Efficient classification and interpolation with neural ODEs
报告专家：Antonio Álvarez López博士（西班牙Universidad Autónoma de Madrid）
报告时间：2024年1月25日上午10:00-11:00
报告地点：西南中心516
报告摘要：Neural ODEs, representing the continuous-time limit of neural networks, have emerged as a natural tool for data-driven supervised learning. They allow for a reinterpretation of several paradigms through the property of simultaneous controllability of $N$ points in the d-dimensional Euclidean space. In this talk, I will present results in two research directions in this area that focus on identifying the optimal architecture (both depth and width) of this model and studying its expressivity. Firstly, we estimate the required number of neurons for efficient cluster-based classification, especially under the worst-case scenario where points are independently and uniformly distributed in $[0,1]^d$. It is known that the task can be accomplished with $O(N)$ neurons. Our work defines an algorithm that classifies clusters of $d$ points from any initial configuration as long as they are in general position, resulting in a complexity of $O(N/d)$ neurons. Second, we explore the interplay between the width $p$ and depth $L$ in interpolating a dataset of $N$ pairs of points. Our findings reveal a balancing trade-off between $p$ and $L$, with $L$ scaling as $O(1+N/p)$.
邀请人：张旭
