Fig. 2: Comparison of forward path KL divergence. | Nature Communications

Fig. 2: Comparison of forward path KL divergence.

From: Flow perturbation to accelerate Boltzmann sampling

Fig. 2

“Constant” uses fixed scaling matrices (0.001). “KL loss” fixes σf(z) at 0.001 and trains \(\left.{{{\boldsymbol{\sigma }}}}_{{{\bf{b}}}}({{\bf{x}}})\right)\) to minimize KL directly, while “\(\left\vert \parallel {{\boldsymbol{\epsilon }}}{\parallel }^{2}-\parallel \tilde{{{\boldsymbol{\epsilon }}}}{\parallel }^{2}\right\vert\)” employs the loss from Eq. (7) to train \(\left.{{{\boldsymbol{\sigma }}}}_{{{\bf{b}}}}({{\bf{x}}})\right)\). “Simplified FP” uses the Simplified FP Entropy estimator (Eq. 9) to compute KL. The “baseline” represents the KL of the base flow model, with entropy calculated via brute-force Jacobian evaluation.

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