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Decentralized optimization and communication compression have exhibited their great potential in accelerating distributed machine learning by mitigating the communication bottleneck in practice. While existing decentralized algorithms with communication compression mostly focus on the problems with only smooth components, we study the decentralized stochastic composite optimization problem with a potentially non-smooth component. A \underline{Prox}imal gradient \underline{L}in\underline{EA}r convergent \underline{D}ecentralized algorithm with compression, Prox-LEAD, is proposed with rigorous theoretical analyses in the general stochastic setting and the finite-sum setting. Our theorems indicate that Prox-LEAD works with arbitrary compression precision, and it tremendously reduces the communication cost almost for free. The superiorities of the proposed algorithms are demonstrated through the comparison with state-of-the-art algorithms in terms of convergence complexities and numerical experiments. Our algorithmic framework also generally enlightens the compressed communication on other primal-dual algorithms by reducing the impact of inexact iterations, which might be of independent interest.

Deep neural networks (DNNs) are effective in solving many real-world problems. Larger DNN models usually exhibit better quality (e.g., accuracy) but their excessive computation results in long inference time. Model sparsification can reduce the computation and memory cost while maintaining model quality. Most existing sparsification algorithms unidirectionally remove weights, while others randomly or greedily explore a small subset of weights in each layer for pruning. The limitations of these algorithms reduce the level of achievable sparsity. In addition, many algorithms still require pre-trained dense models and thus suffer from large memory footprint. In this paper, we propose a novel scheduled grow-and-prune (GaP) methodology without having to pre-train a dense model. It addresses the shortcomings of the previous works by repeatedly growing a subset of layers to dense and then pruning them back to sparse after some training. Experiments show that the models pruned using the proposed methods match or beat the quality of the highly optimized dense models at 80% sparsity on a variety of tasks, such as image classification, objective detection, 3D object part segmentation, and translation. They also outperform other state-of-the-art (SOTA) methods for model sparsification. As an example, a 90% non-uniform sparse ResNet-50 model obtained via GaP achieves 77.9% top-1 accuracy on ImageNet, improving the previous SOTA results by 1.5%. Code available at: https://github.com/boone891214/GaP., Comment: ICLR 2022 camera ready

Communication overhead hinders the scalability of large-scale distributed training. Gossip SGD, where each node averages only with its neighbors, is more communication-efficient than the prevalent parallel SGD. However, its convergence rate is reversely proportional to quantity $1-\beta$ which measures the network connectivity. On large and sparse networks where $1-\beta \to 0$, Gossip SGD requires more iterations to converge, which offsets against its communication benefit. This paper introduces Gossip-PGA, which adds Periodic Global Averaging into Gossip SGD. Its transient stage, i.e., the iterations required to reach asymptotic linear speedup stage, improves from $\Omega(\beta^4 n^3/(1-\beta)^4)$ to $\Omega(\beta^4 n^3 H^4)$ for non-convex problems. The influence of network topology in Gossip-PGA can be controlled by the averaging period $H$. Its transient-stage complexity is also superior to Local SGD which has order $\Omega(n^3 H^4)$. Empirical results of large-scale training on image classification (ResNet50) and language modeling (BERT) validate our theoretical findings., Comment: Accepted to ICML 2021

We consider the decentralized stochastic optimization problems, where a network of $n$ nodes, each owning a local cost function, cooperate to find a minimizer of the globally-averaged cost. A widely studied decentralized algorithm for this problem is decentralized SGD (D-SGD), in which each node averages only with its neighbors. D-SGD is efficient in single-iteration communication, but it is very sensitive to the network topology. For smooth objective functions, the transient stage (which measures the number of iterations the algorithm has to experience before achieving the linear speedup stage) of D-SGD is on the order of ${\Omega}(n/(1-\beta)^2)$ and $\Omega(n^3/(1-\beta)^4)$ for strongly and generally convex cost functions, respectively, where $1-\beta \in (0,1)$ is a topology-dependent quantity that approaches $0$ for a large and sparse network. Hence, D-SGD suffers from slow convergence for large and sparse networks. In this work, we study the non-asymptotic convergence property of the D$^2$/Exact-diffusion algorithm. By eliminating the influence of data heterogeneity between nodes, D$^2$/Exact-diffusion is shown to have an enhanced transient stage that is on the order of $\tilde{\Omega}(n/(1-\beta))$ and $\Omega(n^3/(1-\beta)^2)$ for strongly and generally convex cost functions, respectively. Moreover, when D$^2$/Exact-diffusion is implemented with gradient accumulation and multi-round gossip communications, its transient stage can be further improved to $\tilde{\Omega}(1/(1-\beta)^{\frac{1}{2}})$ and $\tilde{\Omega}(n/(1-\beta))$ for strongly and generally convex cost functions, respectively. These established results for D$^2$/Exact-Diffusion have the best (i.e., weakest) dependence on network topology to our knowledge compared to existing decentralized algorithms. We also conduct numerical simulations to validate our theories.

When applying a stochastic algorithm, one must choose an order to draw samples. The practical choices are without-replacement sampling orders, which are empirically faster and more cache-friendly than uniform-iid-sampling but often have inferior theoretical guarantees. Without-replacement sampling is well understood only for SGD without variance reduction. In this paper, we will improve the convergence analysis and rates of variance reduction under without-replacement sampling orders for composite finite-sum minimization. Our results are in two-folds. First, we develop a damped variant of Finito called Prox-DFinito and establish its convergence rates with random reshuffling, cyclic sampling, and shuffling-once, under both convex and strongly convex scenarios. These rates match full-batch gradient descent and are state-of-the-art compared to the existing results for without-replacement sampling with variance-reduction. Second, our analysis can gauge how the cyclic order will influence the rate of cyclic sampling and, thus, allows us to derive the optimal fixed ordering. In the highly data-heterogeneous scenario, Prox-DFinito with optimal cyclic sampling can attain a sample-size-independent convergence rate, which, to our knowledge, is the first result that can match with uniform-iid-sampling with variance reduction. We also propose a practical method to discover the optimal cyclic ordering numerically., Comment: Accepted by NeurIPS 2021

The scale of deep learning nowadays calls for efficient distributed training algorithms. Decentralized momentum SGD (DmSGD), in which each node averages only with its neighbors, is more communication efficient than vanilla Parallel momentum SGD that incurs global average across all computing nodes. On the other hand, the large-batch training has been demonstrated critical to achieve runtime speedup. This motivates us to investigate how DmSGD performs in the large-batch scenario. In this work, we find the momentum term can amplify the inconsistency bias in DmSGD. Such bias becomes more evident as batch-size grows large and hence results in severe performance degradation. We next propose DecentLaM, a novel decentralized large-batch momentum SGD to remove the momentum-incurred bias. The convergence rate for both non-convex and strongly-convex scenarios is established. Our theoretical results justify the superiority of DecentLaM to DmSGD especially in the large-batch scenario. Experimental results on a variety of computer vision tasks and models demonstrate that DecentLaM promises both efficient and high-quality training.

In this paper we propose a novel network adaption method called Differentiable Network Adaption (DNA), which can adapt an existing network to a specific computation budget by adjusting the width and depth in a differentiable manner. The gradient-based optimization allows DNA to achieve an automatic optimization of width and depth rather than previous heuristic methods that heavily rely on human priors. Moreover, we propose a new elastic search space that can flexibly condense or expand during the optimization process, allowing the network optimization of width and depth in a bi-direction manner. By DNA, we successfully achieve network architecture optimization by condensing and expanding in both width and depth dimensions. Extensive experiments on ImageNet demonstrate that DNA can adapt the existing network to meet different targeted computation requirements with better performance than previous methods. What's more, DNA can further improve the performance of high-accuracy networks obtained by state-of-the-art neural architecture search methods such as EfficientNet and MobileNet-v3.

Motivated by the success of Transformers in natural language processing (NLP) tasks, there emerge some attempts (e.g., ViT and DeiT) to apply Transformers to the vision domain. However, pure Transformer architectures often require a large amount of training data or extra supervision to obtain comparable performance with convolutional neural networks (CNNs). To overcome these limitations, we analyze the potential drawbacks when directly borrowing Transformer architectures from NLP. Then we propose a new \textbf{Convolution-enhanced image Transformer (CeiT)} which combines the advantages of CNNs in extracting low-level features, strengthening locality, and the advantages of Transformers in establishing long-range dependencies. Three modifications are made to the original Transformer: \textbf{1)} instead of the straightforward tokenization from raw input images, we design an \textbf{Image-to-Tokens (I2T)} module that extracts patches from generated low-level features; \textbf{2)} the feed-froward network in each encoder block is replaced with a \textbf{Locally-enhanced Feed-Forward (LeFF)} layer that promotes the correlation among neighboring tokens in the spatial dimension; \textbf{3)} a \textbf{Layer-wise Class token Attention (LCA)} is attached at the top of the Transformer that utilizes the multi-level representations. Experimental results on ImageNet and seven downstream tasks show the effectiveness and generalization ability of CeiT compared with previous Transformers and state-of-the-art CNNs, without requiring a large amount of training data and extra CNN teachers. Besides, CeiT models also demonstrate better convergence with $3\times$ fewer training iterations, which can reduce the training cost significantly\footnote{Code and models will be released upon acceptance.}.

Sparsity in Deep Neural Networks (DNNs) has been widely studied to compress and accelerate the models on resource-constrained environments. It can be generally categorized into unstructured fine-grained sparsity that zeroes out multiple individual weights distributed across the neural network, and structured coarse-grained sparsity which prunes blocks of sub-networks of a neural network. Fine-grained sparsity can achieve a high compression ratio but is not hardware friendly and hence receives limited speed gains. On the other hand, coarse-grained sparsity cannot concurrently achieve both apparent acceleration on modern GPUs and decent performance. In this paper, we are the first to study training from scratch an N:M fine-grained structured sparse network, which can maintain the advantages of both unstructured fine-grained sparsity and structured coarse-grained sparsity simultaneously on specifically designed GPUs. Specifically, a 2:4 sparse network could achieve 2x speed-up without performance drop on Nvidia A100 GPUs. Furthermore, we propose a novel and effective ingredient, sparse-refined straight-through estimator (SR-STE), to alleviate the negative influence of the approximated gradients computed by vanilla STE during optimization. We also define a metric, Sparse Architecture Divergence (SAD), to measure the sparse network's topology change during the training process. Finally, We justify SR-STE's advantages with SAD and demonstrate the effectiveness of SR-STE by performing comprehensive experiments on various tasks. Source codes and models are available at https://github.com/NM-sparsity/NM-sparsity., Comment: ICLR2021

One practice of employing deep neural networks is to apply the same architecture to all the input instances. However, a fixed architecture may not be representative enough for data with high diversity. To promote the model capacity, existing approaches usually employ larger convolutional kernels or deeper network structure, which may increase the computational cost. In this paper, we address this issue by raising the Dynamic Graph Network (DG-Net). The network learns the instance-aware connectivity, which creates different forward paths for different instances. Specifically, the network is initialized as a complete directed acyclic graph, where the nodes represent convolutional blocks and the edges represent the connection paths. We generate edge weights by a learnable module \textit{router} and select the edges whose weights are larger than a threshold, to adjust the connectivity of the neural network structure. Instead of using the same path of the network, DG-Net aggregates features dynamically in each node, which allows the network to have more representation ability. To facilitate the training, we represent the network connectivity of each sample in an adjacency matrix. The matrix is updated to aggregate features in the forward pass, cached in the memory, and used for gradient computing in the backward pass. We verify the effectiveness of our method with several static architectures, including MobileNetV2, ResNet, ResNeXt, and RegNet. Extensive experiments are performed on ImageNet classification and COCO object detection, which shows the effectiveness and generalization ability of our approach., Comment: 13 pages, 3 figures, 6 tables

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important. Previous principles of rule-based modular design simplify the difficulty of building an effective architecture, but constrain the possible topologies in limited spaces. In this paper, we attempt to optimize the connectivity in neural networks. We propose a topological perspective to represent a network into a complete graph for analysis, where nodes carry out aggregation and transformation of features, and edges determine the flow of information. By assigning learnable parameters to the edges which reflect the magnitude of connections, the learning process can be performed in a differentiable manner. We further attach auxiliary sparsity constraint to the distribution of connectedness, which promotes the learned topology focus on critical connections. This learning process is compatible with existing networks and owns adaptability to larger search spaces and different tasks. Quantitative results of experiments reflect the learned connectivity is superior to traditional rule-based ones, such as random, residual, and complete. In addition, it obtains significant improvements in image classification and object detection without introducing excessive computation burden., Comment: 17 pages, 5 figures, to be published in ECCV2020

In this paper, we consider the decentralized dynamic optimization problem defined over a multi-agent network. Each agent possesses a time-varying local objective function, and all agents aim to collaboratively track the drifting global optimal solution that minimizes the summation of all local objective functions. The decentralized dynamic optimization problem can be solved by primal or primal-dual methods, and when the problem degenerates to be static, it has been proved in literature that primal-dual methods are superior to primal ones. This motivates us to ask: are primal-dual methods necessarily better than primal ones in decentralized dynamic optimization? To answer this question, we investigate and compare convergence properties of the primal method, diffusion, and the primal-dual approach, decentralized gradient tracking (DGT). Theoretical analysis reveals that diffusion can outperform DGT in certain dynamic settings. We find that DGT and diffusion are significantly affected by the drifts and the magnitudes of optimal gradients, respectively. In addition, we show that DGT is more sensitive to the network topology, and a badly-connected network can greatly deteriorate its convergence performance. These conclusions provide guidelines on how to choose proper dynamic algorithms in various application scenarios. Numerical experiments are constructed to validate the theoretical analysis., Comment: Submitted for publication; 13 pages; 6 figures

The successful isolation of cyclo-C18 in the experiment means the ground-breaking epoch of carbon rings. Herein, we studied the thermodynamic stabilities of cyclo-Cn (4 $\leq$ n $\leq$ 34) with density functional theory. When n = 4N + 2 (N is integer), cyclo-Cn (10 $\leq$ n $\leq$ 34) were thermodynamically stable. Especially, cyclo-C10 and cyclo-C14 were thermodynamically, kinetically, dynamically, and optically preferred to cyclo-C18, and were the candidates of zero-dimension carbon rings. The carbon atoms were sp hybridization in cyclo-C10, cyclo-C14 and cyclo-C18. Cyclo-C14 and cyclo-C18 had alternating abnormal single and triple bonds, but cyclo-C10 had equal bonds. Cyclo-C10, cyclo-C14, and cyclo-C18 with large aromaticities had out-plane and in-plane pi systems, which were perpendicular to each other. The number of pi electrons in out-plane and in-plane pi systems followed the Huckel rule. Simulated UV-vis-NIR spectra indicated the similar electronic structures of cyclo-C14 and cyclo-C18., Comment: 23 pages, 6 figures, 1 table