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Main Authors: Ge, Luise, Juba, Brendan, Nilsson, Kris, Shao, Alison
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2602.14890
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author Ge, Luise
Juba, Brendan
Nilsson, Kris
Shao, Alison
author_facet Ge, Luise
Juba, Brendan
Nilsson, Kris
Shao, Alison
contents Reconciling the tension between inductive learning and deductive reasoning in first-order relational domains is a longstanding challenge in AI. We study the problem of answering queries in a first-order relational probabilistic logic through a joint effort of learning and reasoning, without ever constructing an explicit model. Traditional lifted inference assumes access to a complete model and exploits symmetry to evaluate probabilistic queries; however, learning such models from partial, noisy observations is intractable in general. We reconcile these two challenges through implicit learning to reason and first-order relational probabilistic inference techniques. More specifically, we merge incomplete first-order axioms with independently sampled, partially observed examples into a bounded-degree fragment of the sum-of-squares (SOS) hierarchy in polynomial time. Our algorithm performs two lifts simultaneously: (i) grounding-lift, where renaming-equivalent ground moments share one variable, collapsing the domain of individuals; and (ii) world-lift, where all pseudo-models (partial world assignments) are enforced in parallel, producing a global bound that holds across all worlds consistent with the learned constraints. These innovations yield the first polynomial-time framework that implicitly learns a first-order probabilistic logic and performs lifted inference over both individuals and worlds.
format Preprint
id arxiv_https___arxiv_org_abs_2602_14890
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Lifted Relational Probabilistic Inference via Implicit Learning
Ge, Luise
Juba, Brendan
Nilsson, Kris
Shao, Alison
Artificial Intelligence
Reconciling the tension between inductive learning and deductive reasoning in first-order relational domains is a longstanding challenge in AI. We study the problem of answering queries in a first-order relational probabilistic logic through a joint effort of learning and reasoning, without ever constructing an explicit model. Traditional lifted inference assumes access to a complete model and exploits symmetry to evaluate probabilistic queries; however, learning such models from partial, noisy observations is intractable in general. We reconcile these two challenges through implicit learning to reason and first-order relational probabilistic inference techniques. More specifically, we merge incomplete first-order axioms with independently sampled, partially observed examples into a bounded-degree fragment of the sum-of-squares (SOS) hierarchy in polynomial time. Our algorithm performs two lifts simultaneously: (i) grounding-lift, where renaming-equivalent ground moments share one variable, collapsing the domain of individuals; and (ii) world-lift, where all pseudo-models (partial world assignments) are enforced in parallel, producing a global bound that holds across all worlds consistent with the learned constraints. These innovations yield the first polynomial-time framework that implicitly learns a first-order probabilistic logic and performs lifted inference over both individuals and worlds.
title Lifted Relational Probabilistic Inference via Implicit Learning
topic Artificial Intelligence
url https://arxiv.org/abs/2602.14890