Non-local　attention　(NLA)　is　a　powerful　technique　for　capturing　long-range　feature　correlations　in　deep　single-image　super-resolution　(SR).　However,　NLA　suffers　from　high　computational　complexity　and　memory　consumption,　as　it　requires　aggregating　all　non-local　feature　information　for　each　query　response　and　recalculating　the　similarity　weight　distribution　for　different　abstraction　levels　of　features.　To　address　these　challenges,　we　propose　a　novel　learnable　collaborative　attention　(LCoA)　that　introduces　inductive　bias　into　non-local　modeling.　Our　LCoA　consists　of　two　components:　learnable　sparse　pattern　(LSP)　and　collaborative　attention　(CoA).　LSP　uses　the　k-means　clustering　algorithm　to　dynamically　adjust　the　sparse　attention　pattern　of　deep　features,　which　reduces　the　number　of　non-local　modeling　rounds　compared　with　existing　sparse　solutions.　CoA　leverages　the　sparse　attention　pattern　and　weights　learned　by　LSP　and　co-optimizes　the　similarity　matrix　across　different　abstraction　levels,　which　avoids　redundant　similarity　matrix　calculations.　The　experimental　results　show　that　our　LCoA　can　reduce　the　non-local　modeling　time　by　about　83%　in　the　inference　stage.　In　addition,　we　integrate　our　LCoA　into　a　deep　learnable　collaborative　attention　network　(LCoAN),　which　achieves　competitive　performance　in　terms　of　inference　time,　memory　consumption,　and　reconstruction　quality　compared　with　other　state-of-the-art　SR　methods.　Our　code　and　pre-trained　LCoAN　models　were　uploaded　to　GitHub　(https://github.com/YigangZhao/LCoAN)　for　validation.　(c)　2024　SPIE　and　IS&T