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Researchers have established that finding approximate stationary points for min-max optimization problems involving quadratic polynomials over a hypercube is PPAD-hard. This complexity holds even for multilinear polynomials with limited variable occurrences and inverse polynomial approximation factors. Consequently, this work presents the first PPAD-hardness results for two-team zero-sum polymatrix games. AI
Researchers have developed a new method to discover discrete algebraic rules from data by framing it as Cayley-table completion. This approach uses a differentiable measure of algebraic complexity, derived from an operator-valued tensor factorization called HyperCube. The method proves that this complexity measure can exactly characterize group structures, resolving a key conjecture and enabling gradient-based discovery without combinatorial search. AI
IMPACT Enables gradient-based discovery of discrete algebraic structures, potentially advancing AI's ability to learn underlying rules from data.