Generative Recursive Reasoning

TL;DR

GRAM (Generative Recursive reAsoning Models) turns recursive latent-state reasoning into a stochastic, multi-trajectory generative process. Where existing Recursive Reasoning Models (RRMs) iteratively refine a single deterministic latent trajectory toward a single answer, GRAM samples a distribution over latent trajectories, enabling multiple hypotheses, alternative solution strategies, and inference-time scaling along two axes: recursive depth and parallel trajectory sampling. The model is trained with amortized variational inference and supports both conditional reasoning $p_\theta(y \mid x)$ and unconditional generation $p_\theta(x)$ . It improves over deterministic recurrent/recursive baselines on structured reasoning and multi-solution constraint-satisfaction tasks.

Key claims

Existing recursive reasoning models perform iterative latent-state refinement with shared transition functions but are largely deterministic, converging to a single prediction along one latent trajectory [Abstract].
GRAM reformulates recursive reasoning as a stochastic latent trajectory, yielding a latent-variable generative model that supports conditional reasoning and (with fixed/absent inputs) unconditional generation [Abstract].
Inference-time compute can be scaled along two independent axes — recursive depth and parallel trajectory sampling — enabling multiple hypotheses for the same input [Abstract].
Trained with amortized variational inference, GRAM outperforms deterministic recurrent and recursive baselines on structured reasoning and multi-solution constraint satisfaction tasks [Abstract].

Method

GRAM keeps the RRM backbone — a shared transition function applied recursively to a latent state — but replaces the deterministic update with a stochastic one, so the latent at each step is sampled from a learned distribution rather than computed by a fixed map. Training is via amortized variational inference: an inference network proposes latent trajectories conditioned on input (and target, during training), and the model is trained to maximize an ELBO over the trajectory distribution. The resulting object is a latent-variable generative model $p_\theta(y \mid x)$ (conditional reasoning) that reduces to $p_\theta(x)$ when the input is fixed or absent, giving unconditional sample generation from the same machinery.

Results

The paper reports improvements over deterministic recurrent and recursive baselines on structured reasoning and multi-solution constraint-satisfaction tasks, and demonstrates an unconditional generation capability that deterministic RRMs do not natively support [Abstract]. Specific benchmark numbers are not extractable from the abstract alone.

Why it’s interesting

Recursive/looped transformers and “thinking longer in latent space” have become a recurring theme — GRAM is one of the cleaner formulations of why you’d want stochasticity in that loop: multi-solution problems (constraint satisfaction, planning) have genuinely multiple correct answers, and a deterministic recurrent model can only commit to one. The two-axis inference-time scaling (depth × parallel samples) is also a useful frame for thinking about test-time compute budgets in latent-reasoning architectures. Matt’s pointer to “looped transformers” is apt: GRAM is essentially what happens when you put a VAE-style latent inside the loop.