MNIST Dataset — Parameter Efficiency at Scale

Setup

Classes

10

Samples

500 (50/class)

Split

70 / 15 / 15

Epochs / LR / Batch

50 / 0.005 / 32

Core Finding

Boolear v8 with L=12 achieves 64.3% test accuracy using 140 parameters — against Linear Softmax's 70.0% test accuracy with 7,850 parameters. That is 91% of the baseline performance at 1.8% of the parameter count — a 56× compression.

Results — Increasing Depth (L)

Model	Params	Test Acc	Train→Test Gap	Time
Linear Softmax	7,850	70.0%	13.7 pp	0.2s
Leaf L8	100	51.4%	7.4 pp	174s
Leaf L12 (best)	140	64.3%	5.1 pp	257s
Leaf L16	180	55.7%	14.6 pp	269s

Tendencies with Increasing Depth

L=8 → L=12: test accuracy jumps +12.9 pp. The model is still underfitting at L=8 — more depth genuinely helps it learn.
L=12 → L=16: test accuracy drops 8.6 pp despite train/val both rising. The model starts to overfit. The train→test gap nearly triples (5.1 pp → 14.6 pp). With only 500 samples, 180 parameters is apparently past the capacity sweet spot for this setting.
Training time grows roughly proportionally to L, but L=12→L=16 shows diminishing returns in time too (257s → 269s, small difference, but accuracy regresses).

What Makes This Interesting

The v8 architecture has no dedicated output weight matrix — the 10-lit expectation values directly become the 10 class logits (plus a 10-element bias). All 140 parameters at L=12 are rotation angles on a 1024-dimensional state vector. The model encodes 784 MNIST features into a quantum-amplitude state and extracts classification signal purely through learned rotations. The fact that this reaches 64% with so few parameters suggests the amplitude encoding is doing genuine work as a structured prior.

The remaining gap to linear (64% vs 70%) appears to be a depth/capacity trade-off: more layers overfit at this dataset size, suggesting the architecture needs either more data, regularization, or a smarter way to scale beyond L=12 without overfitting.

Wine vs. MNIST

Wine is essentially linearly separable in 13-feature space — even 16 parameters can capture the geometry. The amplitude encoding fits 13 features into 16 amplitude slots (3 zeros padding), and v8's learned rotations are sufficient to separate the three classes. There is no information-theoretic gap to close.
MNIST, by contrast, has 784 features and non-linear class structure — there the gap between v8 and linear becomes visible, and the compression/accuracy trade-off becomes the central question.
Together, the two datasets sketch the boundary of where amplitude encoding works without compromise (wine) and where it starts to cost accuracy (MNIST at 500 samples) — while consistently requiring 1–2 orders of magnitude fewer parameters.