Classical energy models solve reasoning puzzles much faster than looped models
Classical Energies Learn to Reason 1,000x Faster than Looped Models
Artificial IntelligenceMachine Learning
Summary
Solving puzzles like Sudoku and mazes with computers can be slow and complicated using current methods called looped models. The authors show that using a classical approach based on energy, called CRAM, can solve these puzzles much faster and with less computing power. CRAM trains quickly, adapts to how hard the puzzle is, and is easier to understand. This method also warns against relying only on simple puzzle tests to measure puzzle-solving models.
What this means in practice
- •For ai developers: Build faster reasoning algorithms for solving constraint puzzles by training energy-based models that use fewer computing resources and adapt to problem difficulty.
- •For game developers: Create puzzle games with integrated solvers that run efficiently on consumer hardware by using fast-trained energy models instead of slower looped models.
Authors
Benjamin Hoover, Hugh Blayney, James C. R. Whittington
Abstract
Looped models have emerged as a prominent paradigm for reasoning, with successes on simple reasoning puzzles such as Sudoku-Extreme and Maze-Unique. However, these models can be unstable, slow to train, and use many parameters and FLOPs to solve simple puzzles. Descent on an energy not only mitigates these issues but also offers advantages: built-in early stopping, compute that adapts to problem difficulty, fast training without differentiating through a solver, and interpretable weights that learn the constraints of the puzzle. Here we demonstrate this with a learned version of Hopfield & Tank's energy from the 80s, which we term CRAM, solves 99.996% of Sudoku-Extreme and 100% of Maze-Unique test puzzles after 42 ms and 132 ms of training on one GPU, at least 1,000x faster than looped models on these tasks. CRAM also matches baseline looped models at their highest accuracy on Sudoku-Extreme using at least 282x fewer inference FLOPs. Our work suggests two things. First, that energies are an extremely promising direction for training reasoning from data. Second, a caution against using trivially solvable benchmarks like Sudoku and Maze to test the scalability of looped reasoning techniques.