Tape-Free Interatomic Potentials: Exact Conservative Forces without Automatic Differentiation

Machine-Learned Interatomic Potentials (MLIPs) compute conservative forces by differentiating the energy with respect to atomic positions using backpropagation, which records intermediate tensors on a "tape" during the forward pass and replays them to produce the forces. Inspired by existing work on "forward" gradients as well as classical force fields, we present a proof-of-concept pattern for building MLIPs that do not rely on automatic differentiation for conservative forces. The pattern couples two ideas: an analytic forward gradient (Jacobian-vector product, JVP), and a weight-tied energy readout that enforces symmetry in the Jacobian, so that the forces follow by propagating the JVP with hand-written chain rules and scattering along edges to preserve net-zero forces. We train and validate on MatPES-r2SCAN, show that the model is stable for (micro)canonical molecular dynamics, and show that with hand-written kernels the deployed model consumes roughly twenty-fold less memory per atom than MACE with cuEquivariance, enabling force evaluations beyond 1M atoms on the DGX Spark.