Related papers: Improving Infinitely Deep Bayesian Neural Networks…
Spiking neural networks (SNNs) have gained prominence for their potential in neuromorphic computing and energy-efficient artificial intelligence, yet optimizing them remains a formidable challenge for gradient-based methods due to their…
Bayesian optimization (BO) is a widely used method for data-driven optimization that generally relies on zeroth-order data of objective function to construct probabilistic surrogate models. These surrogates guide the…
When equipped with efficient optimization algorithms, the over-parameterized neural networks have demonstrated high level of performance even though the loss function is non-convex and non-smooth. While many works have been focusing on…
We propose computationally tractable accelerated first-order methods for Riemannian optimization, extending the Nesterov accelerated gradient (NAG) method. For both geodesically convex and geodesically strongly convex objective functions,…
Nesterov's accelerated gradient method (NAG) achieves faster convergence than gradient descent for convex optimization but lacks monotonicity in function values. To address this, Beck and Teboulle [2009b] proposed a monotonic variant,…
Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes…
We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…
Nesterov's accelerated gradient methods (AGM) have been successfully applied in many machine learning areas. However, their empirical performance on training max-margin models has been inferior to existing specialized solvers. In this…
Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…
Finding the best setup for experiments is the primary concern for Optimal Experimental Design (OED). Here, we focus on the Bayesian experimental design problem of finding the setup that maximizes the Shannon expected information gain. We…
In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…
Bayesian neural networks (BNN) and deep ensembles are principled approaches to estimate the predictive uncertainty of a deep learning model. However their practicality in real-time, industrial-scale applications are limited due to their…
The existence of adversarial examples underscores the importance of understanding the robustness of machine learning models. Bayesian neural networks (BNNs), due to their calibrated uncertainty, have been shown to posses favorable…
Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one…
Recent methods have significantly reduced the performance degradation of Binary Neural Networks (BNNs), but guaranteeing the effective and efficient training of BNNs is an unsolved problem. The main reason is that the estimated gradients…
This research introduces a novel methodology for optimizing Bayesian Neural Networks (BNNs) by synergistically integrating them with traditional machine learning algorithms such as Random Forests (RF), Gradient Boosting (GB), and Support…
In this paper, a general stochastic optimization procedure is studied, unifying several variants of the stochastic gradient descent such as, among others, the stochastic heavy ball method, the Stochastic Nesterov Accelerated Gradient…
We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…
Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…
We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence…