Representation Learning and Similarity of Legal Judgements using Citation Networks

India and many other countries like UK, Australia, Canada follow the ‘common law system’ which gives substantial importance to prior related cases in determining the outcome of the current case. Better similarity methods can help in finding earlier similar cases, which can help lawyers searching for precedents. Prior approaches in computing similarity of legal judgements use a basic representation which is either abag-of-words or dense embedding which is learned by only using the words present in the document. They, however, either neglect or do not emphasize the vital ‘legal’ information in the judgements, e.g. citations to prior cases, act and article numbers or names etc. In this paper, we propose a novel approach to learn the embeddings of legal documents using the citationnetwork of documents. Experimental results demonstrate that the learned embedding is at par with the state-of-the-art methods for document similarity on a standard legal dataset.

A criterion of the existence of an embedding of a monothetic monoid into a topological group

Using properties of unitary Cauchy filters on monothetic monoids, we prove a criterion of the existence of an embedding of such a monoid into a topological group. The proof of the sufficiency is constructive: under the corresponding assumptions, we are building a dense embedding of a given monothetic monoid into a monothetic group.