Unraveling attention via convex duality: Analysis and interpretations of vision transformers

A Sahiner, T Ergen, B Ozturkler… - International …, 2022 - proceedings.mlr.press
Vision transformers using self-attention or its proposed alternatives have demonstrated
promising results in many image related tasks. However, the underpinning inductive bias of …

Revealing the structure of deep neural networks via convex duality

T Ergen, M Pilanci - International Conference on Machine …, 2021 - proceedings.mlr.press
We study regularized deep neural networks (DNNs) and introduce a convex analytic
framework to characterize the structure of the hidden layers. We show that a set of optimal …

Global optimality beyond two layers: Training deep relu networks via convex programs

T Ergen, M Pilanci - International Conference on Machine …, 2021 - proceedings.mlr.press
Understanding the fundamental mechanism behind the success of deep neural networks is
one of the key challenges in the modern machine learning literature. Despite numerous …

Convex geometry and duality of over-parameterized neural networks

T Ergen, M Pilanci - Journal of machine learning research, 2021 - jmlr.org
We develop a convex analytic approach to analyze finite width two-layer ReLU networks.
We first prove that an optimal solution to the regularized training problem can be …

Fast convex optimization for two-layer relu networks: Equivalent model classes and cone decompositions

A Mishkin, A Sahiner, M Pilanci - … Conference on Machine …, 2022 - proceedings.mlr.press
We develop fast algorithms and robust software for convex optimization of two-layer neural
networks with ReLU activation functions. Our work leverages a convex re-formulation of the …

Efficient global optimization of two-layer relu networks: Quadratic-time algorithms and adversarial training

Y Bai, T Gautam, S Sojoudi - SIAM Journal on Mathematics of Data Science, 2023 - SIAM
The nonconvexity of the artificial neural network (ANN) training landscape brings
optimization difficulties. While the traditional back-propagation stochastic gradient descent …

Demystifying batch normalization in relu networks: Equivalent convex optimization models and implicit regularization

T Ergen, A Sahiner, B Ozturkler, J Pauly… - arxiv preprint arxiv …, 2021 - arxiv.org
Batch Normalization (BN) is a commonly used technique to accelerate and stabilize training
of deep neural networks. Despite its empirical success, a full theoretical understanding of …