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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

  • Jan
    19

    CS Colloquium - Kuikui Liu "Spectral Independence: A New Tool to Analyze Markov Chains"

    Department of Computer Science

    12:00 PM

    EVENT DETAILS

    TIME Wednesday, January 19, 2022 at 12:00 PM - 1:00 PM

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    CONTACT Pamela Villalovoz    pmv@northwestern.edu EMAIL

    CALENDAR Department of Computer Science

  • Jan
    24

    CS Colloquium - Andrea Lincoln "Average-Case Fine-Grained Complexity"

    Department of Computer Science

    12:00 PM

    EVENT DETAILS

    TIME Monday, January 24, 2022 at 12:00 PM - 1:00 PM

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    CONTACT Pamela Villalovoz    pmv@northwestern.edu EMAIL

    CALENDAR Department of Computer Science

  • Jan
    26

    CS Colloquium - Nan Tang "From Absolute Good Data to Relative Good Data: Data Preparation for Data-centric AI"

    Department of Computer Science

    12:00 PM

    EVENT DETAILS

    TIME Wednesday, January 26, 2022 at 12:00 PM - 1:00 PM

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    CONTACT Pamela Villalovoz    pmv@northwestern.edu EMAIL

    CALENDAR Department of Computer Science

  • Feb
    7

    CS Colloquium - Yang Song "Learning to Generate Data by Estimating Gradients of the Data Distribution"

    Department of Computer Science

    12:00 PM

    EVENT DETAILS

    TIME Monday, February 7, 2022 at 12:00 PM - 1:00 PM

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    CONTACT Pamela Villalovoz    pmv@northwestern.edu EMAIL

    CALENDAR Department of Computer Science

  • Feb
    16

    CS Colloquium - Alex Wein "Understanding Statistical-vs-Computational Tradeoffs via Low-Degree Polynomials"

    Department of Computer Science

    12:00 PM

    EVENT DETAILS

    TIME Wednesday, February 16, 2022 at 12:00 PM - 1:00 PM

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    CONTACT Pamela Villalovoz    pmv@northwestern.edu EMAIL

    CALENDAR Department of Computer Science

  • Mar
    12

    Winter Classes End

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Saturday, March 12, 2022

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

    CALENDAR University Academic Calendar

  • Mar
    19

    Spring Break Begins

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Saturday, March 19, 2022

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

    CALENDAR University Academic Calendar

  • Mar
    28

    Spring Break Ends

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Monday, March 28, 2022

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

    CALENDAR University Academic Calendar

  • Mar
    29

    Spring Classes Begin 8 a.m.

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Tuesday, March 29, 2022

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

    CALENDAR University Academic Calendar

  • May
    30

    Memorial Day (no classes)

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Monday, May 30, 2022

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

    CALENDAR University Academic Calendar