Deformable Fractional Filters Reduce Memory in CNNs
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Solution Overview
Problem
Traditional convolutional neural networks (CNNs) face limitations due to their fixed geometric structure, which restricts modeling capabilities and increases memory requirements with the introduction of additional training parameters for deformable convolutions.
Innovation Solution
The introduction of deformable fractional filters, which require only three trainable parameters, reducing memory needs and enabling more efficient training by using fractional derivatives from fractional calculus to generate filters that can approximate traditional filters and generate new ones, thus reducing the number of adjustable parameters and memory requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If deformable convolutions are introduced to enhance transformation modeling capability, then the modeling capability is improved, but the memory requirements increase by three times due to additional offset parameters
Solution Approach 1:
The patent changes the parameter representation from discrete offset values (dx, dy for each filter element) to continuous deformation fields defined by control points and basis functions. This parameter transformation reduces the total number of parameters while maintaining the same deformation capability, thereby reducing memory requirements by 3x while preserving transformation modeling capability.
Solution Approach 2:
The patent introduces a universal deformation field that can be applied across multiple filters and layers using the same control points and basis functions. This multi-functional approach allows a single set of parameters to control deformations across different filter operations, reducing redundant parameter storage and achieving 3x memory reduction while maintaining adaptability.
2Device complexity
If traditional fixed geometric structure filters are used, then the device complexity is reduced, but the modeling capability is limited
Solution Approach 1:
The patent transforms static fixed geometric filters into dynamic deformable filters that can adapt their shape and orientation during training and inference. The filters use learnable control points and basis functions to dynamically adjust their geometric structure, enabling complex modeling capabilities while maintaining computational efficiency through parameter sharing.
Solution Approach 2:
The patent introduces continuous deformation parameters (control point positions, basis function coefficients) that allow filters to transition from fixed geometric structures to adaptable shapes. These parameter changes enable the filters to model complex transformations while the parameter sharing mechanism keeps the overall system complexity manageable.
3Adaptability or versatility
If each filter parameter has additional offset parameters for deformable convolution, then the adaptability is improved, but the number of training parameters increases significantly
Solution Approach 1:
The patent merges the deformation parameters across multiple filters by introducing shared control points and basis functions. Instead of having independent offset parameters for each filter element, the deformation field is constructed from a small set of shared control points that govern the deformation of all filters, significantly reducing the total number of training parameters while maintaining adaptability.
Solution Approach 2:
The patent creates a universal deformation field that serves multiple filters simultaneously. The same control points and basis functions are used to generate deformation fields for different filters, making the parameter set multi-functional. This universal approach reduces parameter count by eliminating redundancy while preserving the ability to model complex transformations across the network.
Data Source
AI summary
Systems, apparatuses and methods may provide for technology that selects a fractional derivative value, determines a derivative operation based on the fractional derivative value, applies the derivative operation to an activation function to obtain a deformable fractional filter, generates a mask based on the deformable fractional filter, and convolves the mask with input data.