AlphaCube

AlphaCube is a powerful & flexible Rubik's Cube solver that extends EfficientCube. It uses a Deep Neural Network (DNN) to find optimal/near-optimal solutions for a given scrambled state.

Note

🎮 Try the interactive demo: alphacube.dev

Use Cases

• Solve any scrambled Rubik's Cube configuration with ease
• Find efficient algorithms/solutions, optimizing for either computation speed or ergonomics of the move sequence
• Incorporate into Rubik's Cube apps and tools to provide solving capabilities
• Analyze and study the statistical properties and solution space of the Rubik's Cube puzzle
• Illustrate AI/ML concepts to students. Topics include:
  • discrete diffusion model
  • self-supervised learning
  • combinatorial search with probabilities

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Table of Contents

• AlphaCube
  • Use Cases
  • Table of Contents
  • Installation
  • Usage
    • Basic
    • Better Solutions
    • Applying Ergonomic Bias
    • GPU Acceleration
  • How It Works
  • Contributing
  • License

Installation

Open a terminal and execute the following command:

pip install -U alphacube

Usage

Basic

import alphacube

# Load a trained DNN (default: "small" on cpu, "large" on GPU)
alphacube.load()

# Solve the cube using a given scramble sequence
result = alphacube.solve(
    scramble="D U F2 L2 U' B2 F2 D L2 U R' F' D R' F' U L D' F' D R2",
    beam_width=1024, # Number of candidate solutions to consider at each depth of search
)
print(result)

Output

{
    'solutions': [
        "D L D2 R' U2 D B' D' U2 B U2 B' U' B2 D B2 D' B2 F2 U2 F2"
    ],
    'num_nodes': 19744, # Total search nodes explored
    'time': 1.4068585219999659 # Wall-clock time in seconds
}

Better Solutions

Increasing beam_width explores more candidate solutions, producing shorter (better) solve sequences at the cost of increased computation:

result = alphacube.solve(
    scramble="D U F2 L2 U' B2 F2 D L2 U R' F' D R' F' U L D' F' D R2",
    beam_width=65536,
)
print(result)

Output

{
    'solutions': [
        "D' R' D2 F' L2 F' U B F D L D' L B D2 R2 F2 R2 F'",
        "D2 L2 R' D' B D2 B' D B2 R2 U2 L' U L' D' U2 R' F2 R'"
    ],
    'num_nodes': 968984,
    'time': 45.690575091997744
}

beam_width values between 1024-65536 typically offer a good trade-off between solution quality and speed. Tune according to your needs.

Applying Ergonomic Bias

The ergonomic_bias parameter lets you specify the desirability of each move type, influencing the solver to favor certain moves over others:

# Desirability scale: 0 (lowest) to 1 (highest)
ergonomic_bias = {
    "U": 0.9,   "U'": 0.9,  "U2": 0.8,
    "R": 0.8,   "R'": 0.8,  "R2": 0.75,
    "L": 0.55,  "L'": 0.4,  "L2": 0.3,
    "F": 0.7,   "F'": 0.6,  "F2": 0.6,
    "D": 0.3,   "D'": 0.3,  "D2": 0.2,
    "B": 0.05,  "B'": 0.05, "B2": 0.01,
    "u": 0.45,  "u'": 0.45, "u2": 0.4,
    "r": 0.3,   "r'": 0.3,  "r2": 0.25,
    "l": 0.2,   "l'": 0.2,  "l2": 0.15,
    "f": 0.35,  "f'": 0.3,  "f2": 0.25,
    "d": 0.15,  "d'": 0.15, "d2": 0.1,
    "b": 0.03,  "b'": 0.03, "b2": 0.01
}

result = alphacube.solve(
    scramble="D U F2 L2 U' B2 F2 D L2 U R' F' D R' F' U L D' F' D R2",
    beam_width=65536,
    ergonomic_bias=ergonomic_bias
)
print(result)

Output

{
    'solutions': [
        "u' U' f' R2 U2 R' L' F' R D2 f2 R2 U2 R U L' U R L",
        "u' U' f' R2 U2 R' L' F' R D2 f2 R2 U2 R d F' U f F",
        "u' U' f' R2 U2 R' L' F' R u2 F2 R2 D2 R u f' l u U"
    ],
    'num_nodes': 1078054,
    'time': 56.13087955299852
}

GPU Acceleration

For maximum performance, use the "large" model on a CUDA-enabled GPU (requires PyTorch):

alphacube.load("large")
result = alphacube.solve(
    scramble="D U F2 L2 U' B2 F2 D L2 U R' F' D R' F' U L D' F' D R2",
    beam_width=65536,
)
print(result)

Output

{
    'solutions': ["D F L' F' U2 B2 U F' L R2 B2 U D' F2 U2 R D'"],
    'num_nodes': 903448,
    'time': 20.46845487099995
}

Using a GPU provides an order of magnitude speedup over CPUs, especially for larger models.

Important

When running AlphaCube on a CPU, it's generally recommended to stick with the "small" model, as the larger "base" and "large" models would take considerably more time to find solutions.

Please refer to our documentation for more, especially "Getting Started"

How It Works

At the heart of AlphaCube lies a deep learning method described in "Self-Supervision is All You Need for Solving Rubik's Cube" (TMLR'23), the official code of which is also available as EfficientCube.

The 3 provided models ("small", "base", and "large") are compute-optimally trained in the Half-Turn Metric, This means the model sizes are scaled in tandem with the amount of training data to maximize prediction accuracy for a given computational budget. See Section 7 of the above-mentioned paper for details.

Note

📖 Read more: "How It Works"

Contributing

You are more than welcome to collaborate on AlphaCube. Please read our Contributing Guide to get started.

License

AlphaCube is open source under the MIT License.