Enabling Dynamic Computation in Looped LMs

Looped language models increase effective depth by repeatedly applying a shared block of layers, but existing large-scale recipes require multi-stage training over trillions of tokens, while the benefits of recurrence remain difficult to separate from differences in data and training. In this work, we establish practical training recipes for looped language models, with three main results. (1) We develop a compute-efficient from-scratch pipeline that reduces the training budget from 7.7T tokens in Ouro to 310B tokens while retaining strong reasoning performance. Pretraining followed by high-quality mid-training, together with learning-rate warmup and stronger exit-gate regularization, enables stable recurrent training without prior multi-stage schedules. (2) Under controlled comparisons, our 1.4B LoopLM outperforms a parameter-matched dense model trained on the same data and token budget on all 12 evaluated benchmarks, including +14 points on GSM8K, +10 on MATH, and +22 on DROP. At matched inference compute, it approaches a 3.9B dense model on mathematical reasoning and reading comprehension while using only 36% as many parameters. (3) We introduce a minimal recipe for converting pretrained dense models into looped ones: a single learned input-mixing scalar and a smoothed exit loss, with no step-specific parameters. Applied to Qwen3-1.7B-Base, Looped Qwen improves over an identically continued dense baseline on every evaluated benchmark across two data regimes, with statistically clear gains on GSM8K, MATH, and MMLU-Pro on the curated mixture. Together, these results make looped language models substantially cheaper to train from scratch and practical to introduce into existing pretrained checkpoints, while isolating the gains due to recurrence itself.

A main promise of looped language models (LMs) is depth-adaptive inference. By iterating a block of shared layers a variable number of times, the model can use less compute for "easy" tokens and more for "hard" ones. However, this adaptivity breaks standard batching: tokens in the same batch now require a different number of loops, so there is no unified forward pass, making efficient inference difficult. Standard inference frameworks like vLLM schedule on the token level and cannot handle this because tokens need to be removed from the batch within the forward pass. Loop-level scheduling has been proposed as a solution, but never implemented end to end. The key challenge is that looped architectures also contain non-looped boundary stages (e.g., token embedding and LM head) that must be scheduled at different frequencies than the loop. We introduce continuous depth batching (CDB), which schedules at the granularity of individual loop iterations. CDB handles boundary stages and loop steps in separate priority queues, makes exit decisions one step ahead, and overlaps all scheduling work with GPU computation. On Ouro 1.4B and Huginn 3.5B, CDB can realize up to $99\%$ of the theoretical maximum speed-up from adaptive-depth, translating to $1.5$-$1.9\times$ higher offline throughput and $45$-$90\%$ lower normalized latency under dynamic serving load.

Looped Transformers have attracted substantial attention as a parameter-efficient approach to increasing computational depth through repeated application of shared Transformer blocks. However, their practical advantages over conventional Transformers remain under debate: each additional loop incurs another Transformer pass and requires caching another set of KV states, causing inference FLOPs and KV-cache memory to grow continuously with loop depth. This overhead becomes particularly severe at large loop counts and long context, preventing the parameter efficiency of Looped Transformers from translating into practical inference efficiency. In this paper, we find that much of the additional computation and storage introduced by looping is redundant. As recurrence proceeds, state changes become increasingly concentrated on a small subset of tokens; attention-output differences are dominated by a sparse and stable subset of key columns; and KV residuals between adjacent loops become progressively more amenable to low-bit quantization. Building on these observations, we introduce FlashLoop, a training-free inference framework that reduces cross-loop redundancy through token-sparse updates, sparse attention, and KV-residual quantization. Across several Looped Transformers models, FlashLoop delivers lossless accuracy while achieving up to 1.64$\times$ end-to-end speedup and up to 6$\times$ KV-cache memory reduction, substantially improving the practicality of scaling Looped Transformers to greater computational depths and longer context.