arXiv research

In this paper, we develop an alternating direction method of multipliers (ADMM) for deep neural networks training with sigmoid-type activation functions (called \textit{sigmoid-ADMM pair}), mainly motivated by the gradient-free nature of ADMM in avoiding the saturation of sigmoid-type activations and the advantages of …

New method initializes sigmoidal MLPs for interpretable shapes.

Improved logistic MoE with sigmoid gate shows better sample efficiency.

We developed safe and ranged approximations for ReLU, tanh, and sigmoid functions to reduce neural network training time.

S-GAI initializes MLPs using spectral geometry from data, improving performance.

Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed interval which is independent of the data scope and activation function type. This …

In this paper, we prove that a shallow neural network with a monotone sigmoid, ReLU, ELU, Softplus, or LeakyReLU activation function can arbitrarily well approximate any L^p(p>=2) integrable functions defined on R*[0,1]^n. We also prove that a shallow neural network with a sigmoid, ReLU, ELU, Softplus, or LeakyReLU act…

This note is concerned with accurate and computationally efficient approximations of moments of Gaussian random variables passed through sigmoid or softmax mappings. These approximations are semi-analytical (i.e. they involve the numerical adjustment of parametric forms) and highly accurate (they yield 5% error at most…

Single tree outperforms random forest in testing accuracy.

We propose a differentiable sigmoid function for efficient p-value calculation in clustering.

Proposes a new method to approximate Gaussian inference in classification tasks.

Highly expressive directed latent variable models, such as sigmoid belief networks, are difficult to train on large datasets because exact inference in them is intractable and none of the approximate inference methods that have been applied to them scale well. We propose a fast non-iterative approximate inference metho…

We establish upper bounds for the minimal number of hidden units for which a binary stochastic feedforward network with sigmoid activation probabilities and a single hidden layer is a universal approximator of Markov kernels. We show that each possible probabilistic assignment of the states of $n$ output units, given t…

Sharp lower bounds on shallow neural networks' approximation rates are derived.

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

Improved learning bounds for corrupted data using thresholded gradient descent.

Sigmoid autoencoders can implement associative memory with certain conditions.

We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the model using a latent marked Poisson process and Pólya--Gamma random variables w…

Sigmoid gating is more sample efficient than softmax in mixture of experts.

Study shows MSE with sigmoid can match SCE in classification tasks, especially with noisy data.

Paper develops SINNOs for approximating stochastic processes.

A new KAN variant uses sinusoidal activations to approximate functions.

We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a scaled logistic sigmoid function. We present a tractable representation of the li…

Proposes a method to visualize finer cluster structures in high-dimensional data.

We show that deep narrow Boltzmann machines are universal approximators of probability distributions on the activities of their visible units, provided they have sufficiently many hidden layers, each containing the same number of units as the visible layer. We show that, within certain parameter domains, deep Boltzmann…

There has been a growing interest in expressivity of deep neural networks. However, most of the existing work about this topic focuses only on the specific activation function such as ReLU or sigmoid. In this paper, we investigate the approximation ability of deep neural networks with a broad class of activation functi…

Researchers develop neural networks for approximating functions in Banach spaces.

Efficient inference for nonparametric Hawkes processes using Pólya-Gamma augmentation.

DeepSeekMoE improves language model efficiency with shared experts and normalized gating.

We study layered neural networks of rectified linear units (ReLU) in a modelling framework for stochastic training processes. The comparison with sigmoidal activation functions is in the center of interest. We compute typical learning curves for shallow networks with K hidden units in matching student teacher scenarios…

We develop a new approach to learn the parameters of regression models with hidden variables. In a nutshell, we estimate the gradient of the regression function at a set of random points, and cluster the estimated gradients. The centers of the clusters are used as estimates for the parameters of hidden units. We justif…

Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the graduality of the sigmoid function, the sigmoid gate is not flexible in representing m…

We show that there is a simple (approximately radial) function on $\reals^d$, expressible by a small 3-layer feedforward neural networks, which cannot be approximated by any 2-layer network, to more than a certain constant accuracy, unless its width is exponential in the dimension. The result holds for virtually all kn…

Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step that discards samples from the variational posterior which are assigned low likel…

Deep conditional generative models are developed to simultaneously learn the temporal dependencies of multiple sequences. The model is designed by introducing a three-way weight tensor to capture the multiplicative interactions between side information and sequences. The proposed model builds on the Temporal Sigmoid Be…

We simplify word embeddings by removing sigmoid in SGNS, revealing connections to hyperbolic spaces.

Deep dynamic generative models are developed to learn sequential dependencies in time-series data. The multi-layered model is designed by constructing a hierarchy of temporal sigmoid belief networks (TSBNs), defined as a sequential stack of sigmoid belief networks (SBNs). Each SBN has a contextual hidden state, inherit…

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…

This paper presents a basic property of region dividing of ReLU (rectified linear unit) deep learning when new layers are successively added, by which two new perspectives of interpreting deep learning are given. The first is related to decision trees and forests; we construct a deep learning structure equivalent to a …

We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target distribution, and therefore does not perform its full power on truncated distribu…

Survival trees exhibit end-cut preference, leading to biased splits.

Two methods extend multivariate Kelly optimization to large problem sizes.

We introduce exact macroscopic on-line learning dynamics of two-layer neural networks with ReLU units in the form of a system of differential equations, using techniques borrowed from statistical physics. For the first experiments, numerical solutions reveal similar behavior compared to sigmoidal activation researched …

Paper proposes HTAF for stable training of binary neural networks.

We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly because this approximation tends to underestimate the true variance and other features…

GLU variants improve Transformer performance.

Sharp bounds on neural network approximation rates and widths.

Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in classification for datasets following a linear separability condition. The separab…