The article titled "The Sigmoid Function: From 'e' to Neural Networks" explores the origins and applications of the sigmoid function, a mathematical equation frequently used in data science and machine learning. It traces the function’s development from its foundational exponential form to its modern role in neural network architectures. The piece highlights how this simple yet powerful equation underpins many computational models in the field.
The intuition behind neural networks and why they need activation functions. The post Neural Networks, Explained for Beginners: Start Here If They’ve Confused You appeared first on Towards Data Science .
arXiv:2507. 14177v2 Announce Type: replace-cross Abstract: This paper aims to understand the training solution, which is obtained by the back-propagation algorithm, of two-layer neural networks whose hidden layer is composed of the units with smooth activation functions, including the usual sigmoid type most commonly used before the advent of ReLUs.
They aren’t designed, you can’t help perceiving one anyway, and that makes them an engineering problem almost no one is solving. The post Where Does an AI’s Personality Actually Come From?
A step-by-step journey from calculus-based optimization to Stochastic Gradient Descent The post Why Gradient Descent Became Stochastic appeared first on Towards Data Science .
The article "Diversity of EML-type operators" discusses the EML operator, which can evaluate standard explicit purely transcendental elementary functions, and notes that while most research has focused on the binary EML, many similar variants exist. It enumerates and classifies these variants, clarifies common misconceptions, and proposes a M"obius layer that replaces matrix operations with rational functions. The paper also showcases the activation function eml(x,1/x), enabling separate recovery of exp(x) and ln(x) and thus evaluation of all elementary functions within a rational neural‑network generalization.
Let's discover how neural networks learn, step by step The post Backpropagation Explained for Beginners (Part 1): Building the Intuition appeared first on Towards Data Science .
arXiv:2605. 30370v2 Announce Type: replace-cross Abstract: From their inception in the 1950s, artificial neural networks (ANNs) started using the so-called point neuron model then prevalent in neuroscience, hoping that this analogy would allow for a better emulation of brain function.
The article titled "The AI That Learned to Understand Long After It Stopped Trying" discusses a small, strange discovery in machine learning known as grokking. It highlights how this phenomenon involves an AI developing understanding after ceasing to actively try. The piece was originally published on Towards Data Science.
A clear, math-first walkthrough of how VAEs learn to generate new data The post Variational Autoencoders (VAEs) Explained: From Theory to ELBO and the Reparameterization Trick appeared first on Towards Data Science .
For nearly a decade, this part of neural networks barely changed. DeepSeek is trying to reinvent it.
arXiv:2602.08515v3 Announce Type: replace-cross Abstract: This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partia...
arXiv:2607. 18930v1 Announce Type: cross Abstract: The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error.