Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse

Nicoli, Kim A.; Anders, Christopher J.; Funcke, Lena; Hartung, Tobias; Jansen, Karl; Kessel, Pan; Nakajima, Shinichi; Stornati, Paolo

doi:10.22323/1.396.0338

Cited by 15 publications

(25 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The second term can trivially be obtained by automatic differentiation because the total derivative leads to the same result as the path gradient, i.e. d dθ S(g θ (z)) = θ S(g θ (z)), see (12).…”

Section: Implementation Of Estimatorsmentioning

confidence: 99%

“…In our numerical experiments, we evaluate the degree to which the model q θ approximates the target density p. As explained in Section 1.2, the effective sampling size ( 5) is a natural metric to quantify this. We can estimate the effective sampling size using two approaches [11,12]:…”

Section: Forward and Reverse Effective Sampling Sizementioning

confidence: 99%

“…Furthermore, we demonstrate that a path-gradient estimator can also be used to minimize the forward Kullback-Leibler divergence KL(p, q) which is known to be significantly more robust to mode-collapse, see e.g. [11,12,12], and therefore is the preferable choice to preserve asymptotic guarantees. We show in detailed numerical experiments that our path-gradient method leads to superior training results and is able to significantly alleviate mode dropping.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows

Vaitl¹,

Nicoli²,

Nakajima³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to implement, have lower variance, and lead not only to faster convergence of training but also to better overall approximation results compared to standard total gradient estimators. We also demonstrate that path-gradient training is less susceptible to mode-collapse. In light of our results, we expect that path-gradient estimators will become the new standard method to train normalizing flows for variational inference.

show abstract

Section: Implementation Of Estimatorsmentioning

confidence: 99%

Section: Forward and Reverse Effective Sampling Sizementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows

Vaitl¹,

Nicoli²,

Nakajima³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Bespoke flow architectures tailored to this application have been constructed, including gauge-equivariant architectures designed for Abelian and non-Abelian gauge field theories [30,31], and methods to incorporate fermions [32,46]. Proof-of-principle implementations have demonstrated success in ameliorating important challenges such as critical slowing-down and topological freezing, as well as the computation of thermodynamic quantities, in theories ranging from scalar field theory [5,28,35,39,76] through Yukawa theory [32], to the Schwinger model [9,43] and SU(3) gauge field theory with fermions in two dimensions [46].…”

Section: Introductionmentioning

confidence: 99%

Sampling QCD field configurations with gauge-equivariant flow models

Abbott¹,

Albergo²,

Botev³

et al. 2022

Preprint

View full text Add to dashboard Cite

Machine learning methods based on normalizing flows have been shown to address important challenges, such as critical slowing-down and topological freezing, in the sampling of gauge field configurations in simple lattice field theories. A critical question is whether this success will translate to studies of QCD. This Proceedings presents a status update on advances in this area. In particular, it is illustrated how recently developed algorithmic components may be combined to construct flow-based sampling algorithms for QCD in four dimensions. The prospects and challenges for future use of this approach in at-scale applications are summarized.

show abstract

“…Furthermore, we demonstrate that a path-gradient estimator can also be used to minimize the forward Kullback-Leibler divergence KL(p, q) which is known to be significantly more robust to mode-collapse, see e.g. [11,12], and therefore is the preferable choice to preserve asymptotic guarantees. We show in detailed numerical experiments that our path-gradient method leads to superior training results and is able to significantly alleviate mode dropping.…”

Section: Introductionmentioning

confidence: 99%

Gradients should stay on path: better estimators of the reverse- and forward KL divergence for normalizing flows

Vaitl

Nicoli

Nakajima

et al. 2022

Mach. Learn.: Sci. Technol.

Self Cite

View full text Add to dashboard Cite

We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback--Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to implement, have lower variance, and lead not only to faster convergence of training but also to better overall approximation results compared to standard total gradient estimators. We also demonstrate that path-gradient training is less susceptible to mode-collapse. In light of our results, we expect that path-gradient estimators will become the new standard method to train normalizing flows for variational inference.

show abstract

Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse

Cited by 15 publications

References 25 publications

Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows

Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows

Sampling QCD field configurations with gauge-equivariant flow models

Gradients should stay on path: better estimators of the reverse- and forward KL divergence for normalizing flows

Contact Info

Product

Resources

About