Entropy-RAG

Entropy-Regulated Retrieval-Augmented Reasoning Author: Steven Reid (RRG314 Research Group) License: Apache 2.0 Version: 1.0.0

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Overview

Entropy-RAG is a retrieval-augmented reasoning (RAG) framework based on physical and mathematical principles of entropy regulation. Conventional RAG systems retrieve the top-k most similar documents using cosine similarity alone, which often leads to semantic collapse — overly narrow or repetitive results.

Entropy-RAG models retrieval as an entropy-regulated diffusion process, balancing focus and diversity using an adaptive coupling parameter Ω (Omega). This allows retrieval to behave like a self-stabilizing physical system, maintaining semantic equilibrium across reasoning tasks.

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Theoretical Basis

The system draws from:

• Recursive Entropic Field Theory (REFT): entropy as a regulator of recursive system stability
• RDT Kernel: nonlinear diffusion equation ∂L/∂t = -α·log(L) + D·∇²L
• Topological Adam: optimizer coupling gradients through energy feedback

Entropy-RAG treats retrieval as a diffusion field evolving toward equilibrium, governed by information entropy rather than temperature or noise.

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Design Principles

Entropy-RAG is not a neural network itself. It is a modular retrieval and reasoning layer that can be attached to any language model (Flan-T5, LLaMA, GPT, etc.). Its role is to maintain stability and diversity in reasoning chains.

Main design goals:

• Preserve contextual diversity while staying relevant
• Prevent mode collapse in long or multi-hop retrievals
• Quantify semantic entropy in the information field
• Create a bridge between physics-based and AI-based reasoning

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Features

• Entropy-balanced retrieval with adaptive Ω regulation
• Topic diversity control using entropy feedback
• Works with Hugging Face sentence-transformers
• Evaluation metrics: semantic diversity, lexical entropy, coherence
• Fully differentiable and compatible with fine-tuning pipelines

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Installation

git clone https://github.com/rrg314/entropy-rag.git
cd entropy-rag
pip install -e .

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Quick Start Example

from entropy_rag.entropy_index import build_index
from entropy_rag.retriever import EntropyBalancedSelector, EntropySelectorConfig

docs = [
    "Entropy stabilizes diffusion by regulating potential energy.",
    "Topological Adam introduces alpha-beta coupling in optimization.",
    "Nonlinear PDEs improve stability in differentiable physics."
]

index = build_index(docs, n_topics=3)
selector = EntropyBalancedSelector(index, EntropySelectorConfig(Omega_mode='median'))

results = selector.retrieve('how does entropy stabilize diffusion?', k=5)
for r in results:
    print('-', r)

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Evaluation Example

from entropy_rag.evaluator import evaluate_entropy_rag

queries = [
    'how does entropy regulate diffusion?',
    'why are nonlinear PDEs important for stability?',
]

evaluate_entropy_rag(index, queries)

Example output:

Metric	Mean	Description
Semantic Diversity	0.659	Topic variety
Lexical Entropy	2.187	Vocabulary balance
Context Coherence	0.752	Consistency of retrieved information

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Research Context

Entropy-RAG extends physical entropy models to machine learning. It combines energy-based optimization, diffusion physics, and information theory to form a retrieval engine that self-stabilizes like a physical field system.

Applications include:

• Physics-informed reasoning in neural architectures
• Long-context document retrieval
• Entropy-regulated AI systems for interpretability and balance

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Future Work

• Adaptive Ω-learning from corpus feedback
• Multi-modal (text + image) retrieval
• Symbolic reasoning integration
• Empirical benchmarking vs. standard RAG frameworks

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Citation

Reid, S. (2025). Entropy-Regulated Retrieval-Augmented Reasoning (Entropy-RAG). RRG314 Research Group.

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License

Apache License 2.0 © 2025 Steven Reid See LICENSE for details.