Abstract
<title>Abstract</title> <p>Background Integrating heterogeneous data to find inter-related subsets of attributes is a recurring problem in the life sciences, where the informative agreement between two views—for example omics and clinical data—is often confined to a small subset of attributes. Subset binding addresses this by extending fuzzy association-rule mining to paired itemsets that co-occur across two views. Being built on the Apriori algorithm, however, it inherits two scaling failures: the candidate space grows combinatorially with the number of attributes, and a single large frequent itemset forces all 2^L of its sub-itemsets to be enumerated, exhausting memory. Results We introduce differentiable subset binding (DSB), which recasts the discrete search as gradient optimization of a differentiable cross-view co-occurrence objective. Each binding module is a sparse, learned soft selection of items per view, so an itemset of any size is a fixed-length weight vector and the 2^L blow-up disappears. On the original synthetic benchmark, DSB matches the exhaustive baseline’s perfect recovery, returning the planted patterns as three maximal modules directly rather than as a level-wise rule set that must be reduced post hoc, and recovers a planted itemset of up to 30 items at constant cost where Apriori is intractable; benchmarked against modern multi-view methods it also matches the probabilistic factor model MOFA2 on recovery while returning discrete, directional itemsets rather than dense continuous factors. A sparse-CCA seeding variant scales to the full 3,116-gene liver-toxicity dataset, recovering the methionine/polyamine and heat-shock mechanisms (gene-set enrichment FDR q < 0.05), and on the independent nutrimouse data recovers the canonical PPARα fatty-acid-oxidation program with the correct direction. On TCGA breast cancer, DSB applied to clinical × expression data recovers the canonical basal-like/triple-negative co-expression signature bound to ER-negative/PR-negative/basal status (permutation p < 5×10⁻⁴; basal-marker enrichment p = 8×10⁻¹⁰), whereas sparse, mutually-exclusive somatic-mutation data proves better suited to an additive factor model—delineating a clear data-type boundary for the method. In a direct head-to-head with redescription miners, the greedy miner ReReMi locates the same planted patterns but returns them as hundreds of minimal, largely spurious queries, whereas DSB returns the three complete itemsets with no false positives—empirically grounding the association-versus-equivalence distinction between the two families. Conclusions DSB is a scalable, differentiable complement, decisive for large itemsets, for continuous co-expression bound to phenotype, and for embedding cross-view mining inside a learned pipeline.</p>