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—less than one-tenth of a cent. 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.

Introduction. In-context learning allows a model to acquire a new skill from examples presented at inference time (Brown et al., 2020). In autoregressive language models, chain-of-thought (CoT) prompting complements this capability with a computational workspace: demonstrations specify what to do, while generated intermediate tokens support the computation required to do it (Nye et al., 2021; Wei et al., 2022). Reinforcement learning on verifiable problems has made this combination increasingly powerful, eliciting long reasoning traces, self-verification, and adaptive solution strategies (DeepSeek-AI et al., 2025). It also couples reasoning to serial narration. As reasoning traces have grown, so have token consumption, latency, and inference compute. Every intermediate state must be projected through a discrete vocabulary, emitted autoregressively, and consumed again before computation can continue. Latent reasoning opens a different computational regime. Instead of verbalizing every intermediate result, a model repeatedly transforms its continuous hidden state and decodes only the answer.

Discussion / Conclusion. The system-level result is direct: a 150M-parameter BDH-CQ reaches 29.5% pass@2 on the public ARC-AGI-1 evaluation set at a computed $0.00070 per task. This breaks through the reported cost–accuracy Pareto frontier and establishes a new state of the art in benchmark cost efficiency. The unusually low starting cost also creates room to increase model capacity and reasoning compute while remaining competitive with existing systems. The controlled experiments show what that combination can express. BDH-CQ applies dense task-specific color mappings to all 96 held-out outputs, demonstrating substantial contextual binding capacity. Boundary propagation and copying extrapolate throughout the tested ranges, while ordering and nested containment expose distinct limits. Matched demonstrations eliminate the observed depth-five nesting failures and substantially improve length-eight ordering, showing that coverage in the in-context examples can determine whether a learned operation extrapolates. Composition is more representation-dependent: rotation composes with relocation on all 72 held-out outputs, whereas reflection succeeds on 47/72 and varies sharply across motif families; color swapping is not acquired reliably outside the original fixed layout.