What If Recommender Systems Were Circuits?

Recommender system research largely focused on learning richer user and item representations and designing novel objective functions, while many approaches still model user-item interactions as a simple factorization realized via a dot product. We revisit this factorised component from a probabilistic perspective, asking whether it can support tractable probabilistic inference and learning, without redesigning the underlying recommender architecture. To this end, we introduce CiRe, a plug-in interaction head that replaces the usual dot product with a nonnegative squared circuit, thus delivering a tractable generative model that can be trained with maximum likelihood, avoiding the use of negative sampling and supporting probabilistic queries over user–item interactions. We show that across nine recommender architectures and five datasets, CiRe frequently matches or improves top-k ranking performance with the strongest results combining circuit parametrisation and likelihood training. For simple encoders, removing negative sampling can also reduce training time, whereas richer architectures exhibit different computational trade-offs, which we analyse. Our code is available at https://anonymous.4open.science/r/CiRe-2B56/.