# Let the Data Decide: Supervision Analysis, Capability Trade-offs, and Adaptive Objective Routing in Continued Pre-Training via Off-Policy Distillation

arXiv: https://arxiv.org/abs/2607.16246 · HTML: https://mlsanity.com/paper/2607.16246/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 20 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [MobileBERT: a Compact Task-Agnostic BERT for Resource-Limited Devices](https://mlsanity.com/paper/2004.02984/) (2020)
- [MiniLMv2: Multi-Head Self-Attention Relation Distillation for Compressing Pretrained Transformers](https://mlsanity.com/paper/2012.15828/) (2020)
- [Compact Language Models via Pruning and Knowledge Distillation](https://mlsanity.com/paper/2407.14679/) (2024)
- [LFM2 Technical Report](https://mlsanity.com/paper/2511.23404/) (2025)
- [Pre-training Distillation for Large Language Models: A Design Space Exploration](https://mlsanity.com/paper/2410.16215/) (2024)
- [TAID: Temporally Adaptive Interpolated Distillation for Efficient Knowledge Transfer in Language Models](https://mlsanity.com/paper/2501.16937/) (2025)
- [SelecTKD: Selective Token-Weighted Knowledge Distillation for LLMs](https://mlsanity.com/paper/2510.24021/) (2025)
- [Sparse Logit Sampling: Accelerating Knowledge Distillation in LLMs](https://mlsanity.com/paper/2503.16870/) (2025)
- [LLM-Oriented Token-Adaptive Knowledge Distillation](https://mlsanity.com/paper/2510.11615/) (2025)
- [Distilled Pretraining: A modern lens of Data, In-Context Learning and Test-Time Scaling](https://mlsanity.com/paper/2509.01649/) (2025)
- [Don't Ignore the Tail: Decoupling top-K Probabilities for Efficient Language Model Distillation](https://mlsanity.com/paper/2602.20816/) (2026)
- [SlimQwen: Exploring the Pruning and Distillation in Large MoE Model Pre-training](https://mlsanity.com/paper/2605.08738/) (2026)
- [EGAD: Entropy-Guided Adaptive Distillation for Token-Level Knowledge Transfer](https://mlsanity.com/paper/2605.01732/) (2026)

## Abstract (arXiv)

Off-policy distillation is now central to large language model pre-training, yet how training data, objective parameterization, and model capabilities interact remains poorly characterized. We studies top-k-truncated, temperature-scaled off-policy distillation by decomposing this problem into two questions: an objective-to-capability analysis of how the training objective shapes token-level supervision and downstream performance, and a data-to-objective analysis of how data heterogeneity should inform objective routing. We first show that the language-modeling objective (LLM) and the knowledge-distillation objective (LKD) induce systematically different capability profiles, and trace this divergence to a gradient-level tension between direct observed-token reinforcement and teacher-supported alternative supervision. To quantify this tension, we introduce diagnostic metrics -- support coverage, observed-token probability mass, and teacher-distribution concentration -- and show via controlled sweeps that the support size k governs a coverage-sharpness trade-off, while distillation temperature controls within-support probability allocation. We then examine adaptive objective routing: a domain-level policy that applies LLM to math and code and LKD to general-domain data yields consistent gains over both single-objective baselines, whereas token-level routing based on observed-token probability mass or teacher entropy fails to consistently match the single-objective baseline. These results suggest that effective objective routing depends less on routing granularity than on the quality of the routing signal, reframing continued pre-training via off-policy distillation as a structured, data-conditional supervision-design problem rather than a global hyperparameter choice.