Polar Coordinate Circle Initializer for Neural Network Compression
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Solution Overview
Problem
Existing circular packing algorithms, both deterministic and iterative, face challenges in efficiently covering 2D or 3D shapes and multidimensional classes, leading to slow convergence and high energy consumption during training.
Innovation Solution
A mixed deterministic and iterative approach using a polar coordinate system for initializing parameters, transitioning to a cartesian coordinate system for efficient coverage of user space, and employing an expressive XNOR-based multiplier for neural network model compression.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If traditional random or grid initializers are used for circular packing algorithms, then the implementation is simple, but convergence speed is slow and energy consumption is high
Solution Approach 1:
The patent applies preliminary action by pre-initializing circle parameters using polar coordinates before the iterative optimization process begins. The initializer sets up circle positions, radii, and other parameters in a structured polar coordinate system, which provides a better starting point for convergence compared to random initialization. This preliminary structuring reduces the number of iterations needed and lowers energy consumption during training.
Solution Approach 2:
The patent changes the parameter representation from traditional Cartesian coordinates to polar coordinates for initialization. By representing circle positions as (r, θ) pairs and using polar coordinate system properties, the initializer creates more efficient starting configurations. This parameter transformation enables faster convergence while reducing computational energy requirements.
2Adaptability or versatility
If deterministic approaches like Apollonian packing are used, then circle arrangement follows strict mathematical rules, but flexibility in covering complex shapes is limited
Solution Approach 1:
The patent segments the initialization process into distinct components: polar coordinate definition, circle parameter generation, and Cartesian conversion. By dividing the initialization into these manageable segments, the system maintains mathematical rigor while adapting to complex shapes. Each segment can be independently optimized and combined with iterative methods for versatile shape coverage.
Solution Approach 2:
The patent introduces polar coordinates as an intermediary representation between the deterministic mathematical framework and the flexible iterative optimization. The polar coordinate system serves as a mediator that preserves mathematical structure while enabling adaptation to complex shapes through subsequent iterative refinement in Cartesian coordinates.
3Speed
If iterative algorithms with random initializers are used, then flexibility in multidimensional problems is improved, but convergence speed decreases significantly
Solution Approach 1:
The patent applies preliminary action by pre-initializing circle parameters using polar coordinates before the iterative optimization process begins. The initializer sets up circle positions, radii, and other parameters in a structured polar coordinate system, which provides a better starting point for convergence compared to random initialization. This preliminary structuring reduces the number of iterations needed and lowers energy consumption during training.
Solution Approach 2:
The patent changes the parameter representation from traditional Cartesian coordinates to polar coordinates for initialization. By representing circle positions as (r, θ) pairs and using polar coordinate system properties, the initializer creates more efficient starting configurations. This parameter transformation enables faster convergence while reducing computational energy requirements.
Data Source
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AI summary
An initializer for circle distribution on a 2D surface using a polar coordinate system for image compression, video compression, motion detection, and posture detection. The initializer can also be used for sphere distribution in a 3D shape. The initializer uses a mixed deterministic and iterative / stochastic approach. Using the polar coordinate system for initialization enables coverage of the user space, and after parameters are initialized, the method transitions to a cartesian coordinate system. Methods for using the polar system in CPU units by applying an XNOR/AND architecture for neural network model compression are also described. The neural network includes a perceptron for supervised learning of binary classifiers. The unit responsible for multiplication in a MAC architecture can be replaced with a non-linear expressive function. Thus, a neural network having a non-linear expressive perceptron (quadtron) is described for solving circle distribution and other problems.