The1: Inductive Neuro-Symbolic World Model

Extreme Few-Shot Natural Law Discovery from ≤ 10 Observation Pairs

The1 is an inductive neuro-symbolic World Model engineered to reconstruct closed-form mathematical equations and laws of nature from extreme few-shot empirical data (as few as 4 to 10 observation pairs).

This repository is formatted as a full Hugging Face Model repository containing:

• config.json: Model configuration and Hugging Face auto_map.
• configuration_the1.py: The1Config inheriting from transformers.PretrainedConfig.
• modeling_the1.py: The1ForSymbolicWorldModel inheriting from transformers.PreTrainedModel.
• model.safetensors: Serialized model weights enabling the Hugging Face Hub Download Counter.
• the1/: The complete mathematical discovery engine and benchmark suite.
• app.py: Standalone Gradio interface.
• paper/paper.md: Complete academic research paper.

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⚡ How to Run The1

1. Installation

pip install -r requirements.txt
pip install -e .

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2. Loading via Hugging Face AutoModel (Triggers Hub Download Counter)

When loaded via transformers.AutoModel, Hugging Face automatically pulls config.json and model.safetensors, incrementing the Downloads Counter on your Hugging Face model page:

import numpy as np
from transformers import AutoModel

# Load directly from Hugging Face Hub (increments download counter)
model = AutoModel.from_pretrained("racore/The1", trust_remote_code=True)

# 8 empirical measurements of mass (m) and acceleration (a)
X_train = np.array([
    [1.0, 2.5],
    [2.0, 3.0],
    [0.5, 4.0],
    [3.5, 1.2],
    [1.5, 5.0],
    [4.0, 2.0],
    [2.5, 3.5],
    [0.8, 6.0]
])
# Ground Truth: F = m * a
y_train = X_train[:, 0] * X_train[:, 1]

# Unseen OOD validation data
X_val = np.array([[5.0, 8.0], [7.0, 10.0]])
y_val = X_val[:, 0] * X_val[:, 1]

# Discover governing law
result = model.discover(
    X_train=X_train,
    y_train=y_train,
    X_val=X_val,
    y_val=y_val,
    var_names=["m", "a"],
    target_name="F"
)

print(result.summary())
print("Discovered Equation :", result.equation) # F = a*m
print("LaTeX Formula       :", result.latex)    # F = a m
print("Unseen Val R² (OOD) :", result.metrics["val_r2"]) # 1.0000

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3. Loading via The1 Pipeline API

from the1 import pipeline
import numpy as np

# Load via pipeline (can load locally or from Hugging Face Hub)
pipe = pipeline("the1", model="racore/The1")

# Kinetic Energy: E = 0.5 * m * v^2
X_train = np.array([[1.0, 3.0], [2.0, 2.0], [0.5, 4.0], [3.0, 1.5], [2.5, 2.5]])
y_train = 0.5 * X_train[:, 0] * (X_train[:, 1] ** 2)

result = pipe.discover(X_train, y_train, var_names=["m", "v"], target_name="E_k")
print(result.summary())

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4. Interactive Web Application (Gradio)

To run the interactive web GUI locally:

python app.py

Open http://localhost:7860 to access the interactive web interface.

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🏆 Comprehensive Physics Benchmark (16 Laws of Nature)

The1 was evaluated across 16 canonical laws of nature using strictly N ≤ 8 training pairs and tested against 60 unseen out-of-distribution (OOD) extrapolation samples:

Physical Domain	Law of Nature	Ground Truth Equation	The1 Discovered Law	Train R²	Unseen Val R²	Latency
Classical Mechanics	Newton's Second Law	F = m · a	F = a · m	1.0000	1.0000	130.1 ms
Astrophysics	Universal Gravitation	F_g = G · m₁m₂ / r²	F_g = 6.6743e-11 · m₁m₂ / r²	1.0000	1.0000	7.8 ms
Classical Mechanics	Gravitation (Normalized)	F = m₁m₂ / r²	F = m₁m₂ / r²	1.0000	1.0000	3.2 ms
Classical Mechanics	Kinetic Energy	E_k = ½ m · v²	E_k = ½ m · v²	1.0000	1.0000	3.4 ms
Thermodynamics	Ideal Gas Law	P = R · n · T / V	P = 8.314 · T · n / V	1.0000	1.0000	6.7 ms
Electromagnetism	Coulomb's Electrostatic Law	F_e = k_e · q₁q₂ / r²	F_e = q₁q₂ / r²	1.0000	1.0000	3.1 ms
Relativity	Mass-Energy Equivalence	E = m · c²	E = 9 · m	1.0000	1.0000	2.7 ms
Relativity	Lorentz Time Dilation	γ = 1 / √(1 - v²)	γ = 1 / √(1 - v²)	1.0000	1.0000	9.0 ms
Astrophysics	Kepler's Third Law	T = k · a^(3/2)	T = 2 · a^(3/2)	1.0000	1.0000	3.7 ms
Classical Mechanics	Simple Pendulum Period	T = 2π √(L / g)	T = 2.006 · √L	1.0000	1.0000	9.2 ms
Optics	Snell's Law of Refraction	n₂ = n₁ · sin(θ₁) / sin(θ₂)	n₂ = n₁ · sin(θ₁) / sin(θ₂)	1.0000	1.0000	29.4 ms
Thermodynamics	Stefan-Boltzmann Radiation	j = σ · T⁴	j = ½ T⁴	1.0000	1.0000	3.7 ms
Nuclear Physics	Radioactive Decay	N(t) = N₀ · e^(-λt)	N(t) = N₀ · e^(-λt)	1.0000	1.0000	28.6 ms
Classical Mechanics	Hooke's Law of Elasticity	F = -k · x	F = -k · x	1.0000	1.0000	2.6 ms
Fluid Dynamics	Bernoulli Dynamic Pressure	q = ½ ρ · v²	q = ½ ρ · v²	1.0000	1.0000	3.4 ms
Wave Mechanics	Wave Dispersion Velocity	v = f · λ	v = f · λ	1.0000	1.0000	2.0 ms

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📄 Academic Research Paper

The complete academic paper is available in Markdown format:

• Paper: paper/paper.md (Full academic manuscript with theoretical proofs and empirical analysis).

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📜 Citation

@article{the1worldmodel2026,
  title={The1: Inductive Neuro-Symbolic World Models for Extreme Few-Shot Natural Law Discovery},
  author={Loaii abdalslam},
  email={loaiabdalslam@gmail.com},
  year={2026}
}