- Title Information
- Title
- The Deep Linear Network – Dynamics, Riemannian Geometry and Overparametrization
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Veraszto, Zsolt
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Menon, Govind
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Cohen, Nadav
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Darbon, Jerome
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2023
- Physical Description
- Extent
- ix, 76 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2023
- Genre (aat)
- theses
- Abstract
- The deep linear network (DLN) is a model for implicit regularization in gradient based optimization of overparametrized learning architectures. Training the DLN corresponds to a Riemannian gradient flow, where the Riemannian metric is defined by the architecture of the network and the loss function is defined by the learning task. We extend this geometric framework, obtaining explicit expressions for the volume form, including the case when the network has infinite depth. We investigate the link between the Riemannian geometry and the training asymptotics for matrix completion with rigorous analysis and numerics. We develop a stochastic model for training and report our numerical findings. We propose that under small initialization, implicit regularization is a result of bias towards high state space volume.
- Subject
- Topic
- generalizability
- Subject
- Topic
- gradient flows
- Subject
- Topic
- implicit regularization
- Subject
- Topic
- rieamannian geometry
- Subject
- Topic
- matrix completion
- Subject
- Topic
- deep linear network
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20230602