We present a variation of the Autoencoder (AE) that explicitly maximizes the mutual information between the input data and the hidden representation. The proposed model, the InfoMax Autoencoder (IMAE), by construction is able to learn a robust representation and good prototypes of the data. IMAE is compared both theoretically and then computationally with the state of the art models: the Denoising and Contractive Autoencoders in the one-hidden layer setting and the Variational Autoencoder in the multi-layer case. Computational experiments are performed with the MNIST and Fashion-MNIST datasets and demonstrate particularly the strong clusterization performance of IMAE.
The first neural network defined to explicitly maximize the information between the input and the hidden layer was proposed by Linsker @cite_5 , giving to the objective function the name, . This model is a linear model that actually maximizes only the entropy of the representation, performing Principal Component Analysis (PCA) in the case of Gaussian distributed data. The same objective function was applied by Bell and Sejnowsky @cite_9 , showing that a 1-layer neural network with sigmoid activation performs Independent Component Analysis (ICA).
@cite_5 @cite_9
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The emergence of a feature-analyzing function from the development rules of simple, multilayered networks is explored. It is shown that even a single developing cell of a layered network exhibits a remarkable set of optimization properties that are closely related to issues in statistics, theoretical physics, adaptive signal processing, the formation of knowledge representation in artificial intelligence, and information theory. The network studied is based on the visual system. These results are used to infer an information-theoretic principle that can be applied to the network as a whole, rather than a single cell. The organizing principle proposed is that the network connections develop in such a way as to maximize the amount of information that is preserved when signals are transformed at each processing stage, subject to certain constraints. The operation of this principle is illustrated for some simple cases. > We derive a new self-organizing learning algorithm that maximizes the information transferred in a network of nonlinear units. The algorithm does not assume any knowledge of the input distributions, and is defined here for the zero-noise limit. Under these conditions, information maximization has extra properties not found in the linear case (Linsker 1989). The nonlinearities in the transfer function are able to pick up higher-order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation. This enables the network to separate statistically independent components in the inputs: a higher-order generalization of principal components analysis. We apply the network to the source separation (or cocktail party) problem, successfully separating unknown mixtures of up to 10 speakers. We also show that a variant on the network architecture is able to perform blind deconvolution (cancellation of unknown echoes and reverberation in a speech signal). Finally, we derive dependencies of information transfer on time delays. We suggest that information maximization provides a unifying framework for problems in "blind" signal processing.