For labels taking values in a finite metric space, we introduce techniques new to weak supervision based on pseudo-Euclidean embeddings andtensor decompositions, providing anearly-consistent noise rate estimator.

Aiming to address this limitation, we present Easy2Hard-Bench, a consistently formatted collection of 6 benchmark datasets spanning various domains, such as mathematics and programming problems, chess puzzles, and reasoning questions.

Both strategies suffer from some limitations: the former kind is computationally expensive and difficult to converge, whilst the latter kind optimizes the reconstruction error but ignores the discriminative power of channels.

This work identifies the existence and cause of a type of posterior collapse that frequently occurs in the Bayesian deep learning practice. For a general linear latent variable model that includes linear variational autoencoders as a special case, we precisely identify the nature of posterior collapse to be the competition between the likelihood and the regularization of the mean due to the prior. Our result suggests that posterior collapse may be related to neural collapse and dimensional collapse and could be a subclass of a general problem of learning for deeper architectures.

Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, and canonical correlation analysis are specific instances of GEPs and are widely used in statistical data processing. In this work, we study GEPs under generative priors, assuming that the underlying leading generalized eigenvector lies within the range of a Lipschitz continuous generative model.

Second, current evaluation metrics assume thepresence ofsound sources at alltimes.

However, the training of a sparse DNN encounters great challenges in achieving optimal generalization ability despite the efforts from the state-of-the-art sparse training methodologies. To unravel the mysterious reason behind the difficulty of sparse training, we connect network sparsity with the structure of neural loss functions and identify that the cause of such difficulty lies in a chaotic loss surface.