What question did this study set out to answer?

The paper aims to establish a geometric framework for understanding neural network training as a physical process.

May 10, 20260 citationsOpen Access

The Quantum Geometric Tensor Reveals That Training Is a Physical Process. I. Framework and Diagnostic

Key Points

The paper aims to establish a geometric framework for understanding neural network training as a physical process.
Introduced the Quantum Geometric Tensor (QGT) for describing training dynamics.
Defined a dictionary linking physics and neural network training.
Presented the Information-Geometry Balance Principle (IGBP) as a diagnostic tool.
Identified that standard architectures cannot achieve a nontrivial IGBP due to lacking Berry-bearing sectors.
Demonstrated that Clifford-weighted architectures are capable of producing the necessary geometric properties for the IGBP.

Abstract

This preprint argues that the opacity of neural network training is a framework problem rather than an intrinsic property of the system. It introduces the Quantum Geometric Tensor (QGT) as the instrument for a physical description of training dynamics, with the QGT understood here as a geometric object on parameterized state families rather than as a claim about quantum hardware. The paper defines a dictionary between physics and training, situates that move within the historical construction of macroscopic physics, and shows that machine learning already uses physically meaningful state variables in fragmented form. It then introduces the Information-Geometry Balance Principle (IGBP), a scalar diagnostic measuring the balance between probe-space entropic drive and Berry-curvature resistance. The framework yields an operational event definition, the I-bit, and a set of testable predictions about critical geometric regimes in learning. It also states the key algebraic boundary sharply: standard real-valued architectures cannot produce the Berry-bearing sector required for a nontrivial IGBP, while Clifford-weighted architectures can. This is Paper I of a companion pair. Paper II provides the experimental tests of the framework and diagnostic. --Corrected April 2026 to fix bibliography entries, add public companion DOI references, and freeze the visible preprint date. No substantive scientific claims changed.-Corrected May 2026 to fix berry curvature sign convention and subsequent experiement results.

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