Therefore, many existing SLP vectorization schemes are driven by hand-crafted heuristics (Liu et al., 2012;

A one-layer IGNN with hidden units as 64 is implemented on all data sets.

Thebottom-up-and-top-down ConvRNN architecture is related to the standard U-Net structure (e.g.

Neural Information Processing Systems http://nips.cc/

Deep neural networks can convert ECG page images into analyzable waveforms, yet centralized training often conflicts with cross-institutional privacy and deployment constraints. A cross-silo federated digitization framework is presented that trains a full-model nnU-Net segmentation backbone without sharing images and aggregates updates across sites under realistic non-IID heterogeneity (layout, grid style, scanner profile, noise). The protocol integrates three standard server-side aggregators--FedAvg, FedProx, and FedAdam--and couples secure aggregation with central, user-level differential privacy to align utility with formal guarantees. Key features include: (i) end-to-end full-model training and synchronization across clients; (ii) secure aggregation so the server only observes a clipped, weighted sum once a participation threshold is met; (iii) central Gaussian DP with Renyi accounting applied post-aggregation for auditable user-level privacy; and (iv) a calibration-aware digitization pipeline comprising page normalization, trace segmentation, grid-leakage suppression, and vectorization to twelve-lead signals. Experiments on ECG pages rendered from PTB-XL show consistently faster convergence and higher late-round plateaus with adaptive server updates (FedAdam) relative to FedAvg and FedProx, while approaching centralized performance. The privacy mechanism maintains competitive accuracy while preventing exposure of raw images or per-client updates, yielding deployable, auditable guarantees suitable for multi-institution settings.

We present CuMPerLay, a novel differentiable vectorization layer that enables the integration of Cubical Multiparameter Persistence (CMP) into deep learning pipelines. While CMP presents a natural and powerful way to topologically work with images, its use is hindered by the complexity of multifiltration structures as well as the vectorization of CMP. In face of these challenges, we introduce a new algorithm for vectorizing MP homologies of cubical complexes. Our CuMPerLay decomposes the CMP into a combination of individual, learnable single-parameter persistence, where the bifiltration functions are jointly learned. Thanks to the differentiability, its robust topological feature vectors can be seamlessly used within state-of-the-art architectures such as Swin Transformers. We establish theoretical guarantees for the stability of our vectorization under generalized Wasserstein metrics. Our experiments on benchmark medical imaging and computer vision datasets show the benefit CuMPerLay on classification and segmentation performance, particularly in limited-data scenarios. Overall, CuMPerLay offers a promising direction for integrating global structural information into deep networks for structured image analysis.