What is it?
The space of all possible states (for a pendulum: angle and angular velocity). Each initial state traces a trajectory; drawing them all — the phase portrait — shows the whole behaviour at a glance.
Formulas
- pendulum in phase space
Where it shows up in computing
Symplectic integrators preserve phase-space volume (Liouville), which keeps long simulations physically plausible.
Where is it used?
Computing topics reachable from here, through the chain of ideas that leads to them:
ℒ AI and machine learning
- Attractors→Neural networks★★★★★
- Attractors→Neural networks→Backpropagation★★★★★
- Attractors→Neural networks→Loss landscape★★★★★
- Attractors→Neural networks→Backpropagation→Deep learning★★★★★
- Attractors→Neural networks→Loss landscape→Second-order (Hessian-based) optimization★★★★★
- Attractors→Neural networks→Backpropagation→Deep learning→Convolutional networks (CNNs)★★★★★
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What depends on it
This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.