Synaptic Descent Neural Networks for Online Dynamical Optimization
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Solution Overview
Problem
Existing methods do not effectively harness synaptic computations within artificial neural networks to solve optimization problems by evolving the network's state dynamics, particularly in simulating dynamical systems for gradient descent.
Innovation Solution
Embedding an optimization algorithm's computations into a synapse model within an artificial neural network, where the synapse's state is optimized, and its input is a gradient, allowing the network to evolve towards a solution state or trajectory.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If optimization algorithms are implemented externally to neural networks during training, then model parameters can be optimized effectively, but the neural network cannot solve optimization problems through its own computations during deployment
Solution Approach 1:
The patent merges the optimization algorithm with the neural network by embedding gradient computation and parameter update mechanisms directly into the network architecture. The neural network now performs both inference and optimization functions through its forward and backward passes, eliminating the need for external optimization algorithms during deployment.
Solution Approach 2:
The neural network is designed to perform multiple functions: it acts as both the computational model for inference and the optimization engine for solving problems. By integrating the optimization capability into the network itself, the same structure that performs classification or regression can also autonomously optimize parameters to solve optimization problems.
2Adaptability or versatility
If synapse models use non-linear transformations to capture complex dynamics, then the network can model intricate behaviors, but it becomes intractable to analyze and exploit the computations for network-level information processing
Solution Approach 1:
The patent introduces gradient signals as intermediaries that mediate between the non-linear synapse computations and the optimization objective. By formulating the problem in terms of gradient descent, the complex non-linear dynamics become tractable through the lens of optimization theory, allowing analysis and exploitation of the computations while preserving the ability to model intricate behaviors.
3Productivity
If the neural network evolves state dynamics to solve optimization problems, then it can perform gradient descent online, but this requires embedding optimization computations within the synapse model itself
Solution Approach 1:
The patent makes the synapse model dynamic by allowing its parameters to evolve over time through gradient-based updates. The synapse weights are no longer static but adapt dynamically during network operation, enabling the network to perform online optimization by continuously adjusting its internal state in response to gradient signals.
Data Source
AI summary
The present invention relates to methods and systems for using neural networks to simulate dynamical systems for purposes of solving optimization problems. More specifically, the present invention defines methods and systems that perform a process of “synaptic descent” for performing “synaptic descent”, wherein the state of a given synapse in a neural network is a variable being optimized, the input to the synapse is a gradient defined with respect to this state, and the synapse implements the computations of an optimizer that performs gradient descent over time. Synapse models regulate the dynamics of a given neural network by governing how the output of one neuron is passed as input to another, and since the process of synaptic descent performs gradient descent with respect to state variables defining these dynamics, it can be harnessed to evolve the neural network towards a state or sequence of states that encodes the solution to an optimization problem.