Racer: Hunting GPU Kernel Bugs with Symbolic Equivalence Checking

Abstract:GPU kernels are critical to the performance of today's AI services, yet the same operators are rewritten repeatedly: for each GPU generation, numeric format, serving regime, and kernel language. Every rewrite must preserve the function computed by the implementation it replaces. Today, this obligation depends almost entirely on differential testing: run the new kernel and a trusted reference on randomly sampled tensors, then compare their outputs within a tolerance. This approach has blind spots that additional test cases cannot eliminate. For example, a logical bug may produce an error smaller than the tolerance required to accommodate a correct optimized kernel. We propose symbolic equivalence checking, which executes a kernel and its reference on symbolic inputs, turning each output cell into an exact algebraic expression, and then checks whether the paired expressions agree for all inputs. Because these expressions are exact, symbolic equivalence checking distinguishes floating-point error from logical bugs, while a single check covers the entire input space. We implement Racer, a PTX-level symbolic equivalence checking engine, with three techniques that make this approach practical for production kernels: (1) Shape Reduction to control checking cost, (2) a lockstep CTA scheduler to handle concurrency, and (3) idiom templates with exact numeric refutation for otherwise inconclusive results. Across 2,408 production kernels from 41 collection targets, Racer found 82 real bugs in 23 libraries, including 76 previously unknown bugs and 41 confirmed so far.

Symbolic Computation (cs.SC); Artificial Intelligence (cs.AI)

arXiv:2610.28429 [cs.SC]

(or arXiv:2610.28429v1 [cs.SC] for this version)

https://doi.org/10.48550/arXiv.2610.28429 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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.