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

The aim of this cycle of seminars is twofold. On one side, we want to focus on the applied side of topology. We would like to discuss how deep, abstract mathematical frameworks can be applied to creative contexts, in particular to music, which will be the leitmotif of the three seminars. We aim at showing how topological persistence allows to compute novel, unexpected features, even when applied to a complex and subjective field, as music can be. On the other side, we would like to discuss a simple analysis of musical lyrics, involving both deep learning and topology. We will shoe how the latter can be used to better understand the results coming form a deep learning model. Hopefully, this last purpose will bring to discuss how artificial intelligence and mathematics can be integrated, in order to achieve a better understanding of deep learning.
Gennaio
18
2017
Mattia G. Bergomi
Word embedding: Deep Learning and Computational Topology for the evaluation of context-based semantic change
nel ciclo di seminari: TOPOLOGY, DEEP LEARNING, AND APPLICATIONS TO CREATIVE CONTEXTS
SEMINARIO INTERDISCIPLINARE
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.
organizzato da: M. Ferri
Gennaio
17
2017
Mattia G. Bergomi
Time series topology, a quest towards optimal granularity: automatic stylistic classification
nel ciclo di seminari: TOPOLOGY, DEEP LEARNING, AND APPLICATIONS TO CREATIVE CONTEXTS
SEMINARIO INTERDISCIPLINARE
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.
organizzato da: M. Ferri
Gennaio
16
2017
Mattia G. Bergomi
Persistent homology as a musical fingerprint
nel ciclo di seminari: TOPOLOGY, DEEP LEARNING, AND APPLICATIONS TO CREATIVE CONTEXTS
SEMINARIO INTERDISCIPLINARE
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.
organizzato da: M. Ferri