While ensembling deep neural networks has shown promise in improving generalization performance, scaling current ensemble methods for large models remains challenging. Given that recent progress in deep learning is largely driven by the scale, exemplified by the widespread adoption of large-scale neural network architectures, scalability emerges an increasingly critical issue for machine learning algorithms in the era of large-scale models. In this work, we first showcase the potential of low precision ensembling, where ensemble members are derived from a single model within low precision number systems in a training-free manner. Our empirical analysis demonstrates the effectiveness of our proposed low precision ensembling method compared to existing ensemble approaches.

We first present a topological sorting algorithm that leverages ancestral relationships in linear structural causal models to establish a compact top-down hierarchical ordering, encoding more causal information than linear orderings produced by existing methods.

This paper studies the problem of entropy identity testing: given sample access to a distribution p and a fully described distribution q (both discrete distributions over a domain of size k), and the promise that either p = q or |H (p) H (q)| ε, where H () denotes the Shannon entropy, a tester needs to distinguish between the two cases with high probability.

"why," is crucial for attribution and explanation,

However, the underlying optimization principles and convergence of interactive teaching lack theoretical analysis, and in this regard co-teaching serves as a notable prototype.