arXiv research

We propose K-TanH, a novel, highly accurate, hardware efficient approximation of popular activation function TanH for Deep Learning. K-TanH consists of parameterized low-precision integer operations, such as, shift and add/subtract (no floating point operation needed) where parameters are stored in very small look-up t…

Many neural networks use the tanh activation function, however when given a probability distribution as input, the problem of computing the output distribution in neural networks with tanh activation has not yet been addressed. One important example is the initialization of the echo state network in reservoir computing…

Finite-precision learning of $anh$ networks is limited by the Monte Carlo rate.

Bayesian neural networks show good correlation between out-of-sample performance and Bayesian evidence.

The Rectified Linear Unit (ReLU) is a foundational activation function in artficial neural networks. Recent literature frequently misattributes its origin to the 2018 (initial) version of this paper, which exclusively investigated ReLU at the classification layer. This paper formally corrects the citation record by tra…

Finding minimum distortion of adversarial examples and thus certifying robustness in neural network classifiers for given data points is known to be a challenging problem. Nevertheless, recently it has been shown to be possible to give a non-trivial certified lower bound of minimum adversarial distortion, and some rece…

Random feature maps improve forecasting of chaotic dynamical systems.

New insights into neural network training efficiency.

Upper bounds on fixed points in PWL neural networks with hyperplane analysis.

Neural networks struggle with periodic functions, a new activation fixes this.

We seek to improve the data efficiency of neural networks and present novel implementations of parameterized piece-wise polynomial activation functions. The parameters are the y-coordinates of n+1 Chebyshev nodes per hidden unit and Lagrangian interpolation between the nodes produces the polynomial on [-1, 1]. We show …

Randomly initialized wide neural networks with zero-mean activations are nearly independent, potentially solving AI interpretability limits.

Study fractal and regular geometry in deep neural networks.

New theory explains signal propagation in normalization-free transformers.

Sigmoid-type networks avoid vanishing gradients with regularization and rescaling.

We present a Statistical Mechanics (SM) model of deep neural networks, connecting the energy-based and the feed forward networks (FFN) approach. We infer that FFN can be understood as performing three basic steps: encoding, representation validation and propagation. From the meanfield solution of the model, we obtain a…

Deep networks can approximate various activation functions with modest adjustments.

SGD converges globally to logistic loss minima for two-layer nets.

The performance of artificial neural networks (ANNs) is influenced by weight initialization, the nature of activation functions, and their architecture. There is a wide range of activation functions that are traditionally used to train a neural network, e.g. sigmoid, tanh, and Rectified Linear Unit (ReLU). A widespread…

We propose $\textit{Mish}$, a novel self-regularized non-monotonic activation function which can be mathematically defined as: $f(x)=x\tanh(softplus(x))$. As activation functions play a crucial role in the performance and training dynamics in neural networks, we validated experimentally on several well-known benchmarks…

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…

Investigates least squares estimation in deterministic MoE models.

We investigate the loss surface of neural networks. We prove that even for one-hidden-layer networks with "slightest" nonlinearity, the empirical risks have spurious local minima in most cases. Our results thus indicate that in general "no spurious local minima" is a property limited to deep linear networks, and insigh…

Global convergence of SGD proven for two-layer neural nets with regularization.

The exclusive or (xor) function is one of the simplest examples that illustrate why nonlinear feedforward networks are superior to linear regression for machine learning applications. We review the xor representation and approximation problems and discuss their solutions in terms of probabilistic logic and associative …

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…

In this paper we show all possible ramps where an object can move with constant speed under the effect of gravity and friction. The planar ramp are very easy to describe, just rotate a curve with velocity vector (tanh(as),sech(as)). Recall that tanh(as)^2+sech^2(as) = 1. Therefore, the solution of the planar constant s…

New method improves training of PINNs for PDEs by adding noisy supervision terms.

It is well-known that overparametrized neural networks trained using gradient-based methods quickly achieve small training error with appropriate hyperparameter settings. Recent papers have proved this statement theoretically for highly overparametrized networks under reasonable assumptions. These results either assume…

The paper proves consistency of neural networks with regularization.

Deep Learning is applied to energy markets to predict extreme loads observed in energy grids. Forecasting energy loads and prices is challenging due to sharp peaks and troughs that arise due to supply and demand fluctuations from intraday system constraints. We propose deep spatio-temporal models and extreme value theo…

This paper proposes a novel fault diagnosis approach based on generative adversarial networks (GAN) for imbalanced industrial time series where normal samples are much larger than failure cases. We combine a well-designed feature extractor with GAN to help train the whole network. Aimed at obtaining data distribution a…

Wide hidden layer TCM nets capacity analyzed using RDT and fl RDT.

Study proves deep narrow RNNs can approximate any function, with minimum width independent of data length.

We show that the empirical risk minimization (ERM) problem for neural networks has no solution in general. Given a training set $s_1, \dots, s_n \in \mathbb{R}^p$ with corresponding responses $t_1,\dots,t_n \in \mathbb{R}^q$, fitting a $k$-layer neural network $ν_θ: \mathbb{R}^p \to \mathbb{R}^q$ involves estimation of…

The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain user/item features. A standard approach to modeling this problem is Inductive Matrix Completion where the predicted rating is modeled as an inner product of the user and …

Using back-propagation and its variants to train deep networks is often problematic for new users. Issues such as exploding gradients, vanishing gradients, and high sensitivity to weight initialization strategies often make networks difficult to train, especially when users are experimenting with new architectures. Her…

Exact bounds derived for neural network outputs with noisy inputs.

New findings on neural network identifiability using affine symmetries.

Paper establishes generalization bounds for RNNs and improves existing results.

DIFFRNN verifies RNNs for safety and equivalence.

Lower bound proves ridgeless regression performs poorly near interpolation threshold.

Deep networks with orthogonal weights show stable fluctuations, improving generalization and training speed.

GANs improve anomaly detection in power plants, achieving nearly perfect classification.

The paper analyzes the score field of diffusion models using Burgers dynamics.

New PINNs method improves accuracy in computing Mean Escape Time from bounded domains.

We present a probabilistic framework for nonlinearities, based on doubly truncated Gaussian distributions. By setting the truncation points appropriately, we are able to generate various types of nonlinearities within a unified framework, including sigmoid, tanh and ReLU, the most commonly used nonlinearities in neural…

PDEs constrain smooth functions in neural networks.