MathDB3 problems
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The prefix-free universality penalty conjecture in the error-exponents regime
Prefix-free penalty conjecture. Universal prefix-free codes incur, compared with the optimal rate in equation, a penalty of at best
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Optimality of the universal one-to-one compression rate
Optimal-rate conjecture. The rate obtained by this universal one-to-one compression scheme is optimal; equivalently, a matching converse should hold for the rate above.
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Conjecture that probabilistic circuits improve better Flow-based compression models
Probabilistic-circuit integration conjecture. Although not tested in the experiments, integrating PCs with better Flow models, such as IDF++, could further improve performance.