Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Neural Network Approximation and Learning

Description

This lecture explores the mathematical aspects of neural network approximation and learning, focusing on deep learning experimental revolution, supervised learning basic setup, challenges of high-dimensional learning, reproducing kernel Hilbert spaces, variation-norm spaces, dynamic CLT for shallow neural networks, and upper bounds for deep ReLU networks. The instructor discusses the mean-field limit, global convergence, continuity equation, depth separation, lower bounds for piece-wise oscillatory functions, and future prospects for approximation vs optimization in deep models.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Information engineering

Machine learning: Artificial neural networks

Related concepts (32)

Deep learning

Deep learning is part of a broader family of machine learning methods, which is based on artificial neural networks with representation learning. The adjective "deep" in deep learning refers to the use of multiple layers in the network. Methods used can be either supervised, semi-supervised or unsupervised.

Artificial neural network

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

Feedforward neural network

A feedforward neural network (FNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. Its flow is uni-directional, meaning that the information in the model flows in only one direction—forward—from the input nodes, through the hidden nodes (if any) and to the output nodes, without any cycles or loops, in contrast to recurrent neural networks, which have a bi-directional flow.

Convolutional neural network

Convolutional neural network (CNN) is a regularized type of feed-forward neural network that learns feature engineering by itself via filters (or kernel) optimization. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by using regularized weights over fewer connections. For example, for each neuron in the fully-connected layer 10,000 weights would be required for processing an image sized 100 × 100 pixels.

Rectifier (neural networks)

In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the positive part of its argument: where x is the input to a neuron. This is also known as a ramp function and is analogous to half-wave rectification in electrical engineering. This activation function was introduced by Kunihiko Fukushima in 1969 in the context of visual feature extraction in hierarchical neural networks.

Related lectures (32)

Splines and Machine Learning

Explores supervised learning as an ill-posed problem and the integration of sparse adaptive splines into neural architectures.

Deep Splines: Unifying Framework for Deep Neural Networks

Introduces a functional framework for deep neural networks with adaptive piecewise-linear splines, focusing on biomedical image reconstruction and the challenges of deep splines.

Landscape and Generalisation in Deep Learning

Explores the challenges and insights of deep learning, focusing on loss landscape, generalization, and feature learning.

Perception: Data-Driven Approaches

Explores perception in deep learning for autonomous vehicles, covering image classification, optimization methods, and the role of representation in machine learning.

Nonlinear Supervised Learning