Secure Sigmoid Batch Mapping for Fast, Precise Logistic Regression
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for secure computation of sigmoid functions and logistic regression models face challenges in achieving both high precision and processing speed, with existing approximations requiring rewriting of formulas and increasing computational complexity.
Innovation Solution
A secure sigmoid function calculation system and secure logistic regression calculation system utilizing secure batch mapping with three or more secure computation apparatuses to perform calculations, allowing for precise and efficient computation of sigmoid functions and model parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If approximation using cubic polynomial by fully homomorphic encryption-based secure computation is used, then secure computation of sigmoid function is achieved, but accuracy of approximation is low and processing speed is slow
Solution Approach 1:
The patent changes the parameters of the approximation polynomial dynamically based on the input domain. Instead of using a fixed cubic polynomial, the system selects from multiple pre-computed polynomials (first approximation polynomial for small x, second approximation polynomial for large x) to minimize approximation error while controlling computation complexity. This allows achieving high accuracy without always using high-order polynomials that would slow processing.
Solution Approach 2:
The patent introduces dynamic domain division where the input range is split into multiple sub-domains (small x region and large x region), and different approximation polynomials are selected dynamically based on which region the input falls into. This dynamic adaptation allows the system to use simpler, faster computations for most cases while reserving complex computations only when necessary for high-accuracy requirements.
2Measurement precision
If higher order approximate polynomial is used to increase accuracy, then accuracy of approximation becomes higher, but number of multiplications increases and processing slows down
Solution Approach 1:
The patent applies partial approximation by using lower-order polynomials (first and second approximation polynomials with degrees less than 10) for most computation cases. Instead of always using high-order polynomials to maximize accuracy, the system uses sufficient approximation (partial action) that achieves the required accuracy level with minimal computational complexity, avoiding excessive multiplications that would slow processing.
Solution Approach 2:
The patent performs preliminary computation by pre-computing and storing multiple approximation polynomials with different degrees and their corresponding domains before actual computation. This allows the system to quickly select the appropriate pre-computed polynomial during runtime without performing complex calculations, thereby reducing the number of multiplications needed while maintaining high accuracy.
3Measurement precision
If approximation formula is rewritten according to domain of definition of x, then accuracy is improved, but complexity of computation increases and processing becomes impractical
Solution Approach 1:
The patent performs preliminary action by pre-dividing the input domain into multiple sub-domains (first domain for small x, second domain for large x) and pre-storing the corresponding approximation polynomials before actual computation. This eliminates the need to rewrite approximation formulas during runtime based on the input domain, as the appropriate polynomial is simply retrieved from storage, thereby reducing computational complexity while maintaining high accuracy.
Data Source
AI summary
A secure sigmoid function calculation system is a system in which mapσ is assumed to be secure batch mapping defined by parameters (a0, . . . , ak-1) representing the domain of definition of a sigmoid function σ(x) and parameters (σ(a0), . . . , σ(ak-1)) representing the range of the sigmoid function σ(x) (a0, . . . , ak-1 are real numbers that satisfy a0< . . . <ak-1) and which is configured with three or more secure sigmoid function calculation apparatuses and calculates, from a share [[x→]] of an input vector x→, a share [[y→]] of a value y→ of a sigmoid function for the input vector x→, the system including a secure batch mapping calculating means that calculates the share [[y→]] by [[y→]]=mapσ([[x→]])=([[σ(af(0))]], . . . , [[σ(af(m-1)]]) (where f(i) (0≤i≤m−1) is j that makes aj≤xi<aj+1 hold).