# Representation Learning: A Review and New Perspectives

### Abstract

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

### Notes

Data representation is key to machine learning, and there are entire fields of computer science dedicated to detecting features from data (e.g. computer vision). Recent developments using convolutional network models [@zeiler2014] have shown that convnets can automatically learn features from the data. This automated feature detection is extremely powerful, and provides a lot of value. To allow computers to better understand the world, it is important to figure out how computers can learn optimal representations of the world.

The authors discuss desirable features for a given representation. These include smoothness (\(x \approx y\) should imply that \(f(x) \approx f(y)\)), manifolds (i.e. detecting the relevant dimensions in high-dimensionality data), sparsity, simplicity, and learning factors that help explain aspects of variation, not one off factors. The authors discuss the curse of dimensionality, namely that complication grows exponentially with the number of dimensions, and so for a high-dimensionality object, it is exponentially more difficult to learn a smooth representation when compared to a lower-dimensionality object.

The paper focuses on how expressive certain representations are, comparing models like RBMs, auto-encoders, and multi-layer neural networks to more traditional algorithms like one-hot representations, Gaussian mixtures, and nearest neighbour algorithms, discussing how the former can represent up to \(O(2^k)\) input regions using only \(O(N)\) inputs, while the latter can only represent \(O(N)\) regions using \(O(N)\) inputs. This is both good and bad, as you can have representations that are too precise with some of the more advanced representations.

Deep learning is discussed, focusing on how deep networks evolve their own internal representation of the data.