The Quantum Geometric Tensor Reveals That Training Is a Physical Process. II. Experimental Evidence

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.