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Racer: Hunting GPU Kernel Bugs with Symbolic Equivalence Checking

Vu Tuan Truong, Cheng Tan · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28429 · cited by 0 works (OpenAlex) · open-access PDF

Japanese

GPU カーネルは、現在のAI サービスのパフォーマンスに重要であると確認するが、同じオペレーターは、それぞれの GPU 世代、数値形式、サービング レジーム、カーネル言語のために繰り返し書き換えられています。 すべての再書き換えは、実装によって計算された機能を維持しなければなりません。 今日、この義務はほぼ完全に差異テストに依存しています:新しいカーネルとランダムサンプルテネーターの信頼性のある参照を実行し、その後、許容範囲内で出力を比較します。 このアプローチには、追加のテストケースが排除できない盲点があります。 たとえば、論理的なバグは、正確に最適化されたカーネルを収容するために必要な許容範囲

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Symbolic trajectory evaluation, Computer science, Symbolic execution, Equivalence (formal languages), Model checking, Kernel (algebra)

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