CHLU: The Causal Hamiltonian Learning Unit as a Symplectic Primitive for Deep Learning
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866908887340285952 |
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| author | Jawahar, Pratik Pierini, Maurizio |
| author_facet | Jawahar, Pratik Pierini, Maurizio |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_01768 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | CHLU: The Causal Hamiltonian Learning Unit as a Symplectic Primitive for Deep Learning Jawahar, Pratik Pierini, Maurizio Machine Learning Artificial Intelligence Applied Physics 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. |
| title | CHLU: The Causal Hamiltonian Learning Unit as a Symplectic Primitive for Deep Learning |
| topic | Machine Learning Artificial Intelligence Applied Physics |
| url | https://arxiv.org/abs/2603.01768 |