mlsanityData to 7 Oct 2026

Why Self-Rewarding Works: Theoretical Guarantees for Iterative Alignment of Language Models

arXiv 2601.22513 ↗First posted 30 Jan 2026cs.AIcited by 1

On the map: LLM alignment / RLHF / preference optimisation → LLM preference optimization methods

also in 1 more
Abstract (arXiv)

Self-Rewarding Language Models (SRLMs) achieve notable success in iteratively improving alignment without external feedback. Yet, despite their striking empirical progress, the core mechanisms driving their capabilities remain unelucidated, leaving a critical gap in theoretical understanding. This paper provides the first rigorous theoretical guarantees for SRLMs. We first establish a lower bound that characterizes the fundamental limits of a single update step, revealing a critical dependence on the quality of the initial model. We then derive finite-sample error bounds for the full iterative paradigm, showing that performance improves at a rate of widetildeOleft(1/√nright) with sample size n. Crucially, our analysis reveals that the dependence on the initial model decays exponentially with the number of iterations T. This provides a formal explanation for why self-rewarding succeeds: it robustly overcomes poor initialization by steering the dynamics toward internal stability and consistency. Finally, we instantiate our theoretical framework for the linear softmax model class, yielding tailored guarantees that connect our high-level insights to practical model architectures.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation. Builds on 24 of its 66 references that are in the map. First posted on arXiv 30 Jan 2026.

Builds on

24 of 66 references.

Closest ancestors · 2

Same direction, newest first

  1. 2025Self-Rewarding PPO: Aligning Large Language Models with Demonstrations Only24 Oct
  2. 2025Self-Consistency of the Internal Reward Models Improves Self-Rewarding Language Models13 Feb

Other references · 22

  1. 2015Distilling the Knowledge in a Neural Networkcited by 10,076
  2. 2024A Survey on LLM-as-a-Judgecited by 1,384
  3. 2019How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddingscited by 770
  4. 2022Large Language Models Can Self-Improvecited by 656
  5. 2019ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoringcited by 349
  6. 2024Meta-Rewarding Language Models: Self-Improving Alignment with LLM-as-a-Meta-Judgecited by 202
  7. 2025Learning to Reason without External Rewardscited by 199
  8. 2025The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoningcited by 160
  9. 2025Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivizationcited by 124
  10. 2023What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalizationcited by 112
  11. 2025Self-Rewarding Vision-Language Model via Reasoning Decompositioncited by 95
  12. 2024Model Collapse Demystified: The Case of Regressioncited by 80
10 more
  1. 2025Self-rewarding correction for mathematical reasoningcited by 67
  2. 2024Language Models are Hidden Reasoners: Unlocking Latent Reasoning Capabilities via Self-Rewardingcited by 53
  3. 2024Rate of Model Collapse in Recursive Trainingcited by 22
  4. 2024Heat Death of Generative Models in Closed-Loop Learningcited by 21
  5. 2024Towards a theory of model distillationcited by 14
  6. 2025Large Language Models Encode Semantics and Alignment in Linearly Separable Representationscited by 14
  7. 2025PACR: Progressively Ascending Confidence Reward for LLM Reasoningcited by 9
  8. 2025Confidence as a Reward: Transforming LLMs into Reward Modelscited by 5
  9. 2022Semi-supervised Batch Learning From Logged Datacited by 2
  10. 2022The Best of Both Worlds: Reinforcement Learning with Logarithmic Regret and Policy Switchescited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loopscited by 25

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  1. 2026Theoretical Limits of Language Model Alignment
  2. 2024Dynamic Rewarding with Prompt Optimization Enables Tuning-free Self-Alignment of Language Models
  3. 2024Extensive Self-Contrast Enables Feedback-Free Language Model Alignment
  4. 2025Scalable Best-of-N Selection for Large Language Models via Self-Certainty
  5. 2024RMB: Comprehensively Benchmarking Reward Models in LLM Alignment
  6. 2024Self-Improvement in Language Models: The Sharpening Mechanism
  7. 2024Self-Exploring Language Models: Active Preference Elicitation for Online Alignment
  8. 2026Revisiting the (Sub)Optimality of Best-of-N for Inference-Time Alignment