Deep Tensor Network

• URL: http://arxiv.org/abs/2311.11091v3
• Date: Sun, 31 Aug 2025 04:19:07 GMT
• Title: Deep Tensor Network
• Authors: Yifan Zhang,
• Abstract summary: We introduce the Deep Network, a new architectural framework that reformulates attention by unifying the expressive power of tensor algebra with neural network design.<n>Our approach moves beyond both conventional dot-product attention and subsequent linear-time approximations to capture higher-order statistical dependencies.
• Score: 9.910562011343009
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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