# Specialization after Generalization: Towards Understanding Test-Time Training in Foundation Models

arXiv: https://arxiv.org/abs/2509.24510 · HTML: https://mlsanity.com/paper/2509.24510/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 97 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 30 of 55)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [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)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [MEMO: Test Time Robustness via Adaptation and Augmentation](https://mlsanity.com/paper/2110.09506/) (2021)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Implicit Bias of Gradient Descent on Linear Convolutional Networks](https://mlsanity.com/paper/1806.00468/) (2018)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Linear Representations of Sentiment in Large Language Models](https://mlsanity.com/paper/2310.15154/) (2023)
- [Neural Networks can Learn Representations with Gradient Descent](https://mlsanity.com/paper/2206.15144/) (2022)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)

## Built on by (most cited first, 5 of 5)

- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Expanding the Role of Diffusion Models for Robust Classifier Training](https://mlsanity.com/paper/2602.19931/) (2026)
- [A Decision-Theoretic View of Test-Time Training: When, How Far, and Which Directions to Adapt](https://mlsanity.com/paper/2606.15569/) (2026)
- [Local Sparsity Enables Unsupervised LLM Safety Detection](https://mlsanity.com/paper/2609.20129/) (2026)
- [A Survey on the Linear Representation Hypothesis](https://mlsanity.com/paper/2609.22695/) (2026)

## Abstract (arXiv)

Recent empirical studies have explored the idea of continuing to train a model at test-time for a given task, known as test-time training (TTT), and have found it to yield significant performance improvements. However, there is limited understanding of why and when TTT is effective. Earlier explanations mostly focused on the observation that TTT may help when applied to out-of-distribution adaptation or used with privileged data. However, the growing scale of foundation models with most test data being in-distribution questions these explanations. We instead posit that foundation models remain globally underparameterized, with TTT providing a mechanism for specialization after generalization, focusing capacity on concepts relevant to the test task. Specifically, under the linear representation hypothesis, we propose a model in which TTT achieves a substantially smaller in-distribution test error than global training. We empirically validate our model's key assumptions by training a sparse autoencoder on ImageNet, showing that semantically related data points are explained by only a few shared concepts. Finally, we perform scaling studies across image and language tasks that confirm the practical implications of our model, identifying the regimes where specialization is most effective.