Null-Space Calibration of Auxiliary Evidence for Multi-Behavior Recommendation

Multi-behavior recommendation learns user and item representations from target and auxiliary interactions to improve target prediction. Auxiliary representations may encode preferences not fully reflected in target interactions, but association strength alone does not determine the ranking value of this evidence. A key challenge is to retain target-associated information while learning to use potentially complementary evidence. To this end, we propose Target-referenced Null-space Calibration (TNC), a plug-in module that calibrates auxiliary representations through null-space constraints. Using cross-covariance between paired auxiliary and target representations, TNC constructs a target-associated subspace through truncated singular value decomposition. It retains both the target-associated and null-space components and learns separate calibration gains under target ranking supervision. For a fixed representation, reference, and target-associated gain, adjusting the null-space gain calibrates potentially complementary evidence without changing the prescribed target-associated projection. The module operates between behavior encoding and fusion and is jointly trained with compatible encoders, allowing target supervision to guide both representation learning and calibration. Experiments on three real-world datasets show that integrating TNC improves ranking performance across multiple multi-behavior recommendation backbones. To facilitate reproducibility, our implementation is available in an anonymous repository at this url.