Neural Network Monotonicity Enforcement via Interpolated Data Points
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing neural network models often fail to ensure monotonicity, leading to unpredictable behavior in practical applications, as they either enforce monotonicity only at the boundaries of the input space or in localized regions where training data lies, without efficiently achieving monotonicity across the entire input space.
Innovation Solution
The system employs a computer-implemented method for training neural networks with enforced monotonicity by using a monotonicity penalty that computes gradients based on interpolated and extrapolated data points, including both training and random data, to generate mixed-up data points that densely populate the convex hull and extend beyond the training data manifold, ensuring monotonicity across a larger volume of the input space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If monotonicity is enforced only at boundaries or localized regions using traditional methods, then the implementation complexity is low, but the monotonicity coverage across the input space is insufficient
Solution Approach 1:
The patent extends the monotonicity enforcement from boundary points or localized regions into the interior of the input space by introducing interpolated data points along line segments connecting boundary points. This dimensional extension ensures monotonicity holds throughout the entire input space, not just at boundaries, thereby improving monotonicity coverage without requiring fundamentally new training mechanisms.
Solution Approach 2:
The patent performs preliminary generation of interpolated data points and computation of monotonicity penalties before the main training process. By pre-computing the monotonicity penalty terms based on interpolated points, the actual training phase only requires standard gradient descent, avoiding the need for complex constrained optimization during training and thus limiting the increase in training complexity.
2Reliability
If monotonicity constraints are applied throughout the entire input space using existing methods, then the monotonicity coverage is improved, but the computational overhead increases significantly
Solution Approach 1:
The patent applies different treatment to different regions of the input space: boundary points use standard monotonicity constraints, while interior points are handled through interpolation along line segments. This localized approach ensures monotonicity is enforced where needed (throughout the space) while avoiding the computational burden of applying full constraints uniformly, thus maintaining training efficiency.
Solution Approach 2:
The patent uses interpolated data points as virtual copies or proxies for actual training samples. Instead of requiring dense sampling of the entire input space with real data points, the method generates synthetic interpolated points that capture the monotonicity requirements, reducing the computational load while maintaining comprehensive coverage.
3Reliability
If traditional monotonicity enforcement methods are used, then the training process is simple, but the monotonicity is not maintained in regions beyond training data manifold
Solution Approach 1:
The patent extends monotonicity enforcement beyond the training data manifold by introducing interpolated points along line segments that connect boundary points and extend into the interior of the input space. This dimensional extension ensures monotonicity constraints are applied in regions beyond where training data actually lies, improving monotonicity consistency across the entire input space.
Solution Approach 2:
The patent uses interpolated data points as intermediary elements that bridge the gap between boundary points and the interior regions of the input space. These intermediary points carry the monotonicity constraints from boundaries into the interior, ensuring consistent monotonicity enforcement without requiring direct training data in those regions.
Data Source
AI summary
A computer-implemented system and method for training a neural network with enforced monotonicity are disclosed. An example system includes at least one processor and memory in communication with said at least one processor, wherein the memory stores instructions for providing a data model representing a neural network for predicting an outcome based on input data, the instructions when executed at said at least one processor causes said system to: receive a feature data as input data; predict an outcome based on the input data using the neural network; compute a loss function based on the predicted outcome and an expected outcome associated with the input data, the loss function being dependent on a monotonicity penalty Ω computed based on a set of training data including the feature data and on a set of random data; and update weights of the neural network based on the loss function.