Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.22220

Measuring the Checker: Mutation Analysis for GPU-Kernel Benchmark Oracles

Mingzhe Du·Anh Tuan Luu·Dong Huang·See-Kiong Ng
View original source ↗Read source document ↗Export metadata ↓

Abstract

Benchmarks for LLM-generated GPU kernels decide correctness with a few random inputs and a loose floating-point tolerance, and their verdicts now feed leaderboards and reinforcement-learning rewards. Recent work agrees these checkers are weak and patches them by hand---extra input distributions, fuzzing recipes, tighter tolerances---with no way to \emph{measure} whether any patch suffices. We introduce mutation analysis as an adequacy metric for kernel-benchmark oracles: deterministic rules inject 10{,}303 compilable faults into verified CUDA implementations of 188 KernelBench problems, 7{,}384 of them with an independent kill witness; any test protocol is scored by the fraction it detects. The official check misses \textbf{one in six} witnessed faults (16.9%), deterministically, and the misses are skewed by family: 8.7% of arithmetic faults escape, but 78.6% of precision faults do. The metric explains why (a tolerance blind band growing with reduction size; a measured ceiling on input aggressiveness set by legitimate floating-point variance), audits the strongest existing patch (KernelBench-Verified's gain splits into $+4.0$ points from hidden inputs and $+4.5$ from tighter tolerance, a split its authors could not compute), and exposes a published fuzzing recipe that rejects \emph{correct} kernels 107 times. Optimizing suites over the kill matrix reaches 98.0% detection with two inputs per problem (94.8% held-out), and the measurement's fault taxonomy teaches a test generator more than the raw faults themselves. Across 48 whole architectures, the blindness grows with scale, concentrating in deep homogeneous pipelines, and two problems prove unrefereeable: their official references violate the benchmark's own tolerance against fp64. We release everything as \href{https://huggingface.co/datasets/Elfsong/KernelBench-M}{KernelBench-M}.

Explore related subjects

cs.LGcs.PL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mingzhe Du, Anh Tuan Luu, Dong Huang, See-Kiong Ng. 2026-09-02. Measuring the Checker: Mutation Analysis for GPU-Kernel Benchmark Oracles. https://arxiv.org/abs/2609.22220

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG↗
arXiv2026

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG↗
arXiv2026

ELEMENT: Episodic and Lifelong Exploration via Maximum Entropy

Reinforcement learning agents depend on reward signals whose density is rarely under the designer's control, and when such signals are absent, an agent must generate its own drive to explore. State entropy maximization offers a principled objective for this, but existing methods break down at scale in two ways: the intrinsic reward vanishes once a state has been visited, discouraging revisits to the very gateways that lead onward, and estimating entropy over millions of accumulated observations becomes computationally prohibitive. We address both with Episodic and Lifelong Exploration via Maximum Entropy (ELEMENT), a multiscale intrinsically motivated framework for reward-free exploration that transfers to downstream tasks. ELEMENT couples lifelong entropy maximization with a complementary episodic term acting on a faster timescale. For the episodic term, we derive average episodic state entropy, an intrinsic reward that is the exact minimizer of a tractable upper bound on the reward-decomposition objective; for the lifelong term, we propose a $k$NN graph-based estimator that keeps entropy tractable without forgetting. ELEMENT consistently outperforms state-of-the-art intrinsic reward baselines on state coverage and unsupervised pre-training. Videos, code, and supplementary material: https://sites.google.com/view/element-rl.

cs.LG↗