# Capturing Cardiac Cyclicity through Phase-Equivariant Self-Supervised Learning

arXiv: https://arxiv.org/abs/2608.21147 · HTML: https://mlsanity.com/paper/2608.21147/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 57 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 30 of 41)

- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [Deep Learning for ECG Analysis: Benchmarks and Insights from PTB-XL](https://mlsanity.com/paper/2004.13701/) (2020)
- [Deep Scale-spaces: Equivariance Over Scale](https://mlsanity.com/paper/1905.11697/) (2019)
- [Unlocking State-Tracking in Linear RNNs Through Negative Eigenvalues](https://mlsanity.com/paper/2411.12537/) (2024)
- [Efficient Orthogonal Parametrisation of Recurrent Neural Networks Using Householder Reflections](https://mlsanity.com/paper/1612.00188/) (2016)
- [Unsupervised Learning of Group Invariant and Equivariant Representations](https://mlsanity.com/paper/2202.07559/) (2022)
- [When Does LeJEPA Learn a World Model?](https://mlsanity.com/paper/2605.26379/) (2026)
- [Learning General Representation of 12-Lead Electrocardiogram with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2410.08559/) (2024)
- [Equivariant Representation Learning via Class-Pose Decomposition](https://mlsanity.com/paper/2207.03116/) (2022)
- [Sub-JEPA: Subspace Gaussian Regularization for Stable End-to-End World Models](https://mlsanity.com/paper/2605.09241/) (2026)
- [VISReg: Variance-Invariance-Sketching Regularization for JEPA training](https://mlsanity.com/paper/2606.02572/) (2026)
- [Self-Supervised Pre-Training with Joint-Embedding Predictive Architecture Boosts ECG Classification Performance](https://mlsanity.com/paper/2410.13867/) (2024)
- [Reverso: Efficient Time Series Foundation Models for Zero-shot Forecasting](https://mlsanity.com/paper/2602.17634/) (2026)
- [Subspace-Decomposed JEPAs: Disentangling Progression and Content in Latent World Models](https://mlsanity.com/paper/2605.31111/) (2026)
- [Rectified LpJEPA: Joint-Embedding Predictive Architectures with Sparse and Maximum-Entropy Representations](https://mlsanity.com/paper/2602.01456/) (2026)
- [Wavelet Networks: Scale-Translation Equivariant Learning From Raw Time-Series](https://mlsanity.com/paper/2006.05259/) (2020)
- [Towards a General Intelligence and Interface for Wearable Health Data](https://mlsanity.com/paper/2605.22759/) (2026)
- [SPHERE-JEPA: Spherical Prediction with Homogeneous Embeddings](https://mlsanity.com/paper/2605.26900/) (2026)
- [LeNEPA: No-Augmentation Next-Latent Prediction for Time-Series Representation Learning](https://mlsanity.com/paper/2607.00958/) (2026)
- [Rotary Masked Autoencoders are Versatile Learners](https://mlsanity.com/paper/2505.20535/) (2025)
- [Laya: A LeJEPA Approach to EEG via Latent Prediction over Reconstruction](https://mlsanity.com/paper/2603.16281/) (2026)
- [LuMamba: Latent Unified Mamba for Electrode Topology-Invariant and Efficient EEG Modeling](https://mlsanity.com/paper/2603.19100/) (2026)
- [Temporally Centered SIGReg Improves LeWorldModel Representations for Robot Policy Learning](https://mlsanity.com/paper/2607.26924/) (2026)
- [Learning with Category-Equivariant Architectures for Human Activity Recognition](https://mlsanity.com/paper/2511.01139/) (2025)
- [CardioState-JEPA: Delay-Aware Cross-Modal Learning of a Shared Cardiac Representation](https://mlsanity.com/paper/2608.12944/) (2026)
- [The Rlign Algorithm for Enhanced Electrocardiogram Analysis through R-Peak Alignment for Explainable Classification and Clustering](https://mlsanity.com/paper/2407.15555/) (2024)
- [Sonata: A Hybrid World Model for Inertial Kinematics under Clinical Data Scarcity](https://mlsanity.com/paper/2604.18058/) (2026)

## Abstract (arXiv)

The cyclic structure of physiological processes offers a natural prior for self-supervised representation learning, and the cardiac cycle provides a particularly well-defined setting in which to exploit it. We derive a phase-equivariant self-supervised objective and introduce Winder, a joint-embedding architecture that organises representations into phase-invariant coordinates and phase-rotating harmonic subspaces. Its transport operator is fixed and closed-form, derived from the cycle's geometry rather than learned, and adds no parameters. Evaluated on PTB-XL under a frozen linear-probe protocol, Winder attains diagnostic accuracy within the range reported by state-of-the-art self-supervised methods at a ~1 M parameter footprint, while exhibiting phase-equivariant latent geometry. These findings demonstrate that explicitly encoding cardiac-phase symmetry can preserve diagnostically useful information while yielding a latent geometry that is legible, parameter-efficient, and directly tied to a measurable physiological quantity.