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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.14890 |
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| _version_ | 1866911450720632832 |
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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 |