# GATES: Self-Distillation under Privileged Context with Consensus Gating

arXiv: https://arxiv.org/abs/2602.20574 · HTML: https://mlsanity.com/paper/2602.20574/

## Key facts

- Cited by 35 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 20 of its 31 references that are in the map.
- First posted on arXiv 24 Feb 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, 20 of 20)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Patient Knowledge Distillation for BERT Model Compression](https://mlsanity.com/paper/1908.09355/) (2019)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Revisiting Self-Training for Neural Sequence Generation](https://mlsanity.com/paper/1909.13788/) (2019)
- [SPICE: Self-Play In Corpus Environments Improves Reasoning](https://mlsanity.com/paper/2510.24684/) (2025)
- [Nemotron-CC-Math: A 133 Billion-Token-Scale High Quality Math Pretraining Dataset](https://mlsanity.com/paper/2508.15096/) (2025)

## Built on by (most cited first, 30 of 35)

- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [When Are Teacher Tokens Reliable? Position-Weighted On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2605.21606/) (2026)
- [Respecting Self-Uncertainty in On-Policy Self-Distillation for Efficient LLM Reasoning](https://mlsanity.com/paper/2605.13255/) (2026)
- [Prefix Teach, Suffix Fade: Local Teachability Collapse in Strong-to-Weak On-Policy Distillation](https://mlsanity.com/paper/2605.13643/) (2026)
- [Trajectory-Refined Distillation](https://mlsanity.com/paper/2606.08432/) (2026)
- [Adaptive Teacher Exposure for Self-Distillation in LLM Reasoning](https://mlsanity.com/paper/2605.11458/) (2026)
- [DOPD: Dual On-policy Distillation](https://mlsanity.com/paper/2606.30626/) (2026)
- [Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2605.22263/) (2026)
- [Rethinking Privileged Information in On-Policy Self-Distillation](https://mlsanity.com/paper/2608.18271/) (2026)
- [ReNIO: Reweighting Negative Trajectory Importance for LLM On-Policy Distillation](https://mlsanity.com/paper/2606.23104/) (2026)
- [H2SD: Hybrid Hindsight Self-Distillation](https://mlsanity.com/paper/2607.18955/) (2026)
- [Off-Context GRPO: Learning to Reason on Hard Problems using Privileged Information](https://mlsanity.com/paper/2607.19313/) (2026)
- [OPSD Compresses What RLVR Teaches: A Post-RL Compaction Stage for Reasoning Models](https://mlsanity.com/paper/2605.06188/) (2026)
- [Keep Policy Gradient in Charge: Sibling-Guided Credit Distillation for Long-Horizon Tool-Use Agents](https://mlsanity.com/paper/2606.12634/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [DemoPSD: Disagreement-Modulated Policy Self-Distillation](https://mlsanity.com/paper/2607.02502/) (2026)
- [Consensus as Privileged Context for Label-Free Self-Distillation](https://mlsanity.com/paper/2607.13643/) (2026)
- [Verify Before You Distill: Prompt-Level Teacher Gating for On-Policy Distillation](https://mlsanity.com/paper/2609.02998/) (2026)
- [The Verifier is the Curriculum: Precision Sets the Return on Search in Code Self-Distillation](https://mlsanity.com/paper/2607.09709/) (2026)
- [Matching Supervision to the Student's Learning Capacity: A Unified Framework for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.08176/) (2026)
- [Language Models Need Sleep: Learning to Self-Modify and Consolidate Memories](https://mlsanity.com/paper/2606.03979/) (2026)
- [Geometric Self-Distillation for Reasoning Generalization](https://mlsanity.com/paper/2607.06855/) (2026)
- [Self-Distillation Policy Optimization via Visual Feedback: Bridging Code and Visual Artifacts](https://mlsanity.com/paper/2606.10334/) (2026)
- [Learning from Consensus and Disagreement: Unsupervised On-Policy Self-Distillation with Minority-Trajectory Contrast](https://mlsanity.com/paper/2608.08764/) (2026)
- [Signal Reshaping for GRPO in Weak-Feedback Agentic Code Repair](https://mlsanity.com/paper/2605.07276/) (2026)
- [SR-OPSD: Self-Referenced On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09745/) (2026)
- [Teach Yourself Where to Look: On-Policy Attention Self-Distillation for Reasoning](https://mlsanity.com/paper/2609.33200/) (2026)
- [OSPD: On-Policy Self-Distillation for Persona-Consistent Dialogue](https://mlsanity.com/paper/2609.34418/) (2026)

## Abstract (arXiv)

We study self-distillation in settings where supervision is unreliable: there are no ground truth labels, verifiable rewards, or external graders to evaluate answers. We focus on document-grounded question answering with asymmetric context, where a single model serves as both tutor (with access to a relevant source document during training) and student (answering from the question alone at test time). Rather than assuming tutor correctness, we derive supervision online from tutor consensus by sampling multiple document-grounded reasoning traces and using agreement to gate learning. Conditioned on this reliability signal, we distill knowledge through full tutor reasoning trajectories (not just final answers), providing a dense and stable learning signal. Empirically, this consensus-gated trajectory distillation substantially improves transfer to the document-free student. Held-out in-domain accuracy under asymmetric evaluation improves from 46.0% to 62.0%, and average (maj@8) accuracy on public document-free math benchmarks improves from 20.2% to 35.4%.