# Learned Optimizers for Analytic Continuation

arXiv: https://arxiv.org/abs/2107.13265 · HTML: https://mlsanity.com/paper/2107.13265/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 69 references that are in the map.
- First posted on arXiv 28 Jul 2021.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Efficiently learning Ising models on arbitrary graphs](https://mlsanity.com/paper/1411.6156/) (2014)
- [Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains](https://mlsanity.com/paper/1702.03054/) (2017)
- [Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data](https://mlsanity.com/paper/1702.03056/) (2017)

## Abstract (arXiv)

Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex optimization and replace the ill-posed inverse problem by a sequence of well-conditioned surrogate problems. After training, the learned optimizers are able to give a solution of high quality with low time cost and achieve higher parameter efficiency than heuristic fully-connected networks. The output can also be used as a neural default model to improve the maximum entropy for better performance. Our methods may be easily extended to other high-dimensional inverse problems via large-scale pretraining.