Learning Fingerprints for Medical Time Series with Redundancy-Constrained Information Maximization

Learning meaningful representations from medical time series (MedTS), such as ECG or EEG signals, is a critical challenge. These signals are often high-dimensional, variable-length, and rife with noise. Existing self-supervised approaches, such as Masked Autoencoders (MAEs), are highly effective for pre-training general-purpose encoders. However, they do not explicitly learn compact, fixed-size, or semantically interpretable latent representations, typically relying on heuristic aggregation strategies such as global average pooling or a designated [CLS] token. We propose a novel framework that compresses a variable-length MedTS into a fixed-size set of $k$ latent Fingerprint Tokens. Our architecture employs a cross-attention bottleneck to generate these tokens and is trained with a dual-objective function. The first objective is a reconstruction loss, which ensures the tokens are sufficient statistics for the original data. The second, a diversity penalty based on the Total Coding Rate (TCR), explicitly minimizes the redundancy between tokens, encouraging them to become statistically disentangled representations. We present the theoretical justification for our method, framing it as a novel Disentangled Rate-Distortion problem. This approach produces a low-dimensional, interpretable, and sample-efficient representation, where each token is encouraged to capture an independent factor of variation, paving the way for more robust digital biomarkers.