Elenco seminari del ciclo di seminari
“TOPOLOGY, DEEP LEARNING, AND APPLICATIONS TO CREATIVE CONTEXTS”

Can music be represented as a meaningful geometric and topological object? We propose a strategy to describe some music features as a polyhedral surface obtained by a simplicial interpretation of the Tonnetz. The Tonnetz is a graph largely used in computational musicology to describe the harmonic relationships of notes in equal tuning. In particular, we use persistent homology to describe the persistent properties of music encoded in the aforementioned model. Both the relevance and the characteristics of this approach are discussed by analysing some paradigmatic compositional styles. Eventually, the task of automatic music style classification is addressed by computing the hierarchical clustering of the topological fingerprints associated with some collections of compositions. Keywords: Tonnetz, persistent homology, clustering 75 minutes talk, 45 minutes discussion.

Music can be interpreted as a collection of meaningful events distributed in time. The construction introduced during the first seminar neglects this time-dependent interpretation. Temporal evolution allows the composer to introduce a musical idea, then shape it, and finally proceed to a new scenario. Would it be possible to refine our analysis by representing music in a variable geometry space? We will present a primal attempt to describe this time-dependency in topological terms. First, we will suggest an adaptation of the persistent homology formalism to the analysis and classification of time series. Second, we will analyse different dataset in order to understand the role played by the granularity at which we describe musical events, with respect to our perception. Keywords: Time series, persistent homology, vineyards, Dynamic Time Warping 75 minutes talk, 45 minutes discussion.

Recently, artificial intelligence and deep learning started to occupy a central role in applications. Despite their effectiveness, it is often hard to interpret the inner representation of data provided by these systems. We will present one of the most popular architectures to generate word embeddings: A geometric representation of words dependent on the context in which they can be found in a given dataset. Thereafter, we will take advantage of this model to analyse the semantic shift of words, when used in two different contexts. In particular, we will show how the t-distributed stochastic neighbours embedding can provide a reasonable low-dimensional representation of word embeddings, allowing to explore their most "persistent" regions, through topological methods. Keywords: Artificial intelligence, lyrics, word embedding, semantic shift 75 minutes talk, 45 minutes discussion.