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Title: FLOPs as a Direct Optimization Objective for Learning Sparse Neural Networks

Paper content:
There exists a plethora of techniques for inducing structured sparsity in parametric models during the optimization process, with the final goal of resource-efficient inference.
However, to the best of our knowledge, none target a specific number of floating-point operations (FLOPs) as part of a single end-to-end optimization objective, despite reporting FLOPs as part of the results.
Furthermore, a one-size-fits-all approach ignores realistic system constraints, which differ significantly between, say, a GPU and a mobile phone -- FLOPs on the former incur less latency than on the latter; thus, it is important for practitioners to be able to specify a target number of FLOPs during model compression.
In this work, we extend a state-of-the-art technique to directly incorporate FLOPs as part of the optimization objective and show that, given a desired FLOPs requirement, different neural networks can be successfully trained for image classification.
Neural networks are a class of parametric models that achieve the state of the art across a broad range of tasks, but their heavy computational requirements hinder practical deployment on resourceconstrained devices, such as mobile phones, Internet-of-things (IoT) devices, and offline embedded systems.
Many recent works focus on alleviating these computational burdens, mainly falling under two non-mutually exclusive categories: manually designing resource-efficient models, and automatically compressing popular architectures.
In the latter, increasingly sophisticated techniques have emerged BID3 BID4 BID5 , which have achieved respectable accuracy-efficiency operating points, some even Pareto-better than that of the original network; for example, network slimming BID3 reaches an error rate of 6.20% on CIFAR-10 using VGGNet BID9 with a 51% FLOPs reduction-an error decrease of 0.14% over the original.However, to the best of our knowledge, none of the methods impose a FLOPs constraint as part of a single end-to-end optimization objective.
MorphNets BID0 apply an L 1 norm, shrinkage-based relaxation of a FLOPs objective, but for the purpose of searching and training multiple models to find good network architectures; in this work, we learn a sparse neural network in a single training run.
Other papers directly target device-specific metrics, such as energy usage BID15 , but the pruning procedure does not explicitly include the metrics of interest as part of the optimization objective, instead using them as heuristics.
Falling short of continuously deploying a model candidate and measuring actual inference time, as in time-consuming neural architectural search BID11 , we believe that the number of FLOPs is reasonable to use as a proxy measure for actual latency and energy usage; across variants of the same architecture, Tang et al. suggest that the number of FLOPs is a stronger predictor of energy usage and latency than the number of parameters BID12 .Indeed
, there are compelling reasons to optimize for the number of FLOPs as part of the training objective: First, it would permit FLOPs-guided compression in a more principled manner. Second
, practitioners can directly specify a desired target of FLOPs, which is important in deployment. Thus,
our main contribution is to present a novel extension of the prior state of the art BID6 to incorporate the number of FLOPs as part of the optimization objective, furthermore allowing practitioners to set and meet a desired compression target.

assistant: text: We extend a state-of-the-art technique to directly incorporate FLOPs as part of the optimization objective, and we show that, given a desired FLOPs requirement, different neural networks are successfully trained.