Deep convolutional neural networks are shown to be overkill with high parametric and computational redundancy in many application scenarios, and an increasing number of works have explored model pruning to obtain lightweight and efficient networks. However, most existing pruning approaches are driven by empirical heuristics and rarely consider the joint impact of channels, leading to unguaranteed and suboptimal performance. In this paper, we propose a novel channel pruning method via class-aware trace ratio optimization (CATRO) to reduce the computational burden and accelerate the model inference. Utilizing class information from a few samples, CATRO measures the joint impact of multiple channels by feature space discriminations and consolidates the layer-wise impact of preserved channels. By formulating channel pruning as a submodular set function maximization problem, CATRO solves it efficiently via a two-stage greedy iterative optimization procedure. More importantly, we present theoretical justifications on convergence and performance of CATRO. Experimental results demonstrate that CATRO achieves higher accuracy with similar computation cost or lower computation cost with similar accuracy than other state-of-the-art channel pruning algorithms. In addition, because of its class-aware property, CATRO is suitable to prune efficient networks adaptively for various classification subtasks, enhancing handy deployment and usage of deep networks in real-world applications.
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Filter pruning has been widely used for neural network compression because of its enabled practical acceleration. To date, most of the existing filter pruning works explore the importance of filters via using intra-channel information. In this paper, starting from an inter-channel perspective, we propose to perform efficient filter pruning using Channel Independence, a metric that measures the correlations among different feature maps. The less independent feature map is interpreted as containing less useful information$/$knowledge, and hence its corresponding filter can be pruned without affecting model capacity. We systematically investigate the quantification metric, measuring scheme and sensitiveness$/$reliability of channel independence in the context of filter pruning. Our evaluation results for different models on various datasets show the superior performance of our approach. Notably, on CIFAR-10 dataset our solution can bring $0.75\%$ and $0.94\%$ accuracy increase over baseline ResNet-56 and ResNet-110 models, respectively, and meanwhile the model size and FLOPs are reduced by $42.8\%$ and $47.4\%$ (for ResNet-56) and $48.3\%$ and $52.1\%$ (for ResNet-110), respectively. On ImageNet dataset, our approach can achieve $40.8\%$ and $44.8\%$ storage and computation reductions, respectively, with $0.15\%$ accuracy increase over the baseline ResNet-50 model. The code is available at //github.com/Eclipsess/CHIP_NeurIPS2021.
Optimization is often cast as a deterministic problem, where the solution is found through some iterative procedure such as gradient descent. However, when training neural networks the loss function changes over (iteration) time due to the randomized selection of a subset of the samples. This randomization turns the optimization problem into a stochastic one. We propose to consider the loss as a noisy observation with respect to some reference optimum. This interpretation of the loss allows us to adopt Kalman filtering as an optimizer, as its recursive formulation is designed to estimate unknown parameters from noisy measurements. Moreover, we show that the Kalman Filter dynamical model for the evolution of the unknown parameters can be used to capture the gradient dynamics of advanced methods such as Momentum and Adam. We call this stochastic optimization method KOALA, which is short for Kalman Optimization Algorithm with Loss Adaptivity. KOALA is an easy to implement, scalable, and efficient method to train neural networks. We provide convergence analysis and show experimentally that it yields parameter estimates that are on par with or better than existing state of the art optimization algorithms across several neural network architectures and machine learning tasks, such as computer vision and language modeling.
This paper presents an approach for trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The approach allows for the use of a broad class of model learning tools including deep neural networks to learn uncertain dynamics while still providing guarantees of transient tracking performance throughout the learning phase, including the special case of no learning. Within the proposed approach, a disturbance estimation law is proposed to estimate the pointwise value of the uncertainty, with pre-computable estimation error bounds (EEBs). The learned dynamics, the estimated disturbances, and the EEBs are then incorporated in a robust Riemannian energy condition to compute the control law that guarantees exponential convergence of actual trajectories to desired ones throughout the learning phase, even when the learned model is poor. On the other hand, with improved accuracy, the learned model can be incorporated in a high-level planner to plan better trajectories with improved performance, e.g., lower energy consumption and shorter travel time. The proposed framework is validated on a planar quadrotor navigation example.
Nonlinear parametric systems have been widely used in modeling nonlinear dynamics in science and engineering. Bifurcation analysis of these nonlinear systems on the parameter space are usually used to study the solution structure such as the number of solutions and the stability. In this paper, we develop a new machine learning approach to compute the bifurcations via so-called equation-driven neural networks (EDNNs). The EDNNs consist of a two-step optimization: the first step is to approximate the solution function of the parameter by training empirical solution data; the second step is to compute bifurcations by using the approximated neural network obtained in the first step. Both theoretical convergence analysis and numerical implementation on several examples have been performed to demonstrate the feasibility of the proposed method.
We present and analyze a momentum-based gradient method for training linear classifiers with an exponentially-tailed loss (e.g., the exponential or logistic loss), which maximizes the classification margin on separable data at a rate of $\widetilde{\mathcal{O}}(1/t^2)$. This contrasts with a rate of $\mathcal{O}(1/\log(t))$ for standard gradient descent, and $\mathcal{O}(1/t)$ for normalized gradient descent. This momentum-based method is derived via the convex dual of the maximum-margin problem, and specifically by applying Nesterov acceleration to this dual, which manages to result in a simple and intuitive method in the primal. This dual view can also be used to derive a stochastic variant, which performs adaptive non-uniform sampling via the dual variables.
There has been a surge of interest in continual learning and federated learning, both of which are important in deep neural networks in real-world scenarios. Yet little research has been done regarding the scenario where each client learns on a sequence of tasks from a private local data stream. This problem of federated continual learning poses new challenges to continual learning, such as utilizing knowledge from other clients, while preventing interference from irrelevant knowledge. To resolve these issues, we propose a novel federated continual learning framework, Federated Weighted Inter-client Transfer (FedWeIT), which decomposes the network weights into global federated parameters and sparse task-specific parameters, and each client receives selective knowledge from other clients by taking a weighted combination of their task-specific parameters. FedWeIT minimizes interference between incompatible tasks, and also allows positive knowledge transfer across clients during learning. We validate our \emph{FedWeIT}~against existing federated learning and continual learning methods under varying degrees of task similarity across clients, and our model significantly outperforms them with a large reduction in the communication cost.
In this work, we propose a generally applicable transformation unit for visual recognition with deep convolutional neural networks. This transformation explicitly models channel relationships with explainable control variables. These variables determine the neuron behaviors of competition or cooperation, and they are jointly optimized with the convolutional weight towards more accurate recognition. In Squeeze-and-Excitation (SE) Networks, the channel relationships are implicitly learned by fully connected layers, and the SE block is integrated at the block-level. We instead introduce a channel normalization layer to reduce the number of parameters and computational complexity. This lightweight layer incorporates a simple l2 normalization, enabling our transformation unit applicable to operator-level without much increase of additional parameters. Extensive experiments demonstrate the effectiveness of our unit with clear margins on many vision tasks, i.e., image classification on ImageNet, object detection and instance segmentation on COCO, video classification on Kinetics.
Training large deep neural networks on massive datasets is computationally very challenging. There has been recent surge in interest in using large batch stochastic optimization methods to tackle this issue. The most prominent algorithm in this line of research is LARS, which by employing layerwise adaptive learning rates trains ResNet on ImageNet in a few minutes. However, LARS performs poorly for attention models like BERT, indicating that its performance gains are not consistent across tasks. In this paper, we first study a principled layerwise adaptation strategy to accelerate training of deep neural networks using large mini-batches. Using this strategy, we develop a new layerwise adaptive large batch optimization technique called LAMB; we then provide convergence analysis of LAMB as well as LARS, showing convergence to a stationary point in general nonconvex settings. Our empirical results demonstrate the superior performance of LAMB across various tasks such as BERT and ResNet-50 training with very little hyperparameter tuning. In particular, for BERT training, our optimizer enables use of very large batch sizes of 32868 without any degradation of performance. By increasing the batch size to the memory limit of a TPUv3 Pod, BERT training time can be reduced from 3 days to just 76 minutes (Table 1).
We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activiation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for a broad family of loss functions, with proper random weight initialization, both gradient descent and stochastic gradient descent can find the global minima of the training loss for an over-parameterized deep ReLU network, under mild assumption on the training data. The key idea of our proof is that Gaussian random initialization followed by (stochastic) gradient descent produces a sequence of iterates that stay inside a small perturbation region centering around the initial weights, in which the empirical loss function of deep ReLU networks enjoys nice local curvature properties that ensure the global convergence of (stochastic) gradient descent. Our theoretical results shed light on understanding the optimization of deep learning, and pave the way to study the optimization dynamics of training modern deep neural networks.
Accelerated Randomized Coordinate Descent Algorithms for Stochastic Optimization and Online Learning
We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known randomized online coordinate descent algorithms. Furthermore, the proposed algorithms for stochastic optimization exhibit as good convergence rates as the best known randomized coordinate descent algorithms. We also show simulation results to demonstrate performance of the proposed algorithms.
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