May 7, 2019
James Saunderson
▦ Certifying polynomial nonnegativity via hyperbolic optimization ▦
     Certifying nonnegativity of multivariate polynomials is fundamental to solving optimization problems modeled with polynomials. One well-known way to certify nonnegativity is to express a polynomial as a sum of squares. Furthermore, the search for such a certificate can be carried out via semidefinite optimization. An interesting generalization of semidefinite optimization, that retains many of its good algorithmic properties, is hyperbolic optimization. Are there natural certificates of nonnegativity that we can search for via hyperbolic optimization, and that are not obviously captured by sums of squares? If so, these could have the potential to generate hyperbolic optimization-based relaxations of optimization problems with that may be stronger, in some sense, than semidefinite optimization-based relaxations.
In this talk, I will describe one candidate for such "hyperbolic certificates of nonnegativity", and discuss what is known about their relationship with sums of squares.

September 25, 2019
Jose Antonio Carrillo
▦ Topic to be Announced ▦
     

May 16, 2019
C.-C. Jay Kuo
▦ Interpretable Convolutional Neural Networks (CNNs) via Feedforward Design ▦
     Given a convolutional neural network (CNN) architecture, its network parameters are determined by backpropagation (BP) nowadays. The underlying mechanism remains to be a black-box after a large amount of theoretical investigation. In this talk, I describe a new interpretable and feedforward (FF) design with the LeNet-5 as an example. The FF-trained CNN is a data-centric approach that derives network parameters based on training data statistics layer by layer in one pass. To build the convolutional layers, we develop a new signal transform, called the Saab (Subspace approximation with adjusted bias) transform. The bias in filter weights is chosen to annihilate nonlinearity of the activation function. To build the fully-connected (FC) layers, we adopt a label-guided linear least squared regression (LSR) method. The classification performances of BP- and FF-trained CNNs on the MNIST and the CIFAR-10 datasets are compared. The computational complexity of the FF design is significantly lower than the BP design and, therefore, the FF-trained CNN is ideal for mobile/edge computing. We also comment on the relationship between BP and FF designs by examining the cross-entropy values at nodes of intermediate layers.

Southern California Applied Mathematics Symposium (SOCAMS 2019)

• Meeting Poster