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We present a method of estimating the gradient of an objective function with respect to the synaptic weights of a spiking neural network. The method works by measuring the fluctuations in the objective function in response to dynamic…

Herein the topics of (natural) gradient descent, data decorrelation, and approximate methods for backpropagation are brought into a common discussion. Natural gradient descent illuminates how gradient vectors, pointing at directions of…

This paper presents a framework of successive functional gradient optimization for training nonconvex models such as neural networks, where training is driven by mirror descent in a function space. We provide a theoretical analysis and…

We learn recurrent neural network optimizers trained on simple synthetic functions by gradient descent. We show that these learned optimizers exhibit a remarkable degree of transfer in that they can be used to efficiently optimize a broad…

Deep Spiking Neural Networks (SNNs) present optimization difficulties for gradient-based approaches due to discrete binary activation and complex spatial-temporal dynamics. Considering the huge success of ResNet in deep learning, it would…

Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…

Neural networks can be used to learn the solution of partial differential equations (PDEs) on arbitrary domains without requiring a computational mesh. Common approaches integrate differential operators in training neural networks using a…

Feature learning is thought to be one of the fundamental reasons for the success of deep neural networks. It is rigorously known that in two-layer fully-connected neural networks under certain conditions, one step of gradient descent on the…

We propose a simple yet effective neural network-based framework for global illumination rendering. Recently, rendering techniques that learn neural radiance caches by minimizing the difference (i.e., residual) between the left and right…

In this paper, we first identify activation shift, a simple but remarkable phenomenon in a neural network in which the preactivation value of a neuron has non-zero mean that depends on the angle between the weight vector of the neuron and…

Recent research showed that the dual-pixel sensor has made great progress in defocus map estimation and image defocus deblurring. However, extracting real-time dual-pixel views is troublesome and complex in algorithm deployment. Moreover,…

Neural networks are trained primarily based on their inputs and outputs, without regard for their internal mechanisms. These neglected mechanisms determine properties that are critical for safety, like (i) transparency; (ii) the absence of…

Normalization layers are widely used in deep neural networks to stabilize training. In this paper, we consider the training of convolutional neural networks with gradient descent on a single training example. This optimization problem…

In this work we propose Hebbian-descent as a biologically plausible learning rule for hetero-associative as well as auto-associative learning in single layer artificial neural networks. It can be used as a replacement for gradient descent…

We give a simple proof for the global convergence of gradient descent in training deep ReLU networks with the standard square loss, and show some of its improvements over the state-of-the-art. In particular, while prior works require all…

Neural networks are playing a crucial role in everyday life, with the most modern generative models able to achieve impressive results. Nonetheless, their functioning is still not very clear, and several strategies have been adopted to…

The generalization mystery of overparametrized deep nets has motivated efforts to understand how gradient descent (GD) converges to low-loss solutions that generalize well. Real-life neural networks are initialized from small random values…

Backpropagation is driving today's artificial neural networks (ANNs). However, despite extensive research, it remains unclear if the brain implements this algorithm. Among neuroscientists, reinforcement learning (RL) algorithms are often…

Understanding the properties of neural networks trained via stochastic gradient descent (SGD) is at the heart of the theory of deep learning. In this work, we take a mean-field view, and consider a two-layer ReLU network trained via SGD for…

While deep learning has outperformed other methods for various tasks, theoretical frameworks that explain its reason have not been fully established. To address this issue, we investigate the excess risk of two-layer ReLU neural networks in…