Neural Information Processing Systems http://nips.cc/

Work was done when the author interned at Microsoft.

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As there exist competitive subnetworks within a dense network in concert with Lottery Ticket Hypothesis, we introduce a novel neuron-wise task incremental learning method, namely Data-free Subnetworks (DSN), which attempts to enhance the elastic knowledge transfer across the tasks that sequentially arrive. Specifically, DSN primarily seeks to transfer knowledge to the new coming task from the learned tasks by selecting the affiliated weights of a small set of neurons to be activated, including the reused neurons from prior tasks via neuron-wise masks. And it also transfers possibly valuable knowledge to the earlier tasks via data-free replay.

The recently developed sparse network training methods, such as Lottery Ticket Hypothesis (LTH) and its variants, have shown impressive learning capacity by finding sparse sub-networks from a dense one. While these methods could largely sparsify deep networks, they generally focus more on realizing comparable accuracy to dense counterparts yet neglect network calibration. However, how to achieve calibrated network predictions lies at the core of improving model reliability, especially when it comes to addressing the overconfident issue and out-of-distribution cases. In this study, we propose a novel Distributionally Robust Optimization (DRO) framework to achieve an ensemble of lottery tickets towards calibrated network sparsification. Specifically, the proposed DRO ensemble aims to learn multiple diverse and complementary sparse sub-networks (tickets) with the guidance of uncertainty sets, which encourage tickets to gradually capture different data distributions from easy to hard and naturally complement each other. We theoretically justify the strong calibration performance by showing how the proposed robust training process guarantees to lower the confidence of incorrect predictions. Extensive experimental results on several benchmarks show that our proposed lottery ticket ensemble leads to a clear calibration improvement without sacrificing accuracy and burdening inference costs. Furthermore, experiments on OOD datasets demonstrate the robustness of our approach in the open-set environment.

The success of lottery ticket initializations (Frankle and Carbin, 2019) suggests that small, sparsified networks can be trained so long as the network is initialized appropriately. Unfortunately, finding these winning ticket'' initializations is computationally expensive. One potential solution is to reuse the same winning tickets across a variety of datasets and optimizers. However, the generality of winning ticket initializations remains unclear. Here, we attempt to answer this question by generating winning tickets for one training configuration (optimizer and dataset) and evaluating their performance on another configuration. Perhaps surprisingly, we found that, within the natural images domain, winning ticket initializations generalized across a variety of datasets, including Fashion MNIST, SVHN, CIFAR-10/100, ImageNet, and Places365, often achieving performance close to that of winning tickets generated on the same dataset. Moreover, winning tickets generated using larger datasets consistently transferred better than those generated using smaller datasets. We also found that winning ticket initializations generalize across optimizers with high performance. These results suggest that winning ticket initializations generated by sufficiently large datasets contain inductive biases generic to neural networks more broadly which improve training across many settings and provide hope for the development of better initialization methods.

Despite achieving remarkable efficiency, traditional network pruning techniques often follow manually-crafted heuristics to generate pruned sparse networks. Such heuristic pruning strategies are hard to guarantee that the pruned networks achieve test accuracy comparable to the original dense ones. Recent works have empirically identified and verified the Lottery Ticket Hypothesis (LTH): a randomly-initialized dense neural network contains an extremely sparse subnetwork, which can be trained to achieve similar accuracy to the former. Due to the lack of theoretical evidence, they often need to run multiple rounds of expensive training and pruning over the original large networks to discover the sparse subnetworks with low accuracy loss.

The lottery ticket hypothesis (LTH) has attracted attention because it can explain why over-parameterized models often show high generalization ability. It is known that when we use iterative magnitude pruning (IMP), which is an algorithm to find sparse networks with high generalization ability that can be trained from the initial weights independently, called winning tickets, the initial large learning rate does not work well in deep neural networks such as ResNet. However, since the initial large learning rate generally helps the optimizer to converge to flatter minima, we hypothesize that the winning tickets have relatively sharp minima, which is considered a disadvantage in terms of generalization ability. In this paper, we confirm this hypothesis and show that the PAC-Bayesian theory can provide an explicit understanding of the relationship between LTH and generalization behavior. On the basis of our experimental findings that IMP with a small learning rate finds relatively sharp minima and that the distance from the initial weights is deeply involved in winning tickets, we offer the PAC-Bayes bound using a spike-and-slab distribution to analyze winning tickets. Finally, we revisit existing algorithms for finding winning tickets from a PAC-Bayesian perspective and provide new insights into these methods.

The Strong Lottery Ticket Hypothesis (SLTH) states that randomly-initialised neural networks likely contain subnetworks that perform well without any training. Although unstructured pruning has been extensively studied in this context, its structured counterpart, which can deliver significant computational and memory efficiency gains, has been largely unexplored. One of the main reasons for this gap is the limitations of the underlying mathematical tools used in formal analyses of the SLTH.In this paper, we overcome these limitations: we leverage recent advances in the multidimensional generalisation of the Random Subset-Sum Problem and obtain a variant that admits the stochastic dependencies that arise when addressing structured pruning in the SLTH. We apply this result to prove, for a wide class of random Convolutional Neural Networks, the existence of structured subnetworks that can approximate any sufficiently smaller network.This result provides the first sub-exponential bound around the SLTH for structured pruning, opening up new avenues for further research on the hypothesis and contributing to the understanding of the role of over-parameterization in deep learning.