Definition
A latent space is a space of variables that are not directly observed but are used to represent structure behind the data. An encoder may map an image, sentence, or other example to a point in this space, and a decoder or predictor may use that point to reconstruct data or perform another task.
The geometry comes from the model and objective. Nearby points may produce related outputs, but that property must be tested rather than assumed. Individual coordinates rarely correspond cleanly to human concepts, and a direction that changes one attribute in one region may behave differently elsewhere. Rotation or rescaling can also change the coordinates without changing what the model represents.
Variational autoencoders give the term a probabilistic meaning: the encoder approximates a distribution over latent variables, and training regularizes those variables toward a prior while preserving enough information for reconstruction. Other systems use "latent space" more loosely for an internal feature space without an explicit probability model.
Distinguish it from nearby terms
An embedding is a particular vector representation or the mapping that produces it. Latent space names the space and its modeled variables. Hidden state is a value inside a network computation; it may live in a latent space, but the terms are not interchangeable in every architecture.
Check your understanding
Interpolating between two latent vectors produces smooth-looking images, but one attribute changes abruptly halfway through. What does that reveal about the local geometry, and why does smooth interpolation elsewhere not prove a globally meaningful axis?