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 $\kappa$ surpasses a certain threshold. This regime, characterized as the theta-lazy area, accentuates the predominant influence of the initial scale $\kappa$ 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 $\lim_{m\to\infty}\frac{\log \kappa}{\log m}=\frac{1}{2}$, 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 $\lim_{m\to\infty}\frac{\log \kappa}{\log m}>0$. 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 $\kappa$ in governing the training dynamics of neural networks.

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.

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.

A prior 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.

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.

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.

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.

Structure and Gradient Dynamics Near Global Minima of Two-layer Neural Networks

Under mild assumptions, we investigate the structure of loss landscape of two-layer neural networks near global minima, determine the set of parameters which give perfect generalization, and fully characterize the gradient flows around it. With novel techniques, our work uncovers some simple aspects of the complicated loss landscape and reveals how model, target function, samples and initialization affect the training dynamics differently. Based on these results, we also explain why (overparametrized) neural networks could generalize well.

Exploring Winograd Convolution for Cost-effective Neural Network Fault Tolerance

Winograd is generally utilized to optimize convolution performance and computational efficiency because of the reduced multiplication operations, but the reliability issues brought by winograd are usually overlooked. In this work, we observe the great potential of winograd convolution in improving neural network (NN) fault tolerance. Based on the observation, we evaluate winograd convolution fault tolerance comprehensively from different granularities ranging from models, layers, and operation types for the first time. Then, we explore the use of inherent fault tolerance of winograd convolution for cost-effective NN protection against soft errors. Specifically, we mainly investigate how winograd convolution can be effectively incorporated with classical fault-tolerant design approaches including triple modular redundancy (TMR), fault-aware retraining, and constrained activation functions. According to our experiments, winograd convolution can reduce the fault-tolerant design overhead by 55.77\% on average without any accuracy loss compared to standard convolution, and further reduce the computing overhead by 17.24\% when the inherent fault tolerance of winograd convolution is considered. When it is applied on fault-tolerant neural networks enhanced with fault-aware retraining and constrained activation functions, the resulting model accuracy generally shows significant improvement in presence of various faults.