Vision models show a phase transition where accuracy on a zero syntactic-distance global-semantics task collapses to chance beyond a critical scale and does not recover with larger models or data.
Solution independence and self-referential instances
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
In this paper, we investigate the hitting set problem and demonstrate that solution independence is the crucial property underlying the construction of self-referential instances. As a special case of the hitting set problem, the vertex cover problem lacks the solution independence property. This distinction accounts for its ability to evade exhaustive search, as correlations among candidate solutions can be leveraged to compress the overall search space. In contrast, the dominating set problem on hypergraphs, which is also a special case of the hitting set problem, satisfies the solution independence property, thereby enabling the construction of self-referential instances. Moreover, we prove that these self-referential instances possess an irreducible property, implying that any algorithm for solving such instances must process nearly the entire graph to yield a correct solution.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Claims a finite analogue of Gödel incompleteness in K-SAT by building locally indistinguishable SAT/UNSAT pairs in log-width ensemble, implying sublinear deductive systems require wide clauses and exponential proof sizes, reframing SETH as Gödel projection.
citing papers explorer
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Can Machines Really See Objects in Images? A Study Based on Syntactic Distance and Visual Self-Referential Instances
Vision models show a phase transition where accuracy on a zero syntactic-distance global-semantics task collapses to chance beyond a critical scale and does not recover with larger models or data.
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Self-Referential $K$-SAT and the Finite Analogue of G\"odel's Incompleteness Theorem
Claims a finite analogue of Gödel incompleteness in K-SAT by building locally indistinguishable SAT/UNSAT pairs in log-width ensemble, implying sublinear deductive systems require wide clauses and exponential proof sizes, reframing SETH as Gödel projection.