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Soft Ontology Priors over Latent Concept Posteriors for Weakly Supervised Neuro-Symbolic Learning

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Briefings

A new method uses a soft ontology prior to resolve reasoning shortcuts in weakly supervised neuro-symbolic learning, where distinct concept mappings yield identical likelihoods. By injecting this prior into the training objective alongside task constraints, the method creates a smooth, decomposable probabilistic circuit. Under independent Bernoulli perception, the normalizers of the structured concept posterior reduce to weighted model counts that are linear in the compiled circuit size, as neural leaf weights fold into the circuit before evaluation. The soft compilation strategy places expert axioms in the circuit's weights rather than its support, ensuring noisy axioms only redistribute prior mass without emptying the support. The hard-support counterpart can be made degenerate by a single corrupted axiom. Validation was conducted on an audited six-concept view of the real-world BDD-OIA driving benchmark and controlled NeSy tasks.

Key points

• Neuro-symbolic predictors that supervise only the task label suffer from reasoning shortcuts where distinct concept mappings achieve the same maximum likelihood, leaving the recovered concepts unidentifiable and unsafe for downstream reuse.
• Injecting a soft ontology prior over latent concepts into the training objective creates a smooth, decomposable probabilistic circuit where normalizers reduce to weighted model counts linear in the compiled circuit size under independent Bernoulli perception.

Context

This research addresses a failure mode in neuro-symbolic learning where distinct concept mappings achieve the same maximum likelihood, leaving the recovered concepts unidentifiable and unsafe for downstream reuse. The method injects a soft ontology prior over latent concepts into the training objective alongside task constraints to resolve this issue.

Limitations

Validation was conducted on an audited six-concept view of the real-world BDD-OIA driving benchmark and controlled NeSy tasks. The evidence is from an arXiv preprint (arXiv:2610.30391v1) and the findings are subject to the constraints of preprint status and uncertainty regarding the full scope of the real-world application.

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