# Model-Aware Data Selection from In-and-Out Information Interplay

arXiv: https://arxiv.org/abs/2609.33010 · HTML: https://mlsanity.com/paper/2609.33010/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 26 Sep 2026.

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [Molmo and PixMo: Open Weights and Open Data for State-of-the-Art Vision-Language Models](https://mlsanity.com/paper/2409.17146/) (2024)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [FinanceBench: A New Benchmark for Financial Question Answering](https://mlsanity.com/paper/2311.11944/) (2023)
- [Language Modeling Is Compression](https://mlsanity.com/paper/2309.10668/) (2023)
- [QuRating: Selecting High-Quality Data for Training Language Models](https://mlsanity.com/paper/2402.09739/) (2024)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [Molmo2: Open Weights and Data for Vision-Language Models with Video Understanding and Grounding](https://mlsanity.com/paper/2601.10611/) (2026)
- [OpenCoder: The Open Cookbook for Top-Tier Code Large Language Models](https://mlsanity.com/paper/2411.04905/) (2024)
- [MedCaseReasoning: Evaluating and learning diagnostic reasoning from clinical case reports](https://mlsanity.com/paper/2505.11733/) (2025)

## Abstract (arXiv)

LLMs are effective representations that assimilate vast amounts of knowledge during pretraining, but post-training is necessary for models to reliably access this knowledge and "know what they know." We observe an interesting rank equilibrium between knowledge stored in the weights and the data stream passing through the model. Across all model layers, we find that the hidden states (data stream) follow a U-shaped pattern, showing substantial compression in early layers and a steep rise during the late-layer decoding phase. In contrast, the weight rank follows an inverted U-shaped pattern, with very low rank in the early and late layers and high rank in the middle. We interpret this as an in-and-out information interplay: intermediate activations do not need to carry content that the weights can supply later, so they primarily preserve what the weights cannot provide. Motivated by this observation, we propose a model-aware data selection method, CAP (Counterfactual Assimilation Profile), which can determine whether a data candidate contains information accessible to the current model by utilizing the divergence gap in early- and late-layer representations between model-generated and reference responses. Across math, code, and science domains, CAP delivers 35.4% greater average improvement over the base model than the strongest baseline under different selection budgets. With only 10% of the data pool, CAP surpasses or matches full-pool training on math and science. We further show that CAP transfers to multimodal data selection and is robust to response horizon and noise.