Learning without Overwriting: A Theory of Self-Distillation and Supervised Fine-Tuning in Continual Reasoning

arXiv:2610.05200 · cs.LG · Submitted 2026-10-04 · Read on arXiv

cs.LG

Submitted: 2026-10-04

Updated: 2026-10-04

Code: https://github.com/yuukiizayoi/continual-reasoning-experiments

Terminology

• Distillation — 1× in this paper · explained in 2 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Self-Distillation — 1× in this paper · explained in 7 episodes

Sources

• How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad
• A Quantitative Characterization of Forgetting in Post-Training
• Distributional Biases in Post-Training: A Markovian Analysis of Reasoning Trajectories
• Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting
• Reinforcement Learning via Self-Distillation
• Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning
• Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?
• Reinforcement Fine-Tuning Naturally Mitigates Forgetting in Continual Post-Training
• Self-Distilled Policy Gradient
• An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning
• WizardCoder: Empowering Code Large Language Models with Evol-Instruct
• CRISP: Compressed Reasoning via Iterative Self-Policy Distillation
• On The Statistical Limits of Self-Improving Agents
• Entropy-Preserving Supervised Fine-Tuning via Adaptive Self-Distillation for Large Reasoning Models
• TRACE: A Comprehensive Benchmark for Continual Learning in Large Language Models
• Self-Consistency Improves Chain of Thought Reasoning in Language Models
• Aligning Large Language Models with Human: A Survey
• Provable Benefits of RLVR over SFT for Reasoning Models: Learning to Backtrack Efficiently
• Diversity-Aware Policy Optimization for Large Language Model Reasoning
• Tree of Thoughts: Deliberate Problem Solving with Large Language Models

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