  Of all the vector fields surrounding the minima of recurrent learning setups,
the gradient field with its exploding and vanishing updates appears a poor
choice for optimization, offering little beyond efficient computability. We
seek to improve this suboptimal practice in the context of physics simulations,
where backpropagating feedback through many unrolled time steps is considered
crucial to acquiring temporally coherent behavior. The alternative vector field
we propose follows from two principles: physics simulators, unlike neural
networks, have a balanced gradient flow, and certain modifications to the
backpropagation pass leave the positions of the original minima unchanged. As
any modification of backpropagation decouples forward and backward pass, the
rotation-free character of the gradient field is lost. Therefore, we discuss
the negative implications of using such a rotational vector field for
optimization and how to counteract them. Our final procedure is easily
implementable via a sequence of gradient stopping and component-wise comparison
operations, which do not negatively affect scalability. Our experiments on
three control problems show that especially as we increase the complexity of
each task, the unbalanced updates from the gradient can no longer provide the
precise control signals necessary while our method still solves the tasks. Our
code can be found at https://github.com/tum-pbs/StableBPTT.
