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By tuning the two temperatures, we create loss functions that are non-convex already in the single layer case.

We thank all reviewers for their efforts in reviewing our paper, and for the helpful comments and suggestions. "Id like to see some statistical properties of these new loss functions, and how they are compared to the "The authors are encouraged to present more theoretical & empirical analysis on the robustness of these loss We provide strong empirical evidence of the efficacy of our method, i.e. for dropping the convexity in the We leave this up to future work. Reviewer 3: We will add the additional references you suggested. "There are many possibilities for combining heavy-tailed distributions and robust/consistent divergence. The computational cost is only negligibly larger than the cost of logistic regression.

We introduce a temperature into the exponential function and replace the softmax output layer of neural nets by a high temperature generalization. Similarly, the logarithm in the log loss we use for training is replaced by a low temperature logarithm. By tuning the two temperatures we create loss functions that are non-convex already in the single layer case. When replacing the last layer of the neural nets by our two temperature generalization of logistic regression, the training becomes more robust to noise. We visualize the effect of tuning the two temperatures in a simple setting and show the efficacy of our method on large data sets. Our methodology is based on Bregman divergences and is superior to a related two-temperature method using the Tsallis divergence.