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Unraveling attention via convex duality: Analysis and interpretations of vision transformers
Vision transformers using self-attention or its proposed alternatives have demonstrated
promising results in many image related tasks. However, the underpinning inductive bias of …
promising results in many image related tasks. However, the underpinning inductive bias of …
Revealing the structure of deep neural networks via convex duality
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 …
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
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 …
one of the key challenges in the modern machine learning literature. Despite numerous …
Convex geometry and duality of over-parameterized neural networks
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 …
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
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 …
networks with ReLU activation functions. Our work leverages a convex re-formulation of the …
Implicit convex regularizers of cnn architectures: Convex optimization of two-and three-layer networks in polynomial time
Efficient global optimization of two-layer relu networks: Quadratic-time algorithms and adversarial training
The nonconvexity of the artificial neural network (ANN) training landscape brings
optimization difficulties. While the traditional back-propagation stochastic gradient descent …
optimization difficulties. While the traditional back-propagation stochastic gradient descent …
Demystifying batch normalization in relu networks: Equivalent convex optimization models and implicit regularization
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 …
of deep neural networks. Despite its empirical success, a full theoretical understanding of …