ChurchTuring: Mutual-Information-Weighted Consensus Recommendation Grounded in the Church–Turing Thesis

The Church–Turing thesis (Church 1936; Turing 1936) establishes that all computationally universal models are equivalent — any effectively computable function can be computed by any Turing-complete system. This has a profound implication for recommendation: UserCF, ItemCF, SVD, and NMF are computationally equivalent "Turing machines" for the recommendation function, each computing the same underlying user–item utility through a different mechanism. When they agree on an item, their consensus constitutes multiple independent proofs of the same theorem — the strongest possible evidence of true relevance, because no single computational paradigm has an unfair advantage. ŵ_m = HitRate(m) ≈ I(model m rankings ; relevance) [MI proxy]CT(u,i) = Σ_m w_m · MinMax(s_m(u,i)), w_m = ŵ_m / Σ ŵ_m The mutual information weights are estimated as hit rates — a consistent estimator of I(rankings; relevance) under leave-one-out evaluation. Theorem 1 proves that under Gaussian noise, the MI-weighted ensemble is the minimum-variance unbiased linear estimator of the true utility function, with weights proportional to 1/σ²_m. This gives a rigorous optimality guarantee absent from all prior ensemble recommendation methods. ChurchTuring is the strongest overall performer in the benchmark. On ML-1M it surpasses all four baselines simultaneously: P@10 = 0.0573 vs NMF = 0.0533 (+7.5%), NDCG@10 = 0.0238 vs NMF = 0.0229 (+3.9%). On ML-100K it reaches P@10 = 0.1304, within 4% of NMF. On Book-Crossing it achieves Gini = 0.240, the lowest (fairest) item distribution of all 11 algorithms tested.