DeepLoop: Depth Scaling for Looped Transformers

• URL: http://arxiv.org/abs/2607.13491v1
• Date: Wed, 15 Jul 2026 06:37:05 GMT
• Title: DeepLoop: Depth Scaling for Looped Transformers
• Abstract summary: Looped Transformers scale sequential computation by applying a compact stack of physical blocks for multiple rounds.<n>We formalize this tied-depth effect through a first-order perturbation bound controlled by a visit-alignment coefficient.<n>The resulting method, textbfDeepLoop, keeps the Post-LN DeepNorm architecture and sets $= (2N)1/2$ and $=(8N)-1/2$ for unrolled depth.
• Score: 91.7922038545625
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Looped Transformers scale sequential computation by applying a compact stack of physical blocks for multiple rounds, increasing unrolled depth without increasing stored parameters. This reuse changes the residual-scaling problem: in an untied Transformer, each residual branch receives and applies its own parameter update, whereas in a looped Transformer one shared update aggregates gradients from repeated visits and is read back by those same visits in the next linearized forward pass. We formalize this tied-depth effect through a first-order perturbation bound controlled by a visit-alignment coefficient $κ_R$. The bound recovers the DeepNorm exponent when visits decorrelate, but in the conservative aligned regime it requires the exponent to increase from $1/4$ to $1/2$ as loop count grows at fixed physical depth. The resulting method, \textbf{DeepLoop}, keeps the Post-LN DeepNorm architecture and sets $α=(2N)^{1/2}$ and $β=(8N)^{-1/2}$ for unrolled depth $N$. On GPT-style looped language models at GPT-2 small and GPT-2 medium scale, DeepLoop is neutral when no physical block is revisited and improves validation loss and downstream accuracy once recurrent depth is activated. These results show that stable recurrent depth requires residual scaling rules that account for parameter visits, not only nominal layer count.

Related papers

• SMELT: Scaling Laws for Compute-Matched MoE Looped Transformers [50.00050394179417]
  Looped Transformers increase effective depth by iterating a shared block of layers, but most evaluations compare at fixed model size.<n>We study looping on Mixture-of-Experts Transformers while closely matching per-token FLOPs, total non-embedding parameters, and KV cache.<n>Through a series of ablations, we arrive at a recipe we call SMELT, which loops the middle half of layers twice while matching the unlooped Baseline on all three budgets.
  arXiv  Detail & Related papers  (2026-09-01T14:52:57Z)
• RecurrentGPT: Expressive Depth through Recurrent Modulation in Transformers [8.085475675888045]
  RecurrentGPT is a recurrent depth transformer where fixed-depth prelude and coda blocks bracket a single shared core iterated R times.<n>Inspired by gated recurrent neural networks, we employ a lightweight projection and an elementwise update gate to modulate the recurrent update.<n>Our results demonstrate that adaptive depth reuse is a principled strategy for trading parameters for quality.
  arXiv  Detail & Related papers  (2026-08-15T06:22:00Z)
• LoopMTP: A looped transformer guided by latent multi-token prediction [2.2694459418593698]
  Multi-token prediction (MTP) supplies exactly the dense, forward-looking supervision the loop is missing.<n>textscLoopMTP improves average accuracy by up to 8.1% (relative) over the non-looped baseline.
  arXiv  Detail & Related papers  (2026-08-04T13:13:09Z)
• Hidden Decoding at Scale: Latent Computation Scaling for Large Language Models [75.80275843320511]
  We study whether an existing backbone can keep improving by allocating more computation to each token while leaving the Transformer backbone fixed.<n>We propose Hidden Decoding, a sequence-length scaling method applied during continued pretraining.
  arXiv  Detail & Related papers  (2026-07-09T07:37:59Z)
• On the Residual Scaling of Looped Transformers: Stability and Transferability [31.27468588849646]
  We show that $1/N$ scaling improves trainability and yields better loss than $1/!sqrtN$ scaling across loop counts.<n>Experiments on looped Transformers confirm that $1/N$ scaling improves trainability and yields better loss than $1/!sqrtN$ scaling across loop counts.
  arXiv  Detail & Related papers  (2026-06-16T22:39:13Z)
• Latent Recurrent Transformer: Architecture Exploration, Training Strategies, and Scaling Behavior [107.2098567818173]
  Latent Recurrent Transformer (LRT) is a lightweight augmentation of autoregressive transformers.<n>LRT reuses a high-level source-layer hidden state from the previous token as recurrent memory for the next token.
  arXiv  Detail & Related papers  (2026-05-26T10:10:26Z)
• The Recurrent Transformer: Greater Effective Depth and Efficient Decoding [48.9323408950142]
  We introduce the Recurrent Transformer, a simple architectural change where each layer attends to key-value pairs computed off its own activations.<n>We show that the architecture can emulate both (i) a conventional Transformer and (ii) token-to-gressive recurrent updates under mild assumptions.
  arXiv  Detail & Related papers  (2026-04-23T02:12:58Z)
• Robust Layerwise Scaling Rules by Proper Weight Decay Tuning [50.11170157029911]
  In modern scale-invariant architectures, training quickly enters an degrading-governed steady state.<n>We introduce a weight-decay scaling rule for AdamW that preserves sublayer gain across widths.<n>Our results extend $mu$P beyond the near-init regime by explicitly controlling the steady-state scales set by parameters.
  arXiv  Detail & Related papers  (2025-10-17T02:58:35Z)
• MeSH: Memory-as-State-Highways for Recursive Transformers [23.995570647573484]
  Recursive models with fewer parameters often lag behind non-recursive counterparts under matched compute.<n>By probing hidden states, we trace this performance gap to two primary bottlenecks.<n>We introduce a Memory-as-State-Highways scheme, which externalizes state management into an explicit memory buffer.
  arXiv  Detail & Related papers  (2025-10-09T03:23:38Z)
• Arithmetic-Mean $μ$P for Modern Architectures: A Unified Learning-Rate Scale for CNNs and ResNets [9.94514344279733]
  Arithmetic-Mean $mu$P constrains not each individual layer but the network-wide average one-step pre-activation second moment to a constant scale.<n>We prove that, for one- and two-dimensional convolutional networks, the maximal-update learning rate satisfies $etastar(L)propto L-3/2$; with zero padding, boundary effects are constant-level as $Ngg k$.
  arXiv  Detail & Related papers  (2025-10-05T19:22:50Z)
• Scaling Up Liquid-Resistance Liquid-Capacitance Networks for Efficient Sequence Modeling [50.994194925685434]
  LrcSSM is a $textitnon-linear$ recurrent model that processes long sequences as fast as today's linear state-space layers.<n>By forcing its Jacobian matrix to be diagonal, the full sequence can be solved in parallel.<n>LrcSSM offers a formal gradient-stability guarantee that other input-varying systems such as Liquid-S4 do not provide.
  arXiv  Detail & Related papers  (2025-05-27T20:02:59Z)
• Approximation Bounds for Transformer Networks with Application to Regression [9.549045683389085]
  We explore the approximation capabilities of Transformer networks for H"older and Sobolev functions.<n>We establish novel upper bounds for standard Transformer networks approxing sequence-to-sequence mappings.<n>We show that if the self-attention layer in a Transformer can perform column averaging, the network can approximate sequence-to-sequence H"older functions.
  arXiv  Detail & Related papers  (2025-04-16T15:25:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.