Accurate Models of AMD Matrix Cores

Computer Science > Hardware Architecture [Submitted on 13 Sep 2026 (v1), last revised 15 Sep 2026 (this version, v2)] Title:Accurate Models of AMD Matrix Cores View PDF HTML (experimental)Abstract:Matrix multipliers available on recent GPUs do not conform with the IEEE 754 floating point standard. Features of matrix multipliers differ across vendors and architectures of the same vendor, such as accumulator width, rounding behaviour, normalisation points, intermediate underflow and overflow logic, the handling of subnormals, and the treatment of special inputs. As a result, reproducibility of small matrix multiplier results across devices is not possible and cannot be achieved by software control. Implementation details of matrix multipliers are not documented, making it difficult to interpret discrepancies in the computed results. We characterise the numerical behaviour of matrix multipliers across three AMD GPU architectures: CDNA 1, CDNA 2, and CDNA 3, using the MI100, MI210/250, and MI300A/300X GPUs, respectively. We design test vectors to target numerical features for all supported input formats and provide the derivation and the reasoning for why each vector allows to determine a particular numerical feature based on the outputs of the devices. MATLAB-based software models of the matrix multipliers are then developed for each architecture and validated for bit-level reproducibility against hardware using a randomized test suite consisting of 10 million sets of random input vectors. To achieve this, we applied a previously developed technique to iteratively refine the accuracy of the models in a loop, by randomized testing followed by test-refinement until the model matches the hardware for every test case. Finally, as a proof of concept for what experimental research can be done with the models, we have utilised them in two demonstrative numerical applications, quantifying application-level accuracy differences between AMD matrix cores and the NVIDIA tensor cores. Submission history From: Faizan Ahmad Khattak [view email][v1] Sun, 13 Sep 2026 23:34:01 UTC (1,297 KB) [v2] Tue, 15 Sep 2026 10:33:08 UTC (1,297 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.