TaylorGLO Loss Function Optimization via Taylor Expansion
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Solution Overview
Problem
Existing loss function optimization methods, such as Genetic Loss Optimization (GLO), face challenges in efficiently discovering mutually optimal loss function structures and coefficients, leading to inefficient search spaces and suboptimal performance.
Innovation Solution
The proposed Multivariate Taylor Expansion-based Genetic Loss-Function Optimization (TaylorGLO) uses a novel parameterization for loss functions, representing them as multivariate Taylor expansions, which allows for continuous optimization using Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES).
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Genetic Loss Optimization (GLO) is used to discover loss functions, then loss function optimization is achieved, but the search space becomes inefficient and finding mutually optimal structures and coefficients is challenging
Solution Approach 1:
The patent segments the loss function into a structured hierarchical representation with discrete operational nodes and continuous coefficients. This segmentation allows the optimization system to handle structure and coefficients separately, reducing search space complexity while maintaining optimization accuracy.
Solution Approach 2:
The patent introduces a polynomial representation as an intermediary form between the discrete loss function structure and continuous coefficients. This intermediary enables smooth gradient-based optimization of coefficients while the discrete structure remains separate, resolving the contradiction between optimization precision and search complexity.
2Ease of manufacture
If separate processes are used for evolving loss function structure and optimizing coefficients, then each aspect can be optimized independently, but it becomes challenging to find mutually optimal structure and coefficients
Solution Approach 1:
The patent merges the structure evolution and coefficient optimization into a unified polynomial representation framework. The structured polynomial form allows both discrete structure elements and continuous coefficients to be optimized together through gradient-based methods, achieving mutual optimality while maintaining process modularity.
Solution Approach 2:
The patent transforms the discrete structure parameters into a continuous polynomial parameter space. This parameter transformation enables simultaneous optimization of what were previously separate discrete and continuous components, achieving mutual optimality through unified gradient-based optimization.
3Manufacturing precision
If small changes are made to the genotype in structured search space, then fine-tuning is possible, but it does not always result in small changes in phenotype and can easily make a function invalid
Solution Approach 1:
The patent changes the parameter representation from discrete structural operations to continuous polynomial coefficients. This parameter transformation ensures that small changes in the optimization variables produce small, controlled changes in the loss function phenotype, maintaining validity while enabling fine-tuning.
Solution Approach 2:
The patent creates a polynomial copy or representation of the loss function that preserves the essential behavior while allowing smooth continuous optimization. This polynomial representation acts as a stable intermediary that maintains function validity during optimization iterations.
Data Source
AI summary
A process for optimizing loss functions includes progressively building better sets of parameters for loss functions represented as multivariate Taylor expansions in accordance with an iterative process. The optimization process is built upon CMA-ES. At each generation (i.e., each CMA-ES iteration), a new set of candidate parameter vectors is sampled. These candidate parameter vectors are sampled from a multivariate Gaussian distribution representation that is modeled by the CMA-ES covariance matrix and the current mean vector. The candidates are then each evaluated by training a model (neural network) using the candidates and determining a fitness value for each candidate against a validation data set.