Characterizing the Representational Capacity of Neural Processes
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Computer Science > Machine Learning
Title:Characterizing the Representational Capacity of Neural Processes
Abstract:What functions can Neural Processes represent? We analyze the representational capacity of popular NP architectures: Conditional Neural Processes (CNPs), Attentive Neural Processes (ANPs), Transformer Neural Processes (TNPs), and their latent variants. We prove these architectures form a strict hierarchy. CNP-representable functions are exactly those depending on finitely many expected features of the context distribution. ANPs strictly generalize CNPs via query-dependent reweighting, enabling kernel smoothers. ConvCNPs and ANPs are incomparable; each contains functions outside the other, separated by stationarity versus translation equivariance. TNPs with $L$ self-attention layers capture $L$-hop context interactions. For latent NPs, we show finite-dimensional latents provide coherent sampling but do not circumvent encoder limitations; matching GP posterior distributions requires latent dimension scaling with context size. These results provide a theoretical foundation for architecture selection based on task structure.
| Comments: | To appear at ProbML/AABI 2026 |
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2605.24210 [cs.LG] |
| (or arXiv:2605.24210v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24210
arXiv-issued DOI via DataCite (pending registration)
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