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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

  • Aug
    20

    Alumni Education Webinar: McCormick School of Engineering's Strategic Vision

    McCormick School of Engineering and Applied Science

    12:00 PM

    EVENT DETAILS

    TIME Wednesday, August 20, 2025 at 12:00 PM - 1:00 PM

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    CONTACT Andi Joppie    andi.joppie@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science

  • Sep
    8

    Welcome & Breakfast for New McCormick PhD Students

    McCormick School of Engineering and Applied Science

    9:00 AM LR2 & Tech East Plaza, Technological Institute

    EVENT DETAILS

    TIME Monday, September 8, 2025 at 9:00 AM - 10:00 AM

    LOCATION LR2 & Tech East Plaza, Technological Institute    map it

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    CONTACT Andi Joppie    andi.joppie@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science

  • Sep
    12

    New Undergraduate Fall 2025 Registration

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Friday, September 12, 2025

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

    CALENDAR University Academic Calendar

  • Sep
    15

    Welcome & Luncheon for New Full-time Graduate Students

    McCormick School of Engineering and Applied Science

    11:00 AM Ryan Auditorium & Tech East Plaza, Technological Institute

    EVENT DETAILS

    TIME Monday, September 15, 2025 at 11:00 AM - 12:30 PM

    LOCATION Ryan Auditorium & Tech East Plaza, Technological Institute    map it

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    CONTACT Andi Joppie    andi.joppie@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science

  • Sep
    16

    Fall Classes Begin. Change of Registration (Drop/Add) Late registration for returning students begins

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Tuesday, September 16, 2025

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

    CALENDAR University Academic Calendar

  • Sep
    25

    Bagel Thursday

    Department of Computer Science (CS)

    9:00 AM

    EVENT DETAILS

    TIME Thursday, September 25, 2025 at 9:00 AM - 11:00 AM

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    CONTACT Wynante R Charles    wynante.charles@northwestern.edu EMAIL

    CALENDAR Department of Computer Science (CS)