# Everything in Moderation: Per-Domain Coverage Optima and Alignment-Resistant Domain Gaps in Multi-Domain Mid-Training

arXiv: https://arxiv.org/abs/2609.09081 · HTML: https://mlsanity.com/paper/2609.09081/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 55 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Builds on (most cited first, 30 of 46)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [CLUTRR: A Diagnostic Benchmark for Inductive Reasoning from Text](https://mlsanity.com/paper/1908.06177/) (2019)

## Abstract (arXiv)

Mid-training, the stage between pre-training and alignment, is where a model's per-domain data composition is typically set by data availability rather than principled design. We ask what that decision buys, and whether a later alignment pass can undo it. In a controlled logical-reasoning setting (Qwen3-8B-Base, with a 4B replication; five semantically rule-disjoint KOR-Bench domains) we train 30 allocations spanning the five-domain simplex, 24 sweep configurations plus six withheld from the fit, at five seeds each. Three findings emerge. First, every domain has an interior coverage optimum: the moderate band (10%-40%) is best for all five domains, and a calibrated permutation test for quadratic interiority gives P≈0.010; the fitted mid-training-only curves, with 8B peaks between 9.9% and 35.1%, reproduce for curve shape but not peak location. Second, the gaps survive a fixed-budget alignment pass: compensatory SFT raises 116/120 cells (mean +4.32%) yet bridges 0/240 pairs at a 5% threshold and 30/240 at a 10% ratio, an equal-budget uniform control behaves almost identically, and a permutation null would bridge 13.8±3.3 and 77.9±8.5 pairs (P<0.001). Third, zero coverage collapses mid-training-only accuracy, though a FineWeb-Edu-only control shows the collapse is commingled with generic drift. An exploratory θ^* allocation attains the largest full-pipeline gain (+4.36% vs. +0.80%/+0.64%,pp) but is marginal under Welch test.