CHLU: The Causal Hamiltonian Learning Unit as a Symplectic Primitive for Deep Learning

2026-03-02

AI Summary

This work addresses a fundamental trade-off in deep learning-based time series models between numerical stability and long-term memory retention: discrete architectures like LSTMs suffer from gradient explosion or vanishing, while continuous models such as Neural ODEs experience information decay due to dissipative dynamics. To overcome this limitation, the authors propose the Causal Hamiltonian Learning Unit (CHLU), which— for the first time—integrates relativistic Hamiltonian dynamics with symplectic geometric structure into temporal modeling. By employing symplectic integration, CHLU preserves phase-space volume conservation, theoretically guaranteeing stability over infinite time horizons and enabling controllable noise filtering. Experiments on MNIST generation demonstrate that CHLU achieves both strong representational capacity and robustness, effectively resolving the longstanding conflict between memory preservation and numerical stability inherent in conventional approaches.

Technology Category

• Machine Learning: Causal Learning
• Natural Language Processing: Learning & Optimization for NLP
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Large language models for search
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Current deep learning primitives dealing with temporal dynamics suffer from a fundamental dichotomy: they are either discrete and unstable (LSTMs) \citep{pascanu_difficulty_2013}, leading to exploding or vanishing gradients; or they are continuous and dissipative (Neural ODEs) \citep{dupont_augmented_2019}, which destroy information over time to ensure stability. We propose the \textbf{Causal Hamiltonian Learning Unit} (pronounced: \textit{clue}), a novel Physics-grounded computational learning primitive. By enforcing a Relativistic Hamiltonian structure and utilizing symplectic integration, a CHLU strictly conserves phase-space volume, as an attempt to solve the memory-stability trade-off. We show that the CHLU is designed for infinite-horizon stability, as well as controllable noise filtering. We then demonstrate a CHLU's generative ability using the MNIST dataset as a proof-of-principle.

Problem

• temporal dynamics
• gradient instability
• information dissipation
• memory-stability trade-off
• deep learning primitives

Innovation

• Causal Hamiltonian Learning Unit
• Symplectic Integration
• Hamiltonian Dynamics
• Infinite-horizon Stability
• Phase-space Volume Conservation