Unsupervised learning

Unsupervised learning is a framework in machine learning where, in contrast to supervised learning, algorithms learn patterns exclusively from unlabeled data. Other frameworks in the spectrum of supervisions include weak- or semi-supervision, where a small portion of the data is tagged, and self-supervision. Some researchers consider self-supervised learning a form of unsupervised learning.
Conceptually, unsupervised learning divides into the aspects of data, training, algorithm, and downstream applications. Typically, the dataset is harvested cheaply "in the wild", such as massive text corpus obtained by web crawling, with only minor filtering. This compares favorably to supervised learning, where the dataset is typically constructed manually, which is much more expensive.
There are algorithms designed specifically for unsupervised learning, such as clustering algorithms like k-means, dimensionality reduction techniques like principal component analysis, Boltzmann machine learning, and autoencoders. After the rise of deep learning, most large-scale unsupervised learning has been done by training general-purpose neural network architectures by gradient descent, adapted to performing unsupervised learning by designing an appropriate training procedure.
Sometimes a trained model can be used as-is, but more often they are modified for downstream applications. For example, the generative pretraining method trains a model to generate a textual dataset, before finetuning it for other applications, such as text classification. As another example, autoencoders are trained to produce good features, which can then be used as a module for other models, such as in a latent diffusion model.

Tasks

Tasks are often categorized as discriminative or generative. Often but not always, discriminative tasks use supervised methods and generative tasks use unsupervised ; however, the separation is very hazy. For example, object recognition favors supervised learning but unsupervised learning can also cluster objects into groups. Furthermore, as progress marches onward, some tasks employ both methods, and some tasks swing from one to another. For example, image recognition started off as heavily supervised, but became hybrid by employing unsupervised pre-training, and then moved towards supervision again with the advent of dropout, ReLU, and adaptive learning rates.
A typical generative task is as follows. At each step, a datapoint is sampled from the dataset, and part of the data is removed, and the model must infer the removed part. This is particularly clear for the denoising autoencoders and BERT.

Neural network architectures

Training

During the learning phase, an unsupervised network tries to mimic the data it is given and uses the error in its mimicked output to correct itself. Sometimes the error is expressed as a low probability that the erroneous output occurs, or it might be expressed as an unstable high energy state in the network.
In contrast to supervised methods' dominant use of backpropagation, unsupervised learning also employs other methods including: Hopfield learning rule, Boltzmann learning rule, Contrastive Divergence, Wake Sleep, Variational Inference, Maximum Likelihood, Maximum A Posteriori, Gibbs Sampling, and backpropagating reconstruction errors or hidden state reparameterizations. See the table below for more details.

Energy

An energy function is a macroscopic measure of a network's activation state. In Boltzmann machines, it plays the role of the Cost function. This analogy with physics is inspired by Ludwig Boltzmann's analysis of a gas' macroscopic energy from the microscopic probabilities of particle motion, where k is the Boltzmann constant and T is temperature. In the RBM network the relation is, where and vary over every possible activation pattern and. To be more precise,, where is an activation pattern of all neurons. Hence, some early neural networks bear the name Boltzmann Machine. Paul Smolensky calls the Harmony. A network seeks low energy which is high Harmony.

Networks

This table shows connection diagrams of various unsupervised networks, the details of which will be given in the section Comparison of Networks. Circles are neurons and edges between them are connection weights. As network design changes, features are added on to enable new capabilities or removed to make learning faster. For instance, neurons change between deterministic and stochastic to allow robust output, weights are removed within a layer to hasten learning, or connections are allowed to become asymmetric.

Hopfield	Boltzmann	RBM	Stacked Boltzmann

Helmholtz	Autoencoder	VAE

Of the networks bearing people's names, only Hopfield worked directly with neural networks. Boltzmann and Helmholtz came before artificial neural networks, but their work in physics and physiology inspired the analytical methods that were used.

History

1974	Ising magnetic model proposed by for cognition
1980	Kunihiko Fukushima introduces the neocognitron, which is later called a convolutional neural network. It is mostly used in SL, but deserves a mention here.
1982	Ising variant Hopfield net described as CAMs and classifiers by John Hopfield.
1983	Ising variant Boltzmann machine with probabilistic neurons described by Hinton & Sejnowski following Sherington & Kirkpatrick's 1975 work.
1986	Paul Smolensky publishes Harmony Theory, which is an RBM with practically the same Boltzmann energy function. Smolensky did not give a practical training scheme. Hinton did in mid-2000s.
1995	Hochreiter and Schmidhuber introduce the LSTM neuron for languages.
1995	Dayan & Hinton introduces Helmholtz machine
2013	Kingma, Rezende, & co. introduced Variational Autoencoders as Bayesian graphical probability network, with neural nets as components.

Specific Networks

Here, we highlight some characteristics of select networks. The details of each are given in the comparison table below.

Comparison of networks

	Hopfield	Boltzmann	RBM	Stacked RBM	Helmholtz	Autoencoder	VAE
Usage & notables	CAM, traveling salesman problem	CAM. The freedom of connections makes this network difficult to analyze.	pattern recognition. used in MNIST digits and speech.	recognition & imagination. trained with unsupervised pre-training and/or supervised fine tuning.	imagination, mimicry	language: creative writing, translation. vision: enhancing blurry images	generate realistic data
Neuron	deterministic binary state. Activation =	stochastic binary Hopfield neuron	← same.	← same	← same	language: LSTM. vision: local receptive fields. usually real valued relu activation.	middle layer neurons encode means & variances for Gaussians. In run mode, the output of the middle layer are sampled values from the Gaussians.
Connections	1-layer with symmetric weights. No self-connections.	2-layers. 1-hidden & 1-visible. symmetric weights.	← same. no lateral connections within a layer.	top layer is undirected, symmetric. other layers are 2-way, asymmetric.	3-layers: asymmetric weights. 2 networks combined into 1.	3-layers. The input is considered a layer even though it has no inbound weights. recurrent layers for NLP. feedforward convolutions for vision. input & output have the same neuron counts.	3-layers: input, encoder, distribution sampler decoder. the sampler is not considered a layer
Inference & energy	Energy is given by Gibbs probability measure :	← same	← same		minimize KL divergence	inference is only feed-forward. previous UL networks ran forwards AND backwards	minimize error = reconstruction error - KLD
Training	Δw_ij = s_i*s_j, for +1/-1 neuron	Δw_ij = e*. This is derived from minimizing KLD. e = learning rate, p' = predicted and p = actual distribution.	Δw_ij = e*. This is a form of contrastive divergence w/ Gibbs Sampling. "<>" are expectations.	← similar. train 1-layer at a time. approximate equilibrium state with a 3-segment pass. no back propagation.	wake-sleep 2 phase training	back propagate the reconstruction error	reparameterize hidden state for backprop
Strength	resembles physical systems so it inherits their equations	← same. hidden neurons act as internal representatation of the external world	faster more practical training scheme than Boltzmann machines	trains quickly. gives hierarchical layer of features	mildly anatomical. analyzable w/ information theory & statistical mechanics
Weakness		hard to train due to lateral connections	equilibrium requires too many iterations	integer & real-valued neurons are more complicated.

Hebbian Learning, ART, SOM

The classical example of unsupervised learning in the study of neural networks is Donald Hebb's principle, that is, neurons that fire together wire together. In Hebbian learning, the connection is reinforced irrespective of an error, but is exclusively a function of the coincidence between action potentials between the two neurons. A similar version that modifies synaptic weights takes into account the time between the action potentials. Hebbian Learning has been hypothesized to underlie a range of cognitive functions, such as pattern recognition and experiential learning.
Among neural network models, the self-organizing map and adaptive resonance theory are commonly used in unsupervised learning algorithms. The SOM is a topographic organization in which nearby locations in the map represent inputs with similar properties. The ART model allows the number of clusters to vary with problem size and lets the user control the degree of similarity between members of the same clusters by means of a user-defined constant called the vigilance parameter. ART networks are used for many pattern recognition tasks, such as automatic target recognition and seismic signal processing.