Deep Learning Is Not So Mysterious or Different

A paper by Andrew Wilson and colleagues, submitted to arXiv on March 3, 2025, argues that deep learning's generalization behaviors, such as benign overfitting and double descent, are not unique to neural networks and can be explained by long-standing frameworks like PAC-Bayes and countable hypothesis bounds. The authors propose 'soft inductive biases' as a unifying principle, suggesting that flexible hypothesis spaces with a preference for simpler solutions can encode these behaviors across model classes, though they acknowledge deep learning's distinct strengths in representation learning and mode connectivity.

Computer Science Machine Learning Submitted on 3 Mar 2025 v1 https://arxiv.org/abs/2503.02113v1 , last revised 10 Jul 2025 this version, v2 Title:Deep Learning is Not So Mysterious or Different View PDF /pdf/2503.02113 HTML experimental https://arxiv.org/html/2503.02113v2 Abstract:Deep neural networks are often seen as different from other model classes by defying conventional notions of generalization. Popular examples of anomalous generalization behaviour include benign overfitting, double descent, and the success of overparametrization. We argue that these phenomena are not distinct to neural networks, or particularly mysterious. Moreover, this generalization behaviour can be intuitively understood, and rigorously characterized, using long-standing generalization frameworks such as PAC-Bayes and countable hypothesis bounds. We present soft inductive biases as a key unifying principle in explaining these phenomena: rather than restricting the hypothesis space to avoid overfitting, embrace a flexible hypothesis space, with a soft preference for simpler solutions that are consistent with the data. This principle can be encoded in many model classes, and thus deep learning is not as mysterious or different from other model classes as it might seem. However, we also highlight how deep learning is relatively distinct in other ways, such as its ability for representation learning, phenomena such as mode connectivity, and its relative universality. Submission history From: Andrew Wilson view email /show-email/57319f6c/2503.02113 Mon, 3 Mar 2025 22:56:04 UTC 1,206 KB v1 /abs/2503.02113v1 v2 Thu, 10 Jul 2025 13:56:52 UTC 1,231 KB Current browse context: cs.LG References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender IArxiv Recommender What is IArxiv? https://iarxiv.org/about arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .