We are using JAX [ Bradbury et al., 2018 ]. All the models except for section C.4 have been trained with Softmax loss normalized as Batch Norm: we are using JAX's Stax implementation of Batch Norm which doesn't keep track of Trained on 512 samples of MNIST. MaxPool((2,2), 'V ALID') performs max pooling with'V ALID' padding Trained on CIFAR-10 without data augmentation. The WRN experiments are run on v3-8 TPUs and the rest on P100 GPUs. Here we describe the particularities of each figure.

We test these proposals in modern image classification settings.

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Multivariate loss functions are used to assess performance in many modern prediction tasks, including information retrieval and ranking applications. Convex approximations are typically optimized in their place to avoid NP-hard empirical risk minimization problems. We propose to approximate the training data instead of the loss function by posing multivariate prediction as an adversarial game between a loss-minimizing prediction player and a loss-maximizing evaluation player constrained to match specified properties of training data. This avoids the non-convexity of empirical risk minimization, but game sizes are exponential in the number of predicted variables. We overcome this intractability using the double oracle constraint generation method. We demonstrate the efficiency and predictive performance of our approach on tasks evaluated using the precision at k, the F-score and the discounted cumulative gain.

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While these approaches learn high-quality representations for downstream tasks such as action recognition, their training objectives disregard spatial cues naturally occurring in audio and visual signals.

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