11.1 Part I: Biological and artificial neural networks

Source: Ideas from Computational Physics (Landau, Páez, Bordeianu), Ch. 11 opener + §11.1. Rewritten in original wording. Continues 10.7b. Next: 11.1b.

Automated systems should provide explanations that are technically valid, meaningful and useful… calibrated to the level of risk based on the context. — White House AI Blueprint (2022)

Why this chapter

Brains (≈ $10^{11}$ neurons) solve pattern problems that hard-coded programs struggle with. AI aims to capture that tacit skill; machine learning (ML) trains neural nets from labeled examples; deep learning stacks many layers; generative setups pair a generator with an evaluator. Physics demos here stay deliberately small so you can see the innards.

Problem (chapter arc): model a neuron and a network of neurons, and check whether the net can learn.

Biological neuron

Dendrites collect excitatory / inhibitory pulses. The cell body integrates them; if a threshold is crossed it fires an action potential along the axon (roughly $0$–$30\,\mathrm{mV}$ negative, $1$–$6\,\mathrm{ms}$ wide) — fire or not, then rest. Cortex stacks layers hierarchically (senses → outer layers → deeper maps → response such as face recognition). Biological nets are highly parallel and surprisingly robust: no single clique is usually indispensable.

Artificial nets (McCulloch–Pitts → Perceptron)

McCulloch & Pitts (1943) gave a mathematical neuron and proved nets can be trained. Rosenblatt’s Perceptron (1957) showed learning on an IBM 704 (e.g. left- vs right-marked cards) by tweaking connections after each trial — sensational then, underpowered by 1950s machines.

An artificial net routes data through nodes (neurons). Each node takes several inputs, computes with changeable parameters, and — if criteria are met — sends an output along an edge. Learning = iteratively updating those parameters from prediction error.

Takeaway

Idea	Role
Biological neuron	Integrate → threshold → spike
Artificial node	Weighted sum + activation + bias
Learning	Change weights/biases from error
Deep net	Many hidden layers

Next lessons build a shallow net by hand (forward pass, loss, backprop) before any library black box.

Quiz

NN intro

1 / 4

A biological action potential is best described as…

Pick an answer to see if you are right.

Next: 11.1b NN intro labs.