Learning Interpolations between Boltzmann Densities

Code

• github.com/balintmate/boltzmann-interpolations
  OfficialIn paperjax★ 11

Abstract

We introduce a training objective for continuous normalizing flows that can be used in the absence of samples but in the presence of an energy function. Our method relies on either a prescribed or a learnt interpolation f_t of energy functions between the target energy f_1 and the energy function of a generalized Gaussian f_0(x) = ||x/||_p^p. The interpolation of energy functions induces an interpolation of Boltzmann densities p_t e^-f_t and we aim to find a time-dependent vector field V_t that transports samples along the family p_t of densities. The condition of transporting samples along the family p_t is equivalent to satisfying the continuity equation with V_t and p_t = Z_t^-1e^-f_t. Consequently, we optimize V_t and f_t to satisfy this partial differential equation. We experimentally compare the proposed training objective to the reverse KL-divergence on Gaussian mixtures and on the Boltzmann density of a quantum mechanical particle in a double-well potential.

Reproductions