arXiv cs.AI· Tuan Truong Vu, Cheng Tan·· 12 小时前AI 评分38
Racer：用符号等价性检查猎捕 GPU Kernel Bug
Racer: Hunting GPU Kernel Bugs with Symbolic Equivalence Checking
AI 导读
Racer 是一个 PTX 级符号等价性检查引擎，通过在符号输入上执行 kernel 及其参考实现、将每个输出单元转为精确代数表达式，从而区分浮点误差与逻辑 bug，单次检查即可覆盖整个输入空间。
正文 · 原文
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.
| Subjects: | Symbolic Computation (cs.SC); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.28429 [cs.SC] |
| (or arXiv:2610.28429v1 [cs.SC] for this version) | |
| https://doi.org/10.48550/arXiv.2610.28429 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Cheng Tan [view email]
[v1]
Tue, 20 Oct 2026 15:58:33 UTC (114 KB)
来源：arXiv cs.AI · arxiv.org