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Register a new userMulti-Prize Lottery Ticket Hypothesis: Finding Accurate Binary Neural Networks by Pruning A Randomly Weighted Network
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James Diffenderfer
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Recently, Frankle & Carbin (2019) demonstrated that randomly-initialized dense networks contain subnetworks that once found can be trained to reach test accuracy comparable to the trained dense network. However, finding these high performing trainable subnetworks is expensive, requiring iterative process of training and pruning weights. In this paper, we propose (and prove) a stronger Multi-Prize Lottery Ticket Hypothesis: A sufficiently over-parameterized neural network with random weights contains several subnetworks (winning tickets) that (a) have comparable accuracy to a dense target network with learned weights (prize 1), (b) do not require any further training to achieve prize 1 (prize 2), and (c) is robust to extreme forms of quantization (i.e., binary weights and/or activation) (prize 3). This provides a new paradigm for learning compact yet highly accurate binary neural networks simply by pruning and quantizing randomly weighted full precision neural networks. We also propose an algorithm for finding multi-prize tickets (MPTs) and test it by performing a series of experiments on CIFAR-10 and ImageNet datasets. Empirical results indicate that as models grow deeper and wider, multi-prize tickets start to reach similar (and sometimes even higher) test accuracy compared to their significantly larger and full-precision counterparts that have been weight-trained. Without ever updating the weight values, our MPTs-1/32 not only set new binary weight network state-of-the-art (SOTA) Top-1 accuracy -- 94.8% on CIFAR-10 and 74.03% on ImageNet -- but also outperform their full-precision counterparts by 1.78% and 0.76%, respectively. Further, our MPT-1/1 achieves SOTA Top-1 accuracy (91.9%) for binary neural networks on CIFAR-10. Code and pre-trained models are available at: https://github.com/chrundle/biprop.
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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.
The lottery ticket hypothesis (Frankle and Carbin, 2018), states that a randomly-initialized network contains a small subnetwork such that, when trained in isolation, can compete with the performance of the original network. We prove an even stronger hypothesis (as was also conjectured in Ramanujan et al., 2019), showing that for every bounded distribution and every target network with bounded weights, a sufficiently over-parameterized neural network with random weights contains a subnetwork with roughly the same accuracy as the target network, without any further training.
Pruning methods can considerably reduce the size of artificial neural networks without harming their performance. In some cases, they can even uncover sub-networks that, when trained in isolation, match or surpass the test accuracy of their dense counterparts. Here we study the inductive bias that pruning imprints in such winning lottery tickets. Focusing on visual tasks, we analyze the architecture resulting from iterative magnitude pruning of a simple fully connected network (FCN). We show that the surviving node connectivity is local in input space, and organized in patterns reminiscent of the ones found in convolutional networks (CNN). We investigate the role played by data and tasks in shaping the architecture of pruned sub-networks. Our results show that the winning lottery tickets of FCNs display the key features of CNNs. The ability of such automatic network-simplifying procedure to recover the key features hand-crafted in the design of CNNs suggests interesting applications to other datasets and tasks, in order to discover new and efficient architectural inductive biases.
Lottery Ticket Hypothesis (LTH) raises keen attention to identifying sparse trainable subnetworks, or winning tickets, of training, which can be trained in isolation to achieve similar or even better performance compared to the full models. Despite many efforts being made, the most effective method to identify such winning tickets is still Iterative Magnitude-based Pruning (IMP), which is computationally expensive and has to be run thoroughly for every different network. A natural question that comes in is: can we transform the winning ticket found in one network to another with a different architecture, yielding a winning ticket for the latter at the beginning, without re-doing the expensive IMP? Answering this question is not only practically relevant for efficient once-for-all winning ticket finding, but also theoretically appealing for uncovering inherently scalable sparse patterns in networks. We conduct extensive experiments on CIFAR-10 and ImageNet, and propose a variety of strategies to tweak the winning tickets found from different networks of the same model family (e.g., ResNets). Based on these results, we articulate the Elastic Lottery Ticket Hypothesis (E-LTH): by mindfully replicating (or dropping) and re-ordering layers for one network, its corresponding winning ticket could be stretched (or squeezed) into a subnetwork for another deeper (or shallower) network from the same family, whose performance is nearly the same competitive as the latters winning ticket directly found by IMP. We have also thoroughly compared E-LTH with pruning-at-initialization and dynamic sparse training methods, and discuss the generalizability of E-LTH to different model families, layer types, or across datasets. Code is available at https://github.com/VITA-Group/ElasticLTH.
Recent research has proposed the lottery ticket hypothesis, suggesting that for a deep neural network, there exist trainable sub-networks performing equally or better than the original model with commensurate training steps. While this discovery is insightful, finding proper sub-networks requires iterative training and pruning. The high cost incurred limits the applications of the lottery ticket hypothesis. We show there exists a subset of the aforementioned sub-networks that converge significantly faster during the training process and thus can mitigate the cost issue. We conduct extensive experiments to show such sub-networks consistently exist across various model structures for a restrictive setting of hyperparameters ($e.g.$, carefully selected learning rate, pruning ratio, and model capacity). As a practical application of our findings, we demonstrate that such sub-networks can help in cutting down the total time of adversarial training, a standard approach to improve robustness, by up to 49% on CIFAR-10 to achieve the state-of-the-art robustness.
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