Organizations: 1Korea Advanced Institute of Science and Technology (KAIST)
Abstract
Gaussian Process (GP) kernels are central to Bayesian optimization (BO), yet designing effective kernels for high-dimensional problems still relies on extensive manual engineering. Existing automated approaches struggle in high dimensions for two bottlenecks: their kernel search space is limited to additions and multiplications of base kernels, and LLM-based approaches require conditioning on raw observations, which becomes infeasible due to context-length limits and the difficulty of extracting meaningful patterns. We introduce \textbf{Kernel Discovery}, a LLM-driven evolutionary framework for high-dimensional BO that searches a broader kernel space beyond predefined composition rules and does not require conditioning on observations. Motivated by the observation that directly prompting an LLM to generate kernel code yields syntactically varied but functionally identical kernels, we adopt a two-stage approach: an LLM first proposes novel mathematical forms, then a second LLM call converts each form into validated, executable code. We also propose a leave-one-out continuous ranked probability score (LOO-CRPS) as a selection criterion that penalizes overfitted kernels. On five high-dimensional BO benchmarks, our method achieves an average rank of \textbf{1.2 out of 17}, outperforming competitive baselines. We further analyze the discovered kernels to identify which kernels lead to improvements in high-dimensional BO.
Generating high-performance GPU kernels remains challenging due to the need for both correctness and hardware-aware optimization. While large language models (LLMs) show promise in code generation, they often fail to produce kernels that are both correct and efficient. We propose Kernel Foundry, a diagnosis-driven evolutionary framework for automatic GPU kernel optimization. Our method combines expert-guided, retrieval-augmented initialization with a multi-island evolutionary search, where candidate kernels are iteratively refined using structured diagnostic feedback. A centralized experience library accumulates reusable optimization knowledge to guide subsequent evolution, while explicit mechanisms prevent cheating behaviors that bypass kernel-level computation. Experiments on KernelBench show that our method consistently improves both correctness and performance over strong baselines, achieving up to 100% correctness on Level~2.
Hyperparameter selection remains a key challenge in Bayesian optimization (BO) and Bayesian active learning (AL), as model misspecification can lead to suboptimal performance, while more accurate fully Bayesian treatments typically rely on computationally expensive MCMC sampling. This paper proposes a unified framework, KENDO (Kernel ENsemble Disagreement-aware Operator), that integrates Ensemble Gaussian Processes (EGP) with disagreement-aware acquisition strategies. The central idea is to replace hyperparameter sampling with a kernel ensemble and adaptive Bayesian weighting, combined with disagreement-aware acquisition strategies. Within this unified framework, we instantiate KENDO-BO for BO and KENDO-AL for Bayesian AL, demonstrating that both arise from a common self-correcting mechanism with task-specific acquisition objectives. We further extend the approach to multi-objective optimization via random scalarization that preserves the single-optimizer conditioning structure. Thorough numerical tests on synthetic and real-world benchmarks across single-objective optimization, multi-objective optimization, and active learning demonstrate that (i) KENDO-BO achieves competitive or superior optimization performance compared to state-of-the-art methods while reducing computational overhead by up to 5× and (ii) KENDO-AL achieves superior predictive calibration over MCMC-based active learning baselines with up to 27× speedup.
Heng Zhang, Haotian Xiang, Konstantinos D. Polyzos +2
GPU kernel optimization challenges LLMs beyond standard coding tasks, as it requires an understanding of hardware architecture, parallel computing optimization strategies, and profiling outputs. However, most existing approaches leveraging LLMs for kernel generation apply standard prompting and feedback loops, considering hardware only through profiling feedback. We introduce KernelFoundry, an evolutionary framework that efficiently explores the space of GPU kernels through (1) MAP-Elites quality diversity search with kernel-specific behavioral dimensions to sustain exploration; (2) meta-prompt evolution that co-evolves prompts with kernels to uncover task-specific optimization strategies, and (3) a template-based parameter optimization approach to tune kernels to inputs and hardware. We evaluate this framework on Kernel-Bench, robust-kbench and custom tasks, generating SYCL kernels as a cross-platform GPU programming paradigm, and CUDA kernels for comparison to prior work. Our approach consistently outperforms the baseline methods and achieves an average speedup of 2.3 on KernelBench for SYCL. Moreover, KernelFoundry is implemented as a distributed framework with remote access to diverse hardware, allowing quick benchmarking and featuring a flexible user input layer to support kernel generation for a wide range of real use cases beyond benchmarking.
Nina Wiedemann, Quentin Leboutet, Michael Paulitsch +2