# Long-Sequence Memory with Temporal Kernels and Dense Hopfield Functionals

arXiv: https://arxiv.org/abs/2507.01052 · HTML: https://mlsanity.com/paper/2507.01052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 14 references that are in the map.
- First posted on arXiv 27 Jun 2025.

## Builds on (most cited first, 8 of 8)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Towards AI-Complete Question Answering: A Set of Prerequisite Toy Tasks](https://mlsanity.com/paper/1502.05698/) (2015)
- [Using Fast Weights to Attend to the Recent Past](https://mlsanity.com/paper/1610.06258/) (2016)
- [Dense Associative Memory is Robust to Adversarial Inputs](https://mlsanity.com/paper/1701.00939/) (2017)
- [Long Sequence Hopfield Memory](https://mlsanity.com/paper/2306.04532/) (2023)

## Abstract (arXiv)

In this study we introduce a novel energy functional for long-sequence memory, building upon the framework of dense Hopfield networks which achieves exponential storage capacity through higher-order interactions. Building upon earlier work on long-sequence Hopfield memory models, we propose a temporal kernal K(m, k) to incorporate temporal dependencies, enabling efficient sequential retrieval of patterns over extended sequences. We demonstrate the successful application of this technique for the storage and sequential retrieval of movies frames which are well suited for this because of the high dimensional vectors that make up each frame creating enough variation between even sequential frames in the high dimensional space. The technique has applications in modern transformer architectures, including efficient long-sequence modeling, memory augmentation, improved attention with temporal bias, and enhanced handling of long-term dependencies in time-series data. Our model offers a promising approach to address the limitations of transformers in long-context tasks, with potential implications for natural language processing, forecasting, and beyond.