Paper
CHLU: The Causal Hamiltonian Learning Unit as a Symplectic Primitive for Deep Learning
Authors
Pratik Jawahar, Maurizio Pierini
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.01768v1</id>\n <title>CHLU: The Causal Hamiltonian Learning Unit as a Symplectic Primitive for Deep Learning</title>\n <updated>2026-03-02T11:53:09Z</updated>\n <link href='https://arxiv.org/abs/2603.01768v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.01768v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <category scheme='http://arxiv.org/schemas/atom' term='physics.app-ph'/>\n <published>2026-03-02T11:53:09Z</published>\n <arxiv:comment>Accepted as a short paper at ICLR 2026 (AI & PDE)</arxiv:comment>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Pratik Jawahar</name>\n </author>\n <author>\n <name>Maurizio Pierini</name>\n </author>\n </entry>"
}