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 .
From one gradient to every gradient The post Backpropagation Explained for Beginners (Part 3): How Backpropagation Really Works appeared first on Towards Data Science .
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 .
The idea that makes backpropagation possible. The post Backpropagation Explained for Beginners (Part 2): There Has to Be a Better Way appeared first on Towards Data Science .
arXiv:2509. 14969v2 Announce Type: replace Abstract: We introduce a new adaptive step-size strategy for convex optimization with stochastic gradient that exploits the local geometry of the objective function only by means of a first-order stochastic oracle and without any hyper-parameter tuning.
arXiv:2508. 21571v2 Announce Type: replace Abstract: Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations.
arXiv:2606. 29593v1 Announce Type: cross Abstract: In 1937, Stefan Kaczmarz proposed a simple algorithm for solving systems of linear equations.
arXiv:2608. 07618v1 Announce Type: cross Abstract: Stochastic gradient descent for a loss function discontinuous across lower dimensional manifolds is analyzed by studying its differential equation limit.
The paper develops a diffusion approximation for stochastic gradient descent (SGD) when the optimization target is a functional on the Wasserstein space ℝ2. By lifting the problem to a Hilbert space via Lions differentiability, the authors construct a Gaussian random-field approximation whose velocity field matches the mean and covariance of the original stochastic gradient. They prove that this Gaussian approximation achieves second‑order weak accuracy, providing a rigorous basis for replacing sample‑driven randomness with analytically tractable Gaussian fluctuations in stochastic optimization over probability measures.
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 downside of conference travel The post Last Month’s Machine Learning Lessons Learned appeared first on Towards Data Science .
arXiv:2609.16350v1 Announce Type: new Abstract: Federated stochastic bilevel optimization has been actively studied in recent years due to its widespread applications in machine learning. However, mo...
Patience, Optimism, Discipline, Projects, Teams The post Lessons Learned After 8. 5 Years of ML appeared first on Towards Data Science .