Difference between revisions of "McCulloch-Pitts neuron"

Latest revision as of 13:33, 22 April 2016

Diagram of a McCulloch-Pitts neuron
$\xymatrix{ I_1 \ar[drr]^{w_1} & & \\ \vdots \ar@{.>}[rr] & & ++[o][F-]{\sum} \ar@{<.}[ll]!<0.5em,1.75em> \ar@{<.}[ll]!<0.5em,-1.75em> \ar@{<-}[d]!<0em,1em>_(.9){\theta} \ar[r]^-{\text{net}} & +[o][F-]{\mathcal{A}(\cdot)} \ar[r] & \text{Output}\\ I_n \ar[urr]_{w_n} & & & }$

The McCulloch-Pitts neuron has^[1]:

Inputs: (I1,…,In)∈Rn
- Usually each $I_i$ is confined to $[0,1]\subset\mathbb{R}$ or $[-1,1]\subset\mathbb{R}$
A set of weights, one for each input: $(w_1,\ldots,w_n)\in\mathbb{R}^n$
A bias: $\theta\in\mathbb{R}$
An activation function, A:R→R
- It is more common to see $\mathcal{A}:\mathbb{R}\rightarrow[-1,1]\subset\mathbb{R}$ or sometimes $\mathcal{A}:\mathbb{R}\rightarrow[0,1]\subset\mathbb{R}$ than the entire of $\mathbb{R}$

The output of the neuron is given by:

$\text{Output}:=\mathcal{A}\left(\sum_{i=1}^n(I_iw_i)+\theta\right)$

Jump up ↑ Neural Networks and Statistical Learning - Ke-Lin Du and M. N. S. Swamy

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 {{Neural networks navbox}}
-{{CS Definition|Neural Networks}}{{Statistics Definition|Neural Networks}}
+{{CS Definition|Neural Network}}{{Statistics Definition|Neural Network}}