The result the researchers report
Badash, Boneh, Komargodski and Srivastava present a framework for analyzing GPU arithmetic and reproducing matrix multiplication on a CPU. Their tests examine rounding, treatment of subnormal numbers and the order of accumulation on NVIDIA Tensor Cores.
They report exact reproduction across their tested cases on Ampere, Hopper and Lovelace architectures and several precision formats. The paper is listed as accepted to MLSys 2026. The qualifier “tested cases” is essential: the result is not a guarantee about every GPU, compiler, kernel or future hardware generation.
Why the order of arithmetic matters
Floating-point arithmetic stores a finite approximation to many real numbers. Rounding occurs because the available representation has limits. As a result, changing the grouping or order of operations can change the final stored answer, even when the corresponding expressions are equivalent in exact mathematics. NVIDIA’s floating-point guide discusses precisely this issue.
A useful way to read the problem is to separate mathematical intent from execution details. “Multiply these matrices” names an operation. It does not necessarily specify every rounding decision made while carrying it out. Exact reproduction needs a sufficiently complete account of those decisions.
Reproduction is one layer of an audit
Matching an execution’s arithmetic is different from deciding whether its inputs were appropriate, whether the task was authorized or whether a customer received a satisfactory service. An audit can require all of those answers, but one check does not silently supply the others.
There is also a difference between reproducing a selected operation and reproducing an entire application. Data preparation, control flow and surrounding software still have to be specified if the claim covers them. This is why a reproducibility report is most useful when it describes the boundary of the experiment as carefully as it describes the successful result.
The connection to Pearl
Hawkeye is relevant to the broader problem of verifiable computation. Its publication does not, by itself, establish a Pearl consensus activation. The current node rules and their activation conditions must be checked separately.
The distinction is visible in Pearl Pulse. A byte-commitment check in Proof Lens, an arithmetic reproduction experiment and a validating node’s acceptance decision are different forms of evidence. Keeping them separate lets readers compare progress without inflating any one result into a claim that the whole verification problem has been solved.
The Pearl Pulse view
Independent reproduction can turn trust into a question another party can investigate. If that becomes practical across relevant workloads, cautious operators may find participation easier. Pearl could gain credibility from that progress, provided the verification claims remain as precise as the experiments supporting them. Coverage matters as much as the headline.
Sources & editorial approach
Original reporting and explanation by Pearl Pulse. The editorial perspective is our interpretation; it is separate from the researchers’ findings. Links below lead to the primary sources.