# When Do Concepts Become Functionally Sufficient During Language-Model Training?

arXiv: https://arxiv.org/abs/2608.15323 · HTML: https://mlsanity.com/paper/2608.15323/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 52 references that are in the map.
- First posted on arXiv 15 Aug 2026.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [An Empirical Model of Large-Batch Training](https://mlsanity.com/paper/1812.06162/) (2018)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [Group Fisher Pruning for Practical Network Compression](https://mlsanity.com/paper/2108.00708/) (2021)
- [A Holistic Approach to Unifying Automatic Concept Extraction and Concept Importance Estimation](https://mlsanity.com/paper/2306.07304/) (2023)
- [Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning](https://mlsanity.com/paper/2405.12241/) (2024)
- [Deep Feature Factorization For Concept Discovery](https://mlsanity.com/paper/1806.10206/) (2018)
- [The Shape of Learning: Anisotropy and Intrinsic Dimensions in Transformer-Based Models](https://mlsanity.com/paper/2311.05928/) (2023)
- [EuroBERT: Scaling Multilingual Encoders for European Languages](https://mlsanity.com/paper/2503.05500/) (2025)
- [Tracking the Feature Dynamics in LLM Training: A Mechanistic Study](https://mlsanity.com/paper/2412.17626/) (2024)
- [ModernBERT or DeBERTaV3? Examining Architecture and Data Influence on Transformer Encoder Models Performance](https://mlsanity.com/paper/2504.08716/) (2025)
- [ConSim: Measuring Concept-Based Explanations' Effectiveness with Automated Simulatability](https://mlsanity.com/paper/2501.05855/) (2025)
- [Making Coherence Out of Nothing At All: Measuring the Evolution of Gradient Alignment](https://mlsanity.com/paper/2008.01217/) (2020)
- [FishBack: Pullback Fisher Geometry for Optimal Activation Steering in Transformers](https://mlsanity.com/paper/2605.17231/) (2026)
- [Features that Make a Difference: Leveraging Gradients for Improved Dictionary Learning](https://mlsanity.com/paper/2411.10397/) (2024)
- [How a Bilingual LM Becomes Bilingual: Tracing Internal Representations with Sparse Autoencoders](https://mlsanity.com/paper/2503.06394/) (2025)
- [Revisiting Anisotropy in Language Transformers: The Geometry of Learning Dynamics](https://mlsanity.com/paper/2604.08764/) (2026)

## Built on by (most cited first, 1 of 1)

- [Temporally-Resolved Token Attribution Reveals the Generation Dynamics of Diffusion Language Models](https://mlsanity.com/paper/2610.01177/) (2026)

## Abstract (arXiv)

Understanding a model and its learning mechanisms in depth requires identifying when its internal structures become useful, rather than simply looking at the final state. We study this through concept dynamics: at each layer and checkpoint, we decompose activations, select sparse soft masks, and inject masked reconstructions into the model. Concept analysis is therefore tested functionally: a mask is useful only insofar as it preserves a target under intervention. We compare sufficiency for activation reconstruction, linear decodability, true downstream preservation, and checkpoint transfer under learned alignment. The framework treats decomposition assumptions as hypotheses rather than interpretability guarantees, monitoring functional sufficiency across checkpoints and source-to-final reconstructability under learned alignment. At the shared fixed-penalty operating point across seven models, downstream masks retain substantially less soft mass than reconstruction masks; predictive-distribution shifts remain small.