{"slug": "vanilla-neural-networks", "title": "Vanilla Neural Networks", "summary": "A neural network is a mathematical function of the form y = FNN(x), composed of nested layers where each layer f(x) = g(Wx + b) uses a weight matrix W, bias vector b, and activation function g, with parameters learned via gradient descent.", "body_md": "# Vanilla Neural Networks\n\nA neural network is just a math function: `y = FNN(x)`\n\n.\n\n`FNN`\n\nhas a nested form. Think of it as a stack of layers. A 3-layer neural network that returns a scalar value looks like this:\n\n`y = FNN(x) = f₃(f₂(f₁(x)))`\n\nEach `f`\n\n— `f₁`\n\n, `f₂`\n\n, … `fₙ`\n\n— has the same form:\n\n`f(x) = g(Wx + b)`\n\n`W`\n\n(the weight matrix) and `b`\n\n(a bias vector) are the learned parameters, usually trained via gradient descent. `g`\n\nis the activation function, and it can be chosen differently for each layer.", "url": "https://wpnews.pro/news/vanilla-neural-networks", "canonical_source": "https://julin.ai/2026/08/28/vanilla-neural-networks/", "published_at": "2026-08-27 12:00:00+00:00", "updated_at": "2026-08-27 20:18:46.082793+00:00", "lang": "en", "topics": ["artificial-intelligence", "machine-learning", "neural-networks"], "entities": [], "alternates": {"html": "https://wpnews.pro/news/vanilla-neural-networks", "markdown": "https://wpnews.pro/news/vanilla-neural-networks.md", "text": "https://wpnews.pro/news/vanilla-neural-networks.txt", "jsonld": "https://wpnews.pro/news/vanilla-neural-networks.jsonld"}}