Research map / Learning theory and algorithms / Prediction and decision losses
How regularization affects the critical points in linear networks
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add any positive regularization to the linear-network loss | Continuous-time linear network · General linear transformation learning | critical-point structure | Mixed |
| Use no regularization (λ=0) instead of positive regularization | Continuous-time linear network · Non-singular Σ | critical-point optimality | Helped |
| Add positive regularization | Continuous-time linear network with non-normal R and Σ=I · Non-normal R example | critical-point constancy | Hurt |
| Use a non-constant critical point instead of the constant log(R) solution | Continuous-time linear network · Non-normal R example, T=1 | regularization cost: \frac{\pi^2}{4} < 3.76 | Helped |
| Add positive regularization | Scalar linear network · Scalar case, R > 0 | number of minimizers | Helped |
| Add positive regularization | Linear network for normal R and Σ=I · Normal matrix case | critical-point existence near λ=0 | No clear effect |
| Add positive regularization | Rotation-matrix example · Normal R example | critical-point count | Hurt |
| Continue a non-principal logarithm branch with positive regularization | Rotation-matrix example · Normal R example, n≠0 | critical-point type | Mixed |
| Increase λ beyond the branch turning point | Non-principal branches in the rotation-matrix example · Normal R example | critical-point type | Hurt |
| Use the principal logarithm branch rather than other computed branches | Regularized linear network · Normal R example | objective cost | Helped |
Closest papers by meaning
- Cauchy-Schwarz Regularizers (ICLR 2025 · similarity 0.86)
- Elliptic Loss Regularization (ICLR 2025 · similarity 0.84)
- SGD vs GD: Rank Deficiency in Linear Networks (NeurIPS 2024 · similarity 0.83)
- Exploring The Loss Landscape Of Regularized Neural Networks Via Convex Duality (ICLR 2025 · similarity 0.83)
- Deep linear networks for regression are implicitly regularized towards flat minima (NeurIPS 2024 · similarity 0.83)
- Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer (ICML 2025 · similarity 0.83)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.