Kernel Contracts: A Specification Language for ML Kernel Correctness Across Heterogeneous Silicon

Abstract: Every ML kernel ships with an implicit contract about what it computes. People rarely write the contract down. When two kernels disagree -- when a matmul on AMD produces a different gradient than the same matmul on NVIDIA, when a fused attention kernel silently downcasts an accumulator, when an out-of-bounds access returns zero on one stack and garbage on another -- there is no formal artifact to arbitrate the dispute. Recent empirical work has measured the gap across silicon platforms, but none of it specifies the contract being violated. We present a specification language for kernel contracts. A contract has eight parts: identifier, scope, precondition, postcondition, tolerance, reference oracle, measurement protocol, and violation signature. We use it to state twelve contract classes covering precision, ordering, compiler-induced, and exceptional-value failure modes, each grounded in published empirical evidence. We require a three-state calibration: every contract must admit at least one reference-conforming implementation and at least one contract-violating implementation that passes basic functional tests. We apply the framework to three documented incidents -- Huawei Ascend silent precision coercion, Sakana AI CUDA Engineer reward hacking, AMD out-of-bounds silent acceptance -- and show that each informal diagnosis maps to a specific contract violation with a measurable signature. A kernel contract suite is a normative reference against which conformance can be graded, in the way that ISASecure grades industrial control systems against IEC 62443.