Main Arguments and Concepts in Machine Gnostics ML Models

This document provides definitions and explanations for the main arguments and variables used in Machine Gnostics machine learning and deep learning models. Understanding these concepts will help users grasp the unique characteristics of the Machine Gnostics library, which is based on the non-statistical paradigm of Mathematical Gnostics.

Core Concepts

Machine Gnostics
A machine learning and deep learning library founded on Mathematical Gnostics, a non-statistical paradigm for data analysis.
Mathematical Gnostics
An alternative to traditional statistical methods, focusing on the quantification and estimation of uncertainty in data.

Key Arguments and Gnostic Characteristics

1. Gnostic Characteristics

These are the fundamental variables used to describe data in the gnostic framework. They are divided into two main spaces:

Quantifying Space (Q-space, j):
Describes the variability and irrelevance in the data.
Estimating Space (E-space, i):
Describes the estimation of variability and relevance.

Quantifying Characteristics

fj: Quantifying data variability
Measures the variability present in the data.
hj: Quantifying irrelevance
Measures the irrelevance or error due to variability.

Estimating Characteristics

fi: Estimating data variability
Provides an estimation of the data's variability.
hi: Estimating relevance
Provides an estimation of the data's relevance.

All four variables (\( f_j, h_j, f_i, h_i \)) are called gnostic characteristics.

2. Probability Arguments

pi: Estimating probability
Probability estimate in the context of the gnostic model.
pj: Quantifying probability
Quantifies the probability based on the quantifying characteristics.

3. Information

Ii: Estimating information
Information estimate for the data.
Ij: Quantifying information
Quantifies the information content.

4. Entropy

ei: Estimating entropy
Entropy estimate for the data.
ej: Quantifying entropy
Quantifies the entropy content.
re: Residual entropy
The remaining entropy after estimation, representing the difference between quantification and estimation entropy.

5. Loss Functions

Hc loss: Gnostic mean relevance loss
A loss function based on gnostic relevance, where \( c \) can be \( i \) or \( j \).