arXiv subjects

Tao Luo

Publications and source records attributed to Tao Luo.

At least 109 records · Page 6Linked to original sources

arXiv2024

Performance Study of Various Relay Nodes in 5G Wireless Network

This paper studies performance of various types of relay nodes in a 5G wireless network: conventional amplify-forward repeaters, (semi-)smart/smart amplify-forward repeaters with different levels of side information, and half-duplex/full-duplex decode-forward relay nodes with and without spatial reuse. End-to-end effective signal to interference and noise ratios (SINRs) and achievable rates are derived for these different types of relay nodes. Performance and complexity tradeoffs are discussed with a simulation over a Manhattan topology setting. Over-the-air (OTA) test results corroborates the findings in this paper.

cs.NI↗

arXiv2024

Probing Implicit Bias in Semi-gradient Q-learning: Visualizing the Effective Loss Landscapes via the Fokker--Planck Equation

Semi-gradient Q-learning is applied in many fields, but due to the absence of an explicit loss function, studying its dynamics and implicit bias in the parameter space is challenging. This paper introduces the Fokker--Planck equation and employs partial data obtained through sampling to construct and visualize the effective loss landscape within a two-dimensional parameter space. This visualization reveals how the global minima in the loss landscape can transform into saddle points in the effective loss landscape, as well as the implicit bias of the semi-gradient method. Additionally, we demonstrate that saddle points, originating from the global minima in loss landscape, still exist in the effective loss landscape under high-dimensional parameter spaces and neural network settings. This paper develop a novel approach for probing implicit bias in semi-gradient Q-learning.

cs.LG↗

arXiv2024

Decision Mamba: Reinforcement Learning via Hybrid Selective Sequence Modeling

Recent works have shown the remarkable superiority of transformer models in reinforcement learning (RL), where the decision-making problem is formulated as sequential generation. Transformer-based agents could emerge with self-improvement in online environments by providing task contexts, such as multiple trajectories, called in-context RL. However, due to the quadratic computation complexity of attention in transformers, current in-context RL methods suffer from huge computational costs as the task horizon increases. In contrast, the Mamba model is renowned for its efficient ability to process long-term dependencies, which provides an opportunity for in-context RL to solve tasks that require long-term memory. To this end, we first implement Decision Mamba (DM) by replacing the backbone of Decision Transformer (DT). Then, we propose a Decision Mamba-Hybrid (DM-H) with the merits of transformers and Mamba in high-quality prediction and long-term memory. Specifically, DM-H first generates high-value sub-goals from long-term memory through the Mamba model. Then, we use sub-goals to prompt the transformer, establishing high-quality predictions. Experimental results demonstrate that DM-H achieves state-of-the-art in long and short-term tasks, such as D4RL, Grid World, and Tmaze benchmarks. Regarding efficiency, the online testing of DM-H in the long-term task is 28$\times$ times faster than the transformer-based baselines.

cs.LG↗

arXiv2024

Geometry of Critical Sets and Existence of Saddle Branches for Two-layer Neural Networks

This paper presents a comprehensive analysis of critical point sets in two-layer neural networks. To study such complex entities, we introduce the critical embedding operator and critical reduction operator as our tools. Given a critical point, we use these operators to uncover the whole underlying critical set representing the same output function, which exhibits a hierarchical structure. Furthermore, we prove existence of saddle branches for any critical set whose output function can be represented by a narrower network. Our results provide a solid foundation to the further study of optimization and training behavior of neural networks.

cs.LG↗

arXiv2024

Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) -- DNNs often fit target functions from low to high frequencies -- on high-dimensional benchmark datasets such as MNIST/CIFAR10 and deep neural networks such as VGG16. This F-Principle of DNNs is opposite to the behavior of most conventional iterative numerical schemes (e.g., Jacobi method), which exhibit faster convergence for higher frequencies for various scientific computing problems. With a simple theory, we illustrate that this F-Principle results from the regularity of the commonly used activation functions. The F-Principle implies an implicit bias that DNNs tend to fit training data by a low-frequency function. This understanding provides an explanation of good generalization of DNNs on most real datasets and bad generalization of DNNs on parity function or randomized dataset.

cs.LG↗

arXiv2024

Soft Error Reliability Analysis of Vision Transformers

Vision Transformers (ViTs) that leverage self-attention mechanism have shown superior performance on many classical vision tasks compared to convolutional neural networks (CNNs) and gain increasing popularity recently. Existing ViTs works mainly optimize performance and accuracy, but ViTs reliability issues induced by soft errors in large-scale VLSI designs have generally been overlooked. In this work, we mainly study the reliability of ViTs and investigate the vulnerability from different architecture granularities ranging from models, layers, modules, and patches for the first time. The investigation reveals that ViTs with the self-attention mechanism are generally more resilient on linear computing including general matrix-matrix multiplication (GEMM) and full connection (FC) and show a relatively even vulnerability distribution across the patches. ViTs involve more fragile non-linear computing such as softmax and GELU compared to typical CNNs. With the above observations, we propose a lightweight block-wise algorithm-based fault tolerance (LB-ABFT) approach to protect the linear computing implemented with distinct sizes of GEMM and apply a range-based protection scheme to mitigate soft errors in non-linear computing. According to our experiments, the proposed fault-tolerant approaches enhance ViTs accuracy significantly with minor computing overhead in presence of various soft errors.

cs.CR↗

arXiv2024

Uniform Regularity for Incompressible MHD Equations in a Bounded Domain with Curved Boundary in 3D

For the initial boundary problem of the incompressible MHD equations in a bounded domain with general curved boundary in 3D with the general Navier-slip boundary conditions for the velocity field and the perfect conducting condition for the magnetic field, we establish the uniform regularity of conormal Sobolev norms and Lipschitz norms to addressing the anisotropic regularity of tangential and normal directions, which enable us to prove the vanishing dissipation limit as the viscosity and the magnetic diffusion coefficients tend to zero. We overcome the difficulties caused by the intricate interaction of boundary curvature, velocity field, and magnetic fields and resolve the issue caused by the problem that the viscosity and the magnetic diffusion coefficients are not required to be equal.

math.AP↗

arXiv2024

Demystifying Lazy Training of Neural Networks from a Macroscopic Viewpoint

In this paper, we advance the understanding of neural network training dynamics by examining the intricate interplay of various factors introduced by weight parameters in the initialization process. Motivated by the foundational work of Luo et al. (J. Mach. Learn. Res., Vol. 22, Iss. 1, No. 71, pp 3327-3373), we explore the gradient descent dynamics of neural networks through the lens of macroscopic limits, where we analyze its behavior as width $m$ tends to infinity. Our study presents a unified approach with refined techniques designed for multi-layer fully connected neural networks, which can be readily extended to other neural network architectures. Our investigation reveals that gradient descent can rapidly drive deep neural networks to zero training loss, irrespective of the specific initialization schemes employed by weight parameters, provided that the initial scale of the output function $κ$ surpasses a certain threshold. This regime, characterized as the theta-lazy area, accentuates the predominant influence of the initial scale $κ$ over other factors on the training behavior of neural networks. Furthermore, our approach draws inspiration from the Neural Tangent Kernel (NTK) paradigm, and we expand its applicability. While NTK typically assumes that $\lim_{m\to\infty}\frac{\log κ}{\log m}=\frac{1}{2}$, and imposes each weight parameters to scale by the factor $\frac{1}{\sqrt{m}}$, in our theta-lazy regime, we discard the factor and relax the conditions to $\lim_{m\to\infty}\frac{\log κ}{\log m}>0$. Similar to NTK, the behavior of overparameterized neural networks within the theta-lazy regime trained by gradient descent can be effectively described by a specific kernel. Through rigorous analysis, our investigation illuminates the pivotal role of $κ$ in governing the training dynamics of neural networks.

cs.LG↗

arXiv2024

Table-Lookup MAC: Scalable Processing of Quantised Neural Networks in FPGA Soft Logic

Recent advancements in neural network quantisation have yielded remarkable outcomes, with three-bit networks reaching state-of-the-art full-precision accuracy in complex tasks. These achievements present valuable opportunities for accelerating neural networks by computing in reduced precision. Implementing it on FPGAs can take advantage of bit-level reconfigurability, which is not available on conventional CPUs and GPUs. Simultaneously, the high data intensity of neural network processing has inspired computing-in-memory paradigms, including on FPGA platforms. By programming the effects of trained model weights as lookup operations in soft logic, the transfer of weight data from memory units can be avoided, alleviating the memory bottleneck. However, previous methods face poor scalability - the high logic utilisation limiting them to small networks/sub-networks of binary models with low accuracy. In this paper, we introduce Table Lookup Multiply-Accumulate (TLMAC) as a framework to compile and optimise quantised neural networks for scalable lookup-based processing. TLMAC clusters and maps unique groups of weights to lookup-based processing elements, enabling highly parallel computation while taking advantage of parameter redundancy. Further place and route algorithms are proposed to reduce LUT utilisation and routing congestion. We demonstrate that TLMAC significantly improves the scalability of previous related works. Our efficient logic mapping and high degree of reuse enables entire ImageNet-scale quantised models with full-precision accuracy to be implemented using lookup-based computing on one commercially available FPGA.

cs.AR↗

arXiv2024

A priori Estimates for Deep Residual Network in Continuous-time Reinforcement Learning

Deep reinforcement learning excels in numerous large-scale practical applications. However, existing performance analyses ignores the unique characteristics of continuous-time control problems, is unable to directly estimate the generalization error of the Bellman optimal loss and require a boundedness assumption. Our work focuses on continuous-time control problems and proposes a method that is applicable to all such problems where the transition function satisfies semi-group and Lipschitz properties. Under this method, we can directly analyze the \emph{a priori} generalization error of the Bellman optimal loss. The core of this method lies in two transformations of the loss function. To complete the transformation, we propose a decomposition method for the maximum operator. Additionally, this analysis method does not require a boundedness assumption. Finally, we obtain an \emph{a priori} generalization error without the curse of dimensionality.

cs.LG↗

arXiv2024

On the dynamics of three-layer neural networks: initial condensation

Empirical and theoretical works show that the input weights of two-layer neural networks, when initialized with small values, converge towards isolated orientations. This phenomenon, referred to as condensation, indicates that the gradient descent methods tend to spontaneously reduce the complexity of neural networks during the training process. In this work, we elucidate the mechanisms behind the condensation phenomena occurring in the training of three-layer neural networks and distinguish it from the training of two-layer neural networks. Through rigorous theoretical analysis, we establish the blow-up property of effective dynamics and present a sufficient condition for the occurrence of condensation, findings that are substantiated by experimental results. Additionally, we explore the association between condensation and the low-rank bias observed in deep matrix factorization.

cs.LG↗

arXiv2024

Importance-Aware Image Segmentation-based Semantic Communication for Autonomous Driving

This article studies the problem of image segmentation-based semantic communication in autonomous driving. In real traffic scenes, detecting the key objects (e.g., vehicles, pedestrians and obstacles) is more crucial than that of other objects to guarantee driving safety. Therefore, we propose a vehicular image segmentation-oriented semantic communication system, termed VIS-SemCom, where image segmentation features of important objects are transmitted to reduce transmission redundancy. First, to accurately extract image semantics, we develop a semantic codec based on Swin Transformer architecture, which expands the perceptual field thus improving the segmentation accuracy. Next, we propose a multi-scale semantic extraction scheme via assigning the number of Swin Transformer blocks for diverse resolution features, thus highlighting the important objects' accuracy. Furthermore, the importance-aware loss is invoked to emphasize the important objects, and an online hard sample mining (OHEM) strategy is proposed to handle small sample issues in the dataset. Experimental results demonstrate that the proposed VIS-SemCom can achieve a coding gain of nearly 6 dB with a 60% mean intersection over union (mIoU), reduce the transmitted data amount by up to 70% with a 60% mIoU, and improve the segmentation intersection over union (IoU) of important objects by 4%, compared to traditional transmission scheme.

cs.NI↗

arXiv2023

On Residual Minimization for PDEs: Failure of PINN, Modified Equation, and Implicit Bias

As a popular and easy-to-implement machine learning method for solving differential equations, the physics-informed neural network (PINN) sometimes may fail and find poor solutions which bias against the exact ones. In this paper, we establish a framework of modified equation to explain the failure phenomenon and characterize the implicit bias of a general residual minimization (RM) method. We provide a simple way to derive the modified equation which models the numerical solution obtained by RM methods. Next, we show the modified solution deviates from the original exact solution. The proof uses a by-product of this paper, that is, a necessary and sufficient condition on characterizing the singularity of the coefficients. This equivalent condition can be extended to other types of equations in the future. Finally, we prove, as a complete characterization of the implicit bias, that RM method implicitly biases the numerical solution against the exact solution and towards a modified solution. In this work, we focus on elliptic equations with discontinuous coefficients, but our approach can be extended to other types of equations and our understanding of the implicit bias may shed light on further development of deep learning based methods for solving equations.

math.AP↗

arXiv2023

VQA4CIR: Boosting Composed Image Retrieval with Visual Question Answering

Albeit progress has been made in Composed Image Retrieval (CIR), we empirically find that a certain percentage of failure retrieval results are not consistent with their relative captions. To address this issue, this work provides a Visual Question Answering (VQA) perspective to boost the performance of CIR. The resulting VQA4CIR is a post-processing approach and can be directly plugged into existing CIR methods. Given the top-C retrieved images by a CIR method, VQA4CIR aims to decrease the adverse effect of the failure retrieval results being inconsistent with the relative caption. To find the retrieved images inconsistent with the relative caption, we resort to the "QA generation to VQA" self-verification pipeline. For QA generation, we suggest fine-tuning LLM (e.g., LLaMA) to generate several pairs of questions and answers from each relative caption. We then fine-tune LVLM (e.g., LLaVA) to obtain the VQA model. By feeding the retrieved image and question to the VQA model, one can find the images inconsistent with relative caption when the answer by VQA is inconsistent with the answer in the QA pair. Consequently, the CIR performance can be boosted by modifying the ranks of inconsistently retrieved images. Experimental results show that our proposed method outperforms state-of-the-art CIR methods on the CIRR and Fashion-IQ datasets.

cs.CV↗

arXiv2023

Ultra-Long Sequence Distributed Transformer

Transformer models trained on long sequences often achieve higher accuracy than short sequences. Unfortunately, conventional transformers struggle with long sequence training due to the overwhelming computation and memory requirements. Existing methods for long sequence training offer limited speedup and memory reduction, and may compromise accuracy. This paper presents a novel and efficient distributed training method, the Long Short-Sequence Transformer (LSS Transformer), for training transformer with long sequences. It distributes a long sequence into segments among GPUs, with each GPU computing a partial self-attention for its segment. Then, it uses a fused communication and a novel double gradient averaging technique to avoid the need to aggregate partial self-attention and minimize communication overhead. We evaluated the performance between LSS Transformer and the state-of-the-art Nvidia sequence parallelism on a Wikipedia enwik8 dataset. Results show that our proposed method lead to 5.6x faster and 10.2x more memory-efficient implementation compared to state-of-the-art sequence parallelism on 144 Nvidia V100 GPUs. Moreover, our algorithm scales to an extreme sequence length of 50,112 at 3,456 GPUs, achieving 161% super-linear parallel efficiency and a throughput of 32 petaflops.

cs.DC↗

arXiv2023

Efficient Spiking Neural Networks with Radix Encoding

Spiking neural networks (SNNs) have advantages in latency and energy efficiency over traditional artificial neural networks (ANNs) due to its event-driven computation mechanism and replacement of energy-consuming weight multiplications with additions. However, in order to reach accuracy of its ANN counterpart, it usually requires long spike trains to ensure the accuracy. Traditionally, a spike train needs around one thousand time steps to approach similar accuracy as its ANN counterpart. This offsets the computation efficiency brought by SNNs because longer spike trains mean a larger number of operations and longer latency. In this paper, we propose a radix encoded SNN with ultra-short spike trains. In the new model, the spike train takes less than ten time steps. Experiments show that our method demonstrates 25X speedup and 1.1% increment on accuracy, compared with the state-of-the-art work on VGG-16 network architecture and CIFAR-10 dataset.

cs.NE↗

arXiv2023

On the Free Boundary Problems of 3-D Compressible Euler Equations Coupled or Uncoupled With a Nonlinear Poisson Equation

For the problem of the non-isentropic compressible Euler Equations coupled with a nonlinear Poisson equation with the electric potential satisfying the Dirichlet boundary condition in three spatial dimensions with a general free boundary not restricting to a graph, we identify suitable stability conditions on the electric potential and the pressure under which we obtain a priori estimates on the Sobolev norms of the fluid and electric variables and bounds for geometric quantities of free surface. The stability conditions in this case for a general variable entropy are that the outer normal derivative of the electric potential is positive on the free surface, whereas that on the pressure is negative. In the isentropic case, the stability condition reduces to a single one, the outer normal derivative of the difference of the enthalpy and the electric potential is negative on the free surface. For the free boundary problem of the non-isentropic compressible Euler equations with variable entropy without coupling with the nonlinear Poisson equation, the corresponding higher-order estimates are also obtained under the Taylor sign condition. It is also found that one less derivative is needed to close the energy estimates for the problem for the non-isentropic compressible Euler Equations coupled with a nonlinear Poisson equation when the electric potential satisfies the Dirichlet boundary condition under the stability conditions on the electric potential and the pressure, compared with the problem of the non-isentropic compressible Euler equations.

math.AP↗

arXiv2023

Numerical Stability for Differential Equations with Memory

In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some sufficient conditions for the stability and convergence of some common multi-step methods, and accordingly, a notion of A-stability for differential equations with memory. Finally, we carry out the computational performance of our theory through numerical examples.

math.NA↗