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A random vector functional link network (RVFL) is widely used as a universal approximator for classification and regression problems. The big advantage of RVFL is fast training without backpropagation. This is because the weights and biases…

The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…

We consider strongly convex optimization problems with affine-type restrictions. We build dual problem and solve dual problem by Fast Gradient Method. We use primal-dual structure of this method to construct the solution of the primal…

The expressivity of Graph Neural Networks (GNNs) has been studied broadly in recent years to reveal the design principles for more powerful GNNs. Graph canonization is known as a typical approach to distinguish non-isomorphic graphs, yet…

Neural networks are popular and useful in many fields, but they have the problem of giving high confidence responses for examples that are away from the training data. This makes the neural networks very confident in their prediction while…

This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex…

We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a…

Many supervised machine learning methods are naturally cast as optimization problems. For prediction models which are linear in their parameters, this often leads to convex problems for which many mathematical guarantees exist. Models which…

We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…

Fine-grained visual classification (FGVC) tasks, such as insect and bird identification, demand sensitivity to subtle visual cues while remaining robust to spatial transformations. A key challenge is handling geometric biases and noise,…

Advances in optical and electrophysiological recording technologies have made it possible to record the dynamics of thousands of neurons, opening up new possibilities for interpreting and controlling large neural populations in behaving…

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…

Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as vanishing/exploding gradients. Short of designing new RNN architectures, previous methods for dealing…

In this paper, we theoretically prove that gradient descent can find a global minimum of non-convex optimization of all layers for nonlinear deep neural networks of sizes commonly encountered in practice. The theory developed in this paper…

Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…

Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…

Despite the appeal of deep neural networks that largely replace the traditional handmade filters, they still suffer from isolated cases that cannot be properly handled only by the training of convolutional filters. Abnormal factors,…

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable…