https://arxiv.org/abs/2505.13124 close this message arXiv smileybones arXiv Is Hiring a DevOps Engineer Work on one of the world's most important websites and make an impact on open science. View Jobs Skip to main content Cornell University arXiv Is Hiring a DevOps Engineer View Jobs We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate arxiv logo > cs > arXiv:2505.13124 [ ] Help | Advanced Search [All fields ] Search arXiv logo Cornell University Logo [ ] GO quick links * Login * Help Pages * About Computer Science > Machine Learning arXiv:2505.13124 (cs) [Submitted on 19 May 2025] Title:$m$PC: Scaling Predictive Coding to 100+ Layer Networks Authors:Francesco Innocenti, El Mehdi Achour, Christopher L. Buckley View a PDF of the paper titled $\mu$PC: Scaling Predictive Coding to 100+ Layer Networks, by Francesco Innocenti and 2 other authors View PDF HTML (experimental) Abstract:The biological implausibility of backpropagation (BP) has motivated many alternative, brain-inspired algorithms that attempt to rely only on local information, such as predictive coding (PC) and equilibrium propagation. However, these algorithms have notoriously struggled to train very deep networks, preventing them from competing with BP in large-scale settings. Indeed, scaling PC networks (PCNs) has recently been posed as a challenge for the community (Pinchetti et al., 2024). Here, we show that 100+ layer PCNs can be trained reliably using a Depth-$\mu$P parameterisation (Yang et al., 2023; Bordelon et al., 2023) which we call "$\mu$PC". Through an extensive analysis of the scaling behaviour of PCNs, we reveal several pathologies that make standard PCNs difficult to train at large depths. We then show that, despite addressing only some of these instabilities, $\mu$PC allows stable training of very deep (up to 128-layer) residual networks on simple classification tasks with competitive performance and little tuning compared to current benchmarks. Moreover, $\mu$PC enables zero-shot transfer of both weight and activity learning rates across widths and depths. Our results have implications for other local algorithms and could be extended to convolutional and transformer architectures. Code for $\mu$PC is made available as part of a JAX library for PCNs at this https URL (Innocenti et al., 2024). Comments: 34 pages, 41 figures Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Neural and Evolutionary Computing (cs.NE) ACM classes: I.2.6 Cite as: arXiv:2505.13124 [cs.LG] (or arXiv:2505.13124v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2505.13124 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Francesco Innocenti [view email] [v1] Mon, 19 May 2025 13:54:29 UTC (24,285 KB) Full-text links: Access Paper: View a PDF of the paper titled $\mu$PC: Scaling Predictive Coding to 100+ Layer Networks, by Francesco Innocenti and 2 other authors * View PDF * HTML (experimental) * TeX Source * Other Formats license icon view license Current browse context: cs.LG < prev | next > new | recent | 2025-05 Change to browse by: cs cs.AI cs.NE References & Citations * NASA ADS * Google Scholar * Semantic Scholar a export BibTeX citation Loading... BibTeX formatted citation x [loading... ] Data provided by: Bookmark BibSonomy logo Reddit logo (*) Bibliographic Tools Bibliographic and Citation Tools [ ] Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) [ ] Connected Papers Toggle Connected Papers (What is Connected Papers?) [ ] Litmaps Toggle Litmaps (What is Litmaps?) [ ] scite.ai Toggle scite Smart Citations (What are Smart Citations?) ( ) Code, Data, Media Code, Data and Media Associated with this Article [ ] alphaXiv Toggle alphaXiv (What is alphaXiv?) [ ] Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) [ ] DagsHub Toggle DagsHub (What is DagsHub?) [ ] GotitPub Toggle Gotit.pub (What is GotitPub?) [ ] Huggingface Toggle Hugging Face (What is Huggingface?) [ ] Links to Code Toggle Papers with Code (What is Papers with Code?) [ ] ScienceCast Toggle ScienceCast (What is ScienceCast?) ( ) Demos Demos [ ] Replicate Toggle Replicate (What is Replicate?) [ ] Spaces Toggle Hugging Face Spaces (What is Spaces?) [ ] Spaces Toggle TXYZ.AI (What is TXYZ.AI?) ( ) Related Papers Recommenders and Search Tools [ ] Link to Influence Flower Influence Flower (What are Influence Flowers?) [ ] Core recommender toggle CORE Recommender (What is CORE?) [ ] IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) * Author * Venue * Institution * Topic ( ) About arXivLabs 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. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?) * About * Help * Click here to contact arXiv Contact * Click here to subscribe Subscribe * Copyright * Privacy Policy * Web Accessibility Assistance * arXiv Operational Status Get status notifications via email or slack