# Distilling Directional Verification

arXiv: https://arxiv.org/abs/2610.00997 · HTML: https://mlsanity.com/paper/2610.00997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 33 of its 38 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 30 of 33)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Scaling Diffusion Language Models via Adaptation from Autoregressive Models](https://mlsanity.com/paper/2410.17891/) (2024)
- [Surface Form Competition: Why the Highest Probability Answer Isn't Always Right](https://mlsanity.com/paper/2104.08315/) (2021)
- [Data Programming: Creating Large Training Sets, Quickly](https://mlsanity.com/paper/1605.07723/) (2016)
- [Noisy Channel Language Model Prompting for Few-Shot Text Classification](https://mlsanity.com/paper/2108.04106/) (2021)
- [The pitfalls of next-token prediction](https://mlsanity.com/paper/2403.06963/) (2024)
- [BOND: Aligning LLMs with Best-of-N Distillation](https://mlsanity.com/paper/2407.14622/) (2024)
- [Reverse Training to Nurse the Reversal Curse](https://mlsanity.com/paper/2403.13799/) (2024)
- [Towards a Theoretical Understanding of the 'Reversal Curse' via Training Dynamics](https://mlsanity.com/paper/2405.04669/) (2024)
- [The Factorization Curse: Which Tokens You Predict Underlie the Reversal Curse and More](https://mlsanity.com/paper/2406.05183/) (2024)
- [Is the Reversal Curse a Binding Problem? Uncovering Limitations of Transformers from a Basic Generalization Failure](https://mlsanity.com/paper/2504.01928/) (2025)
- [Exploring Knowledge Purification in Multi-Teacher Knowledge Distillation for LLMs](https://mlsanity.com/paper/2602.01064/) (2026)
- [DART: Draft-Agreement Routing for Training-Free Adaptive Thinking Budgets in Hybrid Reasoning Models](https://mlsanity.com/paper/2606.23181/) (2026)
- [Answer-Conditioned Chains of Thought Degrade Verifiable-Reasoning Distillation in Large Language Models](https://mlsanity.com/paper/2607.14552/) (2026)
- [Cross-Tokenizer Likelihood Scoring Algorithms for Language Model Distillation](https://mlsanity.com/paper/2512.14954/) (2025)

## Abstract (arXiv)

Knowledge distillation aims to transfer the factual knowledge of large language models to smaller models for efficient deployment. Yet a teacher may recall a relation in one direction while failing to generate the answer in the reverse direction. Distillation from its generated answers can therefore propagate this directional limitation to the student. The same teacher can nevertheless recognize such an answer by scoring the relation in the direction it knows. We introduce directional label distillation, in which frozen teachers score candidate answers in that known direction and the best-scoring candidate becomes the student's training target. On facts about parents and their children, known-direction scoring yields more accurate labels than scoring the requested direction, even after tuned corrections for name priors. With prior-corrected scores, the better direction depends on the facts rather than the template, and reverses on mined facts whose notable entity is the parent rather than the child. With the evaluated children's forward facts withheld, students trained on known-direction labels improve open-ended accuracy on their trained queries by 13 to 15 points over students trained on prior-corrected reverse labels. After generated answers are matched to a fixed name list by lexical similarity, students reproduce nearly all selected labels. Their accuracy largely follows label quality. The label advantage holds on unscreened queries and when candidates are retrieved without inserting correct answers. Our findings show that directional verification mitigates the transfer of errors from teacher-generated answers to students by providing more accurate training targets. Code is available at https://github.com/js-lee-AI/directional-verification.