This paper studies quasi-Newton methods for solving nonlinear equations. We propose block variants of both good and bad Broyden's methods, which enjoy explicit local superlinear convergence rates. Our block good Broyden's method has a faster condition-number-free convergence rate than existing Broyden's methods because it takes the advantage of multiple rank modification on Jacobian estimator. On the other hand, our block bad Broyden's method directly estimates the inverse of the Jacobian provably, which reduces the computational cost of the iteration. Our theoretical results provide some new insights on why good Broyden's method outperforms bad Broyden's method in most of the cases. The empirical results also demonstrate the superiority of our methods and validate our theoretical analysis.

Only data collected from the "wrist" is used in our experiment.

This paper proposes a novel contrastive learning framework, called FOCAL, for extracting comprehensive features from multimodal time-series sensing signals through self-supervised training. Existing multimodal contrastive frameworks mostly rely on the shared information between sensory modalities, but do not explicitly consider the exclusive modality information that could be critical to understanding the underlying sensing physics. Besides, contrastive frameworks for time series have not handled the temporal information locality appropriately.

Partitioning a set of elements into an unknown number of mutually exclusive subsets is essential in many machine learning problems.

We investigated DNNs as encoding models of visual areas V1, V2, V4, and IT. We examined 32 visual deep neural networks.

However, these results can be too general to be applicable to natural data distributions. Indeed, humans are quite robust for tasks involving vision.

In most applications, the output labels of learning problems have some structure that is crucial to consider. This includes natural language processing applications, where the output may be a sentence, a sequence of parts-of-speech tags, a parse tree, or a dependency graph.