Relevant Seminars

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Seminar Talk Announcement

  • Tomáš Pevný (Czech Technical University, Prague):

    Understanding the neural networks through rule extraction

    20.05.2025 13:30Room 318 (zoom) @ Institute of Computer Science
    Pod Vodárenskou věží 2
    Praha, 182 00
    Hora Informaticae

    Neural networks are ubiquitous yet they remain opaque for most of its users, who has very little understanding of how they store the knowledge and how the information propagates through. In this talk, I would like to share our findings from our quest to understand these phenomena. Specifically I will show the decision rules realized by neural networks and why it might be difficult to understand them without the knowledge of the data distribution. This will give us intuition why neural networks are robust yet why adversarial samples are so easy to create. Finally, we will use these tools to understand, how the decision rules compose during inference.

  • Thomas Vetterlein (Johannes Kepler University Linz):

    Quantum logic, dagger categories, and the basic model of quantum physics

    30.05.2025 16:00Room 318 (zoom) @ Institute of Computer Science
    Pod Vodárenskou věží 2
    Praha, 182 00
    Applied Mathematical Logic Seminar

    The idea of associating a non-classical logic with the Hilbert-space model of quantum mechanics goes back to the early days of the development of this physical theory. The success has been modest. Propositions about a quantum physical system correspond to the closed subspaces of a complex Hilbert space and hence their inner structure may be described by an orthomodular lattice. There are calculi that are reasonably called logics of orthomodular lattices. However, a convincing logic doing justice to the canonical model has not been found. Rather, undecidability results have become known. The situation is different if one replaces the framework of logic by the framework of category theory. More specifically, what we propose is to consider a dagger category whose objects are orthosets and whose morphisms are adjointable maps between them. The notion of an orthoset is entirely built on the notion of orthogonality, which in turn stands for mutual exclusion. As in logic, we deal with the interrelations between objects that are to be interpreted as Hilbert spaces. Orthoclosed subspaces, which model yes-no properties in quantum logic, correspond to dagger monomorphisms. Sasaki projections, which interpret in certain quantum logics the implication connective, correspond in the categorical approach to adjoints of inclusion maps. The conjunction of mutually exclusive propositions in quantum logics might finally be seen as corresponding to the formation of categorical biproducts. In the talk, we shall present five non-technical assumptions about a dagger category of orthosets that characterise uniquely the standard model of quantum mechanics.

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