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UID:submissions.supercomputing.org_SC25_sess620_post148@linklings.com
SUMMARY:A Formal Characterization of Non-Monotonicity in Tensor Cores
DESCRIPTION:Paul Jiang (Purdue University) and Vivian Zheng (Stony Brook U
 niversity)\n\nModern high performance computing increasingly relies on har
 dware accelerators like NVIDIA Tensor Cores, which employ non-standard int
 ernal arithmetic that can evolve between hardware generations. This non-st
 andard approach can violate the fundamental mathematical property of monot
 onicity, leading to incorrect outputs where adding a larger number produce
 s a smaller result. To address this, we introduce a formal framework using
  satisfiability modulo theories to analyze the hardware design space by sy
 stematically varying hardware features (e.g., number of terms [𝑛], interna
 l padding bits [𝑝]) within a custom bitvector encoding. We derive a precis
 e condition for guaranteed monotonicity, proving that non-monotonicity can
  only occur when 𝑝 ≤ ⌊log2 (𝑛 − 1) − 2⌋. We also derive a formula for the 
 maximum magnitude of error when non-monotonicity can occur. Our results pr
 ovide hardware architects with provably correct design parameters to elimi
 nate such anomalies, ensuring greater numerical stability.\n\nTag: Researc
 h & ACM SRC Posters\n\nRegistration Category: Technical Program Reg Pass\n
 \nSession Chairs: Kento Sato (RIKEN Center for Computational Science (R-CC
 S)); Anja Gerbes (Georg-August-Universität Göttingen); and Chris Schlipali
 us (Pawsey Supercomputing Research Centre; Commonwealth Scientific and Ind
 ustrial Research Organisation (CSIRO), Australia)\n\n
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