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Published June 3, 2026 | Version v1
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Hard-Gating Collapse Dynamics: Selection Hardness as the Organizing Parameter for Robust Sparse Routing

Authors/Creators

Description

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, and
    the 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

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Additional details

Software

Repository URL
https://github.com/Hakan-Saka/artificial-f1
Programming language
Python
Development Status
Active