arXiv subjects

Liwei Wang

Publications and source records attributed to Liwei Wang.

At least 91 records · Page 5Linked to original sources

arXiv2024

Symmetry enforced solution of the many-body Schrödinger equation with deep neural network

The integration of deep neural networks with the Variational Monte Carlo (VMC) method has marked a significant advancement in solving the Schrödinger equation. In this work, we enforce spin symmetry in the neural network-based VMC calculation with modified optimization target. Our method is designed to solve for the ground state and multiple excited states with target spin symmetry at a low computational cost. It predicts accurate energies while maintaining the correct symmetry in strongly correlated systems, even in cases where different spin states are nearly degenerate. Our approach also excels at spin-gap calculations, including the singlet-triplet gap in biradical systems, which is of high interest in photochemistry. Overall, this work establishes a robust framework for efficiently calculating various quantum states with specific spin symmetry in correlated systems, paving the way for novel discoveries in quantum science.

physics.chem-ph↗

arXiv2024

Communication-Efficient Model Aggregation with Layer Divergence Feedback in Federated Learning

Federated Learning (FL) facilitates collaborative machine learning by training models on local datasets, and subsequently aggregating these local models at a central server. However, the frequent exchange of model parameters between clients and the central server can result in significant communication overhead during the FL training process. To solve this problem, this paper proposes a novel FL framework, the Model Aggregation with Layer Divergence Feedback mechanism (FedLDF). Specifically, we calculate model divergence between the local model and the global model from the previous round. Then through model layer divergence feedback, the distinct layers of each client are uploaded and the amount of data transferred is reduced effectively. Moreover, the convergence bound reveals that the access ratio of clients has a positive correlation with model performance. Simulation results show that our algorithm uploads local models with reduced communication overhead while upholding a superior global model performance.

cs.DC↗

arXiv2024

Towards Learning a Generalist Model for Embodied Navigation

Building a generalist agent that can interact with the world is the intriguing target of AI systems, thus spurring the research for embodied navigation, where an agent is required to navigate according to instructions or respond to queries. Despite the major progress attained, previous works primarily focus on task-specific agents and lack generalizability to unseen scenarios. Recently, LLMs have presented remarkable capabilities across various fields, and provided a promising opportunity for embodied navigation. Drawing on this, we propose the first generalist model for embodied navigation, NaviLLM. It adapts LLMs to embodied navigation by introducing schema-based instruction. The schema-based instruction flexibly casts various tasks into generation problems, thereby unifying a wide range of tasks. This approach allows us to integrate diverse data sources from various datasets into the training, equipping NaviLLM with a wide range of capabilities required by embodied navigation. We conduct extensive experiments to evaluate the performance and generalizability of our model. The experimental results demonstrate that our unified model achieves state-of-the-art performance on CVDN, SOON, and ScanQA. Specifically, it surpasses the previous stats-of-the-art method by a significant margin of 29% in goal progress on CVDN. Moreover, our model also demonstrates strong generalizability and presents impressive results on unseen tasks, e.g., embodied question answering and 3D captioning.

cs.CV↗

arXiv2024

GiT: Towards Generalist Vision Transformer through Universal Language Interface

This paper proposes a simple, yet effective framework, called GiT, simultaneously applicable for various vision tasks only with a vanilla ViT. Motivated by the universality of the Multi-layer Transformer architecture (e.g, GPT) widely used in large language models (LLMs), we seek to broaden its scope to serve as a powerful vision foundation model (VFM). However, unlike language modeling, visual tasks typically require specific modules, such as bounding box heads for detection and pixel decoders for segmentation, greatly hindering the application of powerful multi-layer transformers in the vision domain. To solve this, we design a universal language interface that empowers the successful auto-regressive decoding to adeptly unify various visual tasks, from image-level understanding (e.g., captioning), over sparse perception (e.g., detection), to dense prediction (e.g., segmentation). Based on the above designs, the entire model is composed solely of a ViT, without any specific additions, offering a remarkable architectural simplification. GiT is a multi-task visual model, jointly trained across five representative benchmarks without task-specific fine-tuning. Interestingly, our GiT builds a new benchmark in generalist performance, and fosters mutual enhancement across tasks, leading to significant improvements compared to isolated training. This reflects a similar impact observed in LLMs. Further enriching training with 27 datasets, GiT achieves strong zero-shot results over various tasks. Due to its simple design, this paradigm holds promise for narrowing the architectural gap between vision and language. Code and models will be available at \url{https://github.com/Haiyang-W/GiT}.

cs.CV↗

arXiv2024

Tackling Heavy-Tailed Rewards in Reinforcement Learning with Function Approximation: Minimax Optimal and Instance-Dependent Regret Bounds

While numerous works have focused on devising efficient algorithms for reinforcement learning (RL) with uniformly bounded rewards, it remains an open question whether sample or time-efficient algorithms for RL with large state-action space exist when the rewards are \emph{heavy-tailed}, i.e., with only finite $(1+ε)$-th moments for some $ε\in(0,1]$. In this work, we address the challenge of such rewards in RL with linear function approximation. We first design an algorithm, \textsc{Heavy-OFUL}, for heavy-tailed linear bandits, achieving an \emph{instance-dependent} $T$-round regret of $\tilde{O}\big(d T^{\frac{1-ε}{2(1+ε)}} \sqrt{\sum_{t=1}^T ν_t^2} + d T^{\frac{1-ε}{2(1+ε)}}\big)$, the \emph{first} of this kind. Here, $d$ is the feature dimension, and $ν_t^{1+ε}$ is the $(1+ε)$-th central moment of the reward at the $t$-th round. We further show the above bound is minimax optimal when applied to the worst-case instances in stochastic and deterministic linear bandits. We then extend this algorithm to the RL settings with linear function approximation. Our algorithm, termed as \textsc{Heavy-LSVI-UCB}, achieves the \emph{first} computationally efficient \emph{instance-dependent} $K$-episode regret of $\tilde{O}(d \sqrt{H \mathcal{U}^*} K^\frac{1}{1+ε} + d \sqrt{H \mathcal{V}^* K})$. Here, $H$ is length of the episode, and $\mathcal{U}^*, \mathcal{V}^*$ are instance-dependent quantities scaling with the central moment of reward and value functions, respectively. We also provide a matching minimax lower bound $Ω(d H K^{\frac{1}{1+ε}} + d \sqrt{H^3 K})$ to demonstrate the optimality of our algorithm in the worst case. Our result is achieved via a novel robust self-normalized concentration inequality that may be of independent interest in handling heavy-tailed noise in general online regression problems.

cs.LG↗

arXiv2024

A Reduction-based Framework for Sequential Decision Making with Delayed Feedback

We study stochastic delayed feedback in general multi-agent sequential decision making, which includes bandits, single-agent Markov decision processes (MDPs), and Markov games (MGs). We propose a novel reduction-based framework, which turns any multi-batched algorithm for sequential decision making with instantaneous feedback into a sample-efficient algorithm that can handle stochastic delays in sequential decision making. By plugging different multi-batched algorithms into our framework, we provide several examples demonstrating that our framework not only matches or improves existing results for bandits, tabular MDPs, and tabular MGs, but also provides the first line of studies on delays in sequential decision making with function approximation. In summary, we provide a complete set of sharp results for multi-agent sequential decision making with delayed feedback.

cs.LG↗

arXiv2024

On Cyclical MCMC Sampling

Cyclical MCMC is a novel MCMC framework recently proposed by Zhang et al. (2019) to address the challenge posed by high-dimensional multimodal posterior distributions like those arising in deep learning. The algorithm works by generating a nonhomogeneous Markov chain that tracks -- cyclically in time -- tempered versions of the target distribution. We show in this work that cyclical MCMC converges to the desired probability distribution in settings where the Markov kernels used are fast mixing, and sufficiently long cycles are employed. However in the far more common settings of slow mixing kernels, the algorithm may fail to produce samples from the desired distribution. In particular, in a simple mixture example with unequal variance, we show by simulation that cyclical MCMC fails to converge to the desired limit. Finally, we show that cyclical MCMC typically estimates well the local shape of the target distribution around each mode, even when we do not have convergence to the target.

stat.CO↗

arXiv2024

$\widetilde{O}(N^2)$ Representation of General Continuous Anti-symmetric Function

In quantum mechanics, the wave function of fermion systems such as many-body electron systems are anti-symmetric (AS) and continuous, and it is crucial yet challenging to find an ansatz to represent them. This paper addresses this challenge by presenting an ${\widetilde O}(N^2)$ ansatz based on permutation-equivariant functions. We prove that our ansatz can represent any AS continuous functions, and can accommodate the determinant-based structure proposed by Hutter [14], solving the proposed open problems that ${O}(N)$ Slater determinants are sufficient to provide universal representation of AS continuous functions. Together, we offer a generalizable and efficient approach to representing AS continuous functions, shedding light on designing neural networks to learn wave functions.

quant-ph↗

arXiv2024

Asymptotics of the Smallest Eigenvalue Distributions of Freud Unitary Ensembles

We consider the smallest eigenvalue distributions of some Freud unitary ensembles, that is, the probabilities that all the eigenvalues of the Hermitian matrices from the ensembles lie in the interval $(t,\infty)$. This problem is related to the Hankel determinants generated by the Freud weights with a jump discontinuity. By using Chen and Ismail's ladder operator approach, we obtain the discrete systems for the recurrence coefficients of the corresponding orthogonal polynomials. This enables us to derive the large $n$ asymptotics of the recurrence coefficients via Dyson's Coulomb fluid approach. We finally obtain the large $n$ asymptotics of the Hankel determinants and that of the probabilities from their relations to the recurrence coefficients and with the aid of some recent results in the literature.

math-ph↗

arXiv2024

DOF: Accelerating High-order Differential Operators with Forward Propagation

Solving partial differential equations (PDEs) efficiently is essential for analyzing complex physical systems. Recent advancements in leveraging deep learning for solving PDE have shown significant promise. However, machine learning methods, such as Physics-Informed Neural Networks (PINN), face challenges in handling high-order derivatives of neural network-parameterized functions. Inspired by Forward Laplacian, a recent method of accelerating Laplacian computation, we propose an efficient computational framework, Differential Operator with Forward-propagation (DOF), for calculating general second-order differential operators without losing any precision. We provide rigorous proof of the advantages of our method over existing methods, demonstrating two times improvement in efficiency and reduced memory consumption on any architectures. Empirical results illustrate that our method surpasses traditional automatic differentiation (AutoDiff) techniques, achieving 2x improvement on the MLP structure and nearly 20x improvement on the MLP with Jacobian sparsity.

cs.LG↗

arXiv2024

Rethinking the Expressive Power of GNNs via Graph Biconnectivity

Designing expressive Graph Neural Networks (GNNs) is a central topic in learning graph-structured data. While numerous approaches have been proposed to improve GNNs in terms of the Weisfeiler-Lehman (WL) test, generally there is still a lack of deep understanding of what additional power they can systematically and provably gain. In this paper, we take a fundamentally different perspective to study the expressive power of GNNs beyond the WL test. Specifically, we introduce a novel class of expressivity metrics via graph biconnectivity and highlight their importance in both theory and practice. As biconnectivity can be easily calculated using simple algorithms that have linear computational costs, it is natural to expect that popular GNNs can learn it easily as well. However, after a thorough review of prior GNN architectures, we surprisingly find that most of them are not expressive for any of these metrics. The only exception is the ESAN framework, for which we give a theoretical justification of its power. We proceed to introduce a principled and more efficient approach, called the Generalized Distance Weisfeiler-Lehman (GD-WL), which is provably expressive for all biconnectivity metrics. Practically, we show GD-WL can be implemented by a Transformer-like architecture that preserves expressiveness and enjoys full parallelizability. A set of experiments on both synthetic and real datasets demonstrates that our approach can consistently outperform prior GNN architectures.

cs.LG↗

arXiv2024

Deep Learning with Information Fusion and Model Interpretation for Health Monitoring of Fetus based on Long-term Prenatal Electronic Fetal Heart Rate Monitoring Data

Long-term fetal heart rate (FHR) monitoring during the antepartum period, increasingly popularized by electronic FHR monitoring, represents a growing approach in FHR monitoring. This kind of continuous monitoring, in contrast to the short-term one, collects an extended period of fetal heart data. This offers a more comprehensive understanding of fetus's conditions. However, the interpretation of long-term antenatal fetal heart monitoring is still in its early stages, lacking corresponding clinical standards. Furthermore, the substantial amount of data generated by continuous monitoring imposes a significant burden on clinical work when analyzed manually. To address above challenges, this study develops an automatic analysis system named LARA (Long-term Antepartum Risk Analysis system) for continuous FHR monitoring, combining deep learning and information fusion methods. LARA's core is a well-established convolutional neural network (CNN) model. It processes long-term FHR data as input and generates a Risk Distribution Map (RDM) and Risk Index (RI) as the analysis results. We evaluate LARA on inner test dataset, the performance metrics are as follows: AUC 0.872, accuracy 0.816, specificity 0.811, sensitivity 0.806, precision 0.271, and F1 score 0.415. In our study, we observe that long-term FHR monitoring data with higher RI is more likely to result in adverse outcomes (p=0.0021). In conclusion, this study introduces LARA, the first automated analysis system for long-term FHR monitoring, initiating the further explorations into its clinical value in the future.

cs.LG↗

arXiv2024

A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Sampling

Multi-fidelity (MF) methods are gaining popularity for enhancing surrogate modeling and design optimization by incorporating data from various low-fidelity (LF) models. While most existing MF methods assume a fixed dataset, adaptive sampling methods that dynamically allocate resources among fidelity models can achieve higher efficiency in the exploring and exploiting the design space. However, most existing MF methods rely on the hierarchical assumption of fidelity levels or fail to capture the intercorrelation between multiple fidelity levels and utilize it to quantify the value of the future samples and navigate the adaptive sampling. To address this hurdle, we propose a framework hinged on a latent embedding for different fidelity models and the associated pre-posterior analysis to explicitly utilize their correlation for adaptive sampling. In this framework, each infill sampling iteration includes two steps: We first identify the location of interest with the greatest potential improvement using the high-fidelity (HF) model, then we search for the next sample across all fidelity levels that maximize the improvement per unit cost at the location identified in the first step. This is made possible by a single Latent Variable Gaussian Process (LVGP) model that maps different fidelity models into an interpretable latent space to capture their correlations without assuming hierarchical fidelity levels. The LVGP enables us to assess how LF sampling candidates will affect HF response with pre-posterior analysis and determine the next sample with the best benefit-to-cost ratio. Through test cases, we demonstrate that the proposed method outperforms the benchmark methods in both MF global fitting (GF) and Bayesian Optimization (BO) problems in convergence rate and robustness. Moreover, the method offers the flexibility to switch between GF and BO by simply changing the acquisition function.

stat.ML↗

arXiv2024

Beyond Weisfeiler-Lehman: A Quantitative Framework for GNN Expressiveness

Designing expressive Graph Neural Networks (GNNs) is a fundamental topic in the graph learning community. So far, GNN expressiveness has been primarily assessed via the Weisfeiler-Lehman (WL) hierarchy. However, such an expressivity measure has notable limitations: it is inherently coarse, qualitative, and may not well reflect practical requirements (e.g., the ability to encode substructures). In this paper, we introduce a unified framework for quantitatively studying the expressiveness of GNN architectures, addressing all the above limitations. Specifically, we identify a fundamental expressivity measure termed homomorphism expressivity, which quantifies the ability of GNN models to count graphs under homomorphism. Homomorphism expressivity offers a complete and practical assessment tool: the completeness enables direct expressivity comparisons between GNN models, while the practicality allows for understanding concrete GNN abilities such as subgraph counting. By examining four classes of prominent GNNs as case studies, we derive simple, unified, and elegant descriptions of their homomorphism expressivity for both invariant and equivariant settings. Our results provide novel insights into a series of previous work, unify the landscape of different subareas in the community, and settle several open questions. Empirically, extensive experiments on both synthetic and real-world tasks verify our theory, showing that the practical performance of GNN models aligns well with the proposed metric.

cs.LG↗

arXiv2023

Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective

Recent studies have discovered that Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs), particularly when dealing with complex tasks involving mathematics or reasoning. Despite the enormous empirical success, the underlying mechanisms behind CoT and how it unlocks the potential of LLMs remain elusive. In this paper, we take a first step towards theoretically answering these questions. Specifically, we examine the expressivity of LLMs with CoT in solving fundamental mathematical and decision-making problems. By using circuit complexity theory, we first give impossibility results showing that bounded-depth Transformers are unable to directly produce correct answers for basic arithmetic/equation tasks unless the model size grows super-polynomially with respect to the input length. In contrast, we then prove by construction that autoregressive Transformers of constant size suffice to solve both tasks by generating CoT derivations using a commonly used math language format. Moreover, we show LLMs with CoT can handle a general class of decision-making problems known as Dynamic Programming, thus justifying its power in tackling complex real-world tasks. Finally, an extensive set of experiments show that, while Transformers always fail to directly predict the answers, they can consistently learn to generate correct solutions step-by-step given sufficient CoT demonstrations.

cs.LG↗

arXiv2023

Horizon-Free and Instance-Dependent Regret Bounds for Reinforcement Learning with General Function Approximation

To tackle long planning horizon problems in reinforcement learning with general function approximation, we propose the first algorithm, termed as UCRL-WVTR, that achieves both \emph{horizon-free} and \emph{instance-dependent}, since it eliminates the polynomial dependency on the planning horizon. The derived regret bound is deemed \emph{sharp}, as it matches the minimax lower bound when specialized to linear mixture MDPs up to logarithmic factors. Furthermore, UCRL-WVTR is \emph{computationally efficient} with access to a regression oracle. The achievement of such a horizon-free, instance-dependent, and sharp regret bound hinges upon (i) novel algorithm designs: weighted value-targeted regression and a high-order moment estimator in the context of general function approximation; and (ii) fine-grained analyses: a novel concentration bound of weighted non-linear least squares and a refined analysis which leads to the tight instance-dependent bound. We also conduct comprehensive experiments to corroborate our theoretical findings.

cs.LG↗

arXiv2023

Asymptotic Properties of Some Freud Polynomials

We study the asymptotic properties of monic orthogonal polynomials (OPs) with respect to some Freud weights when the degree of the polynomial tends to infinity, including the asymptotics of the recurrence coefficients, the nontrivial leading coefficients of the monic OPs, the associated Hankel determinants and the squares of $L^2$-norm of the monic OPs. These results are derived from the combination of the ladder operator approach, Dyson's Coulomb fluid approach and some recent results in the literature.

math.CA↗

arXiv2023

PRED: Pre-training via Semantic Rendering on LiDAR Point Clouds

Pre-training is crucial in 3D-related fields such as autonomous driving where point cloud annotation is costly and challenging. Many recent studies on point cloud pre-training, however, have overlooked the issue of incompleteness, where only a fraction of the points are captured by LiDAR, leading to ambiguity during the training phase. On the other hand, images offer more comprehensive information and richer semantics that can bolster point cloud encoders in addressing the incompleteness issue inherent in point clouds. Yet, incorporating images into point cloud pre-training presents its own challenges due to occlusions, potentially causing misalignments between points and pixels. In this work, we propose PRED, a novel image-assisted pre-training framework for outdoor point clouds in an occlusion-aware manner. The main ingredient of our framework is a Birds-Eye-View (BEV) feature map conditioned semantic rendering, leveraging the semantics of images for supervision through neural rendering. We further enhance our model's performance by incorporating point-wise masking with a high mask ratio (95%). Extensive experiments demonstrate PRED's superiority over prior point cloud pre-training methods, providing significant improvements on various large-scale datasets for 3D perception tasks. Codes will be available at https://github.com/PRED4pc/PRED.

cs.CV↗