Neural Network Black-Box Integration via Gradient Estimation
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Solution Overview
Problem
Neural networks are limited by the requirement that all functions implemented by their layers must be differentiable, preventing the integration of non-differentiable 'black-box' functions, which are common in legacy code and perform valuable operations, as their differentiability is unknown.
Innovation Solution
A differential approximation of the layer containing the black-box function is generated by estimating its gradient, allowing the neural network to be trained and treated as differentiable, even if the function itself is not, using methods like finite differences to approximate gradients in a multi-dimensional hyperspace.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If all functions in neural network layers must be differentiable, then the neural network can be trained properly, but non-differentiable black-box functions cannot be integrated into the network
Solution Approach 1:
The patent introduces a gradient estimator as an intermediary component that approximates the gradient of black-box functions. This estimator acts as a mediator between the non-differentiable black-box function and the gradient-based training process, allowing the network to be trained without requiring the black-box functions to be differentiable. The gradient estimator provides the necessary gradient information to the training algorithm while the black-box function remains unchanged.
Solution Approach 2:
The patent changes the parameter representation by estimating gradients numerically rather than computing them analytically. Instead of requiring closed-form gradient expressions, the system uses numerical differentiation (finite differences) to approximate gradients. This parameter change in the gradient computation method enables the integration of black-box functions with unknown or non-differentiable mathematical forms.
2Productivity
If existing code programs with unknown differentiability are used, then valuable pre-implemented functions can be leveraged, but they cannot be used in neural network implementations
Solution Approach 1:
The system enables black-box functions to serve themselves by automatically computing their gradients through numerical estimation. The gradient estimator allows each black-box function to provide its own gradient information without requiring external analytical derivation, enabling the function to be integrated and trained autonomously within the neural network framework.
Solution Approach 2:
The patent performs preliminary gradient estimation by computing finite differences before the main training process. By pre-calculating approximate gradients for black-box functions, the system prepares the necessary information in advance, allowing the training algorithm to proceed without waiting for analytical gradient derivations. This preliminary action enables the reuse of existing code programs without compromising the training process.
3Adaptability or versatility
If gradient estimation using finite differences is performed, then non-differentiable functions can be treated as differentiable, but additional computational steps are required
Solution Approach 1:
The patent replaces the mechanical system of analytical gradient computation with a numerical approximation system. Instead of relying on symbolic differentiation and chain rule applications, the system substitutes gradient estimation through finite difference calculations. This substitution simplifies the integration process by replacing complex analytical requirements with straightforward numerical evaluations that can be applied to any black-box function.
Data Source
AI summary
Techniques for incorporating a black-box function into a neural network are described. For example, an image editing function may be the black-box function and may be wrapped into a layer of the neural network. A set of parameters and a source image are provided to the black-box function, and the output image that represents the source image with the set of parameters applied to the source image is output from the black-box function. To address the issue that the black-box function may not be differentiable, a loss optimization may calculate the gradients of the function using, for example, a finite differences calculation, and the gradients are used to train the neural network to ensure the output image is representative of an expected ground truth image.