# Sequential Memory with Temporal Predictive Coding

arXiv: https://arxiv.org/abs/2305.11982 · HTML: https://mlsanity.com/paper/2305.11982/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 69 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Unsupervised Learning of Video Representations using LSTMs](https://mlsanity.com/paper/1502.04681/) (2015)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [Optimal whitening and decorrelation](https://mlsanity.com/paper/1512.00809/) (2015)
- [Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models](https://mlsanity.com/paper/2202.04557/) (2022)
- [Associative Memories via Predictive Coding](https://mlsanity.com/paper/2109.08063/) (2021)
- [Learning on Arbitrary Graph Topologies via Predictive Coding](https://mlsanity.com/paper/2201.13180/) (2022)
- [Continual Learning of Recurrent Neural Networks by Locally Aligning Distributed Representations](https://mlsanity.com/paper/1810.07411/) (2018)
- [Neuroscience-inspired online unsupervised learning algorithms](https://mlsanity.com/paper/1908.01867/) (2019)
- [Constrained Predictive Coding as a Biologically Plausible Model of the Cortical Hierarchy](https://mlsanity.com/paper/2210.15752/) (2022)
- [BayesPCN: A Continually Learnable Predictive Coding Associative Memory](https://mlsanity.com/paper/2205.09930/) (2022)
- [Kernel Memory Networks: A Unifying Framework for Memory Modeling](https://mlsanity.com/paper/2208.09416/) (2022)
- [Generalisation of structural knowledge in the hippocampal-entorhinal system](https://mlsanity.com/paper/1805.09042/) (2018)
- [Predictive Coding Theories of Cortical Function](https://mlsanity.com/paper/2112.10048/) (2021)

## Built on by (most cited first, 16 of 16)

- [Benchmarking Predictive Coding Networks -- Made Simple](https://mlsanity.com/paper/2407.01163/) (2024)
- [Long Sequence Hopfield Memory](https://mlsanity.com/paper/2306.04532/) (2023)
- [Predictive Coding Networks and Inference Learning: Tutorial and Survey](https://mlsanity.com/paper/2407.04117/) (2024)
- [A Sparse Quantized Hopfield Network for Online-Continual Memory](https://mlsanity.com/paper/2307.15040/) (2023)
- [Memory-Integrated Reconfigurable Adapters: A Unified Framework for Settings with Multiple Tasks](https://mlsanity.com/paper/2512.00940/) (2025)
- [Learning Successor Features with Distributed Hebbian Temporal Memory](https://mlsanity.com/paper/2310.13391/) (2023)
- [Learning Sequence Attractors in Recurrent Networks with Hidden Neurons](https://mlsanity.com/paper/2404.02729/) (2024)
- [Predictive Learning in Energy-based Models with Attractor Structures](https://mlsanity.com/paper/2501.13997/) (2025)
- [Deep hybrid models: infer and plan in a dynamic world](https://mlsanity.com/paper/2402.10088/) (2024)
- [Predictive Attractor Models](https://mlsanity.com/paper/2410.02430/) (2024)
- [A General Close-loop Predictive Coding Framework for Auditory Working Memory](https://mlsanity.com/paper/2503.12506/) (2025)
- [Learning Long-Range Dependencies with Temporal Predictive Coding](https://mlsanity.com/paper/2602.18131/) (2026)
- [Leakage and Second-Order Dynamics Improve Hippocampal RNN Replay](https://mlsanity.com/paper/2602.18401/) (2026)
- [Sinkhorn Based Associative Memory Retrieval Using Spherical Hellinger Kantorovich Dynamics](https://mlsanity.com/paper/2603.20656/) (2026)
- [Single State Update Predictive Coding training for Time Series Forecasting and Anomaly Detection](https://mlsanity.com/paper/2608.24697/) (2026)
- [DeltaNet-PC: Test-Time Memory Without Backpropagation Through Time](https://mlsanity.com/paper/2610.15185/) (2026)

## Abstract (arXiv)

Forming accurate memory of sequential stimuli is a fundamental function of biological agents. However, the computational mechanism underlying sequential memory in the brain remains unclear. Inspired by neuroscience theories and recent successes in applying predictive coding (PC) to static memory tasks, in this work we propose a novel PC-based model for sequential memory, called temporal predictive coding (tPC). We show that our tPC models can memorize and retrieve sequential inputs accurately with a biologically plausible neural implementation. Importantly, our analytical study reveals that tPC can be viewed as a classical Asymmetric Hopfield Network (AHN) with an implicit statistical whitening process, which leads to more stable performance in sequential memory tasks of structured inputs. Moreover, we find that tPC exhibits properties consistent with behavioral observations and theories in neuroscience, thereby strengthening its biological relevance. Our work establishes a possible computational mechanism underlying sequential memory in the brain that can also be theoretically interpreted using existing memory model frameworks.