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Added by
Haoyu Ma
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Lottery ticket hypothesis suggests that a dense neural network contains a sparse sub-network that can match the test accuracy of the original dense net when trained in isolation from (the same) random initialization. However, the hypothesis failed to generalize to larger dense networks such as ResNet-50. As a remedy, recent studies demonstrate that a sparse sub-network can still be obtained by using a rewinding technique, which is to re-train it from early-phase training weights or learning rates of the dense model, rather than from random initialization. Is rewinding the only or the best way to scale up lottery tickets? This paper proposes a new, simpler and yet powerful technique for re-training the sub-network, called Knowledge Distillation ticket (KD ticket). Rewinding exploits the value of inheriting knowledge from the early training phase to improve lottery tickets in large networks. In comparison, KD ticket addresses a complementary possibility - inheriting useful knowledge from the late training phase of the dense model. It is achieved by leveraging the soft labels generated by the trained dense model to re-train the sub-network, instead of the hard labels. Extensive experiments are conducted using several large deep networks (e.g ResNet-50 and ResNet-110) on CIFAR-10 and ImageNet datasets. Without bells and whistles, when applied by itself, KD ticket performs on par or better than rewinding, while being nearly free of hyperparameters or ad-hoc selection. KD ticket can be further applied together with rewinding, yielding state-of-the-art results for large-scale lottery tickets.
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We introduce a generalization to the lottery ticket hypothesis in which the notion of sparsity is relaxed by choosing an arbitrary basis in the space of parameters. We present evidence that the original results reported for the canonical basis continue to hold in this broader setting. We describe how structured pruning methods, including pruning units or factorizing fully-connected layers into products of low-rank matrices, can be cast as particular instances of this generalized lottery ticket hypothesis. The investigations reported here are preliminary and are provided to encourage further research along this direction.
Many applications require sparse neural networks due to space or inference time restrictions. There is a large body of work on training dense networks to yield sparse networks for inference, but this limits the size of the largest trainable sparse model to that of the largest trainable dense model. In this paper we introduce a method to train sparse neural networks with a fixed parameter count and a fixed computational cost throughout training, without sacrificing accuracy relative to existing dense-to-sparse training methods. Our method updates the topology of the sparse network during training by using parameter magnitudes and infrequent gradient calculations. We show that this approach requires fewer floating-point operations (FLOPs) to achieve a given level of accuracy compared to prior techniques. We demonstrate state-of-the-art sparse training results on a variety of networks and datasets, including ResNet-50, MobileNets on Imagenet-2012, and RNNs on WikiText-103. Finally, we provide some insights into why allowing the topology to change during the optimization can overcome local minima encountered when the topology remains static. Code used in our work can be found in github.com/google-research/rigl.
$textit{RigL}$, a sparse training algorithm, claims to directly train sparse networks that match or exceed the performance of existing dense-to-sparse training techniques (such as pruning) for a fixed parameter count and compute budget. We implement $textit{RigL}$ from scratch in Pytorch and reproduce its performance on CIFAR-10 within 0.1% of the reported value. On both CIFAR-10/100, the central claim holds -- given a fixed training budget, $textit{RigL}$ surpasses existing dynamic-sparse training methods over a range of target sparsities. By training longer, the performance can match or exceed iterative pruning, while consuming constant FLOPs throughout training. We also show that there is little benefit in tuning $textit{RigL}$s hyper-parameters for every sparsity, initialization pair -- the reference choice of hyperparameters is often close to optimal performance. Going beyond the original paper, we find that the optimal initialization scheme depends on the training constraint. While the Erdos-Renyi-Kernel distribution outperforms the Uniform distribution for a fixed parameter count, for a fixed FLOP count, the latter performs better. Finally, redistributing layer-wise sparsity while training can bridge the performance gap between the two initialization schemes, but increases computational cost.
We propose a new framework for reasoning about generalization in deep learning. The core idea is to couple the Real World, where optimizers take stochastic gradient steps on the empirical loss, to an Ideal World, where optimizers take steps on the population loss. This leads to an alternate decomposition of test error into: (1) the Ideal World test error plus (2) the gap between the two worlds. If the gap (2) is universally small, this reduces the problem of generalization in offline learning to the problem of optimization in online learning. We then give empirical evidence that this gap between worlds can be small in realistic deep learning settings, in particular supervised image classification. For example, CNNs generalize better than MLPs on image distributions in the Real World, but this is because they optimize faster on the population loss in the Ideal World. This suggests our framework is a useful tool for understanding generalization in deep learning, and lays a foundation for future research in the area.
Sparse Neural Networks (NNs) can match the generalization of dense NNs using a fraction of the compute/storage for inference, and also have the potential to enable efficient training. However, naively training unstructured sparse NNs from random initialization results in significantly worse generalization, with the notable exception of Lottery Tickets (LTs) and Dynamic Sparse Training (DST). In this work, we attempt to answer: (1) why training unstructured sparse networks from random initialization performs poorly and; (2) what makes LTs and DST the exceptions? We show that sparse NNs have poor gradient flow at initialization and propose a modified initialization for unstructured connectivity. Furthermore, we find that DST methods significantly improve gradient flow during training over traditional sparse training methods. Finally, we show that LTs do not improve gradient flow, rather their success lies in re-learning the pruning solution they are derived from - however, this comes at the cost of learning novel solutions.
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