arXiv:2601.10334v2 Announce Type: replace-cross Abstract: Supervised convolutional neural networks (CNNs) are widely used to solve imaging inverse problems, achieving state-of-the-art performance in numerous applications. However, despite their empirical success, these methods are poorly understood from a theoretical perspective and often treated as black boxes. To bridge this gap, we analyze trained neural networks through the lens of the Minimum Mean Square Error (MMSE) estimator, incorporating functional constraints that capture two fundamental inductive biases of CNNs: translation equivari
The proliferation of CNNs in critical applications necessitates a deeper theoretical understanding to ensure their reliability and drive further innovation.
A robust theoretical framework for CNNs can unlock significant advancements in AI development, moving beyond empirical success to principled design and deployment.
Approaches to developing and deploying CNNs for inverse problems could shift from purely empirical methods to those grounded in a more analytical and predictable theoretical basis.
- · AI researchers
- · imaging technology sector
- · scientific computing
- · AI models without theoretical grounding
- · purely empirical AI development methods
Improved understanding and reliability of convolutional neural networks for solving inverse problems.
Accelerated development of more robust and less 'black box' AI systems, particularly in sensitive applications.
Enhanced trust in AI-driven solutions within scientific, medical, and industrial imaging, leading to broader adoption and new capabilities.
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Read at arXiv cs.LG