BDH-CQ: In-Context Learning with Recurrent Latent Reasoning

We introduce BDH-CQ, a reasoning model that combines in-context learning with recurrent latent reasoning. Inputs presented at inference time continuously update the model's recurrent memory; the model then solves a query through iterative computation in a high-dimensional latent space, without verbalizing its intermediate reasoning. We evaluate the model on the public ARC-AGI-1 evaluation set and use controlled ARC-like interventions to study what it learns from demonstrations, how consistently it applies an inferred transformation, and which concepts remain difficult. A 150M-parameter configuration reaches 29.5% pass@2 at a computed inference cost of \$0.0007 per task. This operating point breaks through the previously reported ARC-AGI-1 cost-accuracy Pareto frontier, establishing a new state of the art in benchmark cost efficiency.

When to Re-Plan: Subgoal Persistence in Hierarchical Latent Reasoning

Long-horizon reasoning requires a system to commit to medium-horizon intent without becoming rigid: re-plan too often and computation never coheres into multi-step structure; commit too long and the plan goes stale. We study this stability-adaptivity tradeoff in the latent reasoning setting, where multi-step computation occurs inside hidden state rather than externalized token traces. We extend the Hierarchical Reasoning Model (HRM) with a feudal-style manager-worker interface: a slow high-level module periodically emits a normalized directional subgoal that persists for P low-level steps, biasing the worker's hidden-state updates and supplying an intrinsic cosine alignment loss. On ARC and ConceptARC, we find that subgoal persistence -- not subgoal injection alone -- is the central knob: moderate periods P in [3, 6] consistently outperform both very frequent (P=1) and very long horizons, with a clear minimum LM loss at P=3 (1.544 vs. 1.674 at P=1, 1.640 baseline; replicated over 5 seeds at mean 1.595, std 0.045). The intrinsic alignment weight lambda shows a complementary narrow optimum (lambda approximately 0.05). A controlled ablation at past-sweet-spot lambda isolates learned directional structure -- not architectural capacity or auxiliary loss alone -- as the source of interference when the alignment signal exceeds its optimum. Together these findings implicate a design principle for compositional planning in latent reasoning systems: medium-horizon intent must be coherent across enough computational steps for compositional structure to form.