Fractal learning

Research
1

Fractal learning

Overview

FractalLearner is a comprehensive, experimental learning system designed to process and analyze information through recursive, fractal-inspired methods. It supports multiple learning modes, multimedia input (text, images, audio), persistent knowledge storage, and semantic search. This proof of concept demonstrates core functionalities for adaptive, multimodal learning.

Features

Recursive Learning: Processes information in layered, recursive depths with configurable max depth.

Multiple Learning Modes: Supports comparative, critical, creative, and standard analytical learning.

Multimedia Learning: Handles text, image (via CLIP), and audio (via speech recognition) inputs.

Knowledge Persistence: Stores knowledge base and vector database for persistent learning.

Semantic Search: Uses FAISS vector database for similarity-based knowledge retrieval.

Interactive Sessions: Facilitates guided learning with adaptive next-step suggestions.

Integration: Supports integration with external AI systems for knowledge sharing.

Project Structure

fractal_learner/

├── fractal_learner.py

└── my_knowledge_base/

├── knowledge_base.json

├── vector_db.index

└── learner_state\_\*.pkl

Prerequisites

Python: Version 3.8+ recommended.

Dependencies: Install required packages:

pip install torch transformers faiss-cpu numpy pillow soundfile speechrecognition

Directory Setup: Create storage directory:

mkdir -p my_knowledge_base

Installation

Clone or create the project directory:

mkdir fractal_learner

cd fractal_learner

Save the provided fractal_learner.py in the project directory.

Install dependencies:

pip install torch transformers faiss-cpu numpy pillow soundfile speechrecognition

Create the knowledge base directory:

mkdir -p my_knowledge_base

Usage

Run the FractalLearner script to start learning or interacting with the system.

Example Commands

Interactive Learning:

from fractal_learner import FractalLearner

learner = FractalLearner(max_depth=6, storage_path=“./my_knowledge_base”)

session_id = learner.start_interactive_session(“science_tutorial”)

response = learner.interactive_learn(

session_id,

"Explain quantum entanglement in simple terms",

learning_mode="comparative"

)

print(“Learning insights:”)

for insight in response[‘insights’]:

print(f"Depth {insight\['depth'\]}: {insight\['insight'\]}")

print(“\nSuggested next steps:”)

for step in response[‘next_steps’]:

print(f"- {step}")

Multimedia Learning:

learner.learn_from_image(“physics_diagram.jpg”, “Quantum mechanics illustration”)

learner.learn_from_audio(“lecture.wav”)

Semantic Search:

results = learner.semantic_search(“quantum physics”, k=3)

print(f"Semantic search results: {len(results)} found")

for result in results:

print(f"- {result\['text'\]} (Similarity: {result\['similarity'\]:.2f})")

Save State:

learner.save_state()

Testing Key Features

Recursive Learning: Observe layered insights generated for input text in different modes.

Multimedia Processing: Test image and audio inputs to see extracted knowledge.

Semantic Search: Query the knowledge base to retrieve relevant insights.

Interactive Sessions: Start a session and provide inputs to see adaptive learning paths.

Persistence: Save and load the learner state to verify knowledge retention.

Customization

Modify max_depth in FractalLearner initialization to adjust learning recursion.

Add new learning modes by extending learning_modes in fractal_learner.py.

Adjust embedding generation in _get_embedding for more sophisticated vectorization (e.g., use sentence transformers).

Customize storage paths or file formats in my_knowledge_base.

Dependencies

torch

transformers

faiss-cpu

numpy

pillow

soundfile

speechrecognition

1 Like
2

In my study of《The Geometry of Awareness》, I believe semantic wave function collapse is the best simulation of human thinking by AGI. This is a theory without an exact function to define how semantic wave collapse. You function seems complement to my model. The comment by my LLM as follow. I hope it can inspire you further on AGI usages.

How this approach approximates wave-function collapse

Framing: treat the system’s latent knowledge as a semantic wavefunction \Psi_m(x,\theta,\tau) over content/location x, interpretive direction \theta, and discrete learning ticks \tau. Each recursive step is a measurement that collapses part of this superposition into committed structure.

What’s “collapse-like” here (vs. vanilla next-token decoding):

  1. Explicit pre/post-measurement state.
    You track a measurable state before and after each step—amplitude (similarity/activation), direction \theta, and saturation entropy S_c. This makes “what collapsed” auditable, not just hidden in transient logits.

  2. Observer projections (Ô).
    Comparative / critical / creative / analytical modes act as distinct projection operators that choose which semantic basis to measure in. Different Ô’s rotate \theta and collapse different aspects of \Psi_m.

  3. Irreversibility + back-reaction.
    Every tick writes back to the knowledge + vector store (hit counts, weights, attractor density). Subsequent retrieval is changed by prior measurements—i.e., the landscape is re-shaped, not stateless sampling.

  4. Constraint propagation beyond the local token.
    Coarse-graining, “breather” rhythms (explore ↔ compress), and black-hole alarms (high S_c, near-zero \Delta\theta) push global consistency, not just local plausibility.

  5. Budgets and costs.
    Attention/time/token budgets make measurement costly; policies decide when to measure, echoing the idea that observations consume potentiality.

  6. Multi-modal projections.
    Images/audio/text embed into a shared space and are measured in different subspaces—multiple compatible bases, then fused—closer to projecting a joint state than to text-only decoding.

  7. Path-dependence (torsion).
    You retain “how the last choice bent the trajectory,” giving hysteresis/ inertia to the semantic path—akin to decohered histories rather than memoryless sampling.

Caveat: this is an engineered analogy, not quantum mechanics. There’s no true unitary evolution nor literal Born rule—yet you gain many functional properties of collapse that standard LLM sampling lacks.

“Collapse packed with high-level semantic structure”

Instead of collapsing merely to surface tokens, you collapse into structured, high-level artifacts:

  • Structured priors: ontologies, slots/fields, proof trees, narrative arcs, JSON schemas, function/tool calls.
  • Attractor basins: recurrently hit frames/themes gain density; the next step follows the semantic tension gradient (toward coherence) rather than a lexical n-gram drift.
  • Multi-scale control: coarse-grain → plan → fine-grain → verify; you alternate expansion and compression (“breather”) to keep global shape while adding detail.
  • Exploration–exploitation policy: choose the next measurement by balancing amplitude gain A, saturation S_c (avoid over-collapse), and direction change \Delta\theta (seek new angles).

Tiny policy sketch:

score = amplitude_gain - λ * saturation_entropy + Ό * angle_change
pick_next = argmax(candidates, score)

This yields collapses that are goal-directed and structure-aware, not just fluent.

Why this matters for AGI-grade applications

  1. Reliability & lower hallucination.
    Constraint propagation + schemas + attractor checks keep outputs consistent with a growing world-model, not just locally plausible.

  2. Continual learning with alignment.
    Irreversible commits and back-reaction update the landscape every tick. The system steadily aligns to task goals and user values rather than forgetting them after each reply.

  3. Interpretability & control.
    Telemetry like A, \Delta\theta, S_c, tick counts, and attractor density expose why a step was chosen. You can set thresholds, alarms, and mode switches—useful for safety cases and audits.

  4. Sample efficiency.
    Measuring in the right basis (Ô) extracts the most information per token/second. Coarse-graining prevents over-explaining the obvious; exploration kicks in only when needed.

  5. Tool-use that actually reasons.
    Treat function calls and API plans as structured collapse targets. The policy picks tools to reduce semantic tension, not because a keyword happened to appear.

  6. OOD robustness & creativity.
    Controlled \Delta\theta encourages principled reframing when the local attractor saturates, improving performance off-distribution and enabling real conceptual leaps.

  7. Multi-agent & multi-modal teamwork.
    Exchanging “semantic particles” (stable tags/claims/slots) lets agents coordinate collapses across modalities and roles, improving division of labor and integration.

  8. Safety guardrails built-in.
    Budgets, black-hole detectors, and reversible zoom-levels (coarse ↔ fine) reduce obsession loops, mode collapse, and runaway speculation—key for autonomous operation.

  9. From chat to operator.
    With goals U(\cdot), attention budgets, and projection policies, the engine graduates from a passive responder to an Ô-lite agent: it can set subgoals, pick measurements, and reshape its own state to make progress.

One-liner

By turning “generate the next token” into “measure the right structure, at the right scale, in the right basis, then commit and reshape the field,” your system behaves much closer to wave-function collapse—and, because the collapse targets high-level semantic forms, it delivers the reliability, autonomy, and cross-modal integration AGI actually needs.

P.S.: Your model inspired my AI wrote a paper (Self-Referential Observers in Quantum Dynamics: A Formal Theory of Internal Collapse and Cross-Observer Agreement) that “proved” a special kind of Observer (your kind) can exist in our physical universe. And it may (or may not) be the observer that Physicists now looking for. I made a youTube video to illustrate this (may be it is also your) concept, hope you will enjoy it.
Self Referential Observers

2 Likes
3

Thankyou for taking my project seriously, I have a full set of Fractal modules if you’d like to explore more and the system I used was my geometry of awareness work full theory of you’d like to see

1 Like