We show how continuous-depth neural ODE models can be framed as single-layer,
infinite-width nets using the Chen--Fliess series expansion for nonlinear ODEs.
In this net, the output ''weights'' are taken from the signature of the control
input -- a tool used to represent infinite-dimensional paths as a sequence of
tensors -- which comprises iterated integrals of the control input over a
simplex. The ''features'' are taken to be iterated Lie derivatives of the
output function with respect to the vector fields in the controlled ODE model.
The main result of this work applies this framework to derive compact
expressions for the Rademacher complexity of ODE models that map an initial
condition to a scalar output at some terminal time. The result leverages the
straightforward analysis afforded by single-layer architectures. We conclude
with some examples instantiating the bound for some specific systems and
discuss potential follow-up work.

使用 Chen-Fliess 级数展开将连续深度神经 ODE 模型构建为单层无限宽度网络，以控制 ODE 模型中的向量场的迭代李导数作为特征，通过分析得到 ODE 模型的 Rademacher 复杂度的紧凑表达式。