Supplementary Information A The principle of least action and the Euler-Lagrange equation Here, we review the principle of least action and the derivation of the Euler-Lagrange equation [

Now, let us derive the differential equation that gives a solution to the variational problem. This condition yields the Euler-Lagrange equation, d dt @ L @ q = @ L @q . Here, we derive the Noether's learning dynamics by applying Noether's theorem to the A general form of the Noether's theorem relates the dynamics of Noether By evaluating the right hand side of Eq. 23, we get e Now, we harness the covariant property of the Lagrangian formulation, i.e., it preserves the form Plugging this expression obtained from the steady-state condition of Eq.27 Here, we ignore the inertia term in Eq. 16, assuming that the mass (learning rate) is finite but small All the experiments were run using the PyTorch code base. We used Tiny ImageNet dataset to generate all the empirical figures in this work. The key hyperparameters we used are listed with each figure.