# Computational Models of the Neuron  URL:: https://brilliant.org/courses/artificial-neural-networks/learning-and-the-brain-3/computational-models-of-the-neuron/1/ Author:: brilliant.org ## Highlights > w⋅x+b. ([View Highlight](https://read.readwise.io/read/01gj3qrtdf1y7hq2bjq277fvt8)) - Note: A neuron can be defined by the inputs of OTHER neurons, how strong its connections to those neurons are, and a "bias" that determines when a neuron will fire. > A biological interpretation is that the inputs defining x⃗\vec{x}x are the outputs of other neurons, the weights defining w⃗\vec{w}w are the strengths of the connections to those neurons, and the bias bbb impacts the threshold the computing neuron must surpass in order to fire. ([View Highlight](https://read.readwise.io/read/01gj3qpn7jsn4467e7s5nqdtr3)) > A biological interpretation is that the inputs defining x⃗\vec{x}x are the outputs of other neurons, the weights defining w⃗\vec{w}w are the strengths of the connections to those neurons, and the bias bbb impacts the threshold the computing neuron must surpass in order to fire. ([View Highlight](https://read.readwise.io/read/01gj3qtxf95zkj17qqbe87k687)) > The hypersurface w⃗⋅x⃗+b=0\vec{w} \cdot \vec{x} + b = 0w⋅x+b=0 is called the **decision boundary**, since it divides the input vector space into two parts based on whether the input would cause the neuron to fire. This model is known as a linear classifier because this boundary is based on a linear combination of the inputs. ([View Highlight](https://read.readwise.io/read/01gj3qyjvfyd18y2dg3w6daz74)) > Functions like the ones shown avoid counterintuitive jumps and can model continuous values (e.g. a probability): >  ([View Highlight](https://read.readwise.io/read/01gj3r3x15dqpwz9ceky9nys1n)) > The power of ANNs is illustrated by the **universal approximation theorem**, which states that ANNs using activation functions like these can model **any** continuous function, given some general requirements about the size and layout of the ANN. ([View Highlight](https://read.readwise.io/read/01gj3r3n99qhxt2rxcbqb6d68r)) > No matter how complicated a situation is, a sufficiently large ANN with the appropriate parameters can model it ([View Highlight](https://read.readwise.io/read/01gj3r51t25zkcb7g088jxpbbc)) - Note: This would seem to be a huge advantage of [[Artificial intelligence]]s over human ones. --- Title: Computational Models of the Neuron Author: brilliant.org Tags: readwise, articles date: 2024-01-30 --- # Computational Models of the Neuron  URL:: https://brilliant.org/courses/artificial-neural-networks/learning-and-the-brain-3/computational-models-of-the-neuron/1/ Author:: brilliant.org ## AI-Generated Summary A neuron has many inputs but only one output, so it must “integrate” its inputs into one output (a single number). Recall that the inputs to a neuron are generally outputs from other neurons. ## Highlights > w⋅x+b. ([View Highlight](https://read.readwise.io/read/01gj3qrtdf1y7hq2bjq277fvt8)) Note: A neuron can be defined by the inputs of OTHER neurons, how strong its connections to those neurons are, and a "bias" that determines when a neuron will fire. > A biological interpretation is that the inputs defining x⃗\vec{x}x are the outputs of other neurons, the weights defining w⃗\vec{w}w are the strengths of the connections to those neurons, and the bias bbb impacts the threshold the computing neuron must surpass in order to fire. ([View Highlight](https://read.readwise.io/read/01gj3qpn7jsn4467e7s5nqdtr3)) > A biological interpretation is that the inputs defining x⃗\vec{x}x are the outputs of other neurons, the weights defining w⃗\vec{w}w are the strengths of the connections to those neurons, and the bias bbb impacts the threshold the computing neuron must surpass in order to fire. ([View Highlight](https://read.readwise.io/read/01gj3qtxf95zkj17qqbe87k687)) > The hypersurface w⃗⋅x⃗+b=0\vec{w} \cdot \vec{x} + b = 0w⋅x+b=0 is called the **decision boundary**, since it divides the input vector space into two parts based on whether the input would cause the neuron to fire. This model is known as a linear classifier because this boundary is based on a linear combination of the inputs. ([View Highlight](https://read.readwise.io/read/01gj3qyjvfyd18y2dg3w6daz74)) > Functions like the ones shown avoid counterintuitive jumps and can model continuous values (e.g. a probability): >  ([View Highlight](https://read.readwise.io/read/01gj3r3x15dqpwz9ceky9nys1n)) > The power of ANNs is illustrated by the **universal approximation theorem**, which states that ANNs using activation functions like these can model **any** continuous function, given some general requirements about the size and layout of the ANN. ([View Highlight](https://read.readwise.io/read/01gj3r3n99qhxt2rxcbqb6d68r)) > No matter how complicated a situation is, a sufficiently large ANN with the appropriate parameters can model it ([View Highlight](https://read.readwise.io/read/01gj3r51t25zkcb7g088jxpbbc)) Note: This would seem to be a huge advantage of [[Artificial intelligence]]s over human ones.