Optimistic Estimate Uncovers the Potential of Nonlinear Models

We propose an optimistic estimate to evaluate the best possible fitting performance of nonlinear models. It yields an optimistic sample size that quantifies the smallest possible sample size to fit/recover a target function using a nonlinear model. We estimate the optimistic sample sizes for matrix factorization models, deep models, and deep neural networks (DNNs) with fully-connected or convolutional architecture. For each nonlinear model, our estimates predict a specific subset of targets that can be fitted at overparameterization, which are confirmed by our experiments. Our optimistic estimate reveals two special properties of the DNN models -- free expressiveness in width and costly expressiveness in connection. These properties suggest the following architecture design principles of DNNs: (i) feel free to add neurons/kernels; (ii) restrain from connecting neurons. Overall, our optimistic estimate theoretically unveils the vast potential of nonlinear models in fitting at overparameterization. Based on this framework, we anticipate gaining a deeper understanding of how and why numerous nonlinear models such as DNNs can effectively realize their potential in practice in the near future.

Stochastic Modified Equations and Dynamics of Dropout Algorithm

Dropout is a widely utilized regularization technique in the training of neural networks, nevertheless, its underlying mechanism and its impact on achieving good generalization abilities remain poorly understood. In this work, we derive the stochastic modified equations for analyzing the dynamics of dropout, where its discrete iteration process is approximated by a class of stochastic differential equations. In order to investigate the underlying mechanism by which dropout facilitates the identification of flatter minima, we study the noise structure of the derived stochastic modified equation for dropout. By drawing upon the structural resemblance between the Hessian and covariance through several intuitive approximations, we empirically demonstrate the universal presence of the inverse variance-flatness relation and the Hessian-variance relation, throughout the training process of dropout. These theoretical and empirical findings make a substantial contribution to our understanding of the inherent tendency of dropout to locate flatter minima.

DeepFire2: A Convolutional Spiking Neural Network Accelerator on FPGAs

Brain-inspired spiking neural networks (SNNs) replace the multiply-accumulate operations of traditional neural networks by integrate-and-fire neurons, with the goal of achieving greater energy efficiency. Specialized hardware implementations of those neurons clearly have advantages over general-purpose devices in terms of power and performance, but exhibit poor scalability when it comes to accelerating large neural networks. DeepFire2 introduces a hardware architecture which can map large network layers efficiently across multiple super logic regions in a multi-die FPGA. That gives more control over resource allocation and parallelism, benefiting both throughput and energy consumption. Avoiding the use of lookup tables to implement the AND operations of an SNN, prevents the layer size to be limited by logic resources. A deep pipeline does not only lead to an increased clock speed of up to 600 MHz. We double the throughput and power efficiency compared to our previous version of DeepFire, which equates to an almost 10-fold improvement over other previous implementations. Importantly, we are able to deploy a large ImageNet model, while maintaining a throughput of over 1500 frames per second.

Hierarchical Weight Averaging for Deep Neural Networks

Despite the simplicity, stochastic gradient descent (SGD)-like algorithms are successful in training deep neural networks (DNNs). Among various attempts to improve SGD, weight averaging (WA), which averages the weights of multiple models, has recently received much attention in the literature. Broadly, WA falls into two categories: 1) online WA, which averages the weights of multiple models trained in parallel, is designed for reducing the gradient communication overhead of parallel mini-batch SGD, and 2) offline WA, which averages the weights of one model at different checkpoints, is typically used to improve the generalization ability of DNNs. Though online and offline WA are similar in form, they are seldom associated with each other. Besides, these methods typically perform either offline parameter averaging or online parameter averaging, but not both. In this work, we firstly attempt to incorporate online and offline WA into a general training framework termed Hierarchical Weight Averaging (HWA). By leveraging both the online and offline averaging manners, HWA is able to achieve both faster convergence speed and superior generalization performance without any fancy learning rate adjustment. Besides, we also analyze the issues faced by existing WA methods, and how our HWA address them, empirically. Finally, extensive experiments verify that HWA outperforms the state-of-the-art methods significantly.

Phase Diagram of Initial Condensation for Two-layer Neural Networks

The phenomenon of distinct behaviors exhibited by neural networks under varying scales of initialization remains an enigma in deep learning research. In this paper, based on the earlier work by Luo et al.~\cite{luo2021phase}, we present a phase diagram of initial condensation for two-layer neural networks. Condensation is a phenomenon wherein the weight vectors of neural networks concentrate on isolated orientations during the training process, and it is a feature in non-linear learning process that enables neural networks to possess better generalization abilities. Our phase diagram serves to provide a comprehensive understanding of the dynamical regimes of neural networks and their dependence on the choice of hyperparameters related to initialization. Furthermore, we demonstrate in detail the underlying mechanisms by which small initialization leads to condensation at the initial training stage.

Optimization of Image Transmission in a Cooperative Semantic Communication Networks

In this paper, a semantic communication framework for image transmission is developed. In the investigated framework, a set of servers cooperatively transmit images to a set of users utilizing semantic communication techniques. To evaluate the performance of studied semantic communication system, a multimodal metric is proposed to measure the correlation between the extracted semantic information and the original image. To meet the ISS requirement of each user, each server must jointly determine the semantic information to be transmitted and the resource blocks (RBs) used for semantic information transmission. We formulate this problem as an optimization problem aiming to minimize each server's transmission latency while reaching the ISS requirement. To solve this problem, a value decomposition based entropy-maximized multi-agent reinforcement learning (RL) is proposed, which enables servers to coordinate for training and execute RB allocation in a distributed manner to approach to a globally optimal performance with less training iterations. Compared to traditional multi-agent RL, the proposed RL improves the valuable action exploration of servers and the probability of finding a globally optimal RB allocation policy based on local observation. Simulation results show that the proposed algorithm can reduce the transmission delay by up to 16.1% compared to traditional multi-agent RL.

Linear Stability Hypothesis and Rank Stratification for Nonlinear Models

Models with nonlinear architectures/parameterizations such as deep neural networks (DNNs) are well known for their mysteriously good generalization performance at overparameterization. In this work, we tackle this mystery from a novel perspective focusing on the transition of the target recovery/fitting accuracy as a function of the training data size. We propose a rank stratification for general nonlinear models to uncover a model rank as an "effective size of parameters" for each function in the function space of the corresponding model. Moreover, we establish a linear stability theory proving that a target function almost surely becomes linearly stable when the training data size equals its model rank. Supported by our experiments, we propose a linear stability hypothesis that linearly stable functions are preferred by nonlinear training. By these results, model rank of a target function predicts a minimal training data size for its successful recovery. Specifically for the matrix factorization model and DNNs of fully-connected or convolutional architectures, our rank stratification shows that the model rank for specific target functions can be much lower than the size of model parameters. This result predicts the target recovery capability even at heavy overparameterization for these nonlinear models as demonstrated quantitatively by our experiments. Overall, our work provides a unified framework with quantitative prediction power to understand the mysterious target recovery behavior at overparameterization for general nonlinear models.

Desire Backpropagation: A Lightweight Training Algorithm for Multi-Layer Spiking Neural Networks based on Spike-Timing-Dependent Plasticity

Spiking neural networks (SNN) are a viable alternative to conventional artificial neural networks when energy efficiency and computational complexity are of importance. A major advantage of SNNs is their binary information transfer through spike trains. The training of SNN has, however, been a challenge, since neuron models are non-differentiable and traditional gradient-based backpropagation algorithms cannot be applied directly. Furthermore, spike-timing-dependent plasticity (STDP), albeit being a spike-based learning rule, updates weights locally and does not optimize for the output error of the network. We present desire backpropagation, a method to derive the desired spike activity of neurons from the output error. The loss function can then be evaluated locally for every neuron. Incorporating the desire values into the STDP weight update leads to global error minimization and increasing classification accuracy. At the same time, the neuron dynamics and computational efficiency of STDP are maintained, making it a spike-based supervised learning rule. We trained three-layer networks to classify MNIST and Fashion-MNIST images and reached an accuracy of 98.41% and 87.56%, respectively. Furthermore, we show that desire backpropagation is computationally less complex than backpropagation in traditional neural networks.

Beyond Codebook-Based Analog Beamforming at mmWave: Compressed Sensing and Machine Learning Methods

Analog beamforming is the predominant approach for millimeter wave (mmWave) communication given its favorable characteristics for limited-resource devices. In this work, we aim at reducing the spectral efficiency gap between analog and digital beamforming methods. We propose a method for refined beam selection based on the estimated raw channel. The channel estimation, an underdetermined problem, is solved using compressed sensing (CS) methods leveraging angular domain sparsity of the channel. To reduce the complexity of CS methods, we propose dictionary learning iterative soft-thresholding algorithm, which jointly learns the sparsifying dictionary and signal reconstruction. We evaluate the proposed method on a realistic mmWave setup and show considerable performance improvement with respect to code-book based analog beamforming approaches.

Statistical Modeling of Soft Error Influence on Neural Networks

Soft errors in large VLSI circuits pose dramatic influence on computing- and memory-intensive neural network (NN) processing. Understanding the influence of soft errors on NNs is critical to protect against soft errors for reliable NN processing. Prior work mainly rely on fault simulation to analyze the influence of soft errors on NN processing. They are accurate but usually specific to limited configurations of errors and NN models due to the prohibitively slow simulation speed especially for large NN models and datasets. With the observation that the influence of soft errors propagates across a large number of neurons and accumulates as well, we propose to characterize the soft error induced data disturbance on each neuron with normal distribution model according to central limit theorem and develop a series of statistical models to analyze the behavior of NN models under soft errors in general. The statistical models reveal not only the correlation between soft errors and NN model accuracy, but also how NN parameters such as quantization and architecture affect the reliability of NNs. The proposed models are compared with fault simulation and verified comprehensively. In addition, we observe that the statistical models that characterize the soft error influence can also be utilized to predict fault simulation results in many cases and we explore the use of the proposed statistical models to accelerate fault simulations of NNs. According to our experiments, the accelerated fault simulation shows almost two orders of magnitude speedup with negligible simulation accuracy loss over the baseline fault simulations.