# Activation-Conditioned Self-Distillation

arXiv: https://arxiv.org/abs/2609.38342 · HTML: https://mlsanity.com/paper/2609.38342/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 25 of its 26 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 25 of 25)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification](https://mlsanity.com/paper/2504.05419/) (2025)
- [Understanding Reasoning in Thinking Language Models via Steering Vectors](https://mlsanity.com/paper/2506.18167/) (2025)
- [SEAL: Steerable Reasoning Calibration of Large Language Models for Free](https://mlsanity.com/paper/2504.07986/) (2025)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [Purified OPSD: On-Policy Self-Distillation Without Losing How to Think](https://mlsanity.com/paper/2607.02234/) (2026)
- [OGLS-SD: On-Policy Self-Distillation with Outcome-Guided Logit Steering for LLM Reasoning](https://mlsanity.com/paper/2605.12400/) (2026)
- [Adaptive Teacher Exposure for Self-Distillation in LLM Reasoning](https://mlsanity.com/paper/2605.11458/) (2026)
- [Exploring and Exploiting the Inherent Efficiency within Large Reasoning Models for Self-Guided Efficiency Enhancement](https://mlsanity.com/paper/2506.15647/) (2025)
- [One Student, Many Teachers: Multi-Task On-Policy Distillation via Soft-Prompt Privileged Context](https://mlsanity.com/paper/2607.18293/) (2026)
- [S3-CoT: Self-Sampled Succinct Reasoning Enables Efficient Chain-of-Thought LLMs](https://mlsanity.com/paper/2602.01982/) (2026)
- [SafeSteer: Localized On-Policy Distillation for Efficient Safety Alignment](https://mlsanity.com/paper/2606.02530/) (2026)

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

- [Learning from Self-Generated Responses: Reliability--Uncertainty Self-Distillation for Reasoning](https://mlsanity.com/paper/2610.19176/) (2026)

## Abstract (arXiv)

On-policy self-distillation uses a model as its own teacher to provide dense supervision for reasoning, often through reference-solution conditioning. Providing privileged information does not by itself ensure effective token-level supervision throughout long responses. We introduce Activation-Conditioned Self-Distillation (ACSD), which extracts a steering vector by contrasting activations of self-generated trajectories that reach verified correct answers within a generation budget with those of all remaining trajectories. A frozen copy of the base model applies this vector at each prediction position, and the student learns from its next-token distributions on student-generated prefixes. Outcome verification is used for direction construction and calibration; distillation requires neither problem-specific reference text nor teacher parameter updates. The distilled student is used alone at inference. On each of five models, ACSD achieves the highest mean accuracy over four mathematical benchmarks among the evaluated methods. On DeepSeek-R1-0528-Qwen3-8B, mean mathematical accuracy reaches 71.9% and LiveCodeBench v6 pass@12 reaches 70.9%, compared with 69.0% and 66.3% for the reference-conditioned OPSD baseline. Contrasts among correct trajectories also support distillation, and extracted directions can be reused across mathematical training datasets. On fixed student trajectories, ACSD maintains more stable late-position logit-update magnitudes than OPSD.