2019/01/26 by Charles B. Delahunt, Delahunt, Charles B., Courosh Mehanian +3
Computer Science · #Adversarial Robustness in Machine Learning #Anomaly Detection Techniques and Applications #FOS: Computer and information sciences #I.2.0 #I.5.0 #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Data Classification
paper · pdf · doi:10.48550/arxiv.1901.09283
openalex publication_date 2019/01/26 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28
Softmax is a standard final layer used in Neural Nets (NNs) to summarize information encoded in the trained NN and return a prediction. However, Softmax leverages only a subset of the class-specific structure encoded in the trained model and ignores potentially valuable information: During training, models encode an array D of class response distributions, where Dij is the distribution of the jth pre-Softmax readout neuron's responses to the ith class. Given a test sample, Softmax implicitly uses only the row of this array D that corresponds to the readout neurons' responses to the sample's true class. Leveraging more of this array D can improve classifier accuracy, because the likelihoods of two competing classes can be encoded in other rows of D. To explore this potential resource, we develop a hybrid classifier (Softmax-Pooling Hybrid, SPH) that uses Softmax on high-scoring samples, but on low-scoring samples uses a log-likelihood method that pools the information from the full array D. We apply SPH to models trained on a vectorized MNIST dataset to varying levels of accuracy. SPH replaces only the final Softmax layer in the trained NN, at test time only. All training is the same as for Softmax. Because the pooling classifier performs better than Softmax on low-scoring samples, SPH reduces test set error by 6% to 23%, using the exact same trained model, whatever the baseline Softmax accuracy. This reduction in error reflects hidden capacity of the trained NN that is left unused by Softmax.