Loop, Think, & Generalize: Implicit Reasoning in Recurrent-Depth Transformers

Standard Transformers have a fixed computational depth, limiting their ability to generalize to tasks that require variable-depth reasoning. The usual remedy, Chain-of-Thought (CoT), spends tokens to reason, inflating the key--value cache and making latency grow with the step count, so memory becomes the limiting cost when reasoning is served over large query batches. We study a depth-recurrent Transformer that decouples computational depth from parameter count by iterating a shared-weight block, so that each added reasoning step costs flat memory and linear latency, with no token generation. Three ingredients keep the recurrence stable for 20+ thinking steps: a silent thinking objective that supervises only the final output, LayerScale initialization, and an identity-biased gate that opens a gradient highway across steps. We characterize it on three compositional domains with decreasing structural bias: graph reachability (adjacency masking), nested boolean logic (relative positioning), and unstructured relational text (no positional cue). We find a computational frontier: accuracy climbs once the thinking-step count meets the task's complexity, reaching near-perfect performance on the two structured tasks and a lower plateau on unstructured text. How it climbs depends on the structural bias---abruptly from chance on the graph task, gradually on the other two. Depth recurrence extrapolates beyond the training range: it succeeds on the graph task where fixed-depth models barely extrapolate, and on the two sequence tasks comes within two points of fixed-depth Transformers that use $4$--$6.4\times$ more parameters. On the graph task, whose adjacency mask makes propagation depth verifiable, intermediate per-step supervision---a standard recipe for deep iterative models---consistently harms this extrapolation. We release the code for reproducibility.

We investigate the scaling properties of implicit deductive reasoning over Horn clauses in depth-bounded Transformers. By systematically decorrelating provability from spurious features and enforcing algorithmic alignment, we find that in sufficiently deep models with a bidirectional prefix mask, implicit reasoning approaches explicit CoT performance across graph topologies and problem widths, though CoT remains necessary for depth extrapolation.

Large Language Models can perform multi-step reasoning and improve task performance through different forms of intermediate computation, from token-based traces to computation carried out in latent space. However, a question remains open: do these different forms of thinking rely on the same underlying mechanism? To address this, we train and compare five variants of the same GPTNeoX backbone from scratch on an extended multi-hop reasoning task (ProsQA-Ext): a vanilla model, a Chain-of-Thought (CoT) model, a Pause Token model, and two latent-reasoning models that are optimized end-to-end without intermediate reasoning traces. We find that, strong in-distribution (ID) performance does not guarantee depth generalization. Vanilla, CoT, and Pause Token models solve ID problems well, but rely largely on local graph features and generalize poorly to out-of-distribution (OOD) problems with longer hops. In contrast, latent variants generalize better and show internal dynamics consistent with forward reachability propagation on the graph. Causal interventions and circuit analysis localize this computation to a sparse recurrent search circuit in the bottleneck latent model: an attention head retrieves graph relations, an MLP and the residual stream update the reachability state across recurrent steps, while multiple attention heads together then do the candidate matching. Together, these results show that different thinking mechanisms can learn distinct computational solutions, even at similar ID performance. In this setting, latent recurrence supports a reusable forward-search algorithm that generalizes beyond the training depth.