Neural Network Regularization for Skip-Layer Optimization
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Solution Overview
Problem
Neural network-based data analysis techniques face challenges with non-convex optimization problems, multiple local minima, numerical instability, and the need for subjective user involvement, especially when dealing with data that contains strong linear trends, leading to inefficient solutions and sensitivity to noisy data.
Innovation Solution
A novel framework using a regularized objective function for neural networks with skip-layer connections, incorporating a weighted skip-layer and output bias term for de-trending and convex underestimators to stabilize the optimization process, allowing for automatic de-trending and convexification without additional preprocessing, and determining the scaling factor automatically based on the non-convexity measure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional neural network optimization is used for data with strong linear trends, then the neural network can model complex non-linear patterns, but the optimization gets trapped in local minima and performs no better than linear regression
Solution Approach 1:
The patent segments the optimization problem by separating the linear trend component from the non-linear patterns. This is achieved through de-trending the target data before neural network modeling, which divides the original complex optimization problem into two simpler sub-problems: (1) linear trend removal through preprocessing, and (2) non-linear pattern modeling by the neural network. This segmentation prevents the optimizer from being trapped in local minima caused by the strong linear trend.
Solution Approach 2:
The patent applies preliminary de-trending action to the target data before it is fed into the neural network for non-linear pattern modeling. By removing the linear trend component in advance through preprocessing steps (such as fitting a linear model and subtracting it from the target), the optimization process starts from a cleaner state that avoids the local minima problem associated with strong linear trends in the objective function.
2Reliability
If de-trending preprocessing is applied to remove linear trends, then the neural network can focus on non-linear patterns, but additional preprocessing steps increase complexity and require subjective user involvement
Solution Approach 1:
The patent merges the de-trending preprocessing step with the neural network training process by incorporating it as an integral part of the overall modeling framework. Rather than treating de-trending as a separate, manual preprocessing step, it is combined with the optimization process itself, allowing the system to automatically handle linear trend removal as part of the unified training procedure, thereby reducing subjective user involvement.
Solution Approach 2:
The patent enables the neural network system to automatically perform de-trending without requiring subjective user input. By formulating the de-trending process as an automated optimization sub-task that the system handles itself during training, the method eliminates the need for users to manually determine preprocessing parameters or decide when de-trending is necessary, thus reducing complexity and subjectivity.
3Reliability
If weight decay factors are manually tuned to regularize the neural network, then overfitting can be reduced, but significant subjective user involvement is required and solutions become sensitive to noisy data
Solution Approach 1:
The patent implements automatic regularization parameter selection where the system determines the weight decay factor and other regularization parameters autonomously during the training process. This is achieved through automated hyperparameter optimization techniques or adaptive regularization methods that eliminate the need for manual user tuning, thereby reducing subjective involvement while maintaining robustness to noisy data through proper regularization.
Solution Approach 2:
The patent incorporates feedback mechanisms that automatically adjust regularization parameters based on the training progress and model performance. By monitoring the optimization process and automatically modifying weight decay factors in response to observed performance metrics, the system reduces sensitivity to noisy data and eliminates the need for subjective user input, as the parameters are continuously refined through feedback from the training process itself.
Data Source
AI summary
According to one aspect of the invention, target data comprising observations is received. A neural network comprising input neurons, output neurons, hidden neurons, skip-layer connections, and non-skip-layer connections is used to analyze the target data based on an overall objective function that comprises a linear regression part, the neural network's unregularized objective function, and a regularization term. An overall optimized first vector value of a first vector and an overall optimized second vector value of a second vector are determined based on the target data and the overall objective function. The first vector comprises skip-layer weights for the skip-layer connections and output neuron biases, whereas the second vector comprises non-skip-layer weights for the non-skip-layer connections.