From the 1 of 4 linked papers with an AI index.
4 papers
Quotient Dynamics, Effective Curvature, and Implicit Bias in Positive Quadratic Networks
Pengcheng Cheng
The paper studies how the quotient structure of positive quadratic networks influences training dynamics, curvature, recovery guarantees, and implicit bias, providing exact gradien…
Quotient Geometry, Effective Curvature, and Implicit Bias in Simple Shallow Neural Networks
Hang-Cheng Dong, Pengcheng Cheng
Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, resca…
Interpretable Operator Learning for Inverse Problems via Adaptive Spectral Filtering: Convergence and Discretization Invariance
Hang-Cheng Dong, Pengcheng Cheng, Shuhuan Li
Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikho…
Gauge-Equivariant Intrinsic Neural Operators for Geometry-Consistent Learning of Elliptic PDE Maps
Pengcheng Cheng
Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. Howeve…