Neural Ordinary Differential Equations

Neural ODEs replace a fixed stack of hidden layers with a learned derivative field and an adaptive differential-equation solver. Follow the solver contract, the reverse-time adjoint, the continuous normalizing flow, and the numerical limits hidden by the continuous-depth metaphor.

Reading focus: How a residual update becomes a continuous-time derivative field integrated by a black-box adaptive solver. Why the adjoint method can avoid storing the forward solver trajectory, and where numerical reconstruction complicates that promise. What the MNIST, continuous-flow, and irregular-time-series evidence establishes without implying that Neural ODEs replace ordinary residual networks.

NeurIPS 2018 Best Paper. Ricky T. Q. Chen et al.. 13 min read, hard difficulty.