4,119 research outputs found

    Complex-Valued Autoencoders

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    Autoencoders are unsupervised machine learning circuits whose learning goal is to minimize a distortion measure between inputs and outputs. Linear autoencoders can be defined over any field and only real-valued linear autoencoder have been studied so far. Here we study complex-valued linear autoencoders where the components of the training vectors and adjustable matrices are defined over the complex field with the L2L_2 norm. We provide simpler and more general proofs that unify the real-valued and complex-valued cases, showing that in both cases the landscape of the error function is invariant under certain groups of transformations. The landscape has no local minima, a family of global minima associated with Principal Component Analysis, and many families of saddle points associated with orthogonal projections onto sub-space spanned by sub-optimal subsets of eigenvectors of the covariance matrix. The theory yields several iterative, convergent, learning algorithms, a clear understanding of the generalization properties of the trained autoencoders, and can equally be applied to the hetero-associative case when external targets are provided. Partial results on deep architecture as well as the differential geometry of autoencoders are also presented. The general framework described here is useful to classify autoencoders and identify general common properties that ought to be investigated for each class, illuminating some of the connections between information theory, unsupervised learning, clustering, Hebbian learning, and autoencoders.Comment: Final version, journal ref adde

    Complex-Valued Autoencoders for Object Discovery

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    Object-centric representations form the basis of human perception and enable us to reason about the world and to systematically generalize to new settings. Currently, most machine learning work on unsupervised object discovery focuses on slot-based approaches, which explicitly separate the latent representations of individual objects. While the result is easily interpretable, it usually requires the design of involved architectures. In contrast to this, we propose a distributed approach to object-centric representations: the Complex AutoEncoder. Following a coding scheme theorized to underlie object representations in biological neurons, its complex-valued activations represent two messages: their magnitudes express the presence of a feature, while the relative phase differences between neurons express which features should be bound together to create joint object representations. We show that this simple and efficient approach achieves better reconstruction performance than an equivalent real-valued autoencoder on simple multi-object datasets. Additionally, we show that it achieves competitive unsupervised object discovery performance to a SlotAttention model on two datasets, and manages to disentangle objects in a third dataset where SlotAttention fails - all while being 7-70 times faster to train

    Contrastive Training of Complex-Valued Autoencoders for Object Discovery

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    Current state-of-the-art object-centric models use slots and attention-based routing for binding. However, this class of models has several conceptual limitations: the number of slots is hardwired; all slots have equal capacity; training has high computational cost; there are no object-level relational factors within slots. Synchrony-based models in principle can address these limitations by using complex-valued activations which store binding information in their phase components. However, working examples of such synchrony-based models have been developed only very recently, and are still limited to toy grayscale datasets and simultaneous storage of less than three objects in practice. Here we introduce architectural modifications and a novel contrastive learning method that greatly improve the state-of-the-art synchrony-based model. For the first time, we obtain a class of synchrony-based models capable of discovering objects in an unsupervised manner in multi-object color datasets and simultaneously representing more than three objectsComment: 26 pages, 14 figure

    Gated networks: an inventory

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    Gated networks are networks that contain gating connections, in which the outputs of at least two neurons are multiplied. Initially, gated networks were used to learn relationships between two input sources, such as pixels from two images. More recently, they have been applied to learning activity recognition or multi-modal representations. The aims of this paper are threefold: 1) to explain the basic computations in gated networks to the non-expert, while adopting a standpoint that insists on their symmetric nature. 2) to serve as a quick reference guide to the recent literature, by providing an inventory of applications of these networks, as well as recent extensions to the basic architecture. 3) to suggest future research directions and applications.Comment: Unpublished manuscript, 17 page
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