"Parameter Identification for Tear Film Thinning and Breakup" and "Tetrahedral symmetry in the final and penultimate layers of neural network classifiers"
Dec 4, 2020, 10:00 - 11:00 AM
Thanks for participating in our CMAI-MathWorks Workshop last week. It was a very successful event. We have learnt from our colleagues at MathWorks that we had around 250 registrations and 165 participants during the session. You can find the material from the workshop on the CMAI website.
The next and final CMAI Colloquium for this semester will be on
Date: Friday, December 4, 2020 at 10am (Eastern Time)
In this special colloquium, we plan to have two talks (1/2 hour each) from early career researchers.
Zoom Link: Join Zoom Meeting
First Speaker: Rayanne Luke
University of Delaware
Title: Parameter Identification for Tear Film Thinning and Breakup
Abstract: Millions of Americans experience dry eye syndrome, a condition that decreases quality of vision and causes ocular discomfort. A phenomenon associated with dry eye syndrome is tear film breakup (TBU), or the formation of dry spots on the eye. The dynamics of the tear film can be studied using fluorescence imaging. Many parameters affecting tear film thickness and fluorescent intensity distributions within TBU are difficult to measure directly in vivo. We estimate breakup parameters by fitting computed results from thin film fluid PDE models to experimental fluorescent intensity data gathered from normal subjects’ tear films in vivo. Both evaporation and the Marangoni effect can cause breakup. The PDE models include these mechanisms in combination and separately. The parameters are determined by a nonlinear least squares minimization between computed and experimental fluorescent intensity, and they indicate the relative importance of each mechanism. Optimal values for computed breakup variables that cannot be measured in vivo fall near or within accepted experimental ranges for the general corneal region. Our results are a step towards characterizing the mechanisms that cause a wide range of breakup instances and help medical professionals to better understand tear film function and dry eye syndrome.
Second speaker: Dr. Stephan Wojtowytsch
Title: Tetrahedral symmetry in the final and penultimate layers of neural network classifiers
Abstract: A recent empirical study found that the penultimate layer of a well-trained neural network classifier maps training data samples to the vertices of a low-dimensional tetrahedron in a high-dimensional ambient space. We explain this observation from a theoretical perspective in a toy model for deep networks and give complementary examples to show that even the output of a shallow neural network classifier is generally non-uniform over a data class. As deep networks are the composition of a (slightly less) deep network and a shallow network, these example illustrate how a network would fail to output a uniform classifier over the training samples if the data is mapped to sets with inconvenient geometry in an intermediate layer.