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Experimental evidence demonstrates the geometric nature of training in algorithms, suggesting new insights into optimization techniques.
This preprint is the experimental companion to “The Quantum Geometric Tensor Reveals That Training Is a Physical Process. I. Framework and Diagnostic.” It tests the Quantum Geometric Tensor / Information-Geometry Balance Principle (QGT/IGBP) framework in a controlled three-run program on random 3-SAT, with the QGT understood here as a geometric object on parameterized state families rather than as a claim about quantum hardware. The experiment trains matched real-valued and Clifford-weighted architectures first under a physics-blind optimizer, then under physics-aware optimization, and finally under tap-aware closed-loop control with internal observability. The baseline result is exact: standard real-valued models preserve the algebraic flatline Ω = 0, while Clifford-weighted models activate the geometric instrument. Geometric events are already observed in Runs 1 and 2 under passive or lightly controlled training, while Run 3 shows that the critical regime can be steered and reveals the mature full-stack hierarchy. Across the full experiment, the paper reports 17 confirmed I-bit events across 10/18 transformer runs, 3 events across 3/18 TCN runs, and 0 events across all 36 RBM runs. A post hoc topology investigation then finds spectrally structured, Berry-active geometric events but no quantized topological transition on the tested surfaces. The experimental conclusion is that training is a measurable geometric process whose event capability depends jointly on encoding, dynamics, architecture, and observability. -Corrected April 2026 to fix bibliography entries, add public companion DOI references, and freeze the visible preprint date. No substantive scientific claims changed.-Correction May 2026 to fix berry curvature sign convention and subsequent experiment results.
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Dimitry Jean-Noel II (2026) studied this question.
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