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Everyone expected additivity. Hastings produced a random counterexample, and the classical capacity of a quantum channel became genuinely hard.
The answer is 7 when the dimension is a prime power. In dimension 6 nobody can get past 3.
Numerically found in every dimension tried, exactly constructed in many, and proved in none in general.
Held–Karp has stood since 1962. No exact algorithm is known with running time O(1.99^n).
Babai's quasipolynomial algorithm moved the problem, but the gap to polynomial time remains.
Is there any truly subquadratic algorithm for finding three numbers summing to zero?
Are splay trees within a constant factor of the best possible binary search tree, on every access sequence?
Is deterministic communication complexity polylogarithmic in the rank of the communication matrix?
Bayesian optimization with failed function evaluations. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.
HyperBO regret beyond finite-dimensional GP assumptions. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.
Necessary conditions for bounded HyperBO regret. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.
Posterior error bounds for pre-trained Gaussian processes. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.
Fast meta-learning rates with variational task posteriors. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.