arXiv research

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

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 …

Sigmoid autoencoders can implement associative memory with certain conditions.

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

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…

Improved logistic MoE with sigmoid gate shows better sample efficiency.

New method initializes sigmoidal MLPs for interpretable shapes.

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 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 …

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…

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

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…

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…

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

The study explores how Matrix Product States can represent boolean and continuous functions.

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

In adversarial attacks to machine-learning classifiers, small perturbations are added to input that is correctly classified. The perturbations yield adversarial examples, which are virtually indistinguishable from the unperturbed input, and yet are misclassified. In standard neural networks used for deep learning, atta…

Monotonic differentiable sorting networks improve upon previous methods.

It is well known that the initialization of weights in deep neural networks can have a dramatic impact on learning speed. For example, ensuring the mean squared singular value of a network's input-output Jacobian is $O(1)$ is essential for avoiding the exponential vanishing or explosion of gradients. The stronger condi…

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 consider network sparsification as an $L_0$-norm regularized binary optimization problem, where each unit of a neural network (e.g., weight, neuron, or channel, etc.) is attached with a stochastic binary gate, whose parameters are jointly optimized with original network parameters. The Augment-Reinforce-Merge (ARM),…

Python scripts analyze MRAM-based neuromorphic devices' process variation impacts on machine learning accuracy.

SummaryNet automates video summarisation using deep learning.

Activation functions have a notorious impact on neural networks on both training and testing the models against the desired problem. Currently, the most used activation function is the Rectified Linear Unit (ReLU). This paper introduces a new and novel activation function, closely related with the new activation $Swish…

We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the algorithm succeeds with respect to {\em any} distribution on the unit ball in $n$ …

Paper investigates differentiable fuzzy implications and their suitability for learning.

Gated recurrent neural networks have achieved remarkable results in the analysis of sequential data. Inside these networks, gates are used to control the flow of information, allowing to model even very long-term dependencies in the data. In this paper, we investigate whether the original gate equation (a linear projec…

Paper proposes HTAF for stable training of binary neural networks.

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

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

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…

New ACE cost function encourages diversity in neural networks.

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…

We show that any smooth bi-Lipschitz $h$ can be represented exactly as a composition $h_m \circ ... \circ h_1$ of functions $h_1,...,h_m$ that are close to the identity in the sense that each $\left(h_i-\mathrm{Id}\right)$ is Lipschitz, and the Lipschitz constant decreases inversely with the number $m$ of functions com…

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…

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…

The paper approaches the task of handwritten text recognition (HTR) with attentional encoder-decoder networks trained on sequences of characters, rather than words. We experiment on lines of text from popular handwriting datasets and compare different activation functions for the attention mechanism used for aligning i…

Training feedforward neural networks with standard logistic activations is considered difficult because of the intrinsic properties of these sigmoidal functions. This work aims at showing that these networks can be trained to achieve generalization performance comparable to those based on hyperbolic tangent activations…

Overwhelming theoretical and empirical evidence shows that mildly overparametrized neural networks -- those with more connections than the size of the training data -- are often able to memorize the training data with $100\%$ accuracy. This was rigorously proved for networks with sigmoid activation functions and, very …

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

Most deep neural networks use simple, fixed activation functions, such as sigmoids or rectified linear units, regardless of domain or network structure. We introduce differential equation units (DEUs), an improvement to modern neural networks, which enables each neuron to learn a particular nonlinear activation functio…

A new KAN variant uses sinusoidal activations to approximate functions.

FiGS searches over a larger space of architectures for efficient mobile models.

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

Most deep neural networks use simple, fixed activation functions, such as sigmoids or rectified linear units, regardless of domain or network structure. We introduce differential equation units (DEUs), an improvement to modern neural networks, which enables each neuron to learn a particular nonlinear activation functio…

New bounds for shallow neural networks with deterministic parameters.

01 loss neural network improves adversarial robustness on CIFAR10.