coilspy 0.1.0

A Python package for generating self-referencing Bayesian fields, also known as coils.

Probabilistic Coils: Nonreal Self-Referencing Bayesian Fields

Python package for generating and experimenting with probabilistic coils

Table of Contents

• Installation
• General Info
• Coil Behaviors
• Physically-Based Control
• Pseudo Neural Network Parameterization
• Background
• Usage

Installation

General Information

Probabilistic coils are systems of interacting, conserved, nonreal-valued Bayesian fields where the conditionals are themselves dependent on all state and conditional probabilities, thus making coils self-referencing.

Probabilistic coils are inspired by the need for a mathematical framework to describe dynamic, interconnected, non-hierarchical systems. By using conserved Bayesian fields, we can describe the flow of discrete state probabilities. By making these self-referencing, we can describe interdependent probabilistic flows. The generalization into complex and quaternionic number systems offers wider extensibility.

Coil Behaviors

Probabilistic coils exhibit a number of interesting behaviors. One key behavior is sustained aperiodic oscillation. As a result, many coils exhibit chaos.

It should be emphasized that coils behave deterministically, thus irregular phenomenon is a result of interconnectedness.

Physically-Based Control

Coils can be constructed with a variety of physically-based constraints. For example, locality can be enforced, preventing the flow of probability to non-neighboring states. Inertial biases can be imposed, decreasing the flow of probability out of a state.

Locality constraints can also be used to sever coils, resulting in separate interacting conserved subcoils. Parameter symmetry can be used to formulate coils with identical parameterizations.

Neural Network Parameterization

This package demonstrates how neural networks can be used to parameterize coils to generate dynamic fields with desired behavior.

Background

The motivation, background, and derivation of probabilistic coils can be found here:

1. Background

Development Notes

Development with Poetry

I am using Poetry for package management. This is straightforward, with the exception that if we want to use the GPU version of torch, we must do:

poetry source add -p explicit pytorch https://download.pytorch.org/whl/cu121
poetry add --source pytorch torch torchvision