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Register a new userProving the Lottery Ticket Hypothesis: Pruning is All You Need
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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.
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The Lottery Ticket Hypothesis is a conjecture that every large neural network contains a subnetwork that, when trained in isolation, achieves comparable performance to the large network. An even stronger conjecture has been proven recently: Every sufficiently overparameterized network contains a subnetwork that, at random initialization, but without training, achieves comparable accuracy to the trained large network. This latter result, however, relies on a number of strong assumptions and guarantees a polynomial factor on the size of the large network compared to the target function. In this work, we remove the most limiting assumptions of this previous work while providing significantly tighter bounds:the overparameterized network only needs a logarithmic factor (in all variables but depth) number of neurons per weight of the target subnetwork.
Gradient-based meta-learning has proven to be highly effective at learning model initializations, representations, and update rules that allow fast adaptation from a few samples. The core idea behind these approaches is to use fast adaptation and generalization -- two second-order metrics -- as training signals on a meta-training dataset. However, little attention has been given to other possible second-order metrics. In this paper, we investigate a different training signal -- robustness to catastrophic interference -- and demonstrate that representations learned by directing minimizing interference are more conducive to incremental learning than those learned by just maximizing fast adaptation.
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.
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.
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.
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