DENO: Signed Determinantal Evidence Pooling for Correlated Multiple-Instance Learning

Multiple-instance learning (MIL) often involves strongly correlated or redundant instances, yet standard aggregation does not explicitly separate redundant evidence from prevalence information. We introduce DENO, a signed determinantal evidence pooling operator that combines signed instance evidence with a degree-normalized similarity kernel and contrasts log-determinants under opposite evidence tilts. A separate mean-evidence branch retains frequency information. We show that, for exact replicas, the full instance-level determinant reduces exactly to an effective latent-source determinant: uniform replication leaves the determinantal term unchanged, while selective replication can alter the effective source geometry. For near-redundant groups, we bound the approximation error using residual spectral structure and within-group evidence variation. We further develop a boundary-aware ordinal extension and evaluate DENO across five heterogeneous MIL benchmarks, where it attains the highest primary classification point estimate on three tasks and remains competitive on the other two. Controlled duplication experiments show targeted robustness to nuisance multiplicity, and on post-stroke FAC prediction the ordinal variant achieves 75% accuracy and 0.30 MAE versus 45% and 0.70 for mean pooling.