Dissipative Learning Network Weight Adjustment via Fractional Integration
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Solution Overview
Problem
Existing machine learning techniques, such as stochastic gradient descent and equilibrium propagation, face challenges in determining appropriate weights for time varying and dissipative learning networks, making it difficult to align output signals with target values effectively.
Innovation Solution
A method for performing learning in dissipative learning networks involves determining a trajectory and a perturbed trajectory based on target outputs, with gradients calculated by fractionally integrating these trajectories to adjust the weighting arrays, allowing for better alignment of output signals with target values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional weight adjustment methods (stochastic gradient descent, equilibrium propagation) are used in time varying and dissipative learning networks, then the network can theoretically learn, but the weight determination becomes extremely difficult or impossible
Solution Approach 1:
The patent replaces traditional iterative mathematical optimization methods (stochastic gradient descent, equilibrium propagation) with a direct analytical solution based on fractionally integrated trajectories. This substitution transforms the weight determination from an iterative mechanical process into a direct computational approach, making it feasible for time varying and dissipative networks where traditional methods fail.
Solution Approach 2:
The patent introduces fractionally integrated trajectories as a new parameter representation method. By changing from standard trajectory integration to fractional integration, the system can accurately capture the behavior of dissipative and time varying networks, enabling reliable weight determination where previous parameter approaches failed.
2Manufacturing precision
If weights are adjusted to align output signals with target values in time varying and dissipative networks, then learning performance improves, but traditional mathematical models cannot be translated into practical devices
Solution Approach 1:
The patent uses fractionally integrated trajectories as a computational copy or representation of the network's temporal behavior. This copied representation can be directly translated into hardware implementations, bridging the gap between theoretical weight adjustment precision and practical device manufacturing for time varying and dissipative networks.
3Productivity
If standard trajectory integration is used, then computation is simpler, but it fails to capture the dissipative and time varying characteristics of the network
Solution Approach 1:
The patent changes the integration parameter from standard integer-order integration to fractional-order integration. This parameter change enables the trajectory calculation to accurately reflect the dissipative and time varying characteristics of the learning network while maintaining computational feasibility, resolving the trade-off between computation speed and measurement precision.
Data Source
AI summary
A method for performing learning in a dissipative learning network is described. The method includes determining a trajectory for the dissipative learning network and determining a perturbed trajectory for the dissipative learning network based on a plurality of target outputs. Gradients for a portion of the dissipative learning network are determined based on the trajectory and the perturbed trajectory. The portion of the dissipative learning network is adjusted based on the gradients.