# Emergent Symbolic Structure in Health Foundation Models: Extraction, Alignment, and Cross-Modal Transfer

arXiv: https://arxiv.org/abs/2605.07407 · HTML: https://mlsanity.com/paper/2605.07407/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 28 of 28)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Exploiting Similarities among Languages for Machine Translation](https://mlsanity.com/paper/1309.4168/) (2013)
- [Relative representations enable zero-shot latent space communication](https://mlsanity.com/paper/2209.15430/) (2022)
- [A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operations](https://mlsanity.com/paper/2302.03025/) (2023)
- [Getting aligned on representational alignment](https://mlsanity.com/paper/2310.13018/) (2023)
- [Offline bilingual word vectors, orthogonal transformations and the inverted softmax](https://mlsanity.com/paper/1702.03859/) (2017)
- [Large-scale Training of Foundation Models for Wearable Biosignals](https://mlsanity.com/paper/2312.05409/) (2023)
- [PaPaGei: Open Foundation Models for Optical Physiological Signals](https://mlsanity.com/paper/2410.20542/) (2024)
- [Scaling Wearable Foundation Models](https://mlsanity.com/paper/2410.13638/) (2024)
- [Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective](https://mlsanity.com/paper/2106.07115/) (2021)
- [Self-supervised transfer learning of physiological representations from free-living wearable data](https://mlsanity.com/paper/2011.12121/) (2020)
- [Discovering Universal Geometry in Embeddings with ICA](https://mlsanity.com/paper/2305.13175/) (2023)
- [Wearable Accelerometer Foundation Models for Health via Knowledge Distillation](https://mlsanity.com/paper/2412.11276/) (2024)

## Abstract (arXiv)

We show that information can be transferred post-hoc across independently trained health foundation models (FMs), each pretrained on ~20M minutes of wearable sensor data from ~172K participants, by aligning their data-dependent coordinate systems. From frozen embeddings we extract candidate symbol-like components using linear decomposition methods, and align them across models with simple linear maps. Aligned symbols associate selectively with health conditions and physiological attributes, with associations similar across modalities and architectures. A classifier trained on one model's symbols and applied to another retains more than 95% of its in-domain performance, with similar retention in both directions. Overall, our results indicate that independently trained health FMs converge toward a common representation of the same underlying physiology.