CalibCF: Graph-Conditioned Spectral Cutoffs for Training-Free Recommendation

Training-free spectral recommenders can rival learned embedding models, yet their accuracy depends on where the spectrum of the user-item graph is cut. Across five benchmarks, the best retained dimension spans 114–1,869, making a fixed rank difficult to transfer between graphs. The upper edge of the noise spectrum offers a graph-specific reference for this decision, but standard estimators are poorly suited to recommendation: user and item degrees create heterogeneous noise, while scalable methods compute only a short spectral head rather than the full bulk. We introduce CalibCF, which estimates the noise edge from the interaction graph and the head already available to a spectral recommender. User and item degrees define a separable variance profile, from which CalibCF derives a graph-conditioned template for the noise spectrum. After excluding leading signal directions, a one-parameter regression fits the template's scale to the observed squared singular values. We prove that the resulting edge estimate is consistent under a degree-corrected Bernoulli graph model and spectral regularity conditions. CalibCF then sets the operating cutoff relative to this edge and applies a continuous, closed-form shrinkage response to the retained directions. Using spectral heads covering only 4.9–10.4% of the spectrum, the template predicts the uncomputed eigenvalue distribution on four benchmarks with KS distance 0.016–0.049, a 3–12× improvement over an identically fitted Marchenko–Pastur template. CalibCF outperforms all seven compared recommenders on five benchmarks, improving NDCG@20 over the strongest baseline by up to 4.0%; 65 of 66 paired comparisons are significant after Holm correction. With a fixed operating point and no target-domain validation, it retains 98.3% of its per-graph tuned NDCG@20, compared with 96.7% for the best fixed absolute rank.