Diagnostic Benchmarks for Invariant Learning Dynamics: Empirical Validation of the Eidos Architecture

TL;DR

The Eidos architecture achieves>99% accuracy on PSI and 81.67% zero-shot transfer across 30 unseen typefaces without pre-training, validate the "Form-First"hypothesis: generalization in structurally constrained architectures is a property of geometric integrity, not statistical scale.

Abstract

We present the PolyShapes-Ideal (PSI) dataset, a suite of diagnostic benchmarks designed to isolate topological invariance -- the ability to maintain structural identity across affine transformations -- from the textural correlations that dominate standard vision benchmarks. Through three diagnostic probes (polygon classification under noise, zero-shot font transfer from MNIST, and geometric collapse mapping under progressive deformation), we demonstrate that the Eidos architecture achieves >99% accuracy on PSI and 81.67% zero-shot transfer across 30 unseen typefaces without pre-training. These results validate the "Form-First" hypothesis: generalization in structurally constrained architectures is a property of geometric integrity, not statistical scale.

Figures (3)

• Figure 1: Hybrid Architecture (v0.1). Zero-shot font recognition using an early hybrid Eidos variant that retains classical statistical layers. Each cell renders a system font digit (rows: Arial, Times New Roman, Courier New, Comic Sans; columns: digits 0--9). Labels above each cell show P:$n$ (predicted) and T:$n$ (true class); green indicates correct classification, red indicates misclassification. The hybrid model collapses digits 5, 6, 7, and 9 into a narrow attractor basin around digit 1, demonstrating that residual classical layers destroy the topological discrimination required for transfer.
• Figure 2: Pure Eidos Architecture. Same protocol as Figure \ref{['fig:archbefore']}, evaluated after full architectural purification (removal of all classical interpolation layers). The model correctly identifies the majority of digits across all four typefaces. Residual errors concentrate on digits 6 and 7---topologically confusable forms whose open/closed loop distinction is stylistically ambiguous in certain fonts---while structurally unambiguous digits (0, 2, 3, 4, 8) achieve perfect transfer.
• Figure 3: Geometric Collapse Manifolds. Recognition accuracy per digit class under progressive affine deformation (combined rotation, scale, and shear) applied to Comic Sans renderings. X-axis: Geometric Deviation Severity, normalized from 0.0 (no deformation) to 1.0 (maximum). Y-axis: Recognition accuracy (proportion of correct classifications at each severity level). The dashed red line marks the Collapse Threshold at 50% accuracy---below this, the model's commitment to the correct class is no better than chance. Deep Attractor digits (0, 9: closed loops with high topological genus) remain above the collapse threshold across the full severity range, demonstrating wide basins of attraction. Fragile digits (1, 7: open strokes with no closed loops) collapse below threshold before severity reaches 0.2, confirming that their invariant representations depend on angular relations that are destroyed by small shear perturbations. Intermediate digits (2, 3, 4, 5, 6, 8) show graded degradation proportional to their topological complexity---digits with partial closures (6, 8) degrade more slowly than those relying on curvature alone (3, 5).