Benchmarking the tradeoff between neural network accuracy and training time is computationally expensive. Here we show how a multiplicative cyclic learning rate schedule can be used to construct a tradeoff curve in a single training run. We generate cyclic tradeoff curves for combinations of training methods such as Blurpool, Channels Last, Label Smoothing and MixUp, and highlight how these cyclic tradeoff curves can be used to efficiently evaluate the effects of algorithmic choices on network training. In order to make meaningful improvements in neural network training efficiency, ML practitioners must be able to compare between different choices of network architectures, hyperparameters, and training algorithms. One straightforward way to do this is to characterize the tradeoff between accuracy and training time with a "tradeoff curve." Tradeoff curves can be generated by varying the length of training for each model configuration; longer training runs take more time but tend to reach higher quality (Figure 1C). For a fixed model and task configuration, this method of generating tradeoff curves is an estimate of the theoretical Pareto frontier, i.e. the set of all of the best possible tradeoffs between training time and accuracy, where any further attempt to improve one of these metrics worsens the other.

Methods for improving the efficiency of deep network training (i.e. the resources required to achieve a given level of model quality) are of immediate benefit to deep learning practitioners. Distillation is typically used to compress models or improve model quality, but it's unclear if distillation actually improves training efficiency. Can the quality improvements of distillation be converted into training speed-ups, or do they simply increase final model quality with no resource savings? We conducted a series of experiments to investigate whether and how distillation can be used to accelerate training using ResNet-50 trained on ImageNet and BERT trained on C4 with a masked language modeling objective and evaluated on GLUE, using common enterprise hardware (8x NVIDIA A100). We found that distillation can speed up training by up to 1.96x in ResNet-50 trained on ImageNet and up to 1.42x on BERT when evaluated on GLUE. Furthermore, distillation for BERT yields optimal results when it is only performed for the first 20-50% of training. We also observed that training with distillation is almost always more efficient than training without distillation, even when using the poorest-quality model as a teacher, in both ResNet-50 and BERT. Finally, we found that it's possible to gain the benefit of distilling from an ensemble of teacher models, which has O(n) runtime cost, by randomly sampling a single teacher from the pool of teacher models on each step, which only has a O(1) runtime cost. Taken together, these results show that distillation can substantially improve training efficiency in both image classification and language modeling, and that a few simple optimizations to distillation protocols can further enhance these efficiency improvements.

Practitioners frequently observe that pruning improves model generalization. A long-standing hypothesis based on bias-variance trade-off attributes this generalization improvement to model size reduction. However, recent studies on over-parameterization characterize a new model size regime, in which larger models achieve better generalization. Pruning models in this over-parameterized regime leads to a contradiction -- while theory predicts that reducing model size harms generalization, pruning to a range of sparsities nonetheless improves it. Motivated by this contradiction, we re-examine pruning's effect on generalization empirically. We show that size reduction cannot fully account for the generalization-improving effect of standard pruning algorithms. Instead, we find that pruning leads to better training at specific sparsities, improving the training loss over the dense model. We find that pruning also leads to additional regularization at other sparsities, reducing the accuracy degradation due to noisy examples over the dense model. Pruning extends model training time and reduces model size. These two factors improve training and add regularization respectively. We empirically demonstrate that both factors are essential to fully explaining pruning's impact on generalization.

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.

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 and optimizer hyperparameter settings, and we exploit these observations to design custom optimization schemes. However, our results cast doubt on the broader intuition that the presence or absence of barriers when interpolating necessarily relates to the success of optimization.

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.

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.

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, accuracy is the same or higher when randomly shuffling which weights these methods prune within each layer or sampling new initial values. 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 undermines the claimed justifications for these methods and suggests broader challenges with the underlying pruning heuristics, the desire to prune at initialization, or both.

We show that the error of magnitude-pruned networks follows a scaling law, and that this law is of a fundamentally different nature than that of unpruned networks. We functionally approximate the error of the pruned networks, showing that it is predictable in terms of an invariant tying width, depth, and pruning level, such that networks of vastly different sparsities are freely interchangeable. We demonstrate the accuracy of this functional approximation over scales spanning orders of magnitude in depth, width, dataset size, and sparsity for CIFAR-10 and ImageNet. As neural networks become ever larger and more expensive to train, our findings enable a framework for reasoning conceptually and analytically about 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.