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 Adaptive Least Mean Squares Algorithms over Simplicial Complexes

This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we present a topological LMS algorithm that efficiently processes streaming signals observed over time-varying edge subsets. We provide a detailed stochastic analysis of the algorithm, deriving its stability conditions, steady-state mean-square-error, and convergence speed, while exploring the impact of edge sampling on performance. We also propose strategies to design optimal edge sampling probabilities, minimizing rate while ensuring desired estimation accuracy. Assuming partial knowledge of the complex structure (e.g., the underlying graph), we introduce an adaptive topology inference method that integrates with the proposed LMS framework. Additionally, we propose a distributed version of the algorithm and analyze its stability and mean-square-error properties. Empirical results on synthetic and real-world traffic data demonstrate that our approach, in both centralized and distributed settings, outperforms graph-based LMS methods by leveraging higher-order topological features.