Neural Networks for Irregular Data via Differential Operators
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Convolutional neural networks face significant computational costs during inference, particularly when dealing with irregularly sampled data such as point cloud data from sensors or geospatial data, as they require re-gridding and interpolation, which wastes resources and creates artifacts.
Innovation Solution
Designing neural networks with differential operators that conform to the dimensions of the data, using a partial differential equation-inspired framework to perform convolutions directly on irregular grids, allowing for efficient processing of sparse and unstructured data without re-sampling.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If convolution operations are applied on uniform grids using traditional CNN architectures, then computational efficiency is maintained, but the ability to process irregularly sampled data directly is lost requiring re-gridding and interpolation
Solution Approach 1:
The patent transforms the fixed uniform grid parameter into a variable irregular grid structure that adapts to the input data distribution. By representing the grid as a set of points with coordinates (x_i, y_i) rather than fixed indices, the system can process LIDAR point clouds and other irregularly sampled data directly without re-gridding operations
Solution Approach 2:
The patent segments the convolution operation into two distinct phases: (1) a grid-independent feature extraction phase that operates on irregular point sets using distance-based kernels, and (2) a subsequent rendering or projection phase that maps features to uniform grids only when necessary for visualization or compatibility with standard pipelines
2Adaptability or versatility
If re-gridding and interpolation are performed to adapt irregular data to uniform grids, then compatibility with traditional CNNs is achieved, but computational resources are wasted and artifacts are created
Solution Approach 1:
Instead of transforming irregular data to fit uniform grids (traditional approach), the patent inverts the problem by having the convolution operator adapt to the irregular data structure. The kernel is defined in continuous space and evaluated at arbitrary point locations, eliminating the need for interpolation and associated computational waste and artifacts
Solution Approach 2:
The patent introduces a continuous-space kernel function as an intermediary between the discrete irregular data points and the convolution operation. This kernel acts as a mediator that can evaluate features at any spatial location without requiring the data to conform to a fixed grid structure, thereby avoiding interpolation operations
3Productivity
If convolution operations are performed directly on irregular grids, then computational cost is reduced and artifacts are eliminated, but the complexity of implementing differential operators increases
Solution Approach 1:
The patent replaces the mechanical grid-alignment mechanism with a mathematical continuous-field approach. Instead of physically moving or resampling data points to match grid locations, the system uses continuous kernel functions that naturally handle arbitrary point distributions, reducing computational overhead while managing complexity through elegant mathematics
Data Source
AI summary
An illustrative embodiment includes a method for analyzing unstructured multidimensional data with a neural network. The method includes designing the neural network at least in part by defining differential operators conforming with dimensions of the data. The method also includes performing forward propagation at a given convolution layer of the neural network at least in part by: obtaining one or more convolved values at least in part by performing convolution over an object within the data, processing respective convolved values to obtain output, and updating the object based at least in part on the output.