Hard-Gating Collapse Dynamics: Selection Hardness as the Organizing Parameter for Robust Sparse Routing

Hard discrete selection — gating that retains exactly k of n features and suppresses the rest — produces abrupt collapse in task performance as noise increases. This collapse is architecturally invariant: it appears across implementations within the hard-gating class G_hard and is absent in soft attention. We identify selection hardness H_s(G) := H(F_1 | G(F_1)) as the dominant organizing quantity for this collapse behavior: higher H_s corresponds to more discrete, information-destroying gating, and predicts earlier, sharper collapse. F1.1, a minimal extension of hard selection that adds a safety margin of m redundant features, modulates H_s(G_m) without exiting the hard-gating class. Under matched computational budgets (both using 8 effective features), F1.1 outperforms sparsified soft attention (acc=0.755 vs 0.679), establishing a Pareto-superior robustness-compute trade-off. A Saturation Lemma (companion theoretical work) formally predicts that performance differences vanish at extreme noise, explaining the compressed effect size without invalidating the mechanism. Exploratory experiments under high-redundancy regimes show compression of architectural differences, consistent with the regime-dependent interpretation. Together these results establish selection hardness as the dominant organizing quantity for resource-efficient hard-gating architectures within the studied regime. Companion Papers: **Saka, H. (2026a).** Toward a Reframing of the Hard Problem of Consciousness: Subjective Reality, Feeling, andthe Origins of the Conceptual World. Version 7.19. PhilPapers. https://philpapers.org/rec/SAKTAR **Saka, H. (2026b).** Organizational Phenomenology: Artificial F1 and the Geometry of Coherent Agency. Zenodo. https://doi.org/10.5281/zenodo.20555024 **Saka, H. (2026c-Theory).** Artificial F1: Full Computational Model — Selection Hardness, Non-Scalarizability, and Phase Transition in Bounded Evaluative Architectures. https://doi.org/10.5281/zenodo.20524004 Keywords: sparse gating, hard selection, selection hardness, gating collapse,mixture of experts, inductive bias, noise robustness,compute efficiency, phase transition, representation constitution