Computer Science > Machine Learning
arXiv:2310.05918 (cs)
[Submitted on 9 Oct 2023]
Title:Grokking as Compression: A Nonlinear Complexity Perspective
View a PDF of the paper titled Grokking as Compression: A Nonlinear Complexity Perspective, by Ziming Liu and 2 other authors
View PDFAbstract:We attribute grokking, the phenomenon where generalization is much delayed after memorization, to compression. To do so, we define linear mapping number (LMN) to measure network complexity, which is a generalized version of linear region number for ReLU networks. LMN can nicely characterize neural network compression before generalization. Although the $L_2$ norm has been a popular choice for characterizing model complexity, we argue in favor of LMN for a number of reasons: (1) LMN can be naturally interpreted as information/computation, while $L_2$ cannot. (2) In the compression phase, LMN has linear relations with test losses, while $L_2$ is correlated with test losses in a complicated nonlinear way. (3) LMN also reveals an intriguing phenomenon of the XOR network switching between two generalization solutions, while $L_2$ does not. Besides explaining grokking, we argue that LMN is a promising candidate as the neural network version of the Kolmogorov complexity since it explicitly considers local or conditioned linear computations aligned with the nature of modern artificial neural networks.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2310.05918 [cs.LG] |
| (orarXiv:2310.05918v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2310.05918 arXiv-issued DOI via DataCite |
Full-text links:
Access Paper:
- View PDF
- TeX Source
- Other Formats
View a PDF of the paper titled Grokking as Compression: A Nonlinear Complexity Perspective, by Ziming Liu and 2 other authors
Current browse context:
cs.LG
References & Citations
Bookmark
Bibliographic and Citation Tools
Bibliographic Explorer(What is the Explorer?)
Connected Papers(What is Connected Papers?)
Litmaps(What is Litmaps?)
scite Smart Citations(What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv(What is alphaXiv?)
CatalyzeX Code Finder for Papers(What is CatalyzeX?)
DagsHub(What is DagsHub?)
Gotit.pub(What is GotitPub?)
Hugging Face(What is Huggingface?)
Papers with Code(What is Papers with Code?)
ScienceCast(What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower(What are Influence Flowers?)
CORE Recommender(What is CORE?)
IArxiv Recommender(What is IArxiv?)
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.