The UCF Mathematics and Applications Seminar, which takes place every Friday from 10:30am to 11:30am in MSB 318, provides a venue for researchers to present their current work, foster new collaborations, and showcase both foundational mathematics and its applications to graduate and undergraduate students.

Dr. Gerrit Welper will be speaking at this seminar about **approximation and gradient descent results for neural networks**.

**Abstract:** Similar to polynomials and truncated Fourier series, neural networks can be used to approximate arbitrary functions f(x). From this perspective, the talk provides results for the following two questions:

- For a given network size, can we bound the approximation error?
- Can we realize this approximation error by gradient descent training, although the underlying optimization problem is non-convex?

I will also address some preliminary results on generalization errors and nonlinear approximation.

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