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Transcription factor (TF) cooperativity plays a critical role in gene regulation. However, the underlying genomic rules remain unclear, calling for scalable methods to characterize the TF binding site (motif) syntax of regulatory elements. Here, we introduce DeepCompARE, a lightweight model paired with an ablation (ISA) framework for genome-wide analysis of regulatory sequences. Our framework enables precise interpretation of the motif syntax governing chromatin accessibility, enhancer activity, and promoter function. We find that most TF motifs are pairwise independent, indicating a default additive behavior of TFs, and define a cooperativity score to quantify deviations from this baseline. This reveals synergy and redundancy as opposite effects along the same cooperative spectrum. TF redundancy is linked to promoter activity and broad expression, whereas TF synergy is associated with enhancer activity, physical interactions, and cell-type specificity. Our framework provides a quantitative model for TF cooperativity, offering new insights into gene regulatory logic.