Challenges of End-to-End Learning for Phase Retrieval Explained

Core Concepts

Symmetry breaking is crucial for improving end-to-end learning performance in phase retrieval problems.

Abstract

The content discusses the challenges faced in end-to-end learning for phase retrieval, focusing on the importance of symmetry breaking. It explains how intrinsic symmetries can lead to learning difficulties and proposes a novel technique to preprocess training sets before learning. The paper provides insights into the mathematical principles behind symmetry breaking and its application in far-field phase retrieval (FFPR). Experimental results demonstrate the significant improvement in performance after symmetry breaking, validating its effectiveness. Introduction Symmetries in imaging science's forward model. Challenges with data-driven deep learning approaches. Methods Symmetry breaking for learning square root. Symmetry breaking for phase retrieval. Experiments Evaluation dataset: simulated Bragg CDI crystal dataset. Experiment setup using UNet and SiSPRNet models. Results Uniform improvement due to symmetry breaking. Performance boost on training and test sets after symmetry breaking. Related Work Recent research efforts on solving inverse problems using DL. Author Biography Brief biographies of Wenjie Zhang, Yuxiang Wan, Zhong Zhuang, and Ju Sun.

Stats

Given Y = |F(X)|^2 ∈RM1×M2 (R+ means nonnegative reals). To ensure recoverability, M1 ≥ 2N1 − 1 and M2 ≥ 2N2 − 1 are necessary.

Quotes

"Symmetry breaking leads to a much smoother target function, making it easier for DNNs to learn." "In terms of SA-MSE loss, training on unprocessed sets often performs worse than non-data-driven methods."

Key Insights Distilled From

What is Wrong with End-to-End Learning for Phase Retrieval?

by Wenjie Zhang... at arxiv.org 03-26-2024

https://arxiv.org/pdf/2403.15448.pdf

Deeper Inquiries

How can symmetries impact other areas of deep learning beyond phase retrieval?

Symmetries play a crucial role in various areas of deep learning beyond phase retrieval. In computer vision, for example, symmetries such as translation invariance are essential for tasks like object recognition and image classification. By leveraging these symmetries, neural networks can learn more efficiently and effectively from limited data. Symmetry-based regularization techniques can also help prevent overfitting and improve generalization performance in deep learning models. In natural language processing, symmetries like permutation invariance are relevant for tasks involving sequences or sets of data. Models that exploit these symmetries can better capture the inherent structure and relationships within the input data, leading to improved performance on tasks like machine translation or sentiment analysis. Furthermore, in reinforcement learning, exploiting symmetrical properties of environments can lead to more efficient exploration strategies and faster convergence during training. By incorporating symmetry-aware algorithms into reinforcement learning frameworks, agents can learn optimal policies with reduced computational complexity. Overall, understanding and utilizing symmetries effectively across different domains of deep learning can enhance model robustness, accelerate training convergence, and improve overall performance on a wide range of tasks.

What are potential drawbacks or limitations of symmetry-breaking techniques?

While symmetry-breaking techniques offer significant benefits in improving the efficiency and effectiveness of deep learning models when dealing with symmetric data distributions or structures, there are some potential drawbacks to consider: Loss of Information: Symmetry-breaking may involve discarding certain redundant information present due to underlying symmetrical properties. This could potentially lead to loss of valuable insights encoded by those symmetries. Increased Complexity: Implementing symmetry-breaking procedures adds an extra preprocessing step before model training begins. This additional complexity might require more computational resources and time during the training process. Hyperparameter Sensitivity: The success of symmetry-breaking methods often relies on carefully selecting hyperparameters related to how the transformations are applied to break the underlying symmetries. Poor choices here could negatively impact model performance. Domain Specificity: Not all datasets or problems benefit equally from symmetry breaking; its effectiveness may vary depending on the specific characteristics of the data being analyzed. Limited Applicability: Some complex forms of symmetry may be challenging to break effectively without introducing biases or distorting important features within the dataset.

How can the concept of symmetry be applied in unrelated fields but still yield valuable insights?

The concept of symmetry transcends individual disciplines and has broad applications across diverse fields outside traditional scientific domains: 1- Artificial Intelligence (AI) Ethics: Applying ethical principles symmetrically ensures fairness across AI systems. Ensuring equal treatment regardless of demographic attributes maintains ethical standards uniformly. 2- Business Management: Balancing power dynamics symmetrically among team members fosters collaboration. Equitable resource allocation based on contributions promotes organizational harmony. 3- Urban Planning: Designing public spaces symmetrically enhances aesthetics while promoting inclusivity. Distributing infrastructure evenly supports sustainable development goals equitably. 4- Psychology: - Understanding cognitive biases through a lens focused on perceptual asymmetry aids mental health interventions. - Promoting balanced emotional well-being through holistic approaches encourages psychological resilience uniformly across populations. By recognizing patterns that exhibit balance or equivalence within seemingly disparate contexts, valuable insights emerge that drive innovation and foster interdisciplinary collaborations to solve complex challenges holistically across various fields using a unified approach based on fundamental principles such as symmetry.