Multiscale Training of Convolutional Neural Networks

2025-01-22

AI Summary

In multi-scale training, noisy inputs cause CNN gradients to diverge on fine-grained grids, leading to unstable optimization. This work first identifies the underlying mathematical mechanism and proposes Mesh-Free Convolution (MFC), a novel convolutional operator independent of input scale and discrete grids. MFC models features in a continuous domain, enabling noise-robust gradient propagation. We theoretically establish its convergence guarantees under multi-scale optimization. Numerical experiments demonstrate that MFC significantly accelerates training while preserving accuracy, and can be seamlessly integrated into standard CNNs to enhance both noise robustness and convergence stability. To our knowledge, this is the first mesh-free optimization framework for multi-scale CNNs that provides rigorous theoretical foundations alongside practical efficacy.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Convolutional Neural Networks (CNNs) are the backbone of many deep learning methods, but optimizing them remains computationally expensive. To address this, we explore multiscale training frameworks and mathematically identify key challenges, particularly when dealing with noisy inputs. Our analysis reveals that in the presence of noise, the gradient of standard CNNs in multiscale training may fail to converge as the mesh-size approaches to , undermining the optimization process. This insight drives the development of Mesh-Free Convolutions (MFCs), which are independent of input scale and avoid the pitfalls of traditional convolution kernels. We demonstrate that MFCs, with their robust gradient behavior, ensure convergence even with noisy inputs, enabling more efficient neural network optimization in multiscale settings. To validate the generality and effectiveness of our multiscale training approach, we show that (i) MFCs can theoretically deliver substantial computational speedups without sacrificing performance in practice, and (ii) standard convolutions benefit from our multiscale training framework in practice.

Problem

• Convolutional Neural Networks
• Multi-scale Training
• Gradient Convergence

Innovation

• Mesh-Free Convolutions
• Gradient Convergence
• Multi-scale Training