specific fine-tuning while preserving the knowledge of the pre-trained foundation models. Extensive experiments across transfer learning, few-shot learning, and domain generalization show that our proposed approach consistently outperforms existing Bayesian methods, delivering strong performance with affordable computational overhead and offering a practical solution by updating only a small subset of parameters.

Applications · Language, Speech and Dialog

Tianrui Wang, Haoyu Wang, Meng Ge, Cheng Gong, Chunyu Qiang, Ziyang Ma, Zikang Huang, Guanrou Yang, Xiaobao Wang, Eng-Siong Chng 等

While emotional text-to-speech (TTS) has made significant progress, most existing research remains limited to utterance-level emotional expression and fails to support word-level control. Achieving word-level expressive control poses fundamental challenges, primarily due to the complexity of modeling multi-emotion transitions and the scarcity of annotated datasets that capture intra-sentence emotional and prosodic variation. In this paper, we propose WeSCon, the first self-training framework that enables word-level control of both emotion and speaking rate in a pretrained zero-shot TTS model, without relying on datasets containing intra-sentence emotion or speed transitions. Our method introduces a transition-smoothing strategy and a dynamic speed control mechanism to guide the pretrained TTS model in performing word-level expressive synthesis through a multi-round inference process. To further simplify the inference, we incorporate a dynamic emotional attention bias mechanism and fine-tune the model via self-training, thereby activating its ability for word-level expressive control in an end-to-end manner. Experimental results show that WeSCon effectively overcomes data scarcity, achieving state-of-the-art performance in word-level emotional expression control while preserving the strong zero-shot synthesis capabilities of the original TTS model.

Reinforcement Learning · Everything Else

Yuchen Xia, Yunjian Xu

We introduce MOSDT, the first algorithm designed for multi-agent offline safe reinforcement learning (MOSRL), alongside MOSDB, the first dataset and benchmark for this domain. Different from most existing knowledge distillation-based multi-agent RL methods, we propose policy self-distillation (PSD) with a new global information reconstruction scheme by fusing the observation features of all agents, streamlining training and improving parameter efficiency. We adopt full parameter sharing across agents, significantly slashing parameter count and boosting returns up to 38.4-fold by stabilizing training. We propose a new plug-and-play cost binary embedding (CBE) module, which binarizes cumulative costs as safety signals and embeds the signals into return features for efficient information aggregation. On the strong MOSDB benchmark, MOSDT achieves state-of-the-art (SOTA) returns in 14 out of 18 tasks (across all base environments including MuJoCo, Safety Gym, and Isaac Gym) while ensuring complete safety, with only 65% of the execution parameter count of a SOTA single-agent offline safe RL method CDT. Code, dataset, and results are available at this website: https://github.com/Lucian1115/MOSDT.git

Probabilistic Methods · Monte Carlo and Sampling Methods

Guan-Horng Liu, Jaemoo Choi, Yongxin Chen, Benjamin K Miller, Ricky T. Q. Chen

Computational methods for learning to sample from the Boltzmann distribution—where the target distribution is known only up to an unnormalized energy function—have advanced significantly recently. Due to the lack of explicit target samples, however, prior diffusion-based methods, known as _diffusion samplers_, often require importance-weighted estimation or complicated learning processes. Both trade off scalability with extensive evaluations of the energy and model, thereby limiting their practical usage. In this work, we propose **Adjoint Schrödinger Bridge Sampler (ASBS)**, a new diffusion sampler that employs simple and scalable matching-based objectives yet without the need to estimate target samples during training. ASBS is grounded on a mathematical model—the Schrödinger Bridge—which enhances sampling efficiency via kinetic-optimal transportation. Through a new lens of stochastic optimal control theory, we demonstrate how SB-based diffusion samplers can be learned at scale via Adjoint Matching and prove convergence to the global solution. Notably, ASBS generalizes the recent Adjoint Sampling (Havens et al., 2025) to arbitrary source distributions by relaxing the so-called memoryless condition that largely restricts the design space. Through extensive experiments, we demonstrate the effectiveness of ASBS on sampling from classical energy functions, amortized conformer generation, and molecular Boltzmann distributions. Codes are available at https://github.com/facebookresearch/adjoint_samplers

Optimization · Discrete Optimization

Fu Luo, Xi Lin, Mengyuan Zhong, Fei Liu, Zhenkun Wang, Jianyong Sun, Qingfu Zhang

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm that sequentially adds unvisited nodes to partial solutions, this rigid approach often leads to suboptimal results. To overcome this limitation, we explore the idea of the insertion-based paradigm and propose Learning to Construct with Insertion-based Paradigm (L2C-Insert), a novel learning-based method for constructive NCO. Unlike traditional approaches, L2C-Insert builds solutions by strategically inserting unvisited nodes at any valid position in the current partial solution, which can significantly enhance the flexibility and solution quality. The proposed framework introduces three key components: a novel model architecture for precise insertion position prediction, an efficient training scheme for model optimization, and an advanced inference technique that fully exploits the insertion paradigm's flexibility. Extensive experiments on both synthetic and real-world instances of the Travelling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that L2C-Insert consistently achieves superior performance across various problem sizes. The code is available at [https://github.com/CIAM-Group/L2C\_Insert](https://github.com/CIAM-Group/L2C\_Insert).

Social Aspects

mohit sharma, Amit Deshpande, Chiranjib Bhattacharyya, Rajiv Ratn Shah

To fix the `bias in, bias out' problem in fair machine learning, it is important to steer feature distributions of data or internal representations of Large Language Models (LLMs) to \emph{ideal} ones that guarantee group-fair outcomes. Previous work on fair generative models and representation steering could greatly benefit from provable fairness guarantees on the model output. We define a distribution as \emph{ideal} if the minimizer of any cost-sensitive risk on it is guaranteed to have exact group-fair outcomes (e.g., demographic parity, equal opportunity)---in other words, it has no fairness-utility trade-off. We formulate an optimization program for optimal steering by finding the nearest \emph{ideal} distribution in KL-divergence, and provide efficient algorithms for it when the underlying distributions come from well-known parametric families (e.g., normal, log-normal). Empirically, our optimal steering techniques on both synthetic and real-world datasets improve fairness without diminishing utility (and sometimes even improve utility). We demonstrate affine steering of LLM representations to reduce bias in multi-class classification, e.g., occupation prediction from a short biography in Bios dataset (De-Arteaga et al.). Furthermore, we steer internal representations of LLMs towards desired outputs so that it works equally well across different groups.

Theory · Game Theory

Kira Goldner, Taylor Lundy

We initiate the study of multidimensional Bayesian utility maximization, focusing on the unit-demand setting where values are i.i.d. across both items and buyers. The seminal result of Hartline and Roughgarden '08 studies simple, information-robust mechanisms that maximize utility for $n$ i.i.d. agents and $m$ identical items via an approximation to social welfare as an upper bound, and they prove this gap between optimal utility and social welfare is $\Theta(1+\log{n/m})$ in this setting. We extend these results to the multidimensional setting. To do so, we develop simple, prior-independent, approximately-optimal mechanisms, targeting the simplest benchmark of optimal welfare. We give a $(1-1/e)$-approximation when there are more items than buyers, and a $\Theta(\log{n/m})$-approximation when there are more buyers than items, and we prove that this bound is tight in both $n$ and $m$ by reducing the i.i.d. unit-demand setting to the identical items setting. Finally, we include an extensive discussion section on why Bayesian utility maximization is a promising research direction. In particular, we characterize complexities in this setting that defy our intuition from the welfare and revenue literature, and motivate why coming up with a better benchmark than welfare is a hard problem itself.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Johanna Düngler, Amartya Sanyal

Given $n$ i.i.d.random matrices $A_i \in \mathbb{R}^{d \times d}$ that share common expectation $\Sigma$, the objective of Differentially Private Stochastic PCA is to identify a subspace of dimension $k$ that captures the largest variance directions of $\Sigma$, while preserving differential privacy (DP) of each individual $A_i$. Existing methods either (i) require the sample size $n$ to scale super-linearly with dimension $d$, even under Gaussian assumptions on the $A_i$, or (ii) introduce excessive noise for DP even when the intrinsic randomness within $A_i$ is small.~\citet{liu2022dp} addressed these issues for sub-Gaussian data but only for estimating the top eigenvector ($k=1$) using their algorithm DP-PCA. We propose the first algorithm capable of estimating the top $k$ eigenvectors for arbitrary $k \leq d$, whilst overcoming both limitations above. For $k=1$, our algorithm matches the utility guarantees of DP-PCA, achieving near-optimal statistical error even when $n = \tilde{O}(d)$. We further provide a lower bound for general $k > 1$, matching our upper bound up to a factor of $k$, and experimentally demonstrate the advantages of our algorithm over comparable baselines.

Reinforcement Learning · Everything Else

Zhihang Lin, Mingbao Lin, Yuan Xie, Rongrong Ji

This paper introduces Completion Pruning Policy Optimization (CPPO) to accelerate the training of reasoning models based on Group Relative Policy Optimization (GRPO). GRPO, while effective, incurs high training costs due to the need to sample multiple completions for each question. Our experiment and theoretical analysis reveal that the number of completions impacts model accuracy yet increases training time multiplicatively, and not all completions contribute equally to policy training---their contribution depends on their relative advantage. To address these issues, we propose CPPO, which prunes completions with low absolute advantages, significantly reducing the number needed for gradient calculation and updates. Additionally, we introduce a dynamic completion allocation strategy to maximize GPU utilization by incorporating additional questions, further enhancing training efficiency. Experiments show that CPPO achieves up to $7.98\times$ speedup on GSM8K and $3.48\times$ on Math while preserving or even enhancing the accuracy compared to the original GRPO. We release our code at https://github.com/lzhxmu/CPPO.

Theory · Learning Theory

Harin Lee, Min-hwan Oh

We study the problem of infrequent exploration in linear bandits, addressing a significant yet overlooked gap between fully adaptive exploratory methods (e.g., UCB and Thompson Sampling), which explore potentially at every time step, and purely greedy approaches, which require stringent diversity assumptions to succeed. Continuous exploration can be impractical or unethical in safety-critical or costly domains, while purely greedy strategies typically fail without adequate contextual diversity. To bridge these extremes, we introduce a simple and practical framework, INFEX, explicitly designed for infrequent exploration. INFEX executes a base exploratory policy according to a given schedule while predominantly choosing greedy actions in between. Despite its simplicity, our theoretical analysis demonstrates that INFEX achieves instance-dependent regret matching standard provably efficient algorithms, provided the exploration frequency exceeds a logarithmic threshold. Additionally, INFEX is a general, modular framework that allows seamless integration of any fully adaptive exploration method, enabling wide applicability and ease of adoption. By restricting intensive exploratory computations to infrequent intervals, our approach can also enhance computational efficiency. Empirical evaluations confirm our theoretical findings, showing state-of-the-art regret performance and runtime improvements over existing methods.

General Machine Learning · Everything Else

Reza Ramezanpour, Victor Manuel Tenorio Gomez, Antonio G. Marques, Ashutosh Sabharwal, Santiago Segarra

Graphons, as limit objects of dense graph sequences, play a central role in the statistical analysis of network data. However, existing graphon estimation methods often struggle with scalability to large networks and resolution-independent approximation, due to their reliance on estimating latent variables or costly metrics such as the Gromov-Wasserstein distance. In this work, we propose a novel, scalable graphon estimator that directly recovers the graphon via moment matching, leveraging implicit neural representations (INRs). Our approach avoids latent variable modeling by training an INR--mapping coordinates to graphon values--to match empirical subgraph counts (i.e., moments) from observed graphs. This direct estimation mechanism yields a polynomial-time solution and crucially sidesteps the combinatorial complexity of Gromov-Wasserstein optimization. Building on foundational results, we establish a theoretical guarantee: when the observed subgraph motifs sufficiently represent those of the true graphon (a condition met with sufficiently large or numerous graph samples), the estimated graphon achieves a provable upper bound in cut distance from the ground truth. Additionally, we introduce MomentMixup, a data augmentation technique that performs mixup in the moment space to enhance graphon-based learning. Our graphon estimation method achieves strong empirical performance--demonstrating high accuracy on small graphs and superior computational efficiency on large graphs--outperforming state-of-the-art scalable estimators in 75\% of benchmark settings and matching them in the remaining cases. Furthermore, MomentMixup demonstrated improved graph classification accuracy on the majority of our benchmarks.

Applications · Everything Else

Tonglong Wei, Yan Lin, Youfang Lin, Shengnan Guo, Jilin Hu, Haitao Yuan, Gao Cong, Huaiyu Wan

Spatiotemporal trajectory data is crucial for various traffic-related applications. However, issues such as device malfunctions and network instability often result in sparse trajectories that lose detailed movement information compared to their dense counterparts. Recovering missing points in sparse trajectories is thus essential. Despite recent progress, three challenges remain. First, the lack of large-scale dense trajectory datasets hinders the training of a trajectory recovery model. Second, the varying spatiotemporal correlations in sparse trajectories make it hard to generalize across different sampling intervals. Third, extracting road conditions for missing points is non-trivial. To address these challenges, we propose $\textit{PLMTrajRec}$, a novel trajectory recovery model. It leverages the scalability of a pre-trained language model (PLM) and can effectively recover trajectories by fine-tuning with small-scale dense trajectory datasets. To handle different sampling intervals in sparse trajectories, we first convert sampling intervals and movement features into prompts for the PLM to understand. We then introduce a trajectory encoder to unify trajectories of varying intervals into a single interval. To extract road conditions for missing points, we propose an area flow-guided implicit trajectory prompt that represents traffic conditions in each region, and a road condition passing mechanism that infers the road conditions of missing points using the observed ones. Experiments on four public trajectory datasets with three sampling intervals demonstrate the effectiveness, scalability, and generalization ability of PLMTrajRec. Code is available at https://github.com/wtl52656/PLMTrajRec.

Deep Learning · Generative Models and Autoencoders

Dar-Yen Chen, Hmrishav Bandyopadhyay, Kai Zou, Yi-Zhe Song

Negative guidance -- explicitly suppressing unwanted attributes -- remains a fundamental challenge in diffusion models, particularly in few-step sampling regimes. While Classifier-Free Guidance (CFG) works well in standard settings, it fails under aggressive sampling step compression due to divergent predictions between positive and negative branches. We present Normalized Attention Guidance (NAG), an efficient, training-free mechanism that applies extrapolation in attention space with L1-based normalization and refinement. NAG restores effective negative guidance where CFG collapses while maintaining fidelity. Unlike existing approaches, NAG generalizes across architectures (UNet, DiT), sampling regimes (few-step, multi-step), and modalities (image, video), functioning as a \textit{universal} plug-in with minimal computational overhead. Through extensive experimentation, we demonstrate consistent improvements in text alignment (CLIP Score), fidelity (FID, PFID), and human-perceived quality (ImageReward). Our ablation studies validate each design component, while user studies confirm significant preference for NAG-guided outputs. As a model-agnostic inference-time approach requiring no retraining, NAG provides effortless negative guidance for all modern diffusion frameworks -- pseudocode in the Appendix!

Theory · Learning Theory

Binxu Wang, Cengiz Pehlevan

We develop an analytical framework for understanding how the learned distribution evolves during diffusion model training. Leveraging the Gaussian equivalence principle, we derived exact solutions for the gradient-flow dynamics of weights in one or two layer linear or linear convolutional denoiser settings with arbitrary data, where linear networks converge along principal components, and convolutional networks converge along Fourier modes. Remarkably, these solutions allow us to derive the generated distribution in closed-form and its KL-divergence through training. These analytical results expose a pronounced \emph{spectral bias}, i.e. for both weights and generated distributions, the convergence time of a mode follows an inverse power law of its variance. Empirical experiments on both Gaussian and natural image datasets demonstrate that the power-law spectral bias—remain robust even when using deeper or convolutional architectures. Our results underscore the importance of the data covariance in dictating the order and rate at which diffusion models learn different modes of the data, providing potential explanations of why earlier stopping could lead to incorrect details in image generative model.

Probabilistic Methods · Everything Else

Xinyuan Fan, Feiyan Ma, Chenlei Leng, Weichi Wu

Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix and a low-rank graphon--two goals rarely achieved jointly. Our method resolves identification issues and enables an efficient sequential algorithm based on subgraph counts and interpolation. We establish consistency and demonstrate strong empirical performance in terms of computational efficiency and estimation accuracy through simulations and data analysis.

Jisu Nam, Soowon Son, Dahyun Chung, Jiyoung Kim, Siyoon Jin, Junhwa Hur, Seungryong Kim

Recent advancements in video diffusion models based on Diffusion Transformers (DiTs) have achieved remarkable success in generating temporally coherent videos. Yet, a fundamental question persists: how do these models internally establish and represent temporal correspondences across frames? We introduce DiffTrack, the first quantitative analysis framework designed to answer this question. DiffTrack constructs a dataset of prompt-generated video with pseudo ground-truth tracking annotations and proposes novel evaluation metrics to systematically analyze how each component within the full 3D attention mechanism of DiTs (e.g., representations, layers, and timesteps) contributes to establishing temporal correspondences. Our analysis reveals that query-key similarities in specific (but not all) layers play a critical role in temporal matching, and that this matching becomes increasingly prominent throughout denoising. We demonstrate practical applications of DiffTrack in zero-shot point tracking, where it achieves state-of-the-art performance compared to existing vision foundation and self-supervised video models. Further, we extend our findings to motion-enhanced video generation with a novel guidance method that improves temporal consistency of generated videos without additional training. We believe our work offers crucial insights into the inner workings of video DiTs and establishes a foundation for further research and applications leveraging their temporal understanding.

Theory · Learning Theory

Hugo Ninou, Jonathan Kadmon, N Alex Cayco Gajic

Gradient-based algorithms are a cornerstone of artificial neural network training, yet it remains unclear whether biological neural networks use similar gradient-based strategies during learning. Experiments often discover a diversity of synaptic plasticity rules, but whether these amount to an approximation to gradient descent is unclear. Here we investigate a previously overlooked possibility: that learning dynamics may include fundamentally non-gradient "curl"-like components while still being able to effectively optimize a loss function. Curl terms naturally emerge in networks with excitatory-inhibitory connectivity or Hebbian/anti-Hebbian plasticity, resulting in learning dynamics that cannot be framed as gradient descent on any objective. To investigate the impact of these curl terms, we analyze feedforward networks within an analytically tractable student-teacher framework, systematically introducing non-gradient dynamics through rule-flipped neurons. Small curl terms preserve the stability of the original solution manifold, resulting in learning dynamics similar to gradient descent. Beyond a critical value, strong curl terms destabilize the solution manifold. Depending on the network architecture, this loss of stability can lead to chaotic learning dynamics that destroy performance. In other cases, the curl terms can counterintuitively speed up learning compared to gradient descent by allowing the weight dynamics to escape saddles by temporarily ascending the loss. Our results identify specific architectures capable of supporting robust learning via diverse learning rules, providing an important counterpoint to normative theories of gradient-based learning in neural networks.

Deep Learning · Generative Models and Autoencoders

Chaoran Cheng, Yusong Wang, Yuxin Chen, Xiangxin Zhou, Nanning Zheng, Ge Liu

Consistency models are a class of generative models that enable few-step generation for diffusion and flow matching models. While consistency models have achieved promising results on Euclidean domains like images, their applications to Riemannian manifolds remain challenging due to the curved geometry. In this work, we propose the Riemannian Consistency Model (RCM), which, for the first time, enables few-step consistency modeling while respecting the intrinsic manifold constraint imposed by the Riemannian geometry. Leveraging the covariant derivative and exponential-map-based parameterization, we derive the closed-form solutions for both discrete- and continuous-time training objectives for RCM. We then demonstrate theoretical equivalence between the two variants of RCM: Riemannian consistency distillation (RCD) that relies on a teacher model to approximate the marginal vector field, and Riemannian consistency training (RCT) that utilizes the conditional vector field for training. We further propose a simplified training objective that eliminates the need for the complicated differential calculation. Finally, we provide a unique kinematics perspective for interpreting the RCM objective, offering new theoretical angles. Through extensive experiments, we manifest the superior generative quality of RCM in few-step generation on various non-Euclidean manifolds, including flat-tori, spheres, and the 3D rotation group SO(3), spanning a variety of crucial real-world applications such as RNA and protein generation.

Computer Vision · 3D Rendering & Reconstruction

Daniel Jung, Kyoung Mu Lee

Hands are essential to human interaction, and exploring contact between hands and the world can promote comprehensive understanding of their function. Recently, there have been growing number of hand interaction datasets that cover interaction with object, other hand, scene, and body. Despite the significance of the task and increasing high-quality data, how to effectively learn dense hand contact estimation remains largely underexplored. There are two major challenges for learning dense hand contact estimation. First, there exists class imbalance issue from hand contact datasets where majority of regions are not in contact. Second, hand contact datasets contain spatial imbalance issue with most of hand contact exhibited in finger tips, resulting in challenges for generalization towards contacts in other hand regions. To tackle these issues, we present a framework that learns dense HAnd COntact estimation (HACO) from imbalanced data. To resolve the class imbalance issue, we introduce balanced contact sampling, which builds and samples from multiple sampling groups that fairly represent diverse contact statistics for both contact and non-contact vertices. Moreover, to address the spatial imbalance issue, we propose vertex-level class-balanced (VCB) loss, which incorporates spatially varying contact distribution by separately reweighting loss contribution of each vertex based on its contact frequency across dataset. As a result, we effectively learn to predict dense hand contact estimation with large-scale hand contact data without suffering from class and spatial imbalance issue. The codes are available at https://github.com/dqj5182/HACO_RELEASE.

Applications · Everything Else

YINYI WEI, Xiao LI

We present Text2MBL, a text-to-code generation framework that generates executable Building Information Modeling (BIM) code directly from textual descriptions of modular building layout (MBL) design. Unlike conventional layout generation approaches that operate in 2D space, Text2MBL produces fully parametric, semantically rich BIM layouts through on‑the‑fly code instantiation. To address MBLs' unique challenges due to their hierarchical three-tier structure: modules (physical building blocks), units (self-contained dwellings), and rooms (functional spaces), we developed an object-oriented code architecture and fine-tuned large language models to output structured action sequences in code format. To train and evaluate the framework, we curated a dataset of paired descriptions and ground truth layouts drawn from real‑world modular housing projects. Performance were assessed using metrics for executable validity, semantic fidelity, and geometric consistency. By tightly unifying natural language understanding with BIM code generation, Text2MBL establishes a scalable pipeline from high-level conceptual design to automation-ready modular construction workflows. Our implementation is available at https://github.com/CI3LAB/Text2MBL.