# Conformal Prediction for Time Series with Modern Hopfield Networks

arXiv: https://arxiv.org/abs/2303.12783 · HTML: https://mlsanity.com/paper/2303.12783/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 83 references that are in the map.
- First posted on arXiv 22 Mar 2023.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Darts: User-Friendly Modern Machine Learning for Time Series](https://mlsanity.com/paper/2110.03224/) (2021)
- [CLOOB: Modern Hopfield Networks with InfoLOOB Outperform CLIP](https://mlsanity.com/paper/2110.11316/) (2021)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [Modern Hopfield Networks and Attention for Immune Repertoire Classification](https://mlsanity.com/paper/2007.13505/) (2020)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [History Compression via Language Models in Reinforcement Learning](https://mlsanity.com/paper/2205.12258/) (2022)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Txt2Img-MHN: Remote Sensing Image Generation from Text Using Modern Hopfield Networks](https://mlsanity.com/paper/2208.04441/) (2022)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.08756/) (2022)
- [Hopular: Modern Hopfield Networks for Tabular Data](https://mlsanity.com/paper/2206.00664/) (2022)
- [Time series forecasting with Gaussian Processes needs priors](https://mlsanity.com/paper/2009.08102/) (2020)
- [Uncertainty Estimation with Deep Learning for Rainfall-Runoff Modelling](https://mlsanity.com/paper/2012.14295/) (2020)
- [Conformal prediction set for time-series](https://mlsanity.com/paper/2206.07851/) (2022)

## Built on by (most cited first, 30 of 42)

- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Uniform Memory Retrieval with Larger Capacity for Modern Hopfield Models](https://mlsanity.com/paper/2404.03827/) (2024)
- [Outlier-Efficient Hopfield Layers for Large Transformer-Based Models](https://mlsanity.com/paper/2404.03828/) (2024)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [BiSHop: Bi-Directional Cellular Learning for Tabular Data with Generalized Sparse Modern Hopfield Model](https://mlsanity.com/paper/2404.03830/) (2024)
- [Trustworthy Classification through Rank-Based Conformal Prediction Sets](https://mlsanity.com/paper/2407.04407/) (2024)
- [Conv-CoA: Improving Open-domain Question Answering in Large Language Models via Conversational Chain-of-Action](https://mlsanity.com/paper/2405.17822/) (2024)
- [Provably Optimal Memory Capacity for Modern Hopfield Models: Transformer-Compatible Dense Associative Memories as Spherical Codes](https://mlsanity.com/paper/2410.23126/) (2024)
- [Nonparametric Modern Hopfield Models](https://mlsanity.com/paper/2404.03900/) (2024)
- [Kernel-based Optimally Weighted Conformal Time-Series Prediction](https://mlsanity.com/paper/2405.16828/) (2024)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Energy-based Hopfield Boosting for Out-of-Distribution Detection](https://mlsanity.com/paper/2405.08766/) (2024)
- [Bridging Dimensions: Confident Reachability for High-Dimensional Controllers](https://mlsanity.com/paper/2311.04843/) (2023)
- [Flow-based Conformal Prediction for Multi-dimensional Time Series](https://mlsanity.com/paper/2502.05709/) (2025)
- [Conformal Prediction for Time-series Forecasting with Change Points](https://mlsanity.com/paper/2509.02844/) (2025)
- [ResCP: Reservoir Conformal Prediction for Time Series Forecasting](https://mlsanity.com/paper/2510.05060/) (2025)
- [Provably Reliable Conformal Prediction Sets in the Presence of Data Poisoning](https://mlsanity.com/paper/2410.09878/) (2024)
- [Unveiling the Potential of Text in High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2501.07048/) (2025)
- [CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver](https://mlsanity.com/paper/2403.03391/) (2024)
- [Conformal time series decomposition with component-wise exchangeability](https://mlsanity.com/paper/2406.16766/) (2024)
- [HopCast: Calibration of Autoregressive Dynamics Models](https://mlsanity.com/paper/2501.16587/) (2025)
- [Sparse Identification of Nonlinear Dynamics with Conformal Prediction](https://mlsanity.com/paper/2507.11739/) (2025)
- [Conformal Prediction in The Loop: A Feedback-Based Uncertainty Model for Trajectory Optimization](https://mlsanity.com/paper/2510.16376/) (2025)
- [Enhanced Renewable Energy Forecasting using Context-Aware Conformal Prediction](https://mlsanity.com/paper/2510.15780/) (2025)
- [A Gentle Introduction to Conformal Time Series Forecasting](https://mlsanity.com/paper/2511.13608/) (2025)
- [Distribution-informed Online Conformal Prediction](https://mlsanity.com/paper/2512.07770/) (2025)
- [Retrieval-Corrected Conformal Prediction for Time Series](https://mlsanity.com/paper/2608.10553/) (2026)
- [Dual-Splitting Conformal Prediction for Multi-Step Time Series Forecasting](https://mlsanity.com/paper/2503.21251/) (2025)
- [A Systematic Review of Conformal Inference Procedures for Treatment Effect Estimation: Methods and Challenges](https://mlsanity.com/paper/2509.21660/) (2025)
- [AP-OOD: Attention Pooling for Out-of-Distribution Detection](https://mlsanity.com/paper/2602.06031/) (2026)

## Abstract (arXiv)

To quantify uncertainty, conformal prediction methods are gaining continuously more interest and have already been successfully applied to various domains. However, they are difficult to apply to time series as the autocorrelative structure of time series violates basic assumptions required by conformal prediction. We propose HopCPT, a novel conformal prediction approach for time series that not only copes with temporal structures but leverages them. We show that our approach is theoretically well justified for time series where temporal dependencies are present. In experiments, we demonstrate that our new approach outperforms state-of-the-art conformal prediction methods on multiple real-world time series datasets from four different domains.