Datorien L. Anderson | Searcharxiv

arXiv2026

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

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.

cs.CV↗

arXiv2026

Certainty-Validity: A Diagnostic Framework for Discrete Commitment Systems

Standard evaluation metrics for machine learning -- accuracy, precision, recall, and AUROC -- assume that all errors are equivalent: a confident incorrect prediction is penalized identically to an uncertain one. For discrete commitment systems (architectures that select committed states {-W, 0, +W}), this assumption is epistemologically flawed. We introduce the Certainty-Validity (CVS) Framework, a diagnostic method that decomposes model performance into a 2x2 matrix distinguishing high/low certainty from valid/invalid predictions. This framework reveals a critical failure mode hidden by standard accuracy: Confident-Incorrect (CI) behavior, where models hallucinate structure in ambiguous data. Through ablation experiments on Fashion-MNIST, EMNIST, and IMDB, we analyze the "83% Ambiguity Ceiling" -- a stopping point where this specific discrete architecture consistently plateaus on noisy benchmarks. Unlike continuous models that can surpass this ceiling by memorizing texture or statistical noise, the discrete model refuses to commit to ambiguous samples. We show that this refusal is not a failure but a feature: the model stops where structural evidence ends. However, standard training on ambiguous data eventually forces Benign Overfitting, causing a pathological migration from Uncertain-Incorrect (appropriate doubt) to Confident-Incorrect (hallucination). We propose that "good training" for reasoning systems must be defined not by accuracy, but by maximizing the Certainty-Validity Score (CVS) -- ensuring the model knows where to stop.

cs.LG↗