A Unified Framework for Iterative Reasoning and Feedback Convergence (Feb 2025)

Описание: Title: Iterate to Accelerate: A Unified Framework for Iterative Reasoning and Feedback Convergence
Link: http://arxiv.org/abs/2502.03787v1
Date: February 2025

Summary:
This paper introduces a unified framework for iterative reasoning that leverages non-Euclidean geometry, higher-order operator averaging, and adaptive feedback mechanisms. The analysis establishes that a generalized update scheme unifies classical methods and captures modern chain-of-thought reasoning processes, achieving an O(1/n^2) convergence rate under mild assumptions. The paper also demonstrates that feedback architectures are necessary to efficiently approximate certain fixed-point functions.

Key Topics:
Iterative reasoning
Non-Euclidean geometry
Bregman divergences
Operator averaging
Adaptive feedback
Accelerated convergence
Fixed-point approximation
Feedback structures

Chapters:
0:00 - Introduction
1:02 - Key Takeaways
1:13 - Unified Framework Explained
1:27 - Bregman Divergences
4:48 - Fixed Point Functions
7:20 - Iterative Update Scheme
9:10 - Feedback Loops Importance
11:11 - Practical Applications
13:02 - Challenges & Scalability
14:26 - Future Directions
14:50 - Conclusion