Searcharxiv⌕ Search

arXiv subjects

Di He

Publications and source records attributed to Di He.

At least 73 records · Page 4Linked to original sources
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

CORE: Common Random Reconstruction for Distributed Optimization with Provable Low Communication Complexity

With distributed machine learning being a prominent technique for large-scale machine learning tasks, communication complexity has become a major bottleneck for speeding up training and scaling up machine numbers. In this paper, we propose a new technique named Common randOm REconstruction(CORE), which can be used to compress the information transmitted between machines in order to reduce communication complexity without other strict conditions. Especially, our technique CORE projects the vector-valued information to a low-dimensional one through common random vectors and reconstructs the information with the same random noises after communication. We apply CORE to two distributed tasks, respectively convex optimization on linear models and generic non-convex optimization, and design new distributed algorithms, which achieve provably lower communication complexities. For example, we show for linear models CORE-based algorithm can encode the gradient vector to $\mathcal{O}(1)$-bits (against $\mathcal{O}(d)$), with the convergence rate not worse, preceding the existing results.

cs.LG↗
arXiv2023

Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlo

Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic chemistry problems. Here, we report the development of a new NN-VMC method that achieves a remarkable speed-up by more than one order of magnitude, thereby greatly extending the applicability of NN-VMC to larger systems. Our key design is a novel computational framework named Forward Laplacian, which computes the Laplacian associated with neural networks, the bottleneck of NN-VMC, through an efficient forward propagation process. We then demonstrate that Forward Laplacian is not only versatile but also facilitates more developments of acceleration methods across various aspects, including optimization for sparse derivative matrix and efficient neural network design. Empirically, our approach enables NN-VMC to investigate a broader range of atoms, molecules and chemical reactions for the first time, providing valuable references to other ab initio methods. The results demonstrate a great potential in applying deep learning methods to solve general quantum mechanical problems.

physics.comp-ph↗
arXiv2023

Highly Accurate Quantum Chemical Property Prediction with Uni-Mol+

Recent developments in deep learning have made remarkable progress in speeding up the prediction of quantum chemical (QC) properties by removing the need for expensive electronic structure calculations like density functional theory. However, previous methods learned from 1D SMILES sequences or 2D molecular graphs failed to achieve high accuracy as QC properties primarily depend on the 3D equilibrium conformations optimized by electronic structure methods, far different from the sequence-type and graph-type data. In this paper, we propose a novel approach called Uni-Mol+ to tackle this challenge. Uni-Mol+ first generates a raw 3D molecule conformation from inexpensive methods such as RDKit. Then, the raw conformation is iteratively updated to its target DFT equilibrium conformation using neural networks, and the learned conformation will be used to predict the QC properties. To effectively learn this update process towards the equilibrium conformation, we introduce a two-track Transformer model backbone and train it with the QC property prediction task. We also design a novel approach to guide the model's training process. Our extensive benchmarking results demonstrate that the proposed Uni-Mol+ significantly improves the accuracy of QC property prediction in various datasets. We have made the code and model publicly available at \url{https://github.com/dptech-corp/Uni-Mol}.

physics.chem-ph↗
arXiv2023

Personalized Predictive ASR for Latency Reduction in Voice Assistants

Streaming Automatic Speech Recognition (ASR) in voice assistants can utilize prefetching to partially hide the latency of response generation. Prefetching involves passing a preliminary ASR hypothesis to downstream systems in order to prefetch and cache a response. If the final ASR hypothesis after endpoint detection matches the preliminary one, the cached response can be delivered to the user, thus saving latency. In this paper, we extend this idea by introducing predictive automatic speech recognition, where we predict the full utterance from a partially observed utterance, and prefetch the response based on the predicted utterance. We introduce two personalization approaches and investigate the tradeoff between potential latency gains from successful predictions and the cost increase from failed predictions. We evaluate our methods on an internal voice assistant dataset as well as the public SLURP dataset.

cs.CL↗
arXiv2023

A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Tests

Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. To address these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which $\mathsf{SSWL}$ achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. Furthermore, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of WL and Folklore WL (FWL) tests. Our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments demonstrate that $\mathsf{SSWL}$-inspired subgraph GNNs can significantly outperform prior architectures on multiple benchmarks despite great simplicity.

cs.LG↗
arXiv2023

One Transformer Can Understand Both 2D & 3D Molecular Data

Unlike vision and language data which usually has a unique format, molecules can naturally be characterized using different chemical formulations. One can view a molecule as a 2D graph or define it as a collection of atoms located in a 3D space. For molecular representation learning, most previous works designed neural networks only for a particular data format, making the learned models likely to fail for other data formats. We believe a general-purpose neural network model for chemistry should be able to handle molecular tasks across data modalities. To achieve this goal, in this work, we develop a novel Transformer-based Molecular model called Transformer-M, which can take molecular data of 2D or 3D formats as input and generate meaningful semantic representations. Using the standard Transformer as the backbone architecture, Transformer-M develops two separated channels to encode 2D and 3D structural information and incorporate them with the atom features in the network modules. When the input data is in a particular format, the corresponding channel will be activated, and the other will be disabled. By training on 2D and 3D molecular data with properly designed supervised signals, Transformer-M automatically learns to leverage knowledge from different data modalities and correctly capture the representations. We conducted extensive experiments for Transformer-M. All empirical results show that Transformer-M can simultaneously achieve strong performance on 2D and 3D tasks, suggesting its broad applicability. The code and models will be made publicly available at https://github.com/lsj2408/Transformer-M.

cs.LG↗
arXiv2023

Adaptive Endpointing with Deep Contextual Multi-armed Bandits

Current endpointing (EP) solutions learn in a supervised framework, which does not allow the model to incorporate feedback and improve in an online setting. Also, it is a common practice to utilize costly grid-search to find the best configuration for an endpointing model. In this paper, we aim to provide a solution for adaptive endpointing by proposing an efficient method for choosing an optimal endpointing configuration given utterance-level audio features in an online setting, while avoiding hyperparameter grid-search. Our method does not require ground truth labels, and only uses online learning from reward signals without requiring annotated labels. Specifically, we propose a deep contextual multi-armed bandit-based approach, which combines the representational power of neural networks with the action exploration behavior of Thompson modeling algorithms. We compare our approach to several baselines, and show that our deep bandit models also succeed in reducing early cutoff errors while maintaining low latency.

eess.AS↗
arXiv2023

DSVT: Dynamic Sparse Voxel Transformer with Rotated Sets

Designing an efficient yet deployment-friendly 3D backbone to handle sparse point clouds is a fundamental problem in 3D perception. Compared with the customized sparse convolution, the attention mechanism in Transformers is more appropriate for flexibly modeling long-range relationships and is easier to be deployed in real-world applications. However, due to the sparse characteristics of point clouds, it is non-trivial to apply a standard transformer on sparse points. In this paper, we present Dynamic Sparse Voxel Transformer (DSVT), a single-stride window-based voxel Transformer backbone for outdoor 3D perception. In order to efficiently process sparse points in parallel, we propose Dynamic Sparse Window Attention, which partitions a series of local regions in each window according to its sparsity and then computes the features of all regions in a fully parallel manner. To allow the cross-set connection, we design a rotated set partitioning strategy that alternates between two partitioning configurations in consecutive self-attention layers. To support effective downsampling and better encode geometric information, we also propose an attention-style 3D pooling module on sparse points, which is powerful and deployment-friendly without utilizing any customized CUDA operations. Our model achieves state-of-the-art performance with a broad range of 3D perception tasks. More importantly, DSVT can be easily deployed by TensorRT with real-time inference speed (27Hz). Code will be available at \url{https://github.com/Haiyang-W/DSVT}.

cs.CV↗
arXiv2023

Denoising Masked AutoEncoders Help Robust Classification

In this paper, we propose a new self-supervised method, which is called Denoising Masked AutoEncoders (DMAE), for learning certified robust classifiers of images. In DMAE, we corrupt each image by adding Gaussian noises to each pixel value and randomly masking several patches. A Transformer-based encoder-decoder model is then trained to reconstruct the original image from the corrupted one. In this learning paradigm, the encoder will learn to capture relevant semantics for the downstream tasks, which is also robust to Gaussian additive noises. We show that the pre-trained encoder can naturally be used as the base classifier in Gaussian smoothed models, where we can analytically compute the certified radius for any data point. Although the proposed method is simple, it yields significant performance improvement in downstream classification tasks. We show that the DMAE ViT-Base model, which just uses 1/10 parameters of the model developed in recent work arXiv:2206.10550, achieves competitive or better certified accuracy in various settings. The DMAE ViT-Large model significantly surpasses all previous results, establishing a new state-of-the-art on ImageNet dataset. We further demonstrate that the pre-trained model has good transferability to the CIFAR-10 dataset, suggesting its wide adaptability. Models and code are available at https://github.com/quanlin-wu/dmae.

cs.CV↗
arXiv2023

Learning Physics-Informed Neural Networks without Stacked Back-propagation

Physics-Informed Neural Network (PINN) has become a commonly used machine learning approach to solve partial differential equations (PDE). But, facing high-dimensional secondorder PDE problems, PINN will suffer from severe scalability issues since its loss includes second-order derivatives, the computational cost of which will grow along with the dimension during stacked back-propagation. In this work, we develop a novel approach that can significantly accelerate the training of Physics-Informed Neural Networks. In particular, we parameterize the PDE solution by the Gaussian smoothed model and show that, derived from Stein's Identity, the second-order derivatives can be efficiently calculated without back-propagation. We further discuss the model capacity and provide variance reduction methods to address key limitations in the derivative estimation. Experimental results show that our proposed method can achieve competitive error compared to standard PINN training but is significantly faster. Our code is released at https://github.com/LithiumDA/PINN-without-Stacked-BP.

cs.LG↗
arXiv2023

3D Molecular Generation via Virtual Dynamics

Structure-based drug design, i.e., finding molecules with high affinities to the target protein pocket, is one of the most critical tasks in drug discovery. Traditional solutions, like virtual screening, require exhaustively searching on a large molecular database, which are inefficient and cannot return novel molecules beyond the database. The pocket-based 3D molecular generation model, i.e., directly generating a molecule with a 3D structure and binding position in the pocket, is a new promising way to address this issue. Herein, we propose VD-Gen, a novel pocket-based 3D molecular generation pipeline. VD-Gen consists of several carefully designed stages to generate fine-grained 3D molecules with binding positions in the pocket cavity end-to-end. Rather than directly generating or sampling atoms with 3D positions in the pocket like in early attempts, in VD-Gen, we first randomly initialize many virtual particles in the pocket; then iteratively move these virtual particles, making the distribution of virtual particles approximate the distribution of molecular atoms. After virtual particles are stabilized in 3D space, we extract a 3D molecule from them. Finally, we further refine atoms in the extracted molecule by iterative movement again, to get a high-quality 3D molecule, and predict a confidence score for it. Extensive experiment results on pocket-based molecular generation demonstrate that VD-Gen can generate novel 3D molecules to fill the target pocket cavity with high binding affinities, significantly outperforming previous baselines.

q-bio.BM↗
arXiv2023

Matching entropy based disparity estimation from light field

A major challenge for matching-based depth estimation is to prevent mismatches in occlusion and smooth regions. An effective matching window satisfying three characteristics: texture richness, disparity consistency and anti-occlusion should be able to prevent mismatches to some extent. According to these characteristics, we propose matching entropy in the spatial domain of light field to measure the amount of correct information in a matching window, which provides the criterion for matching window selection. Based on matching entropy regularization, we establish an optimization model for depth estimation with a matching cost fidelity term. To find the optimum, we propose a two-step adaptive matching algorithm. First, the region type is adaptively determined to identify occluding, occluded, smooth and textured regions. Then, the matching entropy criterion is used to adaptively select the size and shape of matching windows, as well as the visible viewpoints. The two-step process can reduce mismatches and redundant calculations by selecting effective matching windows. The experimental results on synthetic and real data show that the proposed method can effectively improve the accuracy of depth estimation in occlusion and smooth regions and has strong robustness for different noise levels. Therefore, high-precision depth estimation from 4D light field data is achieved.

cs.CV↗
arXiv2023

Benchmarking Graphormer on Large-Scale Molecular Modeling Datasets

This technical note describes the recent updates of Graphormer, including architecture design modifications, and the adaption to 3D molecular dynamics simulation. With these simple modifications, Graphormer could attain better results on large-scale molecular modeling datasets than the vanilla one, and the performance gain could be consistently obtained on 2D and 3D molecular graph modeling tasks. In addition, we show that with a global receptive field and an adaptive aggregation strategy, Graphormer is more powerful than classic message-passing-based GNNs. Empirically, Graphormer could achieve much less MAE than the originally reported results on the PCQM4M quantum chemistry dataset used in KDD Cup 2021. In the meanwhile, it greatly outperforms the competitors in the recent Open Catalyst Challenge, which is a competition track on NeurIPS 2021 workshop, and aims to model the catalyst-adsorbate reaction system with advanced AI models. All codes could be found at https://github.com/Microsoft/Graphormer.

cs.LG↗
arXiv2022

Online Training Through Time for Spiking Neural Networks

Spiking neural networks (SNNs) are promising brain-inspired energy-efficient models. Recent progress in training methods has enabled successful deep SNNs on large-scale tasks with low latency. Particularly, backpropagation through time (BPTT) with surrogate gradients (SG) is popularly used to achieve high performance in a very small number of time steps. However, it is at the cost of large memory consumption for training, lack of theoretical clarity for optimization, and inconsistency with the online property of biological learning and rules on neuromorphic hardware. Other works connect spike representations of SNNs with equivalent artificial neural network formulation and train SNNs by gradients from equivalent mappings to ensure descent directions. But they fail to achieve low latency and are also not online. In this work, we propose online training through time (OTTT) for SNNs, which is derived from BPTT to enable forward-in-time learning by tracking presynaptic activities and leveraging instantaneous loss and gradients. Meanwhile, we theoretically analyze and prove that gradients of OTTT can provide a similar descent direction for optimization as gradients based on spike representations under both feedforward and recurrent conditions. OTTT only requires constant training memory costs agnostic to time steps, avoiding the significant memory costs of BPTT for GPU training. Furthermore, the update rule of OTTT is in the form of three-factor Hebbian learning, which could pave a path for online on-chip learning. With OTTT, it is the first time that two mainstream supervised SNN training methods, BPTT with SG and spike representation-based training, are connected, and meanwhile in a biologically plausible form. Experiments on CIFAR-10, CIFAR-100, ImageNet, and CIFAR10-DVS demonstrate the superior performance of our method on large-scale static and neuromorphic datasets in small time steps.

cs.NE↗
arXiv2022

Is $L^2$ Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network?

The Physics-Informed Neural Network (PINN) approach is a new and promising way to solve partial differential equations using deep learning. The $L^2$ Physics-Informed Loss is the de-facto standard in training Physics-Informed Neural Networks. In this paper, we challenge this common practice by investigating the relationship between the loss function and the approximation quality of the learned solution. In particular, we leverage the concept of stability in the literature of partial differential equation to study the asymptotic behavior of the learned solution as the loss approaches zero. With this concept, we study an important class of high-dimensional non-linear PDEs in optimal control, the Hamilton-Jacobi-Bellman(HJB) Equation, and prove that for general $L^p$ Physics-Informed Loss, a wide class of HJB equation is stable only if $p$ is sufficiently large. Therefore, the commonly used $L^2$ loss is not suitable for training PINN on those equations, while $L^{\infty}$ loss is a better choice. Based on the theoretical insight, we develop a novel PINN training algorithm to minimize the $L^{\infty}$ loss for HJB equations which is in a similar spirit to adversarial training. The effectiveness of the proposed algorithm is empirically demonstrated through experiments. Our code is released at https://github.com/LithiumDA/L_inf-PINN.

cs.LG↗
arXiv2022

Your Transformer May Not be as Powerful as You Expect

Relative Positional Encoding (RPE), which encodes the relative distance between any pair of tokens, is one of the most successful modifications to the original Transformer. As far as we know, theoretical understanding of the RPE-based Transformers is largely unexplored. In this work, we mathematically analyze the power of RPE-based Transformers regarding whether the model is capable of approximating any continuous sequence-to-sequence functions. One may naturally assume the answer is in the affirmative -- RPE-based Transformers are universal function approximators. However, we present a negative result by showing there exist continuous sequence-to-sequence functions that RPE-based Transformers cannot approximate no matter how deep and wide the neural network is. One key reason lies in that most RPEs are placed in the softmax attention that always generates a right stochastic matrix. This restricts the network from capturing positional information in the RPEs and limits its capacity. To overcome the problem and make the model more powerful, we first present sufficient conditions for RPE-based Transformers to achieve universal function approximation. With the theoretical guidance, we develop a novel attention module, called Universal RPE-based (URPE) Attention, which satisfies the conditions. Therefore, the corresponding URPE-based Transformers become universal function approximators. Extensive experiments covering typical architectures and tasks demonstrate that our model is parameter-efficient and can achieve superior performance to strong baselines in a wide range of applications. The code will be made publicly available at https://github.com/lsj2408/URPE.

cs.LG↗