Low-Rank-Modulated Functa: Exploring the Latent Space of Implicit Neural Representations for Interpretable Ultrasound Video Analysis

Implicit neural representations (INRs) have emerged as a powerful framework for continuous image representation learning. In Functa-based approaches, each image is encoded as a latent modulation vector that conditions a shared INR, enabling strong reconstruction performance. However, the structure and interpretability of the corresponding latent spaces remain largely unexplored. In this work, we investigate the latent space of Functa-based models for ultrasound videos and propose Low-Rank-Modulated Functa (LRM-Functa), a novel architecture that enforces a low-rank adaptation of modulation vectors in the time-resolved latent space. When applied to cardiac ultrasound, the resulting latent space exhibits clearly structured periodic trajectories, facilitating visualization and interpretability of temporal patterns. The latent space can be traversed to sample novel frames, revealing smooth transitions along the cardiac cycle, and enabling direct readout of end-diastolic (ED) and end-systolic (ES) frames without additional model training. We show that LRM-Functa outperforms prior methods in unsupervised ED and ES frame detection, while compressing each video frame to as low as rank k=2 without sacrificing competitive downstream performance on ejection fraction prediction. Evaluations on out-of-distribution frame selection in a cardiac point-of-care dataset, as well as on lung ultrasound for B-line classification, demonstrate the generalizability of our approach. Overall, LRM-Functa provides a compact, interpretable, and generalizable framework for ultrasound video analysis. The code is available at https://github.com/JuliaWolleb/LRM_Functa.