The 31^st NORDIC WORKSHOP ON PROGRAMMING THEORY - NWPT'19
 
13-15 November 2019
Tallinn - Estonia

A compositional approach to Signal Flow Graphs

Wednesday, November 13, 2019, 9:30-10:30

Paweł Sobociński

Tallinn Univ. of Technology, Estonia

Signal flow graphs are a classical state-machine model of computation first proposed by Claude Shannon, and are well-known in control theory and engineering. They have a continuous interpretation, where they compute solutions of systems of homogeneous higher-order differential equations, and a discrete interpretation, where they compute solutions of recurrence relations.

I will give a compositional presentation of the theory of signal flow graphs using standard techniques of programming language semantics. String diagrams provide a rigorous graphical syntax, and a denotational semantics is given as a monoidal functor to an appropriate category of linear relations. Operational semantics can be given using a structural presentation.

Denotational equality will be characterised: i) axiomatically, in terms of an equational theory that shows how the basic syntactic components “interact", ii) and in operational terms as contextual equivalence, via a full abstraction result that relies on recent work that extends the setting from linear to affine relations.

Interpreting and validating machine learning models

Thursday, November 14, 2019, 9:00-10:00

Ando Saabas (Bolt, Estonia)

Bolt, Estonia

Machine learning models are being increasingly used in practical applications, including in fields such as healthcare, manufacturing and transportation. These models, while powerful, can sometimes fail in very unintuitive ways. As the size and complexity of the models increases, it has become more and more important to understand the reasoning of the models, i.e. to validate that the interplay between specification (read: training data) and program (read: the model) is what was intended.

In this talk, I will give an overview of the state of the art in interpreting ML models. In particular, I will explain how tree based models such as random forests or gradient boosted trees can be instrumented to explain their predictions in terms of contributions from each feature in the input feature vector.

Two centuries of formal computation

Friday, November 15, 2019, 9:00-10:00

Jan von Plato

University of Helsinki, Finland

Theories of formal computation preceded actual programmable computers by about one hundred years. The first intimations of such computation go back even further, to one Johann Schultz, professor of mathematics and royal court-preacher in Kant's Königsberg, and to Leibniz. Google books and other online sources have made it possible to illustrate through original sources the long way from Leibniz' formal proof of 2 +2 = 4 to the 1930's that represented formal computation as a species of formal deduction.