What's in a Prior? Learned Proximal Networks for Inverse Problems

• URL: http://arxiv.org/abs/2310.14344v2
• Date: Wed, 27 Mar 2024 20:48:37 GMT
• Title: What's in a Prior? Learned Proximal Networks for Inverse Problems
• Authors: Zhenghan Fang, Sam Buchanan, Jeremias Sulam,
• Abstract summary: Proximal operators are ubiquitous in inverse problems, commonly appearing as part of strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as in the framework of plug-and-play or deep unrolling.
• Score: 9.934876060237345
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as in the framework of plug-and-play or deep unrolling, where they loosely resemble proximal operators. Yet, something essential is lost in employing these purely data-driven approaches: there is no guarantee that a general deep network represents the proximal operator of any function, nor is there any characterization of the function for which the network might provide some approximate proximal. This not only makes guaranteeing convergence of iterative schemes challenging but, more fundamentally, complicates the analysis of what has been learned by these networks about their training data. Herein we provide a framework to develop learned proximal networks (LPN), prove that they provide exact proximal operators for a data-driven nonconvex regularizer, and show how a new training strategy, dubbed proximal matching, provably promotes the recovery of the log-prior of the true data distribution. Such LPN provide general, unsupervised, expressive proximal operators that can be used for general inverse problems with convergence guarantees. We illustrate our results in a series of cases of increasing complexity, demonstrating that these models not only result in state-of-the-art performance, but provide a window into the resulting priors learned from data.

Related papers

• Simplicity bias and optimization threshold in two-layer ReLU networks [24.43739371803548]
  We show that despite overparametrization, networks converge toward simpler solutions rather than interpolating the training data. Our analysis relies on the so called early alignment phase, during which neurons align towards specific directions.
  arXiv  Detail & Related papers  (2024-10-03T09:58:57Z)
• Regularization, early-stopping and dreaming: a Hopfield-like setup to address generalization and overfitting [0.0]
  We look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal neuron-interaction matrices correspond to Hebbian kernels revised by a reiterated unlearning protocol.
  arXiv  Detail & Related papers  (2023-08-01T15:04:30Z)
• Learning Linear Causal Representations from Interventions under General Nonlinear Mixing [52.66151568785088]
  We prove strong identifiability results given unknown single-node interventions without access to the intervention targets. This is the first instance of causal identifiability from non-paired interventions for deep neural network embeddings.
  arXiv  Detail & Related papers  (2023-06-04T02:32:12Z)
• Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning [11.11883703395469]
  This research offers a fresh take on neural operators with a framework Representation equivalent Neural Operators (ReNO) At its core is the concept of operator aliasing, which measures inconsistency between neural operators and their discrete representations. Our findings detail how aliasing introduces errors when handling different discretizations and grids and loss of crucial continuous structures.
  arXiv  Detail & Related papers  (2023-05-31T14:45:34Z)
• Neural networks trained with SGD learn distributions of increasing complexity [78.30235086565388]
  We show that neural networks trained using gradient descent initially classify their inputs using lower-order input statistics. We then exploit higher-order statistics only later during training. We discuss the relation of DSB to other simplicity biases and consider its implications for the principle of universality in learning.
  arXiv  Detail & Related papers  (2022-11-21T15:27:22Z)
• Learning Non-Vacuous Generalization Bounds from Optimization [8.294831479902658]
  We present a simple yet non-vacuous generalization bound from the optimization perspective. We achieve this goal by leveraging that the hypothesis set accessed by gradient algorithms is essentially fractal-like. Numerical studies demonstrate that our approach is able to yield plausible generalization guarantees for modern neural networks.
  arXiv  Detail & Related papers  (2022-06-09T08:59:46Z)
• Self-Ensembling GAN for Cross-Domain Semantic Segmentation [107.27377745720243]
  This paper proposes a self-ensembling generative adversarial network (SE-GAN) exploiting cross-domain data for semantic segmentation. In SE-GAN, a teacher network and a student network constitute a self-ensembling model for generating semantic segmentation maps, which together with a discriminator, forms a GAN. Despite its simplicity, we find SE-GAN can significantly boost the performance of adversarial training and enhance the stability of the model.
  arXiv  Detail & Related papers  (2021-12-15T09:50:25Z)
• Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness [68.97830259849086]
  Most datasets only capture a simpler subproblem and likely suffer from spurious features. We study adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning.
  arXiv  Detail & Related papers  (2021-10-21T07:28:11Z)
• Global Optimization of Objective Functions Represented by ReLU Networks [77.55969359556032]
  Neural networks can learn complex, non- adversarial functions, and it is challenging to guarantee their correct behavior in safety-critical contexts. Many approaches exist to find failures in networks (e.g., adversarial examples), but these cannot guarantee the absence of failures. We propose an approach that integrates the optimization process into the verification procedure, achieving better performance than the naive approach.
  arXiv  Detail & Related papers  (2020-10-07T08:19:48Z)
• Learning the Travelling Salesperson Problem Requires Rethinking Generalization [9.176056742068813]
  End-to-end training of neural network solvers for graph optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently. While state-of-the-art learning-driven approaches perform closely to classical solvers when trained on trivially small sizes, they are unable to generalize the learnt policy to larger instances at practical scales. This work presents an end-to-end neural optimization pipeline that unifies several recent papers in order to identify the principled biases, model architectures and learning algorithms that promote generalization to instances larger than those seen in training.
  arXiv  Detail & Related papers  (2020-06-12T10:14:15Z)
• When Relation Networks meet GANs: Relation GANs with Triplet Loss [110.7572918636599]
  Training stability is still a lingering concern of generative adversarial networks (GANs) In this paper, we explore a relation network architecture for the discriminator and design a triplet loss which performs better generalization and stability. Experiments on benchmark datasets show that the proposed relation discriminator and new loss can provide significant improvement on variable vision tasks.
  arXiv  Detail & Related papers  (2020-02-24T11:35:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.