Recurrent Transformers

Chain-of-thought (CoT) prompting enables reasoning in language models but requires explicit verbalization of intermediate steps. Looped transformers offer an alternative by iteratively refining representations within hidden states. This parameter efficiency comes at a cost, as looped models lack the storage capacity of deeper models which use unique weights per layer. In this work, we investigate transformer models that feature both adaptive per-layer looping, where each transformer block learns to iterate its hidden state via a learned halting mechanism, and gated memory banks, that provide additional learned storage. We find that looping primarily benefits mathematical reasoning, while memory banks help recover performance on commonsense tasks compared to parameter and FLOP matched models. Combining both mechanisms yields a model that outperforms an iso-FLOP baseline, with three times the number of layers, across math benchmarks. Analysis of model internals reveals layer specialization: early layers learn to loop minimally and access memory sparingly, while later layers do both more heavily.

Structured dilated attention has an appealing inference-time efficiency knob: it reduces the FLOPs of attention and the KV cache size by a factor of the dilation size D, while preserving long-range connectivity. While prior work studies it by training each configuration from scratch, directly sparsifying a pretrained attention model into a dilated pattern leads to severe accuracy degradation, preventing flexible reuse across inference scenarios. We introduce RAT+, a dense-pretraining architecture that augments attention with full-sequence recurrence and active recurrence learning. A single RAT+ model is pretrained densely once and can then be flexibly switched at inference time to dilated attention (optionally with local windows) or hybrid layer/head compositions, requiring only a short 1B-token resolution adaptation rather than retraining separate sparse models. At 1.5B parameters trained on 100B tokens, RAT+ closely matches dense accuracy at D = 16, and drops by about 2-3 points at D = 64 on commonsense reasoning and LongBench tasks. We further scale to 2.6B and 7.6B parameters and observe even more promising performance (e.g., a 1-point average accuracy loss with a 64x reduction in attention FLOPs and KV cache size). Code is available at https://github.com/wimh966/rat-plus.

Standard Transformers excel at semantic modeling but struggle with rigid sequential logic and state tracking. Theoretical work establishes that self-attention is limited to $\AC^0$ (under hard attention) or $\TC^0$ (under soft attention), complexity classes that often fail to support robust length generalization on sequential problems without intermediate chain-of-thought \citep{hahn2020theoretical, hao2022formal, merrill2022saturated}. In this work, we introduce Rational Transductors, a dual-stream architecture that augments the Transformer with a matrix-valued recurrence derived from Weighted Finite Automata (WFA). By injecting rational state information into the attention mechanism via a Deep Rational Injection scheme, our framework strictly generalizes the expressive power of Transformers to capture all Regular Languages, $\NC^1$-complete languages (such as the word problem of $S_5$), and fundamental separations like Parity and Modular Counting, while preserving $O(\log T)$ parallel training efficiency. We ground the architecture in a rigorous learning theory: we prove that Random Rational Features act as a universal basis for sequential dependencies, justifying our initialization strategy, while establishing that the Differentiable Rational Feature regime is necessary to close the representational compactness gap. Theoretical analysis and empirical results demonstrate that Rational Transductors solve the ``Regular Gap,'' enabling robust length generalization on algorithmic tasks where standard Transformers fail, without the sequential computational bottlenecks of traditional RNNs.