arXiv subjects

Jonathan Frankle

Publications and source records attributed to Jonathan Frankle.

At least 37 records · Page 2Linked to original sources

arXiv2022

Unmasking the Lottery Ticket Hypothesis: What's Encoded in a Winning Ticket's Mask?

Modern deep learning involves training costly, highly overparameterized networks, thus motivating the search for sparser networks that can still be trained to the same accuracy as the full network (i.e. matching). Iterative magnitude pruning (IMP) is a state of the art algorithm that can find such highly sparse matching subnetworks, known as winning tickets. IMP operates by iterative cycles of training, masking smallest magnitude weights, rewinding back to an early training point, and repeating. Despite its simplicity, the underlying principles for when and how IMP finds winning tickets remain elusive. In particular, what useful information does an IMP mask found at the end of training convey to a rewound network near the beginning of training? How does SGD allow the network to extract this information? And why is iterative pruning needed? We develop answers in terms of the geometry of the error landscape. First, we find that$\unicode{x2014}$at higher sparsities$\unicode{x2014}$pairs of pruned networks at successive pruning iterations are connected by a linear path with zero error barrier if and only if they are matching. This indicates that masks found at the end of training convey the identity of an axial subspace that intersects a desired linearly connected mode of a matching sublevel set. Second, we show SGD can exploit this information due to a strong form of robustness: it can return to this mode despite strong perturbations early in training. Third, we show how the flatness of the error landscape at the end of training determines a limit on the fraction of weights that can be pruned at each iteration of IMP. Finally, we show that the role of retraining in IMP is to find a network with new small weights to prune. Overall, these results make progress toward demystifying the existence of winning tickets by revealing the fundamental role of error landscape geometry.

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arXiv2022

Lottery Tickets on a Data Diet: Finding Initializations with Sparse Trainable Networks

A striking observation about iterative magnitude pruning (IMP; Frankle et al. 2020) is that $\unicode{x2014}$ after just a few hundred steps of dense training $\unicode{x2014}$ the method can find a sparse sub-network that can be trained to the same accuracy as the dense network. However, the same does not hold at step 0, i.e. random initialization. In this work, we seek to understand how this early phase of pre-training leads to a good initialization for IMP both through the lens of the data distribution and the loss landscape geometry. Empirically we observe that, holding the number of pre-training iterations constant, training on a small fraction of (randomly chosen) data suffices to obtain an equally good initialization for IMP. We additionally observe that by pre-training only on "easy" training data, we can decrease the number of steps necessary to find a good initialization for IMP compared to training on the full dataset or a randomly chosen subset. Finally, we identify novel properties of the loss landscape of dense networks that are predictive of IMP performance, showing in particular that more examples being linearly mode connected in the dense network correlates well with good initializations for IMP. Combined, these results provide new insight into the role played by the early phase training in IMP.

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arXiv2022

Strengthening Subcommunities: Towards Sustainable Growth in AI Research

AI's rapid growth has been felt acutely by scholarly venues, leading to growing pains within the peer review process. These challenges largely center on the inability of specific subareas to identify and evaluate work that is appropriate according to criteria relevant to each subcommunity as determined by stakeholders of that subarea. We set forth a proposal that re-focuses efforts within these subcommunities through a decentralization of the reviewing and publication process. Through this re-centering effort, we hope to encourage each subarea to confront the issues specific to their process of academic publication and incentivization. This model has historically been successful for several subcommunities in AI, and we highlight those instances as examples for how the broader field can continue to evolve despite its continually growing size.

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arXiv2022

What can linear interpolation of neural network loss landscapes tell us?

Studying neural network loss landscapes provides insights into the nature of the underlying optimization problems. Unfortunately, loss landscapes are notoriously difficult to visualize in a human-comprehensible fashion. One common way to address this problem is to plot linear slices of the landscape, for example from the initial state of the network to the final state after optimization. On the basis of this analysis, prior work has drawn broader conclusions about the difficulty of the optimization problem. In this paper, we put inferences of this kind to the test, systematically evaluating how linear interpolation and final performance vary when altering the data, choice of initialization, and other optimizer and architecture design choices. Further, we use linear interpolation to study the role played by individual layers and substructures of the network. We find that certain layers are more sensitive to the choice of initialization, but that the shape of the linear path is not indicative of the changes in test accuracy of the model. Our results cast doubt on the broader intuition that the presence or absence of barriers when interpolating necessarily relates to the success of optimization.

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arXiv2021

Trade-offs of Local SGD at Scale: An Empirical Study

As datasets and models become increasingly large, distributed training has become a necessary component to allow deep neural networks to train in reasonable amounts of time. However, distributed training can have substantial communication overhead that hinders its scalability. One strategy for reducing this overhead is to perform multiple unsynchronized SGD steps independently on each worker between synchronization steps, a technique known as local SGD. We conduct a comprehensive empirical study of local SGD and related methods on a large-scale image classification task. We find that performing local SGD comes at a price: lower communication costs (and thereby faster training) are accompanied by lower accuracy. This finding is in contrast from the smaller-scale experiments in prior work, suggesting that local SGD encounters challenges at scale. We further show that incorporating the slow momentum framework of Wang et al. (2020) consistently improves accuracy without requiring additional communication, hinting at future directions for potentially escaping this trade-off.

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arXiv2021

On the Predictability of Pruning Across Scales

We show that the error of iteratively magnitude-pruned networks empirically follows a scaling law with interpretable coefficients that depend on the architecture and task. We functionally approximate the error of the pruned networks, showing it is predictable in terms of an invariant tying width, depth, and pruning level, such that networks of vastly different pruned densities are interchangeable. We demonstrate the accuracy of this approximation over orders of magnitude in depth, width, dataset size, and density. We show that the functional form holds (generalizes) for large scale data (e.g., ImageNet) and architectures (e.g., ResNets). As neural networks become ever larger and costlier to train, our findings suggest a framework for reasoning conceptually and analytically about a standard method for unstructured pruning.

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arXiv2021

Studying the Consistency and Composability of Lottery Ticket Pruning Masks

Magnitude pruning is a common, effective technique to identify sparse subnetworks at little cost to accuracy. In this work, we ask whether a particular architecture's accuracy-sparsity tradeoff can be improved by combining pruning information across multiple runs of training. From a shared ResNet-20 initialization, we train several network copies (\emph{siblings}) to completion using different SGD data orders on CIFAR-10. While the siblings' pruning masks are naively not much more similar than chance, starting sibling training after a few epochs of shared pretraining significantly increases pruning overlap. We then choose a subnetwork by either (1) taking all weights that survive pruning in any sibling (mask union), or (2) taking only the weights that survive pruning across all siblings (mask intersection). The resulting subnetwork is retrained. Strikingly, we find that union and intersection masks perform very similarly. Both methods match the accuracy-sparsity tradeoffs of the one-shot magnitude pruning baseline, even when we combine masks from up to $k = 10$ siblings.

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arXiv2021

The Lottery Tickets Hypothesis for Supervised and Self-supervised Pre-training in Computer Vision Models

The computer vision world has been re-gaining enthusiasm in various pre-trained models, including both classical ImageNet supervised pre-training and recently emerged self-supervised pre-training such as simCLR and MoCo. Pre-trained weights often boost a wide range of downstream tasks including classification, detection, and segmentation. Latest studies suggest that pre-training benefits from gigantic model capacity. We are hereby curious and ask: after pre-training, does a pre-trained model indeed have to stay large for its downstream transferability? In this paper, we examine supervised and self-supervised pre-trained models through the lens of the lottery ticket hypothesis (LTH). LTH identifies highly sparse matching subnetworks that can be trained in isolation from (nearly) scratch yet still reach the full models' performance. We extend the scope of LTH and question whether matching subnetworks still exist in pre-trained computer vision models, that enjoy the same downstream transfer performance. Our extensive experiments convey an overall positive message: from all pre-trained weights obtained by ImageNet classification, simCLR, and MoCo, we are consistently able to locate such matching subnetworks at 59.04% to 96.48% sparsity that transfer universally to multiple downstream tasks, whose performance see no degradation compared to using full pre-trained weights. Further analyses reveal that subnetworks found from different pre-training tend to yield diverse mask structures and perturbation sensitivities. We conclude that the core LTH observations remain generally relevant in the pre-training paradigm of computer vision, but more delicate discussions are needed in some cases. Codes and pre-trained models will be made available at: https://github.com/VITA-Group/CV_LTH_Pre-training.

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arXiv2021

Training BatchNorm and Only BatchNorm: On the Expressive Power of Random Features in CNNs

A wide variety of deep learning techniques from style transfer to multitask learning rely on training affine transformations of features. Most prominent among these is the popular feature normalization technique BatchNorm, which normalizes activations and then subsequently applies a learned affine transform. In this paper, we aim to understand the role and expressive power of affine parameters used to transform features in this way. To isolate the contribution of these parameters from that of the learned features they transform, we investigate the performance achieved when training only these parameters in BatchNorm and freezing all weights at their random initializations. Doing so leads to surprisingly high performance considering the significant limitations that this style of training imposes. For example, sufficiently deep ResNets reach 82% (CIFAR-10) and 32% (ImageNet, top-5) accuracy in this configuration, far higher than when training an equivalent number of randomly chosen parameters elsewhere in the network. BatchNorm achieves this performance in part by naturally learning to disable around a third of the random features. Not only do these results highlight the expressive power of affine parameters in deep learning, but - in a broader sense - they characterize the expressive power of neural networks constructed simply by shifting and rescaling random features.

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arXiv2021

Pruning Neural Networks at Initialization: Why are We Missing the Mark?

Recent work has explored the possibility of pruning neural networks at initialization. We assess proposals for doing so: SNIP (Lee et al., 2019), GraSP (Wang et al., 2020), SynFlow (Tanaka et al., 2020), and magnitude pruning. Although these methods surpass the trivial baseline of random pruning, they remain below the accuracy of magnitude pruning after training, and we endeavor to understand why. We show that, unlike pruning after training, randomly shuffling the weights these methods prune within each layer or sampling new initial values preserves or improves accuracy. As such, the per-weight pruning decisions made by these methods can be replaced by a per-layer choice of the fraction of weights to prune. This property suggests broader challenges with the underlying pruning heuristics, the desire to prune at initialization, or both.

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arXiv2020

Revisiting "Qualitatively Characterizing Neural Network Optimization Problems"

We revisit and extend the experiments of Goodfellow et al. (2014), who showed that - for then state-of-the-art networks - "the objective function has a simple, approximately convex shape" along the linear path between initialization and the trained weights. We do not find this to be the case for modern networks on CIFAR-10 and ImageNet. Instead, although loss is roughly monotonically non-increasing along this path, it remains high until close to the optimum. In addition, training quickly becomes linearly separated from the optimum by loss barriers. We conclude that, although Goodfellow et al.'s findings describe the "relatively easy to optimize" MNIST setting, behavior is qualitatively different in modern settings.

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arXiv2020

Are all negatives created equal in contrastive instance discrimination?

Self-supervised learning has recently begun to rival supervised learning on computer vision tasks. Many of the recent approaches have been based on contrastive instance discrimination (CID), in which the network is trained to recognize two augmented versions of the same instance (a query and positive) while discriminating against a pool of other instances (negatives). The learned representation is then used on downstream tasks such as image classification. Using methodology from MoCo v2 (Chen et al., 2020), we divided negatives by their difficulty for a given query and studied which difficulty ranges were most important for learning useful representations. We found a minority of negatives -- the hardest 5% -- were both necessary and sufficient for the downstream task to reach nearly full accuracy. Conversely, the easiest 95% of negatives were unnecessary and insufficient. Moreover, the very hardest 0.1% of negatives were unnecessary and sometimes detrimental. Finally, we studied the properties of negatives that affect their hardness, and found that hard negatives were more semantically similar to the query, and that some negatives were more consistently easy or hard than we would expect by chance. Together, our results indicate that negatives vary in importance and that CID may benefit from more intelligent negative treatment.

cs.CV↗

arXiv2020

The Lottery Ticket Hypothesis for Pre-trained BERT Networks

In natural language processing (NLP), enormous pre-trained models like BERT have become the standard starting point for training on a range of downstream tasks, and similar trends are emerging in other areas of deep learning. In parallel, work on the lottery ticket hypothesis has shown that models for NLP and computer vision contain smaller matching subnetworks capable of training in isolation to full accuracy and transferring to other tasks. In this work, we combine these observations to assess whether such trainable, transferrable subnetworks exist in pre-trained BERT models. For a range of downstream tasks, we indeed find matching subnetworks at 40% to 90% sparsity. We find these subnetworks at (pre-trained) initialization, a deviation from prior NLP research where they emerge only after some amount of training. Subnetworks found on the masked language modeling task (the same task used to pre-train the model) transfer universally; those found on other tasks transfer in a limited fashion if at all. As large-scale pre-training becomes an increasingly central paradigm in deep learning, our results demonstrate that the main lottery ticket observations remain relevant in this context. Codes available at https://github.com/VITA-Group/BERT-Tickets.

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arXiv2020

Stabilizing the Lottery Ticket Hypothesis

Pruning is a well-established technique for removing unnecessary structure from neural networks after training to improve the performance of inference. Several recent results have explored the possibility of pruning at initialization time to provide similar benefits during training. In particular, the "lottery ticket hypothesis" conjectures that typical neural networks contain small subnetworks that can train to similar accuracy in a commensurate number of steps. The evidence for this claim is that a procedure based on iterative magnitude pruning (IMP) reliably finds such subnetworks retroactively on small vision tasks. However, IMP fails on deeper networks, and proposed methods to prune before training or train pruned networks encounter similar scaling limitations. In this paper, we argue that these efforts have struggled on deeper networks because they have focused on pruning precisely at initialization. We modify IMP to search for subnetworks that could have been obtained by pruning early in training (0.1% to 7% through) rather than at iteration 0. With this change, it finds small subnetworks of deeper networks (e.g., 80% sparsity on Resnet-50) that can complete the training process to match the accuracy of the original network on more challenging tasks (e.g., ImageNet). In situations where IMP fails at iteration 0, the accuracy benefits of delaying pruning accrue rapidly over the earliest iterations of training. To explain these behaviors, we study subnetwork "stability," finding that - as accuracy improves in this fashion - IMP subnetworks train to parameters closer to those of the full network and do so with improved consistency in the face of gradient noise. These results offer new insights into the opportunity to prune large-scale networks early in training and the behaviors underlying the lottery ticket hypothesis

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arXiv2020

Linear Mode Connectivity and the Lottery Ticket Hypothesis

We study whether a neural network optimizes to the same, linearly connected minimum under different samples of SGD noise (e.g., random data order and augmentation). We find that standard vision models become stable to SGD noise in this way early in training. From then on, the outcome of optimization is determined to a linearly connected region. We use this technique to study iterative magnitude pruning (IMP), the procedure used by work on the lottery ticket hypothesis to identify subnetworks that could have trained in isolation to full accuracy. We find that these subnetworks only reach full accuracy when they are stable to SGD noise, which either occurs at initialization for small-scale settings (MNIST) or early in training for large-scale settings (ResNet-50 and Inception-v3 on ImageNet).

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arXiv2020

What is the State of Neural Network Pruning?

Neural network pruning---the task of reducing the size of a network by removing parameters---has been the subject of a great deal of work in recent years. We provide a meta-analysis of the literature, including an overview of approaches to pruning and consistent findings in the literature. After aggregating results across 81 papers and pruning hundreds of models in controlled conditions, our clearest finding is that the community suffers from a lack of standardized benchmarks and metrics. This deficiency is substantial enough that it is hard to compare pruning techniques to one another or determine how much progress the field has made over the past three decades. To address this situation, we identify issues with current practices, suggest concrete remedies, and introduce ShrinkBench, an open-source framework to facilitate standardized evaluations of pruning methods. We use ShrinkBench to compare various pruning techniques and show that its comprehensive evaluation can prevent common pitfalls when comparing pruning methods.

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arXiv2020

Comparing Rewinding and Fine-tuning in Neural Network Pruning

Many neural network pruning algorithms proceed in three steps: train the network to completion, remove unwanted structure to compress the network, and retrain the remaining structure to recover lost accuracy. The standard retraining technique, fine-tuning, trains the unpruned weights from their final trained values using a small fixed learning rate. In this paper, we compare fine-tuning to alternative retraining techniques. Weight rewinding (as proposed by Frankle et al., (2019)), rewinds unpruned weights to their values from earlier in training and retrains them from there using the original training schedule. Learning rate rewinding (which we propose) trains the unpruned weights from their final values using the same learning rate schedule as weight rewinding. Both rewinding techniques outperform fine-tuning, forming the basis of a network-agnostic pruning algorithm that matches the accuracy and compression ratios of several more network-specific state-of-the-art techniques.

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arXiv2020

The Early Phase of Neural Network Training

Recent studies have shown that many important aspects of neural network learning take place within the very earliest iterations or epochs of training. For example, sparse, trainable sub-networks emerge (Frankle et al., 2019), gradient descent moves into a small subspace (Gur-Ari et al., 2018), and the network undergoes a critical period (Achille et al., 2019). Here, we examine the changes that deep neural networks undergo during this early phase of training. We perform extensive measurements of the network state during these early iterations of training and leverage the framework of Frankle et al. (2019) to quantitatively probe the weight distribution and its reliance on various aspects of the dataset. We find that, within this framework, deep networks are not robust to reinitializing with random weights while maintaining signs, and that weight distributions are highly non-independent even after only a few hundred iterations. Despite this behavior, pre-training with blurred inputs or an auxiliary self-supervised task can approximate the changes in supervised networks, suggesting that these changes are not inherently label-dependent, though labels significantly accelerate this process. Together, these results help to elucidate the network changes occurring during this pivotal initial period of learning.

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