Artificial neuron
Mathematical model of a biological neuron, core of neural networks.
An artificial neuron is a mathematical function that serves as the basic building block of an artificial neural network, modeled after a biological neuron. Its inputs correspond to excitatory or inhibitory postsynaptic potentials at dendrites, its weights correspond to synaptic strengths, and its output corresponds to an action potential traveling along an axon.
Typically, each input is multiplied by its own weight, and these weighted values are summed. A bias term—loosely related to a neuron’s threshold potential—is often added to this sum. The result then passes through a nonlinear activation function. Depending on the task, this function might be sigmoid-shaped (common for binary classification), but it can also be another nonlinear function, a piecewise linear function, or a step function. Activation functions are often monotonically increasing, continuous, differentiable, and bounded. However, non-monotonic, unbounded, and oscillating functions with multiple zeros that outperform sigmoidal and ReLU-like functions on many tasks have also been explored recently. The threshold function inspired threshold logic, which is used to build logic circuits that resemble brain processing; new devices like memristors have been extensively used for such logic.
An artificial neuron’s activation function should not be confused with a linear system’s transfer function. Depending on its structure, an artificial neuron may be called a semi-linear unit, Nv neuron, binary neuron, linear threshold function, or McCulloch–Pitts (MCP) neuron. Simple models like the McCulloch–Pitts neuron are sometimes described as "caricature models," because they reflect one or more neurophysiological observations without aiming for realism. Artificial neurons can also refer to artificial cells in neuromorphic engineering that resemble natural physical neurons.
**Basic structure**
For a given artificial neuron \(k\), there are \(m+1\) inputs with signals \(x_0\) through \(x_m\) and weights \(w_{k0}\) through \(w_{km}\). Usually, input \(x_0\) is set to +1, making it a bias input with \(w_{k0} = b_k\). This leaves \(m\) actual inputs: \(x_1\) to \(x_m\). The output of neuron \(k\) is:
\[ y_k = \varphi\left(\sum_{j=0}^{m} w_{kj} x_j\right) \]
where \(\varphi\) is the activation function. This output is analogous to the axon of a biological neuron and propagates to the input of the next lay
- field
- Artificial neural networks, neuromorphic engineering
- known_for
- Elementary unit of artificial neural networks; McCulloch–Pitts model
- type
- Mathematical function / computational model
Lore & Background
The artificial neuron was inspired by biological neural circuitry. Its inputs are analogous to excitatory and inhibitory postsynaptic potentials at neural dendrites, and its weights are analogous to synaptic weights. The output is analogous to a neuron's action potential transmitted along its axon. Usually, each input is separately weighted, and the sum is often added to a bias term before being passed through a nonlinear activation function. Depending on the task, activation functions may have a sigmoid shape, piecewise linear functions, step functions, or other forms. Non-monotonic, unbounded, and oscillating activation functions that outperform sigmoidal and ReLU-like functions on many tasks have also been explored.
The McCulloch–Pitts (MCP) neuron is a restricted artificial neuron operating in discrete time-steps. It has zero or more inputs, each excitatory or inhibitory, and one output. Its output fires if the number of firing excitatory inputs meets or exceeds a threshold and no inhibitory inputs are firing. MCP neurons can represent linearly separable boolean functions like AND, OR, and NOR, but not XOR. Any finite state machine can be simulated by an MCP neural network, and with an infinite tape, they can simulate any Turing machine.
Reader's Guide
Artificial neurons are fundamental to artificial neural networks, which underpin modern machine learning and artificial intelligence. Their design, inspired by biological neurons, allows them to process weighted inputs through an activation function to produce an output. The McCulloch–Pitts model, though a simplified 'caricature,' demonstrated that networks of such neurons could compute logical functions and simulate finite state machines and Turing machines, establishing a theoretical foundation for neural computation. The flexibility of activation functions—from sigmoids for binary classification to more exotic oscillating functions—enables diverse applications. Despite a significant performance gap between biological and artificial neural networks, single biological neurons in the human brain with oscillating activation functions capable of learning XOR have been discovered, highlighting ongoing biological inspiration. Artificial neurons also appear in neuromorphic engineering as artificial cells similar to natural physical neurons.
Did You Know?
- An artificial neuron's inputs are analogous to excitatory and inhibitory postsynaptic potentials at neural dendrites.
- The McCulloch–Pitts neuron can represent linearly separable boolean functions such as AND, OR, and NOR, but not XOR.
- Any finite state machine can be simulated by a McCulloch–Pitts neural network.
- Single biological neurons in the human brain with oscillating activation functions capable of learning XOR have been discovered.
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