mlsanityData to 14 Oct 2026

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

arXiv 2502.03787 ↗First posted 6 Feb 2025cs.LGcited by 1

On the map: LLM reasoning → Test-time compute and efficient thinking

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.

Key facts. Cited by 1 paper 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.

Builds on

4 of 6 references.

References · 4

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  2. 2016Benefits of depth in neural networkscited by 250
  3. 2015The Power of Depth for Feedforward Neural Networkscited by 183
  4. 2024Contextual Feedback Loops: Amplifying Deep Reasoning with Iterative Top-Down Feedbackcited by 1

Built on by

Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025Flowing Through Layers: A Continuous Dynamical Systems Perspective on Transformerscited by 2

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  1. 2026Divergent-Convergent Reasoning: Scaling Test-Time Compute through Structured Solution Synthesis
  2. 2026Reasoning on the Simplex: Geometric Fixed-Point Models
  3. 2026Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models
  4. 2026Test-Time Scaling with Diffusion Language Models via Reward-Guided Stitching
  5. 2026InftyThink+: Effective and Efficient Infinite-Horizon Reasoning via Reinforcement Learning
  6. 2026Reasoning-preserved Efficient Distillation of Large Language Models via Activation-aware Initialization
  7. 2025Parallel Thinking, Sequential Answering: Bridging NAR and AR for Efficient Reasoning
  8. 2026Boosting Inference with Guided Reasoning: Stochastic Exploration for Recursive Models