Tolga Recep Uçar

Mathematics @ Koc University
tucar24@ku.edu.tr

Research

Transformer-based Variational Autoencoders

TUBITAK granted research (2247-C.) Supervised by Prof. Dr. Mehmet Fatih Amasyalı. We propose an alternative VAE architecture inspired by the inner workings of the ubiquitous Transformer. We also diagnose the condition of posterior collapse on the latent space and aggressively train the encoder to create an efficient model overcoming this. Finally the architecture is trained on a large Turkish corpora and tested on various tasks such as sentiment analysis and text classification. Publicly available here.

Orthogonal embedding-based neural network for solving nonlinear differential equations

(Accepted.) We propose a numerical algorithm based on neural networks for solving linear and nonlinear ordinary differential equations. We combine the representational power of orthogonal space of Jacobi polynomials and multilayer perceptrons. Our method presents low-cost and highly accurate approximations with basic training. Some of the tinkering before the actual architecture was designed can be found here.

Proposals

Solving Abel type differential equations using multilayer perceptron
at International Conference on Mathematical Analysis and Applications in Science and Engineering - ICMASC'24
(Portugal, June 20th - 22nd 2024)
Some pictures here

(Accepted for on-site oral presentation and print.) Abstract: We propose machine learning as a new method for solving Abel type differential equations which is an important class of differential equations modeling magnetostatic problems and fluid dynamics. Our method does not rely on extensive formal numeric computing. It is a data-driven algorithm, hence a significant approach as data is more available each day. Our approximation function is a multilayer perceptron and we adjust parameters by backpropagation algorithm. We compare our results with some well-known approximate results.

Titles

Graduate Research and Teaching Assistant: Research on numerical linear algebra and eigenvalue solvers. Assisting and grading Math 102 - Calculus course for undergraduates.

Data Engineer: Cleaning data and structuring it for analysis and modeling at Turkish Airlines. Developing supervised and unsupervised learning solutions for component planning problems.

(and I was a Freelance Python Tutor before this.)

Film theory

Camera as Ideology in 'The Zone of Interest (2023, Glazer)'
Disfunctional Imagery of 'Kinds of Kindness (2024, Lanthimos)'
The Embalmed Sorrow in 'Anora (2024, Baker)'
Quotes from 'Sculpting in Time' by Andrei Tarkovsky

Modernism

Beyond the Psychology of 'About Dry Grasses (2023, Ceylan)'