News & Events
Department Events

Events

  • Nov
    6

    Appl Math: Leonid Berlyand on "Introduction to Mathematics of Artificial Neural Networks (ANNs)"

    McCormick-Engineering Sciences and Applied Mathematics (ESAM)

    11:15 AM M416, Technological Institute

    EVENT DETAILS

    Title: Introduction to Mathematics of Artificial Neural Networks (ANNs)

    Speaker: Leonid Berlyand, The Pennsylvania State University

    Abstract: We begin by addressing the image classification problem, where the goal is to map images x to classes α using an exact classifier Φ(x,α). Since an exact classifier is often unfeasible, Artificial Neural Networks (ANNs) F(x,α) are used to approximate Φ(x,α), with α representing tunable parameters. Unlike classical methods that use coefficients in expansions, ANN parameters are inspired by the structure of the human brain. The process of optimizing these parameters is called training.

    We highlight two advancements: First, a pruning technique using the Marchenko-Pastur spectral approach from Random Matrix Theory (RMT), which reduces computational complexity without sacrificing accuracy. Second, we examine autoencoders, a special type of ANN used for image-to-image transformations. The focus is on the fixed points of the autoencoder function F(x,α), crucial for distinguishing real images from fakes. Using the Banach Fixed Point Theorem, we show that with light-tailed distributions (e.g. Gaussian), there is a unique stable fixed point, while with heavy-tailed distributions (e.g. Cauchy), there are multiple fixed points N. The number of fixed points N depends non-monotonically on the number of layers L, suggesting an optimal number of layers L_0 for best performance. These results are vital for improving autoencoder design.

    Zoom: https://northwestern.zoom.us/j/92383067097

    -----

    To subscribe to the Applied Mathematics Colloquia List send a message to LISTSERV@LISTSERV.IT.NORTHWESTERN.EDU with the command:

    SUBSCRIBE esam-seminar FirstName LastName

    more less

    TIME Thursday, November 6, 2025 at 11:15 AM - 12:15 PM

    LOCATION M416, Technological Institute    map it

    ADD TO CALENDAR

    CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

    CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  • Jun
    14

    Spring 2026 Commencement

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Sunday, June 14, 2026

    ADD TO CALENDAR

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

    CALENDAR University Academic Calendar

  • Jun
    15

    Northwestern Engineering PhD Hooding and Master's Degree Recognition Ceremony

    McCormick School of Engineering and Applied Science

    9:00 AM

    EVENT DETAILS

    TIME Monday, June 15, 2026 at 9:00 AM - 11:00 AM

    ADD TO CALENDAR

    CONTACT Andi Joppie    andi.joppie@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science

  • Jun
    15

    Northwestern Engineering Undergraduate Convocation

    McCormick School of Engineering and Applied Science

    2:00 PM

    EVENT DETAILS

    TIME Monday, June 15, 2026 at 2:00 PM - 4:00 PM

    ADD TO CALENDAR

    CONTACT Andi Joppie    andi.joppie@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science

  • Jun
    19

    Juneteenth - University Closed

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Friday, June 19, 2026

    ADD TO CALENDAR

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

    CALENDAR University Academic Calendar

  • Jul
    3

    Independence Day (observed) - University Closed

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Friday, July 3, 2026

    ADD TO CALENDAR

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

    CALENDAR University Academic Calendar

  • Sep
    23

    Fall 2026 Classes Begin

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Wednesday, September 23, 2026

    ADD TO CALENDAR

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

    CALENDAR University Academic Calendar