HopCast: Calibration of Autoregressive Dynamics Models

2025-01-27

AI Summary

In multi-step autoregressive forecasting, miscalibrated uncertainty propagation severely degrades probabilistic forecast calibration—particularly in physics-informed modeling. To address this, we propose HopCast: the first method to leverage modern Hopfield networks for context-aware residual density modeling of deterministic dynamical systems, enabling calibrated multi-step probabilistic forecasts without explicit uncertainty propagation or trajectory sampling. HopCast seamlessly transforms deterministic models into high-fidelity probabilistic ones. Our contributions are: (1) a novel Hopfield-network-based framework for residual density estimation; and (2) the first systematic benchmark specifically designed for multi-step calibration error evaluation, covering mainstream approaches including deep ensembles. Experiments demonstrate that HopCast significantly improves forecast calibration across diverse benchmarks while maintaining computational efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Deep learning models are often trained to approximate dynamical systems that can be modeled using differential equations. These models are optimized to predict one step ahead and produce calibrated predictions if the predictive model can quantify uncertainty, such as deep ensembles. At inference time, multi-step predictions are generated via autoregression, which needs a sound uncertainty propagation method (e.g., Trajectory Sampling) to produce calibrated multi-step predictions. This paper introduces an approach named HopCast that uses the Modern Hopfield Network (MHN) to learn the residuals of a deterministic model that approximates the dynamical system. The MHN predicts the density of residuals based on a context vector at any timestep during autoregression. This approach produces calibrated multi-step predictions without uncertainty propagation and turns a deterministic model into a calibrated probabilistic model. This work is also the first to benchmark existing uncertainty propagation methods based on calibration errors with deep ensembles for multi-step predictions.

Problem

• Multi-step Prediction
• Uncertainty Estimation
• Deep Learning Models

Innovation

• HopCast
• Modern Hopfield Network (MHN)
• Multi-step Prediction Uncertainty