Основные понятия
Weight sharing in CNNs provides statistical advantages over LCNs and FCNs in translation invariant tasks.
Аннотация
The paper explores the role of weight sharing and locality in convolutional neural networks (CNNs) compared to locally connected neural networks (LCNs) and fully connected neural networks (FCNs) on image-based tasks. It introduces the Dynamic Signal Distribution (DSD) task to model image patches, proving that CNNs require fewer samples due to weight sharing benefits. The study establishes sample complexity separations between these architectures, highlighting the statistical advantages of weight sharing and locality.
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Introduction
- CNNs excel in vision tasks due to architectural biases.
- Previous works lack lower bounds for FCNs on similar tasks.
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Notation
- Definitions of loss function, risk, algorithm, iterative algorithm outlined.
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Equivariant Algorithms
- Concept introduced with motivation from neural network transformations.
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Minimax Framework
- Definition of minimax risk for learning tasks using algorithms.
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FCNs vs LCNs Separation Results
- Proof sketched for FCNs requiring more samples than LCNs on DSD task.
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LCNs vs CNNs Separation Results
- Sketched proof showing LCNs need more samples than CNNs on DSD task.
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Conclusion and Future Work
- Summary of findings and future research directions discussed.
Статистика
For any U, V ∈O(kd), then the KL Divergence between U ◦SSDt and V ◦SSDt is 1−cos(α)/σ2.
Цитаты
"Vision tasks benefit from weight sharing in CNN architecture."
"FCNs incur a multiplicative cost factor due to lacking architectural biases."