Liangming Chen

Liangming Chen, Long Jin, Mingsheng Shang

The question of what kind of convolutional neural network (CNN) structure performs well is fascinating. In this work, we move toward the answer with one more step by connecting zero stability and model performance. Specifically, we found that if a discrete solver of an ordinary differential equation is zero stable, the CNN corresponding to that solver performs well. We first give the interpretation of zero stability in the context of deep learning and then investigate the performance of existing first- and second-order CNNs under different zero-stable circumstances. Based on the preliminary observation, we provide a higher-order discretization to construct CNNs and then propose a zero-stable network (ZeroSNet). To guarantee zero stability of the ZeroSNet, we first deduce a structure that meets consistency conditions and then give a zero stable region of a training-free parameter. By analyzing the roots of a characteristic equation, we theoretically obtain the optimal coefficients of feature maps. Empirically, we present our results from three aspects: We provide extensive empirical evidence of different depth on different datasets to show that the moduli of the characteristic equation's roots are the keys for the performance of CNNs that require historical features; Our experiments show that ZeroSNet outperforms existing CNNs which is based on high-order discretization; ZeroSNets show better robustness against noises on the input. The source code is available at \url{https://github.com/LongJin-lab/ZeroSNet}.

Tao Shi, Liangming Chen, Long Jin et al.

In the training of neural networks, adaptive moment estimation (Adam) typically converges fast but exhibits suboptimal generalization performance. A widely accepted explanation for its defect in generalization is that it often tends to converge to sharp minima. To enhance its ability to find flat minima, we propose its new variant named inverse Adam (InvAdam). The key improvement of InvAdam lies in its parameter update mechanism, which is opposite to that of Adam. Specifically, it computes element-wise multiplication of the first-order and second-order moments, while Adam computes the element-wise division of these two moments. This modification aims to increase the step size of the parameter update when the elements in the second-order moments are large and vice versa, which helps the parameter escape sharp minima and stay at flat ones. However, InvAdam's update mechanism may face challenges in convergence. To address this challenge, we propose dual Adam (DualAdam), which integrates the update mechanisms of both Adam and InvAdam, ensuring convergence while enhancing generalization performance. Additionally, we introduce the diffusion theory to mathematically demonstrate InvAdam's ability to escape sharp minima. Extensive experiments are conducted on image classification tasks and large language model (LLM) fine-tuning. The results validate that DualAdam outperforms Adam and its state-of-the-art variants in terms of generalization performance. The code is publicly available at https://github.com/LongJin-lab/DualAdam.

Mei Liu, Liangming Chen, Xiaohao Du et al.

Deep neural networks often suffer from poor performance or even training failure due to the ill-conditioned problem, the vanishing/exploding gradient problem, and the saddle point problem. In this paper, a novel method by acting the gradient activation function (GAF) on the gradient is proposed to handle these challenges. Intuitively, the GAF enlarges the tiny gradients and restricts the large gradient. Theoretically, this paper gives conditions that the GAF needs to meet, and on this basis, proves that the GAF alleviates the problems mentioned above. In addition, this paper proves that the convergence rate of SGD with the GAF is faster than that without the GAF under some assumptions. Furthermore, experiments on CIFAR, ImageNet, and PASCAL visual object classes confirm the GAF's effectiveness. The experimental results also demonstrate that the proposed method is able to be adopted in various deep neural networks to improve their performance. The source code is publicly available at https://github.com/LongJin-lab/Activated-Gradients-for-Deep-Neural-Networks.

Liangming Chen, Long Jin, Xiujuan Du et al.

In deep learning, it is usually assumed that the optimization process is conducted on a shape-fixed loss surface. Differently, we first propose a novel concept of deformation mapping in this paper to affect the behaviour of the optimizer. Vertical deformation mapping (VDM), as a type of deformation mapping, can make the optimizer enter a flat region, which often implies better generalization performance. Moreover, we design various VDMs, and further provide their contributions to the loss surface. After defining the local M region, theoretical analyses show that deforming the loss surface can enhance the gradient descent optimizer's ability to filter out sharp minima. With visualizations of loss landscapes, we evaluate the flatnesses of minima obtained by both the original optimizer and optimizers enhanced by VDMs on CIFAR-100. The experimental results show that VDMs do find flatter regions. Moreover, we compare popular convolutional neural networks enhanced by VDMs with the corresponding original ones on ImageNet, CIFAR-10, and CIFAR-100. The results are surprising: there are significant improvements on all of the involved models equipped with VDMs. For example, the top-1 test accuracy of ResNet-20 on CIFAR-100 increases by 1.46%, with insignificant additional computational overhead.

Liangming Chen, Long Jin, Xiujuan Du et al.

In deep learning, it is usually assumed that the shape of the loss surface is fixed. Differently, a novel concept of deformation operator is first proposed in this paper to deform the loss surface, thereby improving the optimization. Deformation function, as a type of deformation operator, can improve the generalization performance. Moreover, various deformation functions are designed, and their contributions to the loss surface are further provided. Then, the original stochastic gradient descent optimizer is theoretically proved to be a flat minima filter that owns the talent to filter out the sharp minima. Furthermore, the flatter minima could be obtained by exploiting the proposed deformation functions, which is verified on CIFAR-100, with visualizations of loss landscapes near the critical points obtained by both the original optimizer and optimizer enhanced by deformation functions. The experimental results show that deformation functions do find flatter regions. Moreover, on ImageNet, CIFAR-10, and CIFAR-100, popular convolutional neural networks enhanced by deformation functions are compared with the corresponding original models, where significant improvements are observed on all of the involved models equipped with deformation functions. For example, the top-1 test accuracy of ResNet-20 on CIFAR-100 increases by 1.46%, with insignificant additional computational overhead.