Accurate Models of AMD Matrix Cores

[Submitted connected 13 Sep 2026 (v1), past revised 15 Sep 2026 (this version, v2)]

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Abstract:Matrix multipliers disposable connected caller GPUs do not conform pinch the IEEE 754 floating constituent standard. Features of matrix multipliers disagree crossed vendors and architectures of the aforesaid vendor, specified arsenic accumulator width, rounding behaviour, normalisation points, intermediate underflow and overflow logic, the handling of subnormals, and the curen of typical inputs. As a result, reproducibility of mini matrix multiplier results crossed devices is not imaginable and cannot beryllium achieved by package control. Implementation specifications of matrix multipliers are not documented, making it difficult to construe discrepancies successful the computed results. We characterise the numerical behaviour of matrix multipliers crossed 3 AMD GPU architectures: CDNA 1, CDNA 2, and CDNA 3, utilizing the MI100, MI210/250, and MI300A/300X GPUs, respectively. We creation trial vectors to target numerical features for each supported input formats and supply the derivation and the reasoning for why each vector allows to find a peculiar numerical characteristic based connected the outputs of the devices. MATLAB-based package models of the matrix multipliers are past developed for each architecture and validated for bit-level reproducibility against hardware utilizing a randomized trial suite consisting of 10 cardinal sets of random input vectors. To execute this, we applied a antecedently developed method to iteratively refine the accuracy of the models successful a loop, by randomized testing followed by test-refinement until the exemplary matches the hardware for each trial case. Finally, arsenic a impervious of conception for what experimental investigation tin beryllium done pinch the models, we person utilised them successful 2 demonstrative numerical applications, quantifying application-level accuracy differences betwixt AMD matrix cores and the NVIDIA tensor cores.