arXiv research

Restricted Boltzmann Machine (RBM) is a bipartite graphical model that is used as the building block in energy-based deep generative models. Due to numerical stability and quantifiability of the likelihood, RBM is commonly used with Bernoulli units. Here, we consider an alternative member of exponential family RBM with…

Machine learning classifies topological phases in leaky photonic lattices.

New insights into how linear classifiers and leaky ReLU networks can overfit without harming generalization.

Paper finds conditions for benign overfitting in neural networks.

Study on benign overfitting in leaky ReLUs with moderate input dimensions.

Leaky ReLU activations improve the calibration of Bayesian neural networks.

New methods for uncertainty in neural networks with leaky ReLU activations.

In this paper we investigate the performance of different types of rectified activation functions in convolutional neural network: standard rectified linear unit (ReLU), leaky rectified linear unit (Leaky ReLU), parametric rectified linear unit (PReLU) and a new randomized leaky rectified linear units (RReLU). We evalu…

Study on feature learning in Leaky ResNets, explaining bottleneck structure.

Gradient descent biases towards stable rank networks for nearly-orthogonal data.

This paper investigates the effect of leak in spiking neural networks.

This study investigates how gradient-based methods bias neural networks trained on high-dimensional data.

Learning and memory are intertwined in our brain and their relationship is at the core of several recent neural network models. In particular, the Attention-Gated MEmory Tagging model (AuGMEnT) is a reinforcement learning network with an emphasis on biological plausibility of memory dynamics and learning. We find that …

This study uses neural networks to solve interpolation problems with sparse, infinitely wide layers.

Early training of deep neural networks leads to small, directionally converging weights.

Sparsity inducing regularization is an important part for learning over-complete visual representations. Despite the popularity of $\ell_1$ regularization, in this paper, we investigate the usage of non-convex regularizations in this problem. Our contribution consists of three parts. First, we propose the leaky capped …

New method stabilizes deep neural networks by setting Lyapunov exponent to zero.

Deep nets solve MDPs without high dimensions.

LQF linearizes deep models for better interpretability.

Single neuron with ADA learns XOR and outperforms other functions.

This work bridges theory and practice in spiking reservoirs, identifying robust parameter ranges.

The paper aims to mathematically define and learn abstractions from data.

We empirically investigate the (negative) expected accuracy as an alternative loss function to cross entropy (negative log likelihood) for classification tasks. Coupled with softmax activation, it has small derivatives over most of its domain, and is therefore hard to optimize. A modified, leaky version is evaluated on…

An artificial neuron is modelled as a weighted summation followed by an activation function which determines its output. A wide variety of activation functions such as rectified linear units (ReLU), leaky-ReLU, Swish, MISH, etc. have been explored in the literature. In this short paper, we explore what happens when the…

Visual attention serves as a means of feature selection mechanism in the perceptual system. Motivated by Broadbent's leaky filter model of selective attention, we evaluate how such mechanism could be implemented and affect the learning process of deep reinforcement learning. We visualize and analyze the feature maps of…

We consider a deep ReLU / Leaky ReLU student network trained from the output of a fixed teacher network of the same depth, with Stochastic Gradient Descent (SGD). The student network is \emph{over-realized}: at each layer $l$, the number $n_l$ of student nodes is more than that ($m_l$) of teacher. Under mild conditions…

The seemingly stochastic transient dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference. In vitro neurons, on the other hand, exhibit a highly deterministic response to various types of stimulation. We show that an ensemble of deterministic le…

This paper suggests a learning-theoretic perspective on how synaptic plasticity benefits global brain functioning. We introduce a model, the selectron, that (i) arises as the fast time constant limit of leaky integrate-and-fire neurons equipped with spiking timing dependent plasticity (STDP) and (ii) is amenable to the…

New initialization schemes preserve fractional moments of weights in deep networks, improving training and test performance.

In the recent literature the important role of depth in deep learning has been emphasized. In this paper we argue that sufficient width of a feedforward network is equally important by answering the simple question under which conditions the decision regions of a neural network are connected. It turns out that for a cl…

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high probability, the proposed algorithm with random initialization grants a linear conve…

SGD-trained neural networks generalize well even with adversarial label noise.

Previous work has questioned the conditions under which the decision regions of a neural network are connected and further showed the implications of the corresponding theory to the problem of adversarial manipulation of classifiers. It has been proven that for a class of activation functions including leaky ReLU, neur…

How spiking networks are able to perform probabilistic inference is an intriguing question, not only for understanding information processing in the brain, but also for transferring these computational principles to neuromorphic silicon circuits. A number of computationally powerful spiking network models have been pro…

The biological plausibility of the backpropagation algorithm has long been doubted by neuroscientists. Two major reasons are that neurons would need to send two different types of signal in the forward and backward phases, and that pairs of neurons would need to communicate through symmetric bidirectional connections. …

We study discrete time dynamical systems governed by the state equation $h_{t+1}=φ(Ah_t+Bu_t)$. Here $A,B$ are weight matrices, $φ$ is an activation function, and $u_t$ is the input data. This relation is the backbone of recurrent neural networks (e.g. LSTMs) which have broad applications in sequential learning tasks. …

The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we …

We present a new, unifying approach following some recent developments on the complexity of neural networks with piecewise linear activations. We treat neural network layers with piecewise linear activations as tropical polynomials, which generalize polynomials in the so-called $(\max, +)$ or tropical algebra, with pos…

For a biological agent operating under environmental pressure, energy consumption and reaction times are of critical importance. Similarly, engineered systems are optimized for short time-to-solution and low energy-to-solution characteristics. At the level of neuronal implementation, this implies achieving the desired …

The universal approximation property of various machine learning models is currently only understood on a case-by-case basis, limiting the rapid development of new theoretically justified neural network architectures and blurring our understanding of our current models' potential. This paper works towards overcoming th…

This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GANs), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases. We study a wide range of parametric and nonpar…

Gradient descent fails to train two-layer ReLU networks, leading to poor performance.

An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on the number of nodes in networks with two hidden layers such that linear separabili…

An interesting approach to analyzing neural networks that has received renewed attention is to examine the equivalent kernel of the neural network. This is based on the fact that a fully connected feedforward network with one hidden layer, a certain weight distribution, an activation function, and an infinite number of…

A wide variety of activation functions have been proposed for neural networks. The Rectified Linear Unit (ReLU) is especially popular today. There are many practical reasons that motivate the use of the ReLU. This paper provides new theoretical characterizations that support the use of the ReLU, its variants such as th…

In this paper, we consider parameter recovery for non-overlapping convolutional neural networks (CNNs) with multiple kernels. We show that when the inputs follow Gaussian distribution and the sample size is sufficiently large, the squared loss of such CNNs is $\mathit{~locally~strongly~convex}$ in a basin of attraction…

Smooth calibration improves forecast reliability even with leaked information.

In this paper, we derive a new model of synaptic plasticity, based on recent algorithms for reinforcement learning (in which an agent attempts to learn appropriate actions to maximize its long-term average reward). We show that these direct reinforcement learning algorithms also give locally optimal performance for the…