Yufei Yu

Kelsey L. DiPietro, Ronald D. Haynes, Weizhang Huang et al.

Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial differential equation and the contact events occur in this system as finite time singularities. Primary research interest is in the dependence of the contact set on model parameters and the geometry of the domain. An adaptive numerical strategy is developed based on a moving mesh partial differential equation to dynamically relocate a fixed number of mesh points to increase density where the solution has fine scale detail, particularly in the vicinity of forming singularities. To complement this computational tool, a singular perturbation analysis is used to develop a geometric theory for predicting the possible contact sets. The validity of these two approaches are demonstrated with a variety of test cases.

Peyman Jalali, Nengfeng Zhou, Yufei Yu

Developing explainability methods for Natural Language Processing (NLP) models is a challenging task, for two main reasons. First, the high dimensionality of the data (large number of tokens) results in low coverage and in turn small contributions for the top tokens, compared to the overall model performance. Second, owing to their textual nature, the input variables, after appropriate transformations, are effectively binary (presence or absence of a token in an observation), making the input-output relationship difficult to understand. Common NLP interpretation techniques do not have flexibility in resolution, because they usually operate at word-level and provide fully local (message level) or fully global (over all messages) summaries. The goal of this paper is to create more flexible model explainability summaries by segments of observation or clusters of words that are semantically related to each other. In addition, we introduce a root cause analysis method for NLP models, by analyzing representative False Positive and False Negative examples from different segments. At the end, we illustrate, using a Yelp review data set with three segments (Restaurant, Hotel, and Beauty), that exploiting group/cluster structures in words and/or messages can aid in the interpretation of decisions made by NLP models and can be utilized to assess the model's sensitivity or bias towards gender, syntax, and word meanings.

Rahul Singh, Karan Jindal, Yufei Yu et al.

This paper proposes a strategy to assess the robustness of different machine learning models that involve natural language processing (NLP). The overall approach relies upon a Search and Semantically Replace strategy that consists of two steps: (1) Search, which identifies important parts in the text; (2) Semantically Replace, which finds replacements for the important parts, and constrains the replaced tokens with semantically similar words. We introduce different types of Search and Semantically Replace methods designed specifically for particular types of machine learning models. We also investigate the effectiveness of this strategy and provide a general framework to assess a variety of machine learning models. Finally, an empirical comparison is provided of robustness performance among three different model types, each with a different text representation.

Yufei Yu, Weizhang Huang

The Ambrosio-Tortorelli functional is a phase-field approximation of the Mumford-Shah functional that has been widely used for image segmentation. The approximation has the advantages of being easy to implement, maintaining the segmentation ability, and $Γ$-converging to the Mumford-Shah functional. However, it has been observed in actual computation that the segmentation ability of the Ambrosio-Tortorelli functional varies significantly with different values of the parameter and it even fails to $Γ$-converge to the original functional for some cases. In this paper we present an asymptotic analysis on the gradient flow equation of the Ambrosio-Tortorelli functional and show that the functional can have different segmentation behavior for small but finite values of the regularization parameter and eventually loses its segmentation ability as the parameter goes to zero when the input image is treated as a continuous function. This is consistent with the existing observation as well as the numerical examples presented in this work. A selection strategy for the regularization parameter and a scaling procedure for the solution are devised based on the analysis. Numerical results show that they lead to good segmentation of the Ambrosio-Tortorelli functional for real images.