classic NN takes a vector of data through layers to make a prediction. Backprop adjusts network weights till predictions are right. These network weights form a vector, and training changes this vector till it hits values that mean "trained network".

Neural ODE reframes this: instead of focusing on the weights, focus on how they change. It sees training as finding a path from untrained to trained state. At each step, it uses ODE solvers to compute the next state, continuing for N steps till it reaches values matching training data. This gives you the solution for the trained network.