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How It Works

AlphaCube introduces the following features:

1. Smooth Trade-off Between Latency & Quality​

AlphaCube offers a unique trade-off mechanism that dynamically balances latency and solution quality. As you allocate more time for solving, the generated solutions become increasingly refined.

2. Ergonomic Solve with Biasing​

AlphaCube empowers you to customize the AI solver's behavior by applying an "ergonomic bias." This feature allows you to bias the solver towards finding speed-optimal algorithms, aligning with your preferences and requirements.

These features are underpinned by the probabilistic nature of AlphaCube's fundamental method, as described below.

EfficientCube​

AlphaCube methodologically builds upon EfficientCube (TMLR'23), the state-of-the-art deep learning method for solving goal-predefined combinatorial problems (outperforming DeepCubeA).

At its core, a Deep Neural Network (DNN) is trained to predict next moves that would bring a given state one step closer to the goal. EfficientCube sequentially applies these predicted moves to solve the given challenge.

Conceptual overview of the method introduced by EfficientCube

Under the hood, the DNN emits a probability distribution of optimal moves to evaluate candidate moves.

Probability distribution of optimal moves

EfficientCube evaluates solution candidates based on these probabilities. By employing a search method called beam search, EfficientCube trades off computation time for better/shorter solutions.

Please refer to the original paper and the source code for more details, such as how solution candidates are evaluated.

Speed-optimal solutions​

Leveraging the probabilistic nature of EfficientCube, we can also obtain ergonomic/speed-optimal solutions.

By applying a "ergonomic bias distribution" to the predicted probability distribution of next moves, the AI solver's output can be intentionally skewed towards speed-optimality:

Applying the desirability distribution for biasing

To be more specific, calculating the dot product between the distributions of theoretically optimal moves and ergonomic/desirable moves creates a speed-optimal probability distribution for the next moves. Technically, this approach reframes the Rubik's Cube as a weighted implicit graph, where edge lengths represent their ease of manual execution. Properly controlling this ergonomic bias to your preference gives you not just efficient but also speed-optimal solutions that align with your fingers.