Semantic Perturbations with Normalizing Flows for Improved Generalization

Data augmentation is a widely adopted technique for avoiding overfitting when training deep neural networks. However, this approach requires domain-specific knowledge and is often limited to a fixed set of hard-coded transformations. Recently, several works proposed to use generative models for generating semantically meaningful perturbations to train a classifier. However, because accurate encoding and decoding are critical, these methods, which use architectures that approximate the latent-variable inference, remained limited to pilot studies on small datasets. Exploiting the exactly reversible encoder-decoder structure of normalizing flows, we perform on-manifold perturbations in the latent space to define fully unsupervised data augmentations. We demonstrate that such perturbations match the performance of advanced data augmentation techniques -- reaching 96.6% test accuracy for CIFAR-10 using ResNet-18 and outperform existing methods, particularly in low data regimes -- yielding 10--25% relative improvement of test accuracy from classical training. We find that our latent adversarial perturbations adaptive to the classifier throughout its training are most effective, yielding the first test accuracy improvement results on real-world datasets -- CIFAR-10/100 -- via latent-space perturbations.

A Field Guide to Federated Optimization

Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.

Simultaneous Training of Partially Masked Neural Networks

For deploying deep learning models to lower end devices, it is necessary to train less resource-demanding variants of state-of-the-art architectures. This does not eliminate the need for more expensive models as they have a higher performance. In order to avoid training two separate models, we show that it is possible to train neural networks in such a way that a predefined 'core' subnetwork can be split-off from the trained full network with remarkable good performance. We extend on prior methods that focused only on core networks of smaller width, while we focus on supporting arbitrary core network architectures. Our proposed training scheme switches consecutively between optimizing only the core part of the network and the full one. The accuracy of the full model remains comparable, while the core network achieves better performance than when it is trained in isolation. In particular, we show that training a Transformer with a low-rank core gives a low-rank model with superior performance than when training the low-rank model alone. We analyze our training scheme theoretically, and show its convergence under assumptions that are either standard or practically justified. Moreover, we show that the developed theoretical framework allows analyzing many other partial training schemes for neural networks.

Critical Parameters for Scalable Distributed Learning with Large Batches and Asynchronous Updates

It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and -- in asynchronous implementations -- on the gradient staleness. Especially, it has been observed that the speedup saturates beyond a certain batch size and/or when the delays grow too large. We identify a data-dependent parameter that explains the speedup saturation in both these settings. Our comprehensive theoretical analysis, for strongly convex, convex and non-convex settings, unifies and generalized prior work directions that often focused on only one of these two aspects. In particular, our approach allows us to derive improved speedup results under frequently considered sparsity assumptions. Our insights give rise to theoretically based guidelines on how the learning rates can be adjusted in practice. We show that our results are tight and illustrate key findings in numerical experiments.

Consensus Control for Decentralized Deep Learning

Decentralized training of deep learning models enables on-device learning over networks, as well as efficient scaling to large compute clusters. Experiments in earlier works reveal that, even in a data-center setup, decentralized training often suffers from the degradation in the quality of the model: the training and test performance of models trained in a decentralized fashion is in general worse than that of models trained in a centralized fashion, and this performance drop is impacted by parameters such as network size, communication topology and data partitioning. We identify the changing consensus distance between devices as a key parameter to explain the gap between centralized and decentralized training. We show in theory that when the training consensus distance is lower than a critical quantity, decentralized training converges as fast as the centralized counterpart. We empirically validate that the relation between generalization performance and consensus distance is consistent with this theoretical observation. Our empirical insights allow the principled design of better decentralized training schemes that mitigate the performance drop. To this end, we propose practical training guidelines for the data-center setup as the important first step.

Quasi-Global Momentum: Accelerating Decentralized Deep Learning on Heterogeneous Data

Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks. In realistic learning scenarios, the presence of heterogeneity across different clients' local datasets poses an optimization challenge and may severely deteriorate the generalization performance. In this paper, we investigate and identify the limitation of several decentralized optimization algorithms for different degrees of data heterogeneity. We propose a novel momentum-based method to mitigate this decentralized training difficulty. We show in extensive empirical experiments on various CV/NLP datasets (CIFAR-10, ImageNet, AG News, and SST2) and several network topologies (Ring and Social Network) that our method is much more robust to the heterogeneity of clients' data than other existing methods, by a significant improvement in test performance ($1\% \!-\! 20\%$).

A Linearly Convergent Algorithm for Decentralized Optimization: Sending Less Bits for Free!

Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the entire system. We propose a new randomized first-order method which tackles the communication bottleneck by applying randomized compression operators to the communicated messages. By combining our scheme with a new variance reduction technique that progressively throughout the iterations reduces the adverse effect of the injected quantization noise, we obtain the first scheme that converges linearly on strongly convex decentralized problems while using compressed communication only. We prove that our method can solve the problems without any increase in the number of communications compared to the baseline which does not perform any communication compression while still allowing for a significant compression factor which depends on the conditioning of the problem and the topology of the network. Our key theoretical findings are supported by numerical experiments.

On Communication Compression for Distributed Optimization on Heterogeneous Data

Lossy gradient compression, with either unbiased or biased compressors, has become a key tool to avoid the communication bottleneck in centrally coordinated distributed training of machine learning models. We analyze the performance of two standard and general types of methods: (i) distributed quantized SGD (D-QSGD) with arbitrary unbiased quantizers and (ii) distributed SGD with error-feedback and biased compressors (D-EF-SGD) in the heterogeneous (non-iid) data setting. Our results indicate that D-EF-SGD is much less affected than D-QSGD by non-iid data, but both methods can suffer a slowdown if data-skewness is high. We propose two alternatives that are not (or much less) affected by heterogenous data distributions: a new method that is only applicable to strongly convex problems, and we point out a more general approach that is applicable to linear compressors.

Mime: Mimicking Centralized Stochastic Algorithms in Federated Learning

Federated learning is a challenging optimization problem due to the heterogeneity of the data across different clients. Such heterogeneity has been observed to induce client drift and significantly degrade the performance of algorithms designed for this setting. In contrast, centralized learning with centrally collected data does not experience such drift, and has seen great empirical and theoretical progress with innovations such as momentum, adaptivity, etc. In this work, we propose a general framework Mime which mitigates client-drift and adapts arbitrary centralized optimization algorithms (e.g.\ SGD, Adam, etc.) to federated learning. Mime uses a combination of control-variates and server-level statistics (e.g. momentum) at every client-update step to ensure that each local update mimics that of the centralized method. Our thorough theoretical and empirical analyses strongly establish Mime's superiority over other baselines.

Analysis of SGD with Biased Gradient Estimators

We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates under the Polyak-Lojasiewicz condition. We quantify how the magnitude of the bias impacts the attainable accuracy and convergence rates. Our framework covers many applications where either only biased gradient updates are available or preferred over unbiased ones for performance reasons. For instance, in the domain of distributed learning, biased gradient compression techniques such as top-k compression have been proposed as a tool to alleviate the communication bottleneck and in derivative-free optimization, only biased gradient estimators can be queried. We discuss a few guiding examples that show the broad applicability of our analysis.