{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/local-signal-adaptivity-provable-feature","title":"Local Signal Adaptivity: Provable Feature Learning in Neural Networks Beyond Kernels","arxiv_id":null,"date":"2021-12-01","proceeding":"NeurIPS 2021 12","authors":["Stefani Karp","Ezra Winston","Yuanzhi Li","Aarti Singh"],"abstract":"Neural networks have been shown to outperform kernel methods in practice (including neural tangent kernels). Most theoretical explanations of this performance gap focus on learning a complex hypothesis class; in some cases, it is unclear whether this hypothesis class captures realistic data. In this work, we propose a related, but alternative, explanation for this performance gap in the image classification setting, based on finding a sparse signal in the presence of noise. Specifically, we prove that, for a simple data distribution with sparse signal amidst high-variance noise, a simple convolutional neural network trained using stochastic gradient descent learns to threshold out the noise and find the signal. On the other hand, the corresponding neural tangent kernel, with a fixed set of predetermined features, is unable to adapt to the signal in this manner. We supplement our theoretical results by demonstrating this phenomenon empirically: in CIFAR-10 and MNIST images with various backgrounds, as the background noise increases in intensity, a CNN's performance stays relatively robust, whereas its corresponding neural tangent kernel sees a notable drop in performance. We therefore propose the \"local signal adaptivity\" (LSA) phenomenon as one explanation for the superiority of neural networks over kernel methods.","url_abs":"http://proceedings.neurips.cc/paper/2021/hash/d064bf1ad039ff366564f352226e7640-Abstract.html","url_pdf":"http://proceedings.neurips.cc/paper/2021/file/d064bf1ad039ff366564f352226e7640-Paper.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"local-signal-adaptivity-provable-feature","repo_url":"https://github.com/skarp/local-signal-adaptivity","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":null}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}