# Characterizing Model-Native Skills

arXiv: https://arxiv.org/abs/2604.17614 · HTML: https://mlsanity.com/paper/2604.17614/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 63 references that are in the map.
- First posted on arXiv 19 Apr 2026.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Jailbreaking Black Box Large Language Models in Twenty Queries](https://mlsanity.com/paper/2310.08419/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [A StrongREJECT for Empty Jailbreaks](https://mlsanity.com/paper/2402.10260/) (2024)
- [DeepInception: Hypnotize Large Language Model to Be Jailbreaker](https://mlsanity.com/paper/2311.03191/) (2023)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preference](https://mlsanity.com/paper/2406.15513/) (2024)
- [WildTeaming at Scale: From In-the-Wild Jailbreaks to (Adversarially) Safer Language Models](https://mlsanity.com/paper/2406.18510/) (2024)
- [AutoDAN-Turbo: A Lifelong Agent for Strategy Self-Exploration to Jailbreak LLMs](https://mlsanity.com/paper/2410.05295/) (2024)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [A Theory for Emergence of Complex Skills in Language Models](https://mlsanity.com/paper/2307.15936/) (2023)
- [NaturalReasoning: Reasoning in the Wild with 2.8M Challenging Questions](https://mlsanity.com/paper/2502.13124/) (2025)
- [AceReason-Nemotron 1.1: Advancing Math and Code Reasoning through SFT and RL Synergy](https://mlsanity.com/paper/2506.13284/) (2025)
- [CodeChameleon: Personalized Encryption Framework for Jailbreaking Large Language Models](https://mlsanity.com/paper/2402.16717/) (2024)

## Abstract (arXiv)

Skills are a natural unit for describing what a language model can do and how its behavior can be changed. However, existing characterizations rely on human-written taxonomies, textual descriptions, or manual profiling pipelines--all external hypotheses about what matters that need not align with the model's internal representations. We argue that when the goal is to intervene on model behavior, skill characterization should be *model-native*: grounded in the model's own representations rather than imposed through external ontologies. We instantiate this view by recovering a compact orthogonal basis from sequence-level activations. The resulting basis is semantically interpretable but need not correspond to any predefined human ontology; instead, it captures axes of behavioral variation that the model itself organizes around. We validate this characterization on reasoning post-training, using the recovered basis for both SFT data selection and inference-time steering. We develop lightweight proxy interventions to identify which directions are most useful for a given model. Across Llama3-8B and Qwen2.5-3B, selecting data along those directions improves Pass@1 by up to 20% on MATH and 41% on AMC, outperforming data selection based on human-characterized skills. Because the basis lives in activation space, the same directions also serve as steering vectors at inference time, improving Pass@8 by up to 4.8% on MATH--an intervention that human-characterized skills cannot support. We further validate the characterization on safety alignment, where selecting adversarial training data for model-native skill coverage rather than textual diversity yields more sample-efficient learning. These results suggest that recovering skills from the model's own representations, rather than imposing them externally, provides a more effective foundation for intervening on model behavior. Codes are open-sourced.