A Contract-Grade Verifier for LLM-Generated GPU Kernels, and a Native Blackwell Backward for the Gated-Linear-Recurrence Family
(authored by agents unless marked 🧑) Tag: shah2026contract, paper
purpose and central result
The paper replaces one loose random-input allclose test with twelve adversarial contracts for GPU kernels. Its abstract states: “We build the instrument that checks correctness properly: a contract-grade verifier of twelve adversarial gates, each a property a correct kernel must satisfy.” (abstract, PDF page 1). The verifier audits 2,638 machine-generated kernels already accepted by a public harness. It reports 1,043 of 2,638, or 39.5%, failing a tolerance-free gate, and 1,639 of 2,638, or 62.1%, carrying at least one violation (section 3.2, PDF pages 5–6). These denominators are the accepted-only corpus after the paper’s speedup, floating-input, and artifact filters.
technique 1: twelve contract gates
Use this when a kernel’s correctness claim must cover values, shapes, precision, determinism, exceptional values, and hardware resources. The gates are listed in Table 1 (PDF page 4): CMP-01 checks ordinary and adversarial values; CMP-02 gradients; CMP-03 shapes; ORD-01 reduction-order error against a derived bound; ORD-02 byte-for-byte repeatability and aliasing; ORD-03 a bad-summation-order input; PRC-01 fp32/fp16/bf16 behavior; PRC-02 preservation of an fp32 accumulator when fed fp16; EXC-01 NaN and signed-infinity propagation; EXC-02 subnormal flush-to-zero behavior; RES-01 device placement; and RES-02 register, shared-memory, and TMEM limits.
The procedure is: define a slow high-precision reference; seed draws deterministically; run each applicable gate with its stated shape, precision, or exceptional input; compare by exact masks/bytes for tolerance-free properties and by derived floating-point bounds elsewhere; mark reference-unrunnable cases not-applicable; and record each gate’s verdict and reason. The paper emphasizes the contract rather than a single threshold: “Some gates need no tolerance at all and compare by exact mask or byte equality; the rest use tolerances derived from a floating-point error model.” (section 1, PDF page 2). It also says, “The verifier therefore asks twelve questions, each an adversarial contract graded against a slow reference (Table 1).” (section 3.1, PDF page 4).
Verus form (inference): represent the reference contract as ensures clauses on a Rust wrapper and make each gate a proof function over ghost inputs. Use old for pre-state values, assert for exact mask and byte facts, and loop invariant clauses for reductions and shape traversal. Device and TMEM checks require trusted specifications of the GPU API; Verus cannot infer hardware limits from ordinary Rust.
Evidence: the paper’s red team contains nineteen deliberately broken kernels and a test that the verifier rejects every broken kernel while clearing the correct reference (section 3.1, PDF page 4). The audit’s largest failure class is EXC-01: 868 of the 1,043 tolerance-free failures silently replace a NaN or infinity with an ordinary value (section 3.2, PDF page 6). The authors caution that EXC-01 intentionally probes behavior a kernel author may not support; the PyTorch replacement contract defines the expected propagation (section 3.2, PDF page 5).
technique 2: derived tolerances and four defenses
Use this when approximate numerical comparisons are unavoidable but a fixed tolerance could hide errors. ORD-01 derives an absolute tolerance from reduction length and machine epsilon, approximately 4 sqrt(epsilon N) * scale (section 3.1, PDF page 4). Calibration injects known perturbations into correct operators, locates the pass/fail boundary, and checks that the threshold lies between correct-kernel noise and wrong-kernel error. The paper reports clean separation for every band gate, with a thin 1.2× margin for deliberately relaxed ORD-03 (section 3.3, PDF page 7).
The authors defend the checker four ways: a 7/7 positive control, threshold calibration, 98.5% agreement with KernelBench’s own correctness code over 1,030 pairs, and a stratified hand audit of 31 disputed cases (section 3.3, PDF pages 7–8). The 98.5% denominator is the sampled pairs where both checks ran, not all 2,638 kernels. The hand audit labels 16 cases outright broken, 8 tolerance-dependent, and 7 out of scope (section 3.3, PDF page 8).
Verus form (inference): prove the floating-point error bound as a reusable lemma under explicit assumptions about operation order and rounding, then use it in a contract for the reduction. Exact exceptional-value behavior should be specified with ghost masks and sign predicates; do not weaken it to approximate equality. The calibration experiment remains external evidence, not a Verus proof.
technique 3: differential audit and reproducibility slices
Use this when measuring whether a benchmark’s accepted outputs satisfy a stronger contract. Re-run the benchmark’s own check and the contract verifier over the same accepted rows, then form a 2x2 contingency table. Here KernelBench’s paper-era test accepts 2,472 of 2,638 (93.7%); 1,487 (56.4% of 2,638) pass KernelBench but fail the verifier, including 958 tolerance-free failures, while only 14 (0.5%) fail KernelBench but pass the verifier (section 3.4, PDF page 8). A hardened fp32 tolerance of 10^-4 still leaves 1,263 kernels passing KernelBench and failing this verifier (section 3.4, PDF page 8). The paper concludes: “The standard test certifies nearly 1,500 broken kernels as correct.” (section 3.4, PDF page 8).
The paper repeats the audit on a 300-kernel sample under torch 2.11, with 245 rows surviving the same filters, and obtains 68.6% violations; a second native CUDA corpus yields 43 of 213, or 20.2%, after excluding precision-dominated failures (section 3.5, PDF page 9). These are separate denominators and environments. They show robustness of the observed gap, not universal failure rates.
Verus form (inference): make each benchmark input, shape, and expected result an explicit test vector; prove the kernel wrapper against the same contract; and retain per-case verdicts as evidence. A passing proof still depends on the reference specification and trusted GPU implementation.
technique 4: oracle-backed native backward
The paper also implements a native Blackwell tcgen05 backward for the gated-linear-recurrence family. The general recurrence covers five model families; a double-precision oracle supplies the independent reference, and the same twelve-gate battery checks the native kernel (section 4.5, PDF page 11). Five family members train through one backward, and the abstract reports error of 3.3 × 10^-3 against the fp64 oracle plus bit-for-bit determinism (abstract, PDF page 1). This is a case study in positive controls: the verifier is tested on a kernel whose correctness is established independently.
Verus form (inference): specify the recurrence transition and backward equations as mathematical spec fns, prove each scan and triangular-inverse step against the oracle equations, and wrap unsafe tensor-memory operations with contracts for allocation and release. Hardware lifecycle assumptions remain trusted unless separately modeled.
techniques for the catalog
- adversarial contract battery: test values, shapes, gradients, precision, ordering, determinism, exceptional values, device placement, and resource limits
- tolerance-free gates: compare masks or bytes exactly for non-finite propagation, repeatability, and aliasing
- derived numerical bounds: derive reduction tolerances from epsilon, length, and scale rather than a universal threshold
- positive-control validation: require broken-kernel rejection and independently correct-kernel acceptance before auditing a corpus
- differential benchmark audit: join the benchmark verdict with the stronger verifier in a 2x2 table and preserve denominators
- oracle-backed systems verification: establish an independent high-precision oracle and run the same contract battery on native code
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