Self-similarity　is　valuable　to　the　exploration　of　non-local　textures　in　single　image　super-resolution　(SISR).　Researchers　usually　assume　that　the　importance　of　non-local　textures　is　positively　related　to　their　similarity　scores.　In　this　paper,　we　surprisingly　found　that　when　repairing　severely　damaged　query　textures,　some　non-local　textures　with　low-similarity　which　are　closer　to　the　target　can　provide　more　accurate　and　richer　details　than　the　high-similarity　ones.　In　these　cases,　low-similarity　does　not　mean　inferior　but　is　usually　caused　by　different　scales　or　orientations.　Utilizing　this　finding,　we　proposed　a　Global　Learnable　Attention　(GLA)　to　adaptively　modify　similarity　scores　of　non-local　textures　during　training　instead　of　only　using　a　fixed　similarity　scoring　function　such　as　the　dot　product.　The　proposed　GLA　can　explore　non-local　textures　with　low-similarity　but　more　accurate　details　to　repair　severely　damaged　textures.　Furthermore,　we　propose　to　adopt　Super-Bit　Locality-Sensitive　Hashing　(SB-LSH)　as　a　preprocessing　method　for　our　GLA.　With　the　SB-LSH,　the　computational　complexity　of　our　GLA　is　reduced　from　quadratic　to　asymptotic　linear　with　respect　to　the　image　size.　In　addition,　the　proposed　GLA　can　be　integrated　into　existing　deep　SISR　models　as　an　efficient　general　building　block.　Based　on　the　GLA,　we　constructed　a　Deep　Learnable　Similarity　Network　(DLSN),　which　achieves　state-of-the-art　performance　for　SISR　tasks　of　different　degradation　types　(e.g.,　blur　and　noise).　Our　code　and　a　pre-trained　DLSN　have　been　uploaded　to　GitHub†　for　validation.　©　1979-2012　IEEE.