# Iterate to Accelerate: A Unified Framework for Iterative Reasoning and Feedback Convergence

arXiv: https://arxiv.org/abs/2502.03787 · HTML: https://mlsanity.com/paper/2502.03787/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 4 of its 6 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 4 of 4)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Benefits of depth in neural networks](https://mlsanity.com/paper/1602.04485/) (2016)
- [The Power of Depth for Feedforward Neural Networks](https://mlsanity.com/paper/1512.03965/) (2015)
- [Contextual Feedback Loops: Amplifying Deep Reasoning with Iterative Top-Down Feedback](https://mlsanity.com/paper/2412.17737/) (2024)

## Built on by (most cited first, 1 of 1)

- [Flowing Through Layers: A Continuous Dynamical Systems Perspective on Transformers](https://mlsanity.com/paper/2502.05656/) (2025)

## Abstract (arXiv)

We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness and contractivity assumptions, a generalized update scheme not only unifies classical methods such as mirror descent and dynamic programming but also captures modern chain-of-thought reasoning processes in large language models. In particular, we prove that our accelerated iterative update achieves an O(1/t2) convergence rate in the absence of persistent perturbations, and we further demonstrate that feedback (iterative) architectures are necessary to approximate certain fixed-point functions efficiently. These theoretical insights bridge classical acceleration techniques with contemporary applications in neural computation and optimization.