１．講演会名称：第12回　CMSAIコロキウム

２．開催日時　：2023年12月19日（火）17時10分～18時10分

３．講演会場　：ファカルティルーム（7号館3階）
　　　　　　　　※対面及びZoom配信

　参加登録URL；
　https://us02web.zoom.us/meeting/register/tZcocO2urzIvGtP-y8o9YbhDvAfE6SLsHVPW

４．講演者　　：Roy Sigelmann 氏（Research Assistant/ Johns Hopkins University, USA）

５．講演題目　：「A Recurrence-Based Lyapunov Direct Method for Stability Analysis」

要旨： Incorporating neural memory models based on attractor dynamics into neural networks has been conjectured to keep the computational network smaller and more practical to train. However, state-of-the-art memory models are not scalable in terms of encompassing richer and larger memories. At the crux of this, the dependence of neural models is the reliance on existence of a Lyapunov function, a function whose value monotonically decreases along the trajectories of the dynamical system. Unfortunately, finding a Lyapunov function is often tricky and requires ingenuity, domain knowledge, or significant computational power. At the core of this challenge is the fact that the method requires every sub-level set to be forward invariant, thus implicitly coupling the geometry of the function and the trajectories of the system. We seek to disentangle this dependence by developing a direct method that substitutes the concept of invariance with the more flexible notion of recurrence. We show that, under mild conditions, the recurrence of sub-level sets is sufficient to guarantee stability and introduce the appropriate stronger notions to obtain asymptotic stability and exponential stability, which in turn may enable new types of memory models.