Deep Tensor Network
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912560497819648 |
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| author | Zhang, Yifan |
| author_facet | Zhang, Yifan |
| contents | The quadratic complexity of dot-product attention introduced in Transformer remains a fundamental bottleneck impeding the progress of foundation models toward unbounded context lengths. Addressing this challenge, we introduce the Deep Tensor Network, a new architectural framework that fundamentally reformulates attention by unifying the expressive power of tensor algebra with neural network design. Our approach moves beyond both conventional dot-product attention and subsequent linear-time approximations to capture higher-order statistical dependencies. We introduce two core operators derived from this framework: \emph{Tensor Attention}, which models complex token-mixing via data-dependent polynomial kernels, and Tensor Interaction, a novel mechanism for adaptive channel-mixing. We demonstrate that these operators are powered by second-order summaries that entirely bypass the formation of $n \times n$ matrices, enabling a causality-preserving streaming implementation with $O(d^2)$ per-token updates and $O(d^2)$ state. This efficiency rivals that of modern State Space Models while retaining an attention-like formulation. The Deep Tensor Network thus provides a principled and powerful new class of building blocks for next-generation sequence models, bridging the gap between scalable computation and rich, expressive interaction modeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11091 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deep Tensor Network Zhang, Yifan Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Quantum Physics The quadratic complexity of dot-product attention introduced in Transformer remains a fundamental bottleneck impeding the progress of foundation models toward unbounded context lengths. Addressing this challenge, we introduce the Deep Tensor Network, a new architectural framework that fundamentally reformulates attention by unifying the expressive power of tensor algebra with neural network design. Our approach moves beyond both conventional dot-product attention and subsequent linear-time approximations to capture higher-order statistical dependencies. We introduce two core operators derived from this framework: \emph{Tensor Attention}, which models complex token-mixing via data-dependent polynomial kernels, and Tensor Interaction, a novel mechanism for adaptive channel-mixing. We demonstrate that these operators are powered by second-order summaries that entirely bypass the formation of $n \times n$ matrices, enabling a causality-preserving streaming implementation with $O(d^2)$ per-token updates and $O(d^2)$ state. This efficiency rivals that of modern State Space Models while retaining an attention-like formulation. The Deep Tensor Network thus provides a principled and powerful new class of building blocks for next-generation sequence models, bridging the gap between scalable computation and rich, expressive interaction modeling. |
| title | Deep Tensor Network |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Quantum Physics |
| url | https://arxiv.org/abs/2311.11091 |