We describe a probabilistic approach to the task of placing objects, described by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the high-dimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribution as well as possible when the same operation is performed on the low-dimensional "images" of the objects. A natural cost function is a sum of Kullback-Leibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the low-dimensional images.

The performance of symbolic inference tasks has long been a challenge to connectionists. In this paper, we present an extended survey of this area. Existing connectionist inference systems are reviewed, with particular reference to how they perform variable binding and rulebased reasoning and whether they involve distributed or localist representations. The benefits and disadvantages of different representations and systems are outlined, and conclusions drawn regarding the capabilities of connectionist inference systems when compared with symbolic inference systems or when used for cognitive modelling.

The representation of hierarchically structured knowledge in systems using distributed patterns of activity is an abiding concern for the connectionist solution of cognitively rich problems. Here, we use statistical unsupervised learning to consider semantic aspects of structured knowledge representation. We meld unsupervised learning notions formulated for multilinear models with tensor product ideas for representing rich information. We apply the model to images of faces.

Many Knowledge Bases (KBs) are now readily available and encompass colossal quantities of information thanks to either a long-term funding effort (e.g. WordNet, OpenCyc) or a collaborative process (e.g. Freebase, DBpedia). However, each of them is based on a different rigorous symbolic framework which makes it hard to use their data in other systems. It is unfortunate because such rich structured knowledge might lead to a huge leap forward in many other areas of AI like natural language processing (word-sense disambiguation, natural language understanding,...), vision (scene classification, image semantic annotation,...) or collaborative filtering. In this paper, we present a learning process based on an innovative neural network architecture designed to embed any of these symbolic representations into a more flexible continuous vector space in which the original knowledge is kept and enhanced. These learnt embeddings would allow data from any KB to be easily used in recent machine learning methods for prediction and information retrieval. We illustrate our method on WordNet and Freebase and also present a way to adapt it to knowledge extraction from raw text.

We describe a way of learning matrix representations of objects and relationships. The goal of learning is to allow multiplication of matrices to represent symbolic relationships between objects and symbolic relationships between relationships, which is the main novelty of the method. We demonstrate that this leads to excellent generalization in two different domains: modular arithmetic and family relationships. We show that the same system can learn first-order propositions such as (2,5) ∈ +3 or (Christopher, Penelope) ∈ has wife, and higher-order propositions such as (3,+3) ∈ plus and (+3, −3) ∈ inverse or (has husband, has wife) ∈ higher oppsex. We further demonstrate that the system understands how higher-order propositions are related to first-order ones by showing that it can correctly answer questions about first-order propositions involving the relations +3 or has wife even though it has not been trained on any first-order examples involving these relations. 1