  Consider a learning algorithm, which involves an internal call to an
optimization routine such as a generalized eigenvalue problem, a cone
programming problem or even sorting. Integrating such a method as a layer(s)
within a trainable deep neural network (DNN) in an efficient and numerically
stable way is not straightforward -- for instance, only recently, strategies
have emerged for eigendecomposition and differentiable sorting. We propose an
efficient and differentiable solver for general linear programming problems
which can be used in a plug and play manner within DNNs as a layer. Our
development is inspired by a fascinating but not widely used link between
dynamics of slime mold (physarum) and optimization schemes such as steepest
descent. We describe our development and show the use of our solver in a video
segmentation task and meta-learning for few-shot learning. We review the
existing results and provide a technical analysis describing its applicability
for our use cases. Our solver performs comparably with a customized projected
gradient descent method on the first task and outperforms the differentiable
CVXPY-SCS solver on the second task. Experiments show that our solver converges
quickly without the need for a feasible initial point. Our proposal is easy to
implement and can easily serve as layers whenever a learning procedure needs a
fast approximate solution to a LP, within a larger network.
