Vector Symbolic Representations for Dynamical System Simulation
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Solution Overview
Problem
Existing methods for simulating and predicting dynamical systems using neural networks are limited in representing and handling combinations of discrete and continuous data elements, particularly in high-dimensional spaces, and fail to effectively model complex interactions and trajectories involving multiple objects.
Innovation Solution
The introduction of a method and system utilizing spatial semantic pointers (SSPs) with temporal fractional binding, collection, and decoding subsystems to represent, simulate, and predict the behavior of dynamical systems in continuous spaces of arbitrary dimensionality, enabling the simulation of continuous trajectories and interactions between objects and obstacles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If recurrent neural networks are used to model dynamical systems with discrete variables, then the system can learn and model dynamics of discrete data, but it cannot effectively represent and simulate continuous data elements and arbitrary dynamical systems
Solution Approach 1:
The system segments the representation of dynamical systems into distinct components: discrete variables are represented by one-hot encoded vectors, continuous variables are represented by separate vector embeddings, and their combination forms composite state representations. This segmentation allows each type of data to be handled appropriately while maintaining a unified framework for arbitrary dynamical systems.
Solution Approach 2:
The patent embeds both discrete and continuous variables into a high-dimensional continuous vector space, transitioning from discrete symbolic representations to continuous geometric representations. This dimensional transformation enables the use of continuous mathematics and neural network operations to model arbitrary dynamical systems with mixed discrete-continuous states.
2Reliability
If vector symbolic architecture is used for discrete data structures, then discrete input-output transformations can be performed, but it cannot simulate and predict arbitrary dynamical systems with continuous data elements
Solution Approach 1:
The system changes the parameter representation from purely discrete symbolic vectors to continuous vector embeddings with learned parameters. Continuous variables are represented as continuous vectors that can be transformed through neural network operations, while discrete variables maintain their symbolic nature through one-hot encoding. This parameter change enables reliable discrete transformations while adding versatility for continuous data handling.
Solution Approach 2:
The patent creates a composite representation framework that combines discrete one-hot encoded vectors with continuous vector embeddings. This composite approach allows the system to maintain the reliability of discrete symbolic processing while incorporating the versatility of continuous data representation, enabling accurate simulation of arbitrary dynamical systems with mixed variable types.
3Measurement precision
If high-dimensional vector representations are used for each discrete variable, then discrete data can be represented, but the system cannot efficiently represent combinations of discrete and continuous elements
Solution Approach 1:
The patent merges discrete one-hot encoded vectors with continuous variable embeddings into unified composite state representations. These combined representations efficiently encode both discrete and continuous elements in a single vector structure, allowing the system to maintain measurement precision for discrete variables while reducing the complexity of managing separate representation systems.
Data Source
AI summary
The present invention relates to methods and systems for simulating and predicting dynamical systems with vector symbolic representations of continuous spaces. More specifically, the present invention specifies methods for simulating and predicting such dynamics through the definition of temporal fractional binding, collection, and decoding subsystems that collectively function to both create vector symbolic representations of multi-object trajectories, and decode these representations to simulate or predict the future states of these trajectories. Systems composed of one or more of these temporal fractional binding, collection, and decoding subsystems are combined to simulate or predict the behavior of at least one dynamical system that involves the motion of at least one object.