Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Native Gardens In Southern California, Center For Urban Resilience
Native Gardens In Southern California, Center For Urban Resilience
Module 10: Garden Ecology
No abstract provided.
Stochastic Maximum Principle For Partial Information Optimal Investment And Dividend Problem Of An Insurer, Yanping Ma
Stochastic Maximum Principle For Partial Information Optimal Investment And Dividend Problem Of An Insurer, Yanping Ma
Mathematics Faculty Works
We study an optimal investment and dividend problem of an insurer, where the aggregate insurance claims process is modeled by a pure jump Lévy process. We allow the management of the dividend payment policy and the investment of surplus in a continuous-time financial market, which is composed of a risk free asset and a risky asset. The information available to the insurer is partial information. We generalize this problem as a partial information regular-singular stochastic control problem, where the control variable consists of regular control and singular control. Then maximum principles are established to give sufficient and necessary optimality conditions …
The Multilinear Structure Of Relu Networks, Thomas Laurent
The Multilinear Structure Of Relu Networks, Thomas Laurent
Mathematics Faculty Works
We study the loss surface of neural networks equipped with a hinge loss criterion and ReLU or leaky ReLU nonlinearities. Any such network defines a piecewise multilinear form in parameter space. By appealing to harmonic analysis we show that all local minima of such network are non-differentiable, except for those minima that occur in a region of parameter space where the loss surface is perfectly flat. Non-differentiable minima are therefore not technicalities or pathologies; they are heart of the problem when investigating the loss of ReLU networks. As a consequence, we must employ techniques from nonsmooth analysis to study these …
Deep Linear Networks With Arbitrary Loss: All Local Minima Are Global, Thomas Laurent
Deep Linear Networks With Arbitrary Loss: All Local Minima Are Global, Thomas Laurent
Mathematics Faculty Works
We consider deep linear networks with arbitrary convex differentiable loss. We provide a short and elementary proof of the fact that all local minima are global minima if the hidden layers are either 1) at least as wide as the input layer, or 2) at least as wide as the output layer. This result is the strongest possible in the following sense: If the loss is convex and Lipschitz but not differentiable then deep linear networks can have sub-optimal local minima.
Facilitators And Outcomes Of Stem-Education Groups Working Toward Disciplinary Integration, Anna E. Bargagliotti
Facilitators And Outcomes Of Stem-Education Groups Working Toward Disciplinary Integration, Anna E. Bargagliotti
Mathematics Faculty Works
There is a growing societal recognition of the need for transdisciplinary scholarly collaboration which can enhance undergraduate physics, science, and engineering education. A regional conference/network with 100 university education researchers in physics and other STEM fields was formed to address three themes (problemsolving, computational thinking, and equity) with multiple goals including to strive for transdisciplinary publications. As part of an ongoing participant observation study, phone interviews were conducted 3-4 months later. One year later, publications that were completed as a result of the conference were analyzed for their disciplinary integration. The papers showed evidence of interdispliciplanry collaboration but transdiciplinary collaboration …