Singular Learning and Occam's Razor in Deep Monomial Networks
A new paper applies singular learning theory to deep monomial networks, showing that critical points correspond to subnetworks, providing a mathematical explanation for neural networks' implicit bias towards simpler functions.
[2606.28464] Singular Learning and Occam's Razor in Deep Monomial Networks
[Submitted on 26 Jun 2026]
Title:Singular Learning and Occam's Razor in Deep Monomial Networks
View a PDF of the paper titled Singular Learning and Occam's Razor in Deep Monomial Networks, by Kathl\'en Kohn and 4 other authors
View PDF HTML (experimental)
Abstract:In the optimization of neural networks, gradient dynamics are influenced by critical points that arise from the model's architecture. These critical points occur where the Jacobian of the model's parametrization is rank-deficient, and are the most pronounced singularities studied in Singular Learning Theory. We investigate such points in deep fully-connected networks with monomial activations via tools from polynomial algebra such as Mason's Theorem. We show that, for sufficiently large activation degree, criticality occurs precisely at subnetworks, i.e., at parameter configurations where some neurons are inactive or redundant. This offers a mathematical perspective on the implicit bias in deep neural networks, explaining the tendency of these models to converge toward simpler functions.
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2606.28464 [cs.LG]
(or arXiv:2606.28464v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.28464
arXiv-issued DOI via DataCite
Submission history
From: Giovanni Luca Marchetti [view email] [v1] Fri, 26 Jun 2026 13:40:14 UTC (34 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Singular Learning and Occam's Razor in Deep Monomial Networks, by Kathl\'en Kohn and 4 other authors
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.LG
new | recent | 2026-06
Change to browse by:
cs
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
Loading...
Data provided by:
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?)
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?)