A Sheaf-Theoretic Framework for Distributed Multi-Site Channel Charting

Channel charting (CC) enables data-driven user localization in wireless networks by embedding channel state information (CSI) into low-dimensional representations. In multi-cell scenarios, each base station independently learns a local chart via neural encoders, leading to misaligned representation spaces across overlapping coverage areas. This lack of consistency hinders network-level tasks such as user tracking, handover prediction, and resource allocation. To address this issue, we propose a principled framework for multi-site channel charting based on topological signal processing. We model the collection of local charts as a network sheaf, which encodes consistency constraints across the network and enables the coherent integration of locally learned representations into a shared global structure. This formulation introduces an interpretable inductive bias that promotes alignment across base stations while preserving local geometric fidelity. Building on this model, we develop a multi-site channel charting architecture and an alternating optimization algorithm that jointly updates neural encoders and inter-site orthogonal transport maps, with theoretical guarantees on consistency. Experimental results validate the effectiveness of the proposed approach, demonstrating improved cross-site alignment without degrading the quality of local embeddings.

SEMASIA: A Large-Scale Dataset of Semantically Structured Latent Representations

Latent representations learned by neural networks often exhibit semantic structure, where concept similarity is reflected by geometric proximity in embedding space. However, comparing such spaces across models remains difficult: changes in architecture, pretraining data, objective, or random seed can yield embeddings with similar content but incompatible geometry. This latent space alignment problem is central to interpretability, transfer and multimodal learning, federated systems, and semantic communication; however, progress remains limited by the lack of large-scale, model-diverse, and metadata-rich benchmarks. To address this gap, we introduce SEMASIA, a large-scale collection of latent representations extracted from approximately 1,700 pretrained vision models across eight standard image-classification benchmarks. SEMASIA pairs embeddings with structured metadata describing architectures, training regimes, pretraining sources, and model scale. We demonstrate three applications of the resource. First, we analyze the conceptual organization of individual latent spaces, showing consistent prototype-like clustering and hierarchical semantic neighborhoods across models and datasets. Second, we benchmark supervised alignment mappings between latent spaces using reconstruction error and downstream task performance. Third, we perform a large-scale regression analysis of how pretraining-data complexity, specialization, transfer learning, augmentation, and model scale relate to geometric and probing properties of embeddings. By coupling representational scale with standardized metadata, SEMASIA provides a reproducible foundation for studying latent geometry, evaluating alignment methods, and developing next-generation heterogeneous and interoperable AI systems.

Topological Dictionary Learning

The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology into the dictionary structure via concatenated sub-dictionaries, each as a polynomial of Hodge Laplacians, yielding localized spectral topological filter frames. The learning problem is cast to jointly infer the underlying cell complex and optimize the dictionary coefficients and the sparse signal representation. We efficiently solve the problem via iterative alternating algorithms. Numerical results on both synthetic and real data show the effectiveness of the proposed procedure in jointly learning the sparse representations and the underlying relational structure of topological signals.