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Deep spiking neural networks (SNNs) hold great potential for improving the latency and energy efficiency of deep neural networks through event-based computation. However, training such networks is difficult due to the non-differentiable…

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether…

This work contributes to the development of a new data-driven method (D-DM) of feedforward neural networks (FNNs) learning. This method was proposed recently as a way of improving randomized learning of FNNs by adjusting the network…

Deep neural networks, including recurrent networks, have been successfully applied to human activity recognition. Unfortunately, the final representation learned by recurrent networks might encode some noise (irrelevant signal components,…

Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Program (SDP). The main…

Many complex real-world tasks are composed of several levels of sub-tasks. Humans leverage these hierarchical structures to accelerate the learning process and achieve better generalization. In this work, we study the inductive bias and…

Deep multitask networks, in which one neural network produces multiple predictive outputs, can offer better speed and performance than their single-task counterparts but are challenging to train properly. We present a gradient normalization…

Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Neural networks have been achieving high generalization performance on many tasks despite being highly over-parameterized. Since classical statistical learning theory struggles to explain this behavior, much effort has recently been focused…

A crucial property for achieving secure, trustworthy and interpretable deep learning systems is their robustness: small changes to a system's inputs should not result in large changes to its outputs. Mathematically, this means one strives…

For Bayesian optimization (BO) on high-dimensional data with complex structure, neural network-based kernels for Gaussian processes (GPs) have been used to learn flexible surrogate functions by the high representation power of deep…

Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in computational science and engineering. Despite well over…

Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…

The goal of this tutorial is to introduce key models, algorithms, and open questions related to the use of optimization methods for solving problems arising in machine learning. It is written with an INFORMS audience in mind, specifically…

Automated deep neural network architecture design has received a significant amount of recent attention. However, this attention has not been equally shared by one of the fundamental building blocks of a deep neural network, the neurons. In…

Many important computer vision tasks are naturally formulated to have a non-differentiable objective. Therefore, the standard, dominant training procedure of a neural network is not applicable since back-propagation requires the gradients…

This paper tackles the problem of training a deep convolutional neural network of both low-bitwidth weights and activations. Optimizing a low-precision network is very challenging due to the non-differentiability of the quantizer, which may…

In this paper, we present a branch and bound algorithm for extracting approximate solutions to Global Polynomial Optimization (GPO) problems with bounded feasible sets. The algorithm is based on a combination of SOS/Moment relaxations and…

The highly structured energy landscape of the loss as a function of parameters for deep neural networks makes it necessary to use sophisticated optimization strategies in order to discover (local) minima that guarantee reasonable…