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  • Nov
    30

    IDEAL Seminar - Benjamin Lovitz, University of Waterloo

    Department of Computer Science

    3:00 PM

    EVENT DETAILS

    Tuesday, November 30 at 3:00 pm CDT
    Speaker: Benjamin Lovitz, University of Waterloo
    Title: A generalization of Kruskal's theorem on tensor decomposition
    Type: This is a Hybrid talk
    Location:Mudd 3514

    Abstract:

    Tensors are natural generalizations of matrices to higher-way arrays. Decompositions of tensors into sums of product (rank-one) tensors are useful in many areas for compressing and interpreting the information stored in a tensor. The tensor rank, which naturally generalizes matrix rank, is the smallest number of product tensors that can decompose a given tensor. In contrast to matrices, tensor rank decompositions are often unique (up to trivialities). Uniqueness is useful in applications, as it corresponds to a unique interpretation of the information stored in a tensor. I will review a concrete application of uniqueness in unsupervised learning.
    Kruskal's theorem states that a sum of product tensors constitutes a unique tensor rank decomposition if the so-called k-ranks of the product tensors are large. We prove a "splitting theorem" for sets of product tensors, in which the k-rank condition of Kruskal's theorem is weakened to the standard notion of rank, and the conclusion of uniqueness is relaxed to the statement that the set of product tensors splits (i.e. is disconnected as a matroid). Our splitting theorem implies a generalization of Kruskal's theorem. While several extensions of Kruskal's theorem are already present in the literature, all of these use Kruskal's original permutation lemma, and hence still cannot certify uniqueness when the k-ranks are below a certain threshold. Our generalization uses a completely new (matroidal) proof technique, contains many of these extensions, and can certify uniqueness below this threshold.

    This talk is based on joint work with Pavel Gubkin and Fedor Petrov.

    Biography:
    Benjamin is a fourth-year PhD candidate in the Institute for Quantum Computing at the University of Waterloo. He studies tensors, with applications in algebraic statistics and quantum information theory. He is supported by the government of Ontario and the University of Waterloo through an Ontario Graduate Scholarship.

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    TIME Tuesday, November 30, 2021 at 3:00 PM - 4:00 PM

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    CONTACT Pam Villalovoz    pmv@northwestern.edu EMAIL

    CALENDAR Department of Computer Science

  • Nov
    29

    Fall Classes resume 8 a.m.

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Monday, November 29, 2021

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

    CALENDAR University Academic Calendar

  • Nov
    29

    CS Distinguished Lecture Series - Claire Mathieu "Two-sided matching markets with correlated random preferences"

    Department of Computer Science

    12:00 PM

    EVENT DETAILS

    TIME Monday, November 29, 2021 at 12:00 PM - 1:00 PM

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    CONTACT Pamela Villalovoz    pmv@northwestern.edu EMAIL

    CALENDAR Department of Computer Science

  • Dec
    4

    Fall classes end

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Saturday, December 4, 2021

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

    CALENDAR University Academic Calendar

  • Dec
    11

    Northwestern Engineering PhD Hooding and Master's Recognition Ceremony

    McCormick School of Engineering and Applied Science

    4:00 PM Pick-Staiger Concert Hall

    EVENT DETAILSmore info

    TIME Saturday, December 11, 2021 at 4:00 PM - 5:30 PM

    LOCATION Pick-Staiger Concert Hall    map it

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    CONTACT Northwestern Engineering Events    northwestern-engineering-events@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science

  • Dec
    27

    Winter Recess - University Closed

    University Academic Calendar

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    EVENT DETAILS

    TIME Monday, December 27, 2021

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

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  • Dec
    28

    Winter Recess - University Closed

    University Academic Calendar

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    EVENT DETAILS

    TIME Tuesday, December 28, 2021

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

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  • Dec
    29

    Winter Recess - University Closed

    University Academic Calendar

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    EVENT DETAILS

    TIME Wednesday, December 29, 2021

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

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  • Dec
    30

    Winter Recess - University Closed

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Thursday, December 30, 2021

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

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  • Jan
    3

    Winter Classes begin 8 a.m.

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    EVENT DETAILS

    TIME Monday, January 3, 2022

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

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