提出四类稀疏性区分，揭示稀疏FNO的效率陷阱
Selection, Representation, and Execution in Sparse Fourier Neural Operators
- 分离表示、参数、理论复杂度与实测延迟四类稀疏性
- 83%参数压缩后仍比密集基线慢，因执行路径未真正变快
- 强调真稀疏需兼顾精度与实际加速，适合模型部署优化研究者
稀疏表示通常期望使模型更小且推理成本更低。但对于傅里叶神经算子（FNOs），这些目标并不等价或总能对齐：移除学习算子的部分内容可能不会改变底层变换和密集计算，而改变模型评估网格则可能引入额外开销。因此，我们区分了表示稀疏性、存储参数稀疏性、理论操作次数稀疏性和实测运行时稀疏性，并对多种实现稀疏FNO的路径进行了独立测试。粗化执行网格可降低理论成本但不减少实测延迟，添加修正项虽恢复精度却使模型变慢。即使参数减少83%，在常规执行下仍慢于密集基线。这些结果促使我们提出更严格的有效稀疏定义：部署的算子必须保持解的准确性，并将缩减的支持域映射到真正更低成本的执行路径。
原文摘要 · Abstract (English)
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.
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