Structured Knowledge Accumulation: The Principle of Entropic Least Action in Forward-Only Neural Learning
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909564848308224 |
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| author | Quantiota, Bouarfa Mahi |
| author_facet | Quantiota, Bouarfa Mahi |
| contents | This paper aims to extend the Structured Knowledge Accumulation (SKA) framework recently proposed by \cite{mahi2025ska}. We introduce two core concepts: the Tensor Net function and the characteristic time property of neural learning. First, we reinterpret the learning rate as a time step in a continuous system. This transforms neural learning from discrete optimization into continuous-time evolution. We show that learning dynamics remain consistent when the product of learning rate and iteration steps stays constant. This reveals a time-invariant behavior and identifies an intrinsic timescale of the network. Second, we define the Tensor Net function as a measure that captures the relationship between decision probabilities, entropy gradients, and knowledge change. Additionally, we define its zero-crossing as the equilibrium state between decision probabilities and entropy gradients. We show that the convergence of entropy and knowledge flow provides a natural stopping condition, replacing arbitrary thresholds with an information-theoretic criterion. We also establish that SKA dynamics satisfy a variational principle based on the Euler-Lagrange equation. These findings extend SKA into a continuous and self-organizing learning model. The framework links computational learning with physical systems that evolve by natural laws. By understanding learning as a time-based process, we open new directions for building efficient, robust, and biologically-inspired AI systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structured Knowledge Accumulation: The Principle of Entropic Least Action in Forward-Only Neural Learning Quantiota, Bouarfa Mahi Machine Learning 68T07 This paper aims to extend the Structured Knowledge Accumulation (SKA) framework recently proposed by \cite{mahi2025ska}. We introduce two core concepts: the Tensor Net function and the characteristic time property of neural learning. First, we reinterpret the learning rate as a time step in a continuous system. This transforms neural learning from discrete optimization into continuous-time evolution. We show that learning dynamics remain consistent when the product of learning rate and iteration steps stays constant. This reveals a time-invariant behavior and identifies an intrinsic timescale of the network. Second, we define the Tensor Net function as a measure that captures the relationship between decision probabilities, entropy gradients, and knowledge change. Additionally, we define its zero-crossing as the equilibrium state between decision probabilities and entropy gradients. We show that the convergence of entropy and knowledge flow provides a natural stopping condition, replacing arbitrary thresholds with an information-theoretic criterion. We also establish that SKA dynamics satisfy a variational principle based on the Euler-Lagrange equation. These findings extend SKA into a continuous and self-organizing learning model. The framework links computational learning with physical systems that evolve by natural laws. By understanding learning as a time-based process, we open new directions for building efficient, robust, and biologically-inspired AI systems. |
| title | Structured Knowledge Accumulation: The Principle of Entropic Least Action in Forward-Only Neural Learning |
| topic | Machine Learning 68T07 |
| url | https://arxiv.org/abs/2504.03214 |