title: LLBoost: Last Layer Perturbation to Boost Pre-trained Neural Networks
abstract:     While deep networks have produced state-of-the-art results in several domains from image classification to machine translation, hyper-parameter selection remains a significant computational bottleneck.  In order to produce the best possible model, practitioners often search across random seeds or use ensemble methods.  As models get larger, any method to improve neural network performance that involves re-training becomes intractable.  For example, computing the training accuracy of FixResNext-101 (829 million parameters) on ImageNet takes roughly 1~day when using 1~GPU.   
      In this work, we present LLBoost, a theoretically-grounded, computationally-efficient method to boost the validation accuracy of pre-trained over-parameterized models without impacting the original training accuracy.  LLBoost adjusts the last layer of a neural network by adding a term that is orthogonal to the training feature matrix, which is constructed by applying all layers but the last to the training data.  We provide an efficient implementation of LLBoost on the GPU and demonstrate that LLBoost, run using only 1 GPU, improves the test/validation accuracy of pre-trained models on CIFAR10, ImageNet32, and ImageNet.  In the over-parameterized linear regression setting, we prove that LLBoost reduces the generalization error of any interpolating solution with high probability without affecting training error.  
authors: Adityanarayanan Radhakrishnan Neha Prasad Caroline Uhler
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