Amr Hegazy, Amr Alanwar, Mostafa Elhoushics.CL cs.LG
Scaling transformer language models creates an inherent tension between expressivity and memory efficiency. While unique weights across layers preserve functional specialization---from input-grounding to abstract refinement---they incur a substantial memory footprint. Conversely, standard depth-sharing enforces uniform transformations that collapse representational diversity and degrade modeling quality. We introduce Gated Recurrent Transformer, a recurrent depth transformer where fixed-depth prelude and coda blocks bracket a single shared core iterated R times. Inspired by gated recurrent neural networks, we employ a lightweight projection and an elementwise update gate---conditioned on the hidden state, the fixed prelude output, and noise resampled at every step---to modulate the recurrent update. This allows the model to specialize the input to the same few layers across recurrences, rather than requiring many unique layers to achieve functional diversity. Under an isoFLOPS constraint, a 3-layer Gated Recurrent Transformer matches the accuracy of a 12-layer GPT-2 Small baseline with similar training and inference FLOPs, and leads MoR and heavy-tail depth sampling in all nine scale-by-budget cells; at medium and large scale it approaches dense quality at the standard token budget and overtakes it at medium scale once that budget is doubled. Under an isoPARAMS constraint, deeper recurrence achieves a 2.76 validation loss versus 2.84 for a non-recurrent counterpart at matched parameter and data budget. Our results demonstrate that adaptive depth reuse is a principled strategy for trading parameters for quality: at large scale, 63% fewer parameters and 59% less peak decoding memory for a 10% increase in compiled generation latency.
We test whether the "compositional ignition" reported in latent-reasoning models is real computation, an instrument artifact, or inherited from verbal training data. We grow an independent realization of a published 30M-parameter recurrent-depth reasoner from scratch (same recipe and seed), film its development, certify fidelity through a pre-registered whole-signature gate, and measure resolution in two channels at once: the vocabulary readout and the hidden state. The ignition is real and lives at the readout: arrival time rises lawfully with problem depth, resolution is sharp and holds, and the signature reproduces across two same-seed realizations with divergent training trajectories. At commitment the decision margin jumps 5.8-8.0 logits in one iteration, exceeding the 90th percentile of near-threshold non-event steps in 96% of cases; the signed margin's zero-crossing there is definitional and carries no evidential weight, so the evidence is that conditioned magnitude. The hidden-state direction snaps in raw geometry, meeting its pre-registered criterion (in the decoder's LayerNorm coordinates it attenuates just below our bar, so the composite decoder-coordinate claim is not confirmed), and then freezes in both (descriptively so in decoder coordinates; angular steps 52.9 to 1.2 degrees over eight iterations), while subsequent displacement is predominantly radial (0.961 of squared-norm) and readout-null to a measured bound (radial logit effect <=5.7e-6). An earlier velocity-trough claim is withdrawn: pre-registered normalization controls showed it coordinate-dependent. Intermediates were never recoverable through the tied readout (relay 0.00). All criteria were frozen before their data; the predictions ledger, including this paper's own withdrawn headline, ships in the companion repository.
A dense, pretrained language model can be retrofitted with recurrent depth and learn an iterative latent transition that persists after outcome-only annealing. Qwen2.5-0.5B-Instruct is split into a Prelude, a weight-tied Recurrent Block, and a Coda, with an identity-preserving one-loop path and a re-entry bridge on later loops. At loop 1 the retrofit remains non-inferior to its base on a preregistered ARC battery. Three findings. First, the mechanism is a reusable procedure rather than terminal-answer lookup, and installs at two budgets: 6M trained parameters over frozen base weights and 180M full-block. With intermediate-step supervision, the model computes one task step per loop and persists when only final answers are graded. The adapter matched the full block overall (83.8% versus 84.0%), led through depth 11, and trailed beyond. Verbal fine-tuning reached 79-86% on controlled verbal renderings (zero-shot transfer was minimal), and adapter verbal training begun from the installed mechanism outpaced matched fresh training by 18.6 points, including on a held-out test set. Second, the operation extrapolates to roughly 1.5 times its supervised depth, holding 70% accuracy through depth 18. Third, a same-size scratchpad-trained model matched the recurrent model within its learned horizon but collapsed beyond it. The recurrent model won overall, 84% versus 72%, retained 53% versus 2.5% beyond depth 10, and answered 7.6 times faster. An iterative transformer can therefore perform deeper reasoning in latent space faster than comparable or larger models fine-tuned on the same task, in a system-level comparison. A second task, running the rule in reverse, exposed the limits: the inverse was learnable in isolation, but no continuation acquired it while preserving the installed mechanism and general capability, a catastrophic-interference boundary. Learned depth selection remains open.
Bum Jun Kim, Kohei Hayashi, Shunsuke Kamiya +3cs.LG cs.CL
Looped Transformers create a useful train- and test-time compute axis by reusing the same Transformer block over recurrent depth, increasing effective depth at a fixed parameter count. However, that shared block must then govern an entire trajectory of varying hidden states over trained and extrapolated depths. Furthermore, in additive-injection looped Transformers, an input-conditioned signal is reintroduced at every recurrent step, so applying the shared transition at an input-conditioned reference can still move the hidden state. In this paper, we propose Source-Centered State Evolution (SCSE), which is designed to reconcile input conditioning with reference-preserving shared recurrence. Specifically, SCSE retains input dependence through its learned anchor and initial deviation, allows nonzero deviations to drive recurrent computation while mapping zero deviation to zero, and guarantees exact anchor invariance through its zero-deviation mask. The designated anchor is thereby a one-step fixed point by construction. The zero-deviation forcing bias is the next deviation produced from the anchor itself and vanishes in SCSE, while nonzero deviations remain active and support state-dependent recurrent computation. Our theory shows that the zero-deviation forcing bias is a design degree of freedom whose task effect can be harmful, neutral, or beneficial; SCSE resolves this choice in favor of exact anchor invariance by setting the bias to zero. Across WikiText-2, WikiText-103, direct web-corpus pretraining, held-out web-text transfer, and LAMBADA completion, SCSE improves the controlled recurrent quality frontier. Ablation studies identify the learned anchor and the anchor-coordinate deviation recurrence as the primary contributors to the gain, and a trained-model case study grounds the anchor-response diagnostic in observed recurrent motion.