The Memory Wall as Force-Ratio Imbalance: From Failure-Line Intersection to Resident Reduction Algebra

Abstract

The memory wall as force-ratio imbalance (v2.0, upgraded from the PIM reduction proposal v1.0). Part I: a dimensionless force-ratio criterion R'_wall=ΣE_byte(i)/(E_FLOP×AI_i); three structural results: the wall stays two orders of magnitude across six process generations (45nm 173× → 4nm 37-74×, structural not process-bound); cache-dilution ceiling E_DRAM/E_L1=128× with zero dilution for streaming workloads; unlimited reuse converges to an L1 wall R_min=b_op·E_L1/E_FLOP (the ultimate boundary is not DRAM but L1). Two-dimensional adsorption picture: residence time τ × transfer cost R', engineering tax 8 orders above the adsorption barrier. Part II: resident reduction algebra - reduction as commutative monoid, legality criterion, completeness theorem and converse design boundary; resident reduction saves 2K× adsorption transfers and 9.5-10.2× energy. All figures hand-verified 2026-08-15 (Horowitz ISSCC 2014 / CAQA 6e full text / NVIDIA official specs / arXiv 2604.27808 / IEEE Micro 2022 / JSSC 2023). Chinese version is the companion translation.