Any-Dimensional Learning by Sampling

arXiv:2607.07680 · math.ST, cs.LG, math.PR, stat.TH · Submitted 2026-07-08 · Read on arXiv

math.ST, cs.LG, math.PR, stat.TH

Submitted: 2026-07-08

Updated: 2026-09-08

Comments: Improved sketching rates for transformers and generalization rates for polynomials

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Generalization — 87× in this paper · explained in 13 episodes
• Transformer — 25× in this paper · explained in 2 episodes
• Hypergraph — 8× in this paper · explained in 2 episodes
• Point Clouds — 6× in this paper · explained in 2 episodes
• Transferability — 6× in this paper · explained in 4 episodes
• Accuracy — 5× in this paper · explained in 1 episode
• Generalization Bounds — 4× in this paper · explained in 2 episodes
• Homogeneity — 4× in this paper · explained in 2 episodes
• Wasserstein Distance — 3× in this paper · explained in 4 episodes
• Adjacency Matrix — 2× in this paper · explained in 1 episode
• Consistency — 2× in this paper · explained in 3 episodes
• Exchangeability — 2× in this paper · explained in 2 episodes
• Hamming Distance — 2× in this paper · explained in 2 episodes
• Ambient Dimension — 1× in this paper · explained in 1 episode
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Distribution Shift — 1× in this paper · explained in 5 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Foundation Model — 1× in this paper · explained in 3 episodes
• Foundation Models — 1× in this paper · explained in 7 episodes
• GNNs — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Transformer Architecture — 1× in this paper · explained in 2 episodes

Sources

• Graph limits and exchangeable random graphs
• Limits of Weighted Graphs via Random Quotients
• Any-Dimensional Polynomial Optimization via de Finetti Theorems
• On Transferring Transferability: Towards a Theory for Size Generalization
• Length Generalization Bounds for Transformers
• Function graph transformers universally approximate operators between function spaces
• Invariant Kernels: Rank Stabilization and Generalization Across Dimensions
• Approximation Theory for Lipschitz Continuous Transformers

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