Item:Q156 - Revision history

Rongzhou: /* wbsetclaim-update:2||1 */ Property:P4: $\begin{aligned}\text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\\text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\\text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\\text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\\text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\\text{The arti...

2026-08-17T19:10:25Z

‎Changed claim: LaTeX source (P4): $\begin{aligned}\text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\\text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\\text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\\text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\\text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\\text{The arti...

← Older revision		Revision as of 19:10, 17 August 2026
Property / LaTeX source		Property / LaTeX source
	\begin{aligned}\text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\\text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\\text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\\text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\\text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\\text{The artificial neuron output is } y = \sigma(z) \in \mathbb{R} \\\text{Typical activations: } \sigma(z) = \mathbf{1}_{z \ge 0} \text{ (step)}, \quad \sigma(z) = (1+e^{-z})^{-1} \text{ (sigmoid)}, \quad \sigma(z) = \max(0,z) \text{ (ReLU)}\end{aligned}		$\begin{aligned}\text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\\text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\\text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\\text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\\text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\\text{The artificial neuron output is } y = \sigma(z) \in \mathbb{R} \\\text{Typical activations: } \sigma(z) = \mathbf{1}_{z \ge 0} \text{ (step)}, \quad \sigma(z) = (1+e^{-z})^{-1} \text{ (sigmoid)}, \quad \sigma(z) = \max(0,z) \text{ (ReLU)}\end{aligned}$

Rongzhou: /* wbsetclaim-update:2||1 */ Property:P4: \begin{aligned}\text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\\text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\\text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\\text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\\text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\\text{The artif...

2026-08-17T19:09:48Z

‎Changed claim: LaTeX source (P4): \begin{aligned}\text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\\text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\\text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\\text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\\text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\\text{The artif...

← Older revision		Revision as of 19:09, 17 August 2026
Property / LaTeX source		Property / LaTeX source
	$ \begin{aligned} \text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\ \text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\ \text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\ \text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\ \text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\ \text{The artificial neuron output is } y = \sigma(z) \in \mathbb{R} \\ \text{Typical activations: } \sigma(z) = \mathbf{1}_{z \ge 0} \text{ (step)}, \quad \sigma(z) = (1+e^{-z})^{-1} \text{ (sigmoid)}, \quad \sigma(z) = \max(0,z) \text{ (ReLU)} \end{aligned} $		\begin{aligned}\text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\\text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\\text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\\text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\\text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\\text{The artificial neuron output is } y = \sigma(z) \in \mathbb{R} \\\text{Typical activations: } \sigma(z) = \mathbf{1}_{z \ge 0} \text{ (step)}, \quad \sigma(z) = (1+e^{-z})^{-1} \text{ (sigmoid)}, \quad \sigma(z) = \max(0,z) \text{ (ReLU)}\end{aligned}

Rongzhou: Added content item: Formula: Artificial Neuron

2026-08-17T19:08:41Z

Added content item: Formula: Artificial Neuron

← Older revision	Revision as of 19:08, 17 August 2026
	Property / instance of
		mathematical expression
	Property / instance of: mathematical expression / rank
		Normal rank
	Property / LaTeX source
		$ \begin{aligned} \text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\ \text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\ \text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\ \text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\ \text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\ \text{The artificial neuron output is } y = \sigma(z) \in \mathbb{R} \\ \text{Typical activations: } \sigma(z) = \mathbf{1}_{z \ge 0} \text{ (step)}, \quad \sigma(z) = (1+e^{-z})^{-1} \text{ (sigmoid)}, \quad \sigma(z) = \max(0,z) \text{ (ReLU)} \end{aligned} $
	Property / LaTeX source: $ \begin{aligned} \text{Let } \mathbf{x} = (x_1,\dots,x_n)^\top \in \mathbb{R}^n \text{ be the input vector} \\ \text{Let } \mathbf{w} = (w_1,\dots,w_n)^\top \in \mathbb{R}^n \text{ be the weight vector} \\ \text{Let } b \in \mathbb{R} \text{ be the scalar bias} \\ \text{The affine pre‑activation is } z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^n w_i x_i + b \\ \text{Choose a non‑linear activation } \sigma: \mathbb{R} \to \mathbb{R} \\ \text{The artificial neuron output is } y = \sigma(z) \in \mathbb{R} \\ \text{Typical activations: } \sigma(z) = \mathbf{1}_{z \ge 0} \text{ (step)}, \quad \sigma(z) = (1+e^{-z})^{-1} \text{ (sigmoid)}, \quad \sigma(z) = \max(0,z) \text{ (ReLU)} \end{aligned} $ / rank
		Normal rank
	Property / source
		Rong Martin-Siebler ZHOU
	Property / source: Rong Martin-Siebler ZHOU / rank
		Normal rank
	Property / describes
		programming language
	Property / describes: programming language / rank
		Normal rank

Rongzhou: Added content item: Formula: Artificial Neuron

2026-08-17T19:08:41Z

Added content item: Formula: Artificial Neuron

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