In this paper, we theoretically and empirically characterize obstructions to training encoders with geometric latent spaces. We show that local optima can arise due to singularities (e.g.

Adversarially robust classification, that has been of much recent interest, is typically formulated as follows.

These selections serve as subgoals that indicate subtasks and guide policy.

An alternative approach, Generative Adversarial Networks (GANs), has become popular across severaldomains, particularly Computer Vision, owing tobreakthrough realism intheimages they output[e.g.,19,65]. This is the case in NLP where, unlike computer vision, a measure of likelihood called perplexityhas been theprevailing metric fortraining and evaluating language models fordecades.

Our proof relies on anewtype of synthetic data generator,Sequential Synthetic14 Data Generators, which we believe may be of interest of their own right.

Our bound addresses the second question; it suggests that learning algorithms that bias towards models with small variation across the source threat model exhibit smaller drop in robustness to particularunforeseenattacks.

Modelers use automatic differentiation (AD) of computation graphs to implement complex deep learning models without defining gradient computations.