Certainty-Validity: A Diagnostic Framework for Discrete Commitment Systems

Abstract: 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.