# Learning Network Sheaves for AI-native Semantic Communication

arXiv: https://arxiv.org/abs/2512.03248 · HTML: https://mlsanity.com/paper/2512.03248/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Builds on (most cited first, 17 of 17)

- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [Deep Learning Enabled Semantic Communication Systems](https://mlsanity.com/paper/2006.10685/) (2020)
- [Relative representations enable zero-shot latent space communication](https://mlsanity.com/paper/2209.15430/) (2022)
- [Linearly Mapping from Image to Text Space](https://mlsanity.com/paper/2209.15162/) (2022)
- [Text-To-Concept (and Back) via Cross-Model Alignment](https://mlsanity.com/paper/2305.06386/) (2023)
- [Semantics-Empowered Communication for Networked Intelligent Systems](https://mlsanity.com/paper/2007.11579/) (2020)
- [Harnessing the Universal Geometry of Embeddings](https://mlsanity.com/paper/2505.12540/) (2025)
- [Latent Space Translation via Semantic Alignment](https://mlsanity.com/paper/2311.00664/) (2023)
- [Goal-Oriented and Semantic Communication in 6G AI-Native Networks: The 6G-GOALS Approach](https://mlsanity.com/paper/2402.07573/) (2024)
- [Towards Optimal Transport with Global Invariances](https://mlsanity.com/paper/1806.09277/) (2018)
- [Semantic Channel Equalizer: Modelling Language Mismatch in Multi-User Semantic Communications](https://mlsanity.com/paper/2308.03789/) (2023)
- [Goal-oriented Communications for the IoT: System Design and Adaptive Resource Optimization](https://mlsanity.com/paper/2310.13948/) (2023)
- [Parallel and Distributed Successive Convex Approximation Methods for Big-Data Optimization](https://mlsanity.com/paper/1805.06963/) (2018)
- [Learning Sheaf Laplacian Optimizing Restriction Maps](https://mlsanity.com/paper/2501.19207/) (2025)
- [Latent Space Alignment for AI-Native MIMO Semantic Communications](https://mlsanity.com/paper/2507.16680/) (2025)
- [Frame-Based Zero-Shot Semantic Channel Equalization for AI-Native Communications](https://mlsanity.com/paper/2507.17835/) (2025)
- [Semantic Channel Equalization Strategies for Deep Joint Source-Channel Coding](https://mlsanity.com/paper/2510.04674/) (2025)

## Built on by (most cited first, 4 of 4)

- [Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves](https://mlsanity.com/paper/2605.06395/) (2026)
- [SEMASIA: A Large-Scale Dataset of Semantically Structured Latent Representations](https://mlsanity.com/paper/2605.09485/) (2026)
- [Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling](https://mlsanity.com/paper/2608.01318/) (2026)
- [Sheaf-Based Federated Representation Learning](https://mlsanity.com/paper/2608.10016/) (2026)

## Abstract (arXiv)

Recent advances in AI call for a paradigm shift from bit-centric communication to goal- and semantics-oriented architectures, paving the way for AI-native 6G networks. In this context, we address a key open challenge: enabling heterogeneous AI agents to exchange compressed latent-space representations while mitigating semantic noise and preserving task-relevant meaning. We cast this challenge as learning both the communication topology and the alignment maps that govern information exchange among agents, yielding a learned network sheaf equipped with orthogonal maps. This learning process is further supported by a semantic denoising end compression module that constructs a shared global semantic space and derives sparse, structured representations of each agent's latent space. This corresponds to a nonconvex dictionary learning problem solved iteratively with closed-form updates. Experiments with mutiple AI agents pre-trained on real image data show that the semantic denoising and compression facilitates AI agents alignment and the extraction of semantic clusters, while preserving high accuracy in downstream task. The resulting communication network provides new insights about semantic heterogeneity across agents, highlighting the interpretability of our methodology.