  In this study, we examine the efficacy of post-hoc local attribution methods
in identifying features with predictive power from irrelevant ones in domains
characterized by a low signal-to-noise ratio (SNR), a common scenario in
real-world machine learning applications. We developed synthetic datasets
encompassing symbolic functional, image, and audio data, incorporating a
benchmark on the {\it (Model \(\times\) Attribution\(\times\) Noise Condition)}
triplet. By rigorously testing various classic models trained from scratch, we
gained valuable insights into the performance of these attribution methods in
multiple conditions. Based on these findings, we introduce a novel extension to
the notable recursive feature elimination (RFE) algorithm, enhancing its
applicability for neural networks. Our experiments highlight its strengths in
prediction and feature selection, alongside limitations in scalability. Further
details and additional minor findings are included in the appendix, with
extensive discussions. The codes and resources are available at
\href{https://github.com/geshijoker/ChaosMining/}{URL}.
