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 and 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 $\mathit{\text{sufficient}}\mathit{\text{statistics}}$ 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 $\mathit{\text{disentangled}}$ representations. We present the theoretical justification for our method, framing it as a novel $\mathbf{\text{Disentangled}}\mathbf{\text{Rate-Distortion}}$ 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.