A First Step Towards Even More Sparse Encodings of Probability Distributions

arXiv cs.AI / 4/1/2026

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Key Points

  • The paper addresses the inefficiency of representing lifted probability distributions, which typically require exponentially large tables or lists of values.
  • It proposes a two-stage approach: first reduce the number of values in a distribution to increase sparsity, then extract a logical (first-order) formula for each remaining value.
  • The extracted formulas are further minimized, enabling much sparser encodings while aiming to retain the distribution’s core information.
  • Experimental evaluation suggests sparsity can grow substantially by using a small set of short formulas instead of dense enumerations, alongside improved generalization of the original distribution.

Abstract

Real world scenarios can be captured with lifted probability distributions. However, distributions are usually encoded in a table or list, requiring an exponential number of values. Hence, we propose a method for extracting first-order formulas from probability distributions that require significantly less values by reducing the number of values in a distribution and then extracting, for each value, a logical formula to be further minimized. This reduction and minimization allows for increasing the sparsity in the encoding while also generalizing a given distribution. Our evaluation shows that sparsity can increase immensely by extracting a small set of short formulas while preserving core information.