稀疏傅里叶神经算子中的选择、表示与执行
Selection, Representation, and Execution in Sparse Fourier Neural Operators
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中文总结 AI 辅助
本文通过实证研究分析稀疏FNO中表示、参数、操作数、运行时的稀疏性差异，发现粗化执行网格降理论成本但不减延迟、减参数83%仍慢于基线，提出有用稀疏性需保精度且映射到廉价执行路径的定义。
中文摘要 AI 辅助
稀疏表示通常被期望能减小模型规模并降低推理成本，但对于傅里叶神经算子（Fourier Neural Operators, FNOs）而言，这些目标并不等价或始终一致：移除学习到的算子部分可能会保留底层变换和密集计算不变，而改变模型评估所用的网格则可能引入自身的开销。因此，我们区分了表示、存储参数、理论操作数和实测运行时中的稀疏性，并对稀疏FNO的若干实现路径开展实证研究，分别测试它们之间的每一步转变。粗化执行网格会降低理论成本，但不会减少实测延迟；添加校正项可恢复精度，代价是使模型变慢。即使参数减少83%，在常规执行下仍比密集基线更慢。这些结果促使人们对有用的稀疏性给出更严格的定义：部署的算子必须保持解的精度，并将其缩减后的支撑集映射到真正更廉价的执行路径上。
英文摘要
Sparse representations are often expected to make models smaller and also reduce inference cost. For Fourier Neural Operators (FNOs), these objectives are not equivalent or do not always align: removing parts of the learned operator can leave the underlying transforms and dense computations unchanged, while changing the grid on which the model is evaluated can introduce overhead of its own. We therefore distinguish sparsity in the representation, in the stored parameters, in the theoretical operation count, and in measured runtime, and present an empirical study of several routes toward sparse FNOs that tests each transition between them separately. Coarsening the execution grid reduces the theoretical cost without reducing measured latency, and adding a correction term recovers accuracy at the cost of making the model slower. Even an 83\% parameter reduction remains slower than the dense baseline under ordinary execution. These results motivate a stricter definition of useful sparsity: the deployed operator must preserve solution accuracy and map its reduced support to a genuinely cheaper execution path.
发表机构
- Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究所）
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