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Applications · Everything Else

Haohan Zou, Jie Feng, Hao Zhao, Yuanyuan Shi

Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited interpretability. To address these, we propose an end-to-end framework using transformers to construct analytical Lyapunov functions (local), which simplifies formal verification, enhances interpretability, and provides valuable insights for control engineers. Our framework consists of a transformer-based trainer that generates candidate Lyapunov functions and a falsifier that verifies candidate expressions and refines the model via risk-seeking policy gradient. Unlike Alfarano et al. (2024), which utilizes pre-training and seeks global Lyapunov functions for low-dimensional systems, our model is trained from scratch via reinforcement learning (RL) and succeeds in finding local Lyapunov functions for *high-dimensional* and *non-polynomial* systems. Given the symbolic nature of the Lyapunov function candidates, we employ efficient optimization methods for falsification during training and formal verification tools for the final verification. We demonstrate the efficiency of our approach on a range of nonlinear dynamical systems with up to ten dimensions and show that it can discover Lyapunov functions not previously identified in the control literature. Full implementation is available on [Github](https://github.com/JieFeng-cse/Analytical-Lyapunov-Function-Discovery).

Optimization · Non-Convex

Jiaqi Leng, Bin Shi

With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between accelerated gradient methods and damped heavy-ball motion, particularly within the framework of Hamiltonian dynamics, has inspired the development of innovative quantum algorithms for continuous optimization. One such algorithm, Quantum Hamiltonian Descent (QHD), leverages quantum tunneling to escape saddle points and local minima, facilitating the discovery of global solutions in complex optimization landscapes. However, QHD faces several challenges, including slower convergence rates compared to classical gradient methods and limited robustness in highly non-convex problems due to the non-local nature of quantum states. Furthermore, the original QHD formulation primarily relies on function value information, which limits its effectiveness. Inspired by insights from high-resolution differential equations that have elucidated the acceleration mechanisms in classical methods, we propose an enhancement to QHD by incorporating gradient information, leading to what we call gradient-based QHD. This gradient-based QHD achieves faster convergence and significantly increases the likelihood of identifying global solutions. Numerical simulations on challenging problem instances demonstrate that this gradient-based QHD outperforms existing quantum and classical methods by at least an order of magnitude.

Theory · Learning Theory

Nuoya Xiong, Aarti Singh

Reinforcement Learning with Human Feedback (RLHF) is a widely used fine-tuning approach that aligns machine learning models, particularly Language Models (LMs) with human preferences. There are typically multiple objectives driving the preference, hence humans find it easier to express per-objective comparisons rather than a global preference between two choices, e.g. compare two papers on their novelty, clarity, correctness, etc. Multi-Objective RLHF aims to use per-objective preference feedback and achieve a Pareto optimal tradeoff among these objectives by aggregating them into a single unified objective for optimization. However, nearly all prior works rely on linear aggregation, which rules out policies that favor specific objectives such as the worst one. The only existing approach using non-linear aggregation is computationally expensive due to its reward-based nature and the need for retraining whenever the aggregation parameters change. In this work, we address this limitation by transforming the non-linear aggregation maximization problem into a series of sub-problems. Each sub-problem involves only linear aggregation, making it computationally efficient to solve. We further extend our framework to handle multi-group scenarios, where each group has distinct weights for the objectives. Our method enables achieving consensus or maximizing the aggregated objective across all groups. Theoretically, we demonstrate that our algorithmic framework achieves sublinear regret and can be easily adapted to a reward-free algorithm. Empirically, leveraging our theoretical insights, we propose a nearly training-free algorithm once the optimal policies for individual objectives are obtained.

General Machine Learning · Clustering

Haowen Ma, Zhiguo Long, Hua Meng

Density-based mode-seeking methods generate a density-ascending dependency from low-density points towards higher-density neighbors.Current mode-seeking methods identify modes by breaking some dependency connections, but relying heavily on local data characteristics, requiring case-by-case threshold settings or human intervention to be effective for different datasets. To address this issue, we introduce a novel concept called typicality, by exploring the locally defined dependency from a global perspective, to quantify how confident a point would be a mode. We devise an algorithm that effectively and efficiently identifies modes with the help of the global-view typicality. To implement and validate our idea, we design a clustering method called TANGO, which not only leverages typicality to detect modes, but also utilizes graph-cut with an improved path-based similarity to aggregate data into the final clusters. Moreover, this paper also provides some theoretical analysis on the proposed algorithm. Experimental results on several synthetic and extensive real-world datasets demonstrate the effectiveness and superiority of TANGO. The code is available at https://github.com/SWJTU-ML/TANGO_code.

Deep Learning · Generative Models and Autoencoders

Deqian Kong, Minglu Zhao, Dehong Xu, Bo Pang, Shu Wang, Edouardo Honig, Zhangzhang Si, Chuan Li, Jianwen Xie, Sirui Xie 等

We propose a novel class of language models, Latent Thought Models (LTMs), which incorporate explicit latent thought vectors that follow an explicit prior model in latent space. These latent thought vectors guide the autoregressive generation of ground tokens through a Transformer decoder. Training employs a dual-rate optimization process within the classical variational Bayes framework: fast learning of local variational parameters for the posterior distribution of latent vectors (inference-time computation), and slow learning of global decoder parameters. Empirical studies reveal that LTMs possess additional scaling dimensions beyond traditional Large Language Models (LLMs), such as the number of iterations in inference-time computation and number of latent thought vectors. Higher sample efficiency can be achieved by increasing training compute per token, with further gains possible by trading model size for more inference steps. Designed based on these scaling properties, LTMs demonstrate superior sample and parameter efficiency compared to autoregressive models and discrete diffusion models. They significantly outperform these counterparts in validation perplexity and zero-shot language modeling tasks. Additionally, LTMs exhibit emergent few-shot in-context reasoning capabilities that scale with model size, and achieve competitive performance in conditional and unconditional text generation. The project page is available at [https://deqiankong.github.io/blogs/ltm](https://deqiankong.github.io/blogs/ltm).

Reinforcement Learning · Multi-agent

Zhiyao Zhang, Myeung Suk Oh, Hairi, Ziyue Luo, Alvaro Velasquez, Jia (Kevin) Liu

Actor-critic methods for decentralized multi-agent reinforcement learning (MARL) facilitate collaborative optimal decision making without centralized coordination, thus enabling a wide range of applications in practice. To date, however, most theoretical convergence studies for existing actor-critic decentralized MARL methods are limited to the guarantee of a stationary solution under the linear function approximation. This leaves a significant gap between the highly successful use of deep neural actor-critic for decentralized MARL in practice and the current theoretical understanding. To bridge this gap, in this paper, we make the first attempt to develop a deep neural actor-critic method for decentralized MARL, where both the actor and critic components are inherently non-linear. We show that our proposed method enjoys a global optimality guarantee with a finite-time convergence rate of $\mathcal{O}(1/T)$, where $T$ is the total iteration times. This marks the first global convergence result for deep neural actor-critic methods in the MARL literature. We also conduct extensive numerical experiments, which verify our theoretical results.

Optimization · Large Scale, Parallel and Distributed

Hongyao Chen, Tianyang Xu, Xiaojun Wu, Josef Kittler

Batch Normalisation (BN) is widely used in conventional deep neural network training to harmonise the input-output distributions for each batch of data.However, federated learning, a distributed learning paradigm, faces the challenge of dealing with non-independent and identically distributed data among the client nodes. Due to the lack of a coherent methodology for updating BN statistical parameters, standard BN degrades the federated learning performance.To this end, it is urgent to explore an alternative normalisation solution for federated learning. In this work, we resolve the dilemma of the BN layer in federated learning by developing a customised normalisation approach, Hybrid Batch Normalisation (HBN). HBN separates the update of statistical parameters (*i.e.*, means and variances used for evaluation) from that of learnable parameters (*i.e.*, parameters that require gradient updates), obtaining unbiased estimates of global statistical parameters in distributed scenarios. In contrast with the existing solutions, we emphasise the supportive power of global statistics for federated learning. The HBN layer introduces a learnable hybrid distribution factor, allowing each computing node to adaptively mix the statistical parameters of the current batch with the global statistics. Our HBN can serve as a powerful plugin to advance federated learning performance.It reflects promising merits across a wide range of federated learning settings, especially for small batch sizes and heterogeneous data. Code is available at https://github.com/Hongyao-Chen/HybridBN.

General Machine Learning · Sequential, Network, and Time Series Modeling

Daoyu Wang, Mingyue Cheng, Zhiding Liu, Qi Liu

Self-supervised learning has garnered increasing attention in time series analysis for benefiting various downstream tasks and reducing reliance on labeled data. Despite its effectiveness, existing methods often struggle to comprehensively capture both long-term dynamic evolution and subtle local patterns in a unified manner. In this work, we propose \textbf{TimeDART}, a novel self-supervised time series pre-training framework that unifies two powerful generative paradigms to learn more transferable representations. Specifically, we first employ a causal Transformer encoder, accompanied by a patch-based embedding strategy, to model the evolving trends from left to right. Building on this global modeling, we further introduce a denoising diffusion process to capture fine-grained local patterns through forward diffusion and reverse denoising. Finally, we optimize the model in an autoregressive manner. As a result, TimeDART effectively accounts for both global and local sequence features in a coherent way.We conduct extensive experiments on public datasets for time series forecasting and classification. The experimental results demonstrate that TimeDART consistently outperforms previous compared methods, validating the effectiveness of our approach.Our code is available at \url{https://github.com/Melmaphother/TimeDART}.

Deep Learning · Theory

Etienne Boursier, Nicolas Flammarion

Understanding generalization of overparametrized models remains a fundamental challenge in machine learning. The literature mostly studies generalization from an interpolation point of view, taking convergence towards a global minimum of the training loss for granted. This interpolation paradigm does not seem valid for complex tasks such as in-context learning or diffusion. It has instead been empirically observed that the trained models go from global minima to spurious local minima of the training loss as the number of training samples becomes larger than some level we call optimization threshold. This paper explores theoretically this phenomenon in the context of two-layer ReLU networks. We demonstrate that, despite overparametrization, networks might converge towards simpler solutions rather than interpolating training data, which leads to a drastic improvement on the test loss. Our analysis relies on the so called early alignment phase, during which neurons align toward specific directions. This directional alignment leads to a simplicity bias, wherein the network approximates the ground truth model without converging to the global minimum of the training loss. Our results suggest this bias, resulting in an optimization threshold from which interpolation is not reached anymore, is beneficial and enhances the generalization of trained models.

Theory · Game Theory

Fivos Kalogiannis, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Ian Gemp, Georgios Piliouras

We contribute the first provable guarantees of global convergence to Nash equilibria (NE) in two-player zero-sum convex Markov games (cMGs) by using independent policy gradient methods. Convex Markov games, recently defined by Gemp et al.(2024), extend Markov decision processes to multi-agent settings with preferences that are convex over occupancy measures, offering a broad framework for modeling generic strategic interactions. However, even the fundamental min-max case of cMGs presents significant challenges, including inherent nonconvexity, the absence of Bellman consistency, and the complexity of the infinite horizon.Our results follow a two-step approach. First, leveraging properties of hidden-convex–hidden-concave functions, we show that a simple nonconvex regularization transforms the min-max optimization problem into a nonconvex–proximal Polyak-Łojasiewicz (NC-pPL) objective. Crucially, this regularization can stabilize the iterates of independent policy gradient methods and ultimately lead them to converge to equilibria. Second, building on this reduction, we address the general constrained min-max problems under NC-pPL and two-sided pPL conditions, providing the first global convergence guarantees for stochastic nested and alternating gradient descent-ascent methods, which we believe may be of independent interest.

Theory · Learning Theory

Wei Shen, Ruida Zhou, Jing Yang, Cong Shen

Although transformers have demonstrated impressive capabilities for in-context learning (ICL) in practice, theoretical understanding of the underlying mechanism that allows transformers to perform ICL is still in its infancy. This work aims to theoretically study the training dynamics of transformers for in-context classification tasks. We demonstrate that, for in-context classification of Gaussian mixtures under certain assumptions, a single-layer transformer trained via gradient descent converges to a globally optimal model at a linear rate. We further quantify the impact of the training and testing prompt lengths on the ICL inference error of the trained transformer. We show that when the lengths of training and testing prompts are sufficiently large, the prediction of the trained transformer approaches the ground truth distribution of the labels. Experimental results corroborate the theoretical findings.

Deep Learning · Large Language Models

Hongyi Liu, Rajarshi Saha, Zhen Jia, Youngsuk Park, Jiaji Huang, Shoham Sabach, Yu-Xiang Wang, George Karypis

Large Language Models (LLMs) have demonstrated exceptional performance in natural language processing tasks, yet their massive size makes serving them inefficient and costly. Semi-structured pruning has emerged as an effective method for model acceleration, but existing approaches are suboptimal because they focus on local, layer-wise optimizations using heuristic rules, failing to leverage global feedback. We present ProxSparse, a learning-based framework for mask selection enabled by regularized optimization. ProxSparse transforms the rigid, non-differentiable mask selection process into a smoother optimization procedure, allowing gradual mask exploration with flexibility. ProxSparse does not involve additional weight updates once the mask is determined. Our extensive evaluations on 7 widely used models show that ProxSparse consistently outperforms previously proposed semi-structured mask selection methods with significant improvement, demonstrating the effectiveness of our learned approach towards semi-structured pruning.

Deep Learning · Large Language Models

Zeyu Tang, Zhenhao Chen, Xiangchen Song, Loka Li, Yunlong Deng, Yifan Shen, Guangyi Chen, Peter Spirtes, Kun Zhang

The autoregressive decoding for text generation in large language models (LLMs), while widely used, is inherently suboptimal due to the lack of a built-in mechanism to perform refinement and/or correction of the generated content. In this paper, we consider optimality in terms of the joint probability over the generated response, when jointly considering all tokens at the same time. We theoretically characterize the potential deviation of the autoregressively generated response from its globally optimal counterpart that is of the same length. Our analysis suggests that we need to be cautious when noticeable uncertainty arises during text generation, which may signal the sub-optimality of the generation history. To address the pitfall of autoregressive decoding for text generation, we propose an approach that incorporates a sliding reflection window and a pausing criterion, such that refinement and generation can be carried out interchangeably as the decoding proceeds. Our selective refinement framework strikes a balance between efficiency and optimality, and our extensive experimental results demonstrate the effectiveness of our approach.

Deep Learning · Sequential Models, Time series

Mehmet Yiğit Balık, Maksim Sinelnikov, Priscilla Ong, Harri Lähdesmäki

High-dimensional time-series datasets are common in domains such as healthcare and economics. Variational autoencoder (VAE) models, where latent variables are modeled with a Gaussian process (GP) prior, have become a prominent model class to analyze such correlated datasets. However, their applications are challenged by the inherent cubic time complexity that requires specific GP approximation techniques, as well as the general challenge of modeling both shared and individual-specific correlations across time. Though inducing points enhance GP prior VAE scalability, optimizing them remains challenging, especially since discrete covariates resist gradient‑based methods. In this work, we propose a scalable basis function approximation technique for GP prior VAEs that mitigates these challenges and results in linear time complexity, with a global parametrization that eliminates the need for amortized variational inference and the associated amortization gap, making it well-suited for conditional generation tasks where accuracy and efficiency are crucial. Empirical evaluations on synthetic and real-world benchmark datasets demonstrate that our approach not only improves scalability and interpretability but also drastically enhances predictive performance.

Deep Learning · Theory

Letong Hong, Zhangyang “Atlas” Wang

Maximal Update Parameterization ($\mu$P) has shown significant promise in allowing zero-shot hyperparameter transfer across neural network scales, reducing the prohibitive cost of hyperparameter tuning for large models. However, the theoretical foundation behind the observed approximate transferability of hyperparameters remains underexplored. Relying on a width-dominance regime, which ensures that as width grows, certain terms of the learning dynamics dominate, we establish the first fundamental separation of scales in $\mu$P between macro-variables (e.g. loss landscapes) and micro-variables (e.g. individual weights). Our formulation explains why hyperparameter tuning can be effectively performed in early training stages, i.e., \textit{early statistics effectively approximate global hyperparameter optima}, implying the potential to further reduce the training costs required for searching optimal hyperparameters. We further apply our main theory to explain an empirical deep learning phenomenon discovered independently by prior work.

Guojin Zhong, pan wang, Jin Yuan, Zhiyong Li, Long Chen

Recently, generative models have shown considerable promise in unsupervised time series anomaly detection. Nonetheless, the task of effectively capturing complex temporal patterns and minimizing false alarms becomes increasingly challenging when dealing with non-stationary time series, characterized by continuously fluctuating statistical attributes and joint distributions. To confront these challenges, we underscore the benefits of multi-resolution modeling, which improves the ability to distinguish between anomalies and non-stationary behaviors by leveraging correlations across various resolution scales. In response, we introduce a **M**ulti-Res**o**lution **De**composable Diffusion **M**odel (MODEM), which integrates a coarse-to-fine diffusion paradigm with a frequency-enhanced decomposable network to adeptly navigate the intricacies of non-stationarity. Technically, the coarse-to-fine diffusion model embeds cross-resolution correlations into the forward process to optimize diffusion transitions mathematically. It then innovatively employs low-resolution recovery to guide the reverse trajectories of high-resolution series in a coarse-to-fine manner, enhancing the model's ability to learn and elucidate underlying temporal patterns. Furthermore, the frequency-enhanced decomposable network operates in the frequency domain to extract globally shared time-invariant information and time-variant temporal dynamics for accurate series reconstruction. Extensive experiments conducted across five real-world datasets demonstrate that our proposed MODEM achieves state-of-the-art performance and can be generalized to other time series tasks.

Theory · Deep Learning

Yu Huang, Zixin Wen, Yuejie Chi, Yingbin Liang

Self-supervised learning has become a cornerstone in computer vision, primarily divided into reconstruction-based methods like masked autoencoders (MAE) and discriminative methods such as contrastive learning (CL). Recent empirical observations reveal that MAE and CL capture different types of representations: CL tends to focus on global patterns, while MAE adeptly captures **both global and subtle local** information simultaneously. Despite a flurry of recent empirical investigations to shed light on this difference, theoretical understanding remains limited, especially on the dominant architecture **vision transformers** (ViTs). In this paper, to provide rigorous insights, we model the visual data distribution by considering two types of spatial features: dominant global features and comparatively minuscule local features, and study the impact of imbalance among these features. We analyze the training dynamics of one-layer softmax-based ViTs on both MAE and CL objectives using gradient descent. Our analysis shows that as the degree of feature imbalance varies, ViTs trained with the MAE objective effectively learn both global and local features to achieve near-optimal reconstruction, while the CL-trained ViTs favor predominantly global features, even under mild imbalance. These results provide a theoretical explanation for distinct behaviors of MAE and CL observed in empirical studies.

Applications · Computer Vision

Ziqi Lu, Heng Yang, Danfei Xu, Boyi Li, Boris Ivanovic, Marco Pavone, Yue Wang

Emerging 3D geometric foundation models, such as DUSt3R, offer a promising approach for in-the-wild 3D vision tasks.However, due to the high-dimensional nature of the problem space and scarcity of high-quality 3D data,these pre-trained models still struggle to generalize to many challenging circumstances,such as limited view overlap or low lighting.To address this, we propose LoRA3D, an efficient self-calibration pipeline to *specialize* the pre-trained models to target scenes using their own multi-view predictions.Taking sparse RGB images as input, we leverage robust optimization techniques to refine multi-view predictions and align them into a global coordinate frame.In particular, we incorporate prediction confidence into the geometric optimization process, automatically re-weighting the confidence to better reflect point estimation accuracy. We use the calibrated confidence to generate high-quality pseudo labels for the calibrating views and fine-tune the models using low-rank adaptation (LoRA) on the pseudo-labeled data.Our method does not require any external priors or manual labels. It completes the self-calibration process on a **single standard GPU within just 5 minutes**.Each low-rank adapter requires only **18MB** of storage. We evaluated our method on **more than 160 scenes** from the Replica, TUM and Waymo Open datasets,achieving up to **88\% performance improvement** on 3D reconstruction, multi-view pose estimation and novel-view rendering.For more details, please visit our project page at https://520xyxyzq.github.io/lora3d/.

Xin Dong, Yonggan Fu, Shizhe Diao, Wonmin Byeon, ZIJIA CHEN, Ameya Mahabaleshwarkar, Shih-Yang Liu, Matthijs Van keirsbilck, Min-Hung Chen, Yoshi Suhara 等

We propose Hymba, a family of small language models featuring a hybrid-head parallel architecture that integrates attention mechanisms and state space models (SSMs) within the same layer, offering parallel and complementary processing of the same inputs. In this hybrid-head module, attention heads provide high-resolution recall, while SSM heads facilitate efficient context summarization. Additionally, we introduce learnable meta tokens, which are prepended to prompts to store critical meta information, guiding subsequent tokens and alleviating the “forced-to-attend” burden associated with attention mechanisms. Thanks to the global context summarized by SSMs, the attention heads in our model can be further optimized through cross-layer key-value (KV) sharing and a mix of global and local attention, resulting in a compact cache size without compromising accuracy. Notably, Hymba achieves state-of-the-art performance among small LMs: Our Hymba-1.5B-Base model surpasses all sub-2B public models and even outperforms Llama-3.2-3B, achieving 1.32\% higher average accuracy, an 11.67$\times$ reduction in cache size, and 3.49$\times$ higher throughput.

Applications · Chemistry and Drug Discovery

Zichen Wang, Yaokun Ji, Jianing Tian, Shuangjia Zheng

Antibodies are essential proteins responsible for immune responses in organisms, capable of specifically recognizing antigen molecules of pathogens. Recent advances in generative models have significantly enhanced rational antibody design. However, existing methods mainly create antibodies from scratch without template constraints, leading to model optimization challenges and unnatural sequences. To address these issues, we propose a retrieval-augmented diffusion framework, termed RADAb, for efficient antibody design. Our method leverages a set of structural homologous motifs that align with query structural constraints to guide the generative model in inversely optimizing antibodies according to desired design criteria. Specifically, we introduce a structure-informed retrieval mechanism that integrates these exemplar motifs with the input backbone through a novel dual-branch denoising module, utilizing both structural and evolutionary information. Additionally, we develop a conditional diffusion model that iteratively refines the optimization process by incorporating both global context and local evolutionary conditions. Our approach is agnostic to the choice of generative models. Empirical experiments demonstrate that our method achieves state-of-the-art performance in multiple antibody inverse folding and optimization tasks, offering a new perspective on biomolecular generative models.