Transformer Neural Processes - Kernel Regression

• URL: http://arxiv.org/abs/2411.12502v3
• Date: Tue, 11 Feb 2025 11:03:24 GMT
• Title: Transformer Neural Processes - Kernel Regression
• Authors: Daniel Jenson, Jhonathan Navott, Mengyan Zhang, Makkunda Sharma, Elizaveta Semenova, Seth Flaxman,
• Abstract summary: We introduce the Transformer Neural Process - Kernel Regression (TNP-KR), a scalable Neural Process (NP)<n>TNP-KR features a Kernel Regression Block (KR-Block), a simple, parameter, and efficient transformer block with complexity $O(n_c2 + n_c n_t)$, and two novel attention mechanisms: scan attention (SA), a memory-efficient scan-based bias, and deep kernel attention (DKA), a Performer-style attention that implicitly incoporates a distance bias.<n>These enhancements enable both TNP-KR variants to perform inference with 100K
• Score: 2.309018557701645
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Neural Processes (NPs) are a rapidly evolving class of models designed to directly model the posterior predictive distribution of stochastic processes. Originally developed as a scalable alternative to Gaussian Processes (GPs), which are limited by $O(n^3)$ runtime complexity, the most accurate modern NPs can often rival GPs but still suffer from an $O(n^2)$ bottleneck due to their attention mechanism. We introduce the Transformer Neural Process - Kernel Regression (TNP-KR), a scalable NP featuring: (1) a Kernel Regression Block (KRBlock), a simple, extensible, and parameter efficient transformer block with complexity $O(n_c^2 + n_c n_t)$, where $n_c$ and $n_t$ are the number of context and test points, respectively; (2) a kernel-based attention bias; and (3) two novel attention mechanisms: scan attention (SA), a memory-efficient scan-based attention that when paired with a kernel-based bias can make TNP-KR translation invariant, and deep kernel attention (DKA), a Performer-style attention that implicitly incoporates a distance bias and further reduces complexity to $O(n_c)$. These enhancements enable both TNP-KR variants to perform inference with 100K context points on over 1M test points in under a minute on a single 24GB GPU. On benchmarks spanning meta regression, Bayesian optimization, image completion, and epidemiology, TNP-KR with DKA outperforms its Performer counterpart on nearly every benchmark, while TNP-KR with SA achieves state-of-the-art results.

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