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.

Distributed training of Deep Learning models has been critical to many recent successes in the field. Current standard methods primarily rely on synchronous centralized algorithms which induce major communication bottlenecks and synchronization locks at scale.

In what's turning out to be a great quarter for corporate earnings growth, company executives and investors alike are focused on something else entirely: the threat from artificial intelligence. Mentions of AI disruption on management calls almost doubled compared to the previous quarter, an analysis of transcripts shows. While the technology hasn't yet noticeably reduced earnings estimates, investors aren't waiting around and instead are selling any company perceived to be at risk. Last week, commercial real estate company CBRE Group published better-than-expected earnings. In a call with analysts following the results, its chief executive officer said it's possible AI will reduce demand for office space in the long term. The comments sparked a 20% selloff in the stock over two days.

It is worth noting thatSafe LoRAis a training-free and data-free approach, as it only requires the knowledge of the weights from the base and aligned LLMs.

Adaptivity to the difficulties of a problem is a key property in sequential decision-making problems to broaden the applicability of algorithms.

Adaptivity to the difficulties of a problem is a key property in sequential decision-making problems to broaden the applicability of algorithms.