{"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/algebranets","title":"AlgebraNets","arxiv_id":"2006.07360","date":"2020-06-12","proceeding":null,"authors":["Jordan Hoffmann","Simon Schmitt","Simon Osindero","Karen Simonyan","Erich Elsen"],"abstract":"Neural networks have historically been built layerwise from the set of functions in ${f: \\mathbb{R}^n \\to \\mathbb{R}^m }$, i.e. with activations and weights/parameters represented by real numbers, $\\mathbb{R}$. Our work considers a richer set of objects for activations and weights, and undertakes a comprehensive study of alternative algebras as number representations by studying their performance on two challenging problems: large-scale image classification using the ImageNet dataset and language modeling using the enwiki8 and WikiText-103 datasets. We denote this broader class of models as AlgebraNets. Our findings indicate that the conclusions of prior work, which explored neural networks constructed from $\\mathbb{C}$ (complex numbers) and $\\mathbb{H}$ (quaternions) on smaller datasets, do not always transfer to these challenging settings. However, our results demonstrate that there are alternative algebras which deliver better parameter and computational efficiency compared with $\\mathbb{R}$. We consider $\\mathbb{C}$, $\\mathbb{H}$, $M_{2}(\\mathbb{R})$ (the set of $2\\times2$ real-valued matrices), $M_{2}(\\mathbb{C})$, $M_{3}(\\mathbb{R})$ and $M_{4}(\\mathbb{R})$. Additionally, we note that multiplication in these algebras has higher compute density than real multiplication, a useful property in situations with inherently limited parameter reuse such as auto-regressive inference and sparse neural networks. We therefore investigate how to induce sparsity within AlgebraNets. We hope that our strong results on large-scale, practical benchmarks will spur further exploration of these unconventional architectures which challenge the default choice of using real numbers for neural network weights and activations.","url_abs":"https://arxiv.org/abs/2006.07360v2","url_pdf":"https://arxiv.org/pdf/2006.07360v2.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":"algebranets","repo_url":"https://github.com/andravin/algebranets","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok"}}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"language-modeling","task_name":"Language Modeling"},{"task_slug":"language-modelling","task_name":"Language Modelling"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2006.07360","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}