Distributed Learning over Unreliable Networks

Most of today's distributed machine learning systems assume {\em reliable networks}: whenever two machines exchange information (e.g., gradients or models), the network should guarantee the delivery of the message. At the same time, recent work exhibits the impressive tolerance of machine learning algorithms to errors or noise arising from relaxed communication or synchronization. In this paper, we connect these two trends, and consider the following question: {\em Can we design machine learning systems that are tolerant to network unreliability during training?} With this motivation, we focus on a theoretical problem of independent interest---given a standard distributed parameter server architecture, if every communication between the worker and the server has a non-zero probability $p$ of being dropped, does there exist an algorithm that still converges, and at what speed? In the context of prior art, this problem can be phrased as {\em distributed learning over random topologies}. The technical contribution of this paper is a novel theoretical analysis proving that distributed learning over random topologies can achieve comparable convergence rate to centralized or distributed learning over reliable networks. Further, we prove that the influence of the packet drop rate diminishes with the growth of the number of \textcolor{black}{parameter servers}. We map this theoretical result onto a real-world scenario, training deep neural networks over an unreliable network layer, and conduct network simulation to validate the system improvement by allowing the networks to be unreliable.

Communication Compression for Decentralized Training

Optimizing distributed learning systems is an art of balancing between computation and communication. There have been two lines of research that try to deal with slower networks: {\em communication compression} for low bandwidth networks, and {\em decentralization} for high latency networks. In this paper, We explore a natural question: {\em can the combination of both techniques lead to a system that is robust to both bandwidth and latency?} Although the system implication of such combination is trivial, the underlying theoretical principle and algorithm design is challenging: unlike centralized algorithms, simply compressing exchanged information, even in an unbiased stochastic way, within the decentralized network would accumulate the error and fail to converge. In this paper, we develop a framework of compressed, decentralized training and propose two different strategies, which we call {\em extrapolation compression} and {\em difference compression}. We analyze both algorithms and prove both converge at the rate of $O(1/\sqrt{nT})$ where $n$ is the number of workers and $T$ is the number of iterations, matching the convergence rate for full precision, centralized training. We validate our algorithms and find that our proposed algorithm outperforms the best of merely decentralized and merely quantized algorithm significantly for networks with {\em both} high latency and low bandwidth.

D$^2$: Decentralized Training over Decentralized Data

While training a machine learning model using multiple workers, each of which collects data from their own data sources, it would be most useful when the data collected from different workers can be {\em unique} and {\em different}. Ironically, recent analysis of decentralized parallel stochastic gradient descent (D-PSGD) relies on the assumption that the data hosted on different workers are {\em not too different}. In this paper, we ask the question: {\em Can we design a decentralized parallel stochastic gradient descent algorithm that is less sensitive to the data variance across workers?} In this paper, we present D$^2$, a novel decentralized parallel stochastic gradient descent algorithm designed for large data variance \xr{among workers} (imprecisely, "decentralized" data). The core of D$^2$ is a variance blackuction extension of the standard D-PSGD algorithm, which improves the convergence rate from $O\left({\sigma \over \sqrt{nT}} + {(n\zeta^2)^{\frac{1}{3}} \over T^{2/3}}\right)$ to $O\left({\sigma \over \sqrt{nT}}\right)$ where $\zeta^{2}$ denotes the variance among data on different workers. As a result, D$^2$ is robust to data variance among workers. We empirically evaluated D$^2$ on image classification tasks where each worker has access to only the data of a limited set of labels, and find that D$^2$ significantly outperforms D-PSGD.

Recurrent computations for visual pattern completion

Making inferences from partial information constitutes a critical aspect of cognition. During visual perception, pattern completion enables recognition of poorly visible or occluded objects. We combined psychophysics, physiology and computational models to test the hypothesis that pattern completion is implemented by recurrent computations and present three pieces of evidence that are consistent with this hypothesis. First, subjects robustly recognized objects even when rendered <15% visible, but recognition was largely impaired when processing was interrupted by backward masking. Second, invasive physiological responses along the human ventral cortex exhibited visually selective responses to partially visible objects that were delayed compared to whole objects, suggesting the need for additional computations. These physiological delays were correlated with the effects of backward masking. Third, state-of-the-art feed-forward computational architectures were not robust to partial visibility. However, recognition performance was recovered when the model was augmented with attractor-based recurrent connectivity. These results provide a strong argument of plausibility for the role of recurrent computations in making visual inferences from partial information.