![]() State-of-the-art, while also achieving a superior non-adversarial accuracy. 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 cross entropy loss function is the most commonly used loss function in classification, Cross entropy is used to measure the difference between two probability distributions, It is used to measure the difference between the learned distribution and the real distribution. So, with some simple highschool level math, we have solved the numerical flaw in the basic Binary Cross-Entropy function and created a Stable Binary Cross-Entropy Loss and Cost function. These bounds depend on quantities called minimizability gaps. Take a moment to understand this and try to piece it together with the piecewise stable Binary Cross-Entropy Loss function from Fig.58. 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 Loss), generalized cross-entropy, the mean absolute error and otherĬross-entropy-like loss functions. 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 The lesser the loss, the better the model for prediction. For example, we have 10 classes to choose from when. Multi-class cross entropy loss is used in multi-class classification, such as the MNIST digits classification problem from Chapter 2, Deep Learning and. With the logistic loss applied to the outputs of a neural network, when the Cross entropy is used to determine how the loss can be minimized to get a better prediction. Cross-entropy is a loss function we can use to train a model when the output is one of several classes. 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. ![]()
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