FacultyVenkat ChandrasekaranMathieu Desbrun Thomas Hou Houman Owhadi Peter Schröder Andrew Stuart Joel Tropp Von Karman
Franca Hoffmann 
Lunch Seminars(Will be held at 12 noon in Annenberg 213, unless otherwise specified.)
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 wellknown 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 optimizationbased relaxations of optimization problems with that may be stronger, in some sense, than semidefinite optimizationbased 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 ▦ Other Seminars
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 blackbox after a large amount of theoretical investigation. In this talk, I describe a new interpretable and feedforward (FF) design with the LeNet5 as an example. The FFtrained CNN is a datacentric 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 fullyconnected (FC) layers, we adopt a labelguided linear least squared regression (LSR) method. The classification performances of BP and FFtrained CNNs on the MNIST and the CIFAR10 datasets are compared. The computational complexity of the FF design is significantly lower than the BP design and, therefore, the FFtrained CNN is ideal for mobile/edge computing. We also comment on the relationship between BP and FF designs by examining the crossentropy values at nodes of intermediate layers. Meetings and Workshops 
