2025/07/17 by Vittorio Cipriani, Cipriani, Vittorio, Valentino Delle Rose +5
Computer Science · #Data Mining Algorithms and Applications #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Logic (math.LO) #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.2507.13054
openalex publication_date 2025/07/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
We study PAC and online learnability of hypothesis classes formed by copies of a countably infinite graph G, where each copy is induced by permuting G's vertices. This corresponds to learning a graph's labeling, knowing its structure and label set. We consider classes where permutations move only finitely many vertices. Our main result shows that PAC learnability of all such finite-support copies implies online learnability of the full isomorphism type of G, and is equivalent to the condition of automorphic triviality. We also characterize graphs where copies induced by swapping two vertices are not learnable, using a relaxation of the extension property of the infinite random graph. Finally, we show that, for all G and k>2, learnability for k-vertex permutations is equivalent to that for 2-vertex permutations, yielding a four-class partition of infinite graphs, whose complexity we also determine using tools coming from both descriptive set theory and computability theory.