distribution-search

Constructing a probability distribution with specific KL divergence and entropy targets involves applying feasibility analysis and closed-form parameterizations. This Skill uses softmax and exponential-family logits to find solutions that satisfy your statistical constraints during numerical optimization and model calibration.

Parameterizing a discrete token distribution is best achieved using two-group or multi-group closed-form parameterizations, or continuous parameterizations for large vocabularies. This approach calibrates the distribution to match a known prior while minimizing parameter complexity and satisfying divergence tolerances.

Yes, you can use gradient-free optimizers and discrete grid searches for matching probability distributions to moment constraints. These optimization strategies are recommended for effectively navigating mixed discrete and continuous parameter spaces during distribution construction.

Verifying that a probability distribution satisfies normalization and divergence tolerances requires applying numerical checks for positivity and KL/entropy tolerances. This robust verification process identifies common pitfalls and ensures mathematically consistent solutions for large-scale problems.

Yes, this approach supports feasibility and degrees-of-freedom analysis for statistical constraints. It assesses whether your constraints are solvable and determines exactly how many parameters are required before attempting numerical optimization and model calibration.