Transformer Neural Processes - Kernel Regression
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914480563159040 |
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| author | Jenson, Daniel Navott, Jhonathan Zhang, Mengyan Sharma, Makkunda Semenova, Elizaveta Flaxman, Seth |
| author_facet | Jenson, Daniel Navott, Jhonathan Zhang, Mengyan Sharma, Makkunda Semenova, Elizaveta Flaxman, Seth |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transformer Neural Processes - Kernel Regression Jenson, Daniel Navott, Jhonathan Zhang, Mengyan Sharma, Makkunda Semenova, Elizaveta Flaxman, Seth Machine Learning Artificial Intelligence 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. |
| title | Transformer Neural Processes - Kernel Regression |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2411.12502 |