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Learning Network Sheaves for AI-native Semantic Communication

Enrico Grimaldi, Mario Edoardo Pandolfo, Gabriele D'Acunto, Sergio Barbarossa, Paolo Di Lorenzo

TL;DR

This work tackles semantic misalignment across heterogeneous pre-trained AI agents by proposing a two-stage framework that learns both the communication topology and edge maps via a network sheaf, complemented by a global semantic dictionary for denoising. The methodology combines a sheaf-theoretic model with orthogonal edge maps and a dictionary-learning step (including a log-determinant regularizer and ADMM/SCA solvers) to produce denoised, compression-friendly embeddings and a sparse, interpretable topology. Empirical results on CIFAR-10 with ten agents show that substantial semantic compression can be achieved with minimal loss in downstream accuracy, while revealing semantic clusters and interpretable edge structures that reflect agents' architectural relationships. The approach advances AI-native semantic networks by enabling controllable, interpretable, and scalable semantic exchange under topology learning and semantic denoising.

Abstract

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.

Learning Network Sheaves for AI-native Semantic Communication

TL;DR

This work tackles semantic misalignment across heterogeneous pre-trained AI agents by proposing a two-stage framework that learns both the communication topology and edge maps via a network sheaf, complemented by a global semantic dictionary for denoising. The methodology combines a sheaf-theoretic model with orthogonal edge maps and a dictionary-learning step (including a log-determinant regularizer and ADMM/SCA solvers) to produce denoised, compression-friendly embeddings and a sparse, interpretable topology. Empirical results on CIFAR-10 with ten agents show that substantial semantic compression can be achieved with minimal loss in downstream accuracy, while revealing semantic clusters and interpretable edge structures that reflect agents' architectural relationships. The approach advances AI-native semantic networks by enabling controllable, interpretable, and scalable semantic exchange under topology learning and semantic denoising.

Abstract

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.

Paper Structure

This paper contains 8 sections, 11 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Sheaf Learning for Network Semantic Alignment
  4. Semantic Denoising via Dictionary Learning
  5. Results
  6. Accuracy-compression trade-off
  7. Semantic denoising for topology learning
  8. Conclusion

Figures (3)

  • Figure 1: Average semantic accuracy of the architecture families (left y-axis) and communication network edges (right y-axis) along the sparsity level $d'$ for the edge-loss threshold $\tau=0.8$.
  • Figure 2: Semantic signatures induced by the global dictionary when setting $d'=d=384$ (no compression), for each model $i=0,\,1,\, \dots,\, 9$ listed in Table \ref{['tab:agent_models']}.
  • Figure 3: Distribution of edge misalignment losses with (lower panel) and without (upper panel) dictionary learning (shown for $d'=200$), illustrating the emergence of bimodality and improved separation between homophilic and heterophilic edges.