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We further report the results of a series of experimentsĭemonstrating that our adversarial robustness algorithms outperform the current Theoretical analysis, we also present an extensive empirical analysis comparingĬomp-sum losses. Regularized smooth adversarial comp-sum loss. Leads to new adversarial robustness algorithms that consist of minimizing a We show that these loss functions are beneficial in theĪdversarial setting by proving that they admit $H$-consistency bounds. We also introduce a new family of loss functions, smooth adversarialĬomp-sum losses, that are derived from their comp-sum counterparts by adding inĪ related smooth term. Make them more explicit, we give a specific analysis of these gaps for comp-sum The perplexity for this stupid language model is even larger I have fixed it in the blog post. These bounds depend on quantities called minimizability gaps. 'If the number of words in the sentences T10 and the size of word corpus M106, PP (S)107', but (106)101060. We further show that our boundsĪre tight. Loss, for the specific hypothesis set $H$ used. Zero-one loss estimation error in terms of the estimation error of a surrogate These are non-asymptotic guarantees that upper bound the We give the first $H$-consistency bounds for We propose to reconstruct PET images by minimizing a. Unlike Softmax loss it is independent for each vector component (class), meaning that the loss computed for every CNN output vector component is not affected by other component values. The cross-entropy or Kullback-Leiber distance is a measure of dissimilarity between two images.

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Loss), generalized cross-entropy, the mean absolute error and otherĬross-entropy-like loss functions. It is a Sigmoid activation plus a Cross-Entropy loss. Loss functions, comp-sum losses, that includes cross-entropy (or logistic But, what guarantees can we rely on when using cross-entropyĪs a surrogate loss? We present a theoretical analysis of a broad family of With the logistic loss applied to the outputs of a neural network, when the

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Download a PDF of the paper titled Cross-Entropy Loss Functions: Theoretical Analysis and Applications, by Anqi Mao and 2 other authors Download PDF Abstract: Cross-entropy is a widely used loss function in applications.

Cross entropy