A 10-million-parameter model called GRAM achieves 97% accuracy on hard Sudoku puzzles, surpassing deterministic recursive models three times its size. The key innovation is stochastic recursion that explores multiple reasoning paths in parallel rather than a single deterministic chain.
Key facts
- GRAM: 10 million parameters, 97% on hard Sudoku.
- Best prior recursive model: 87.4% accuracy on same Sudoku.
- 20 parallel samples outperforms 320 recursion steps.
- Sudoku generation: 99% valid puzzles in 16 steps.
- Diffusion baseline: 91% valid with 55M params and 1000 steps.
Most AI reasoning models are trapped on a single train of thought, and GRAM ("Generative Recursive Reasoning") is the first to break that by letting the model think in parallel universes simultaneously [per @rohanpaul_ai]. The problem is that all existing recursive models are fully deterministic, meaning given the same input they always follow the exact same reasoning path and can never escape a wrong trajectory or discover more than 1 valid answer.
GRAM fixes this by injecting learned randomness at each refinement step, so the model samples a slightly different direction each time rather than snapping to 1 fixed next state, which produces a spread of diverse reasoning trajectories. At test time the model runs many of these paths in parallel and selects the best one using a small reward predictor trained alongside the main model, adding a "width" scaling axis on top of the usual "depth" axis of running more recursion steps.
On hard Sudoku puzzles, GRAM with 10M parameters hits 97% accuracy versus 87.4% for the best prior recursive model, and with only 20 parallel samples it outperforms every deterministic baseline even at 320 recursion steps. On tasks with many valid answers like N-Queens, deterministic recursive models collapse as the number of solutions grows, while GRAM maintains near-perfect accuracy throughout.
The same stochastic framework also acts as a generator: given a blank board, GRAM produces valid Sudoku puzzles 99% of the time using 16 steps, versus 1,000 steps and 55M parameters for the best diffusion baseline at just 91%.
The unique take: GRAM challenges the prevailing assumption that more parameters and deeper recursion are the only ways to improve reasoning. By adding a width axis through parallel stochastic trajectories, it achieves superlinear scaling efficiency — a 3x parameter disadvantage is neutralized by 20 parallel samples. This suggests that for many reasoning tasks, compute may be better spent on parallel exploration than on scaling model size or recursion depth alone.
What to watch
Watch for open-source implementations of GRAM on GitHub and whether larger models (100M+ parameters) using the same stochastic recursion paradigm can match or exceed chain-of-thought performance on general reasoning benchmarks like GSM8K or MATH. A paper with ablation studies on the reward predictor's architecture would clarify the scalability ceiling.
