{"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/on-the-connection-of-benford-s-law-and-neural","title":"Rethinking Neural Networks With Benford's Law","arxiv_id":"2102.03313","date":"2021-02-05","proceeding":null,"authors":["Surya Kant Sahu","Abhinav Java","Arshad Shaikh","Yannic Kilcher"],"abstract":"Benford's Law (BL) or the Significant Digit Law defines the probability distribution of the first digit of numerical values in a data sample. This Law is observed in many naturally occurring datasets. It can be seen as a measure of naturalness of a given distribution and finds its application in areas like anomaly and fraud detection. In this work, we address the following question: Is the distribution of the Neural Network parameters related to the network's generalization capability? To that end, we first define a metric, MLH (Model Enthalpy), that measures the closeness of a set of numbers to Benford's Law and we show empirically that it is a strong predictor of Validation Accuracy. Second, we use MLH as an alternative to Validation Accuracy for Early Stopping, removing the need for a Validation set. We provide experimental evidence that even if the optimal size of the validation set is known before-hand, the peak test accuracy attained is lower than not using a validation set at all. Finally, we investigate the connection of BL to Free Energy Principle and First Law of Thermodynamics, showing that MLH is a component of the internal energy of the learning system and optimization as an analogy to minimizing the total energy to attain equilibrium.","url_abs":"https://arxiv.org/abs/2102.03313v4","url_pdf":"https://arxiv.org/pdf/2102.03313v4.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":"on-the-connection-of-benford-s-law-and-neural","repo_url":"https://github.com/The-Learning-Machines/RethinkingNNsWithBL","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"average-pooling","method_name":"Average Pooling"},{"method_slug":"batch-normalization","method_name":"Batch Normalization"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"early-stopping","method_name":"Early Stopping"},{"method_slug":"global-average-pooling","method_name":"Global Average Pooling"},{"method_slug":"grouped-convolution","method_name":"Grouped Convolution"},{"method_slug":"kaiming-initialization","method_name":"Kaiming Initialization"},{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"resnext","method_name":"ResNeXt"},{"method_slug":"resnext-block","method_name":"ResNeXt Block"},{"method_slug":"residual-connection","method_name":"Residual Connection"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2102.03313","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}