Conditional computational barrier exists for learning k=1 invariant subspaces in samplable multi-environment instances under sparse recovery hardness; minimax risk is Theta(k(d-k)/(n|E|)) with phase transition at n* ~ k(d-k)/(|E| gamma^2).
Finding a large hidden clique in a random graph
2 Pith papers cite this work. Polarity classification is still indexing.
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2026 2verdicts
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Establishes n^{1-ε}-hardness of approximation for dichromatic number and acyclic number on tournaments, plus polynomial-time approximations for ℓ-dicolorable digraphs and special dense cases.
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Is Spurious Correlation Removal Always Learnable?
Conditional computational barrier exists for learning k=1 invariant subspaces in samplable multi-environment instances under sparse recovery hardness; minimax risk is Theta(k(d-k)/(n|E|)) with phase transition at n* ~ k(d-k)/(|E| gamma^2).
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Hardness and Approximation for Coloring Digraphs
Establishes n^{1-ε}-hardness of approximation for dichromatic number and acyclic number on tournaments, plus polynomial-time approximations for ℓ-dicolorable digraphs and special dense cases.