Authors: Xiangdong Zhang, Xiaohan Qin, Sunan Zou, Tuo Dai, Xiaoming Shi, Huaijin Wu, Yebin Yang, Zhuo Xia, +5 more
Abstract
Hyper-Connections (HC) expand the residual stream of Transformers into N parallel streams, providing a form of memory scaling beyond model width and depth. Manifold-Constrained HC (mHC) stabilizes this formulation at scale. The large gains from N=1 to N=4 suggest residual-stream expansion as a promising scaling axis. However, existing HC-family methods typically stop at N=4. Our experiments reveal why: scaling mHC beyond this point yields diminishing performance gains and rapidly increasing training cost. We attribute this limitation to two bottlenecks: insufficient write-back information for an expanding number of streams and residual-mixing generation whose cost scales cubically with N. To address both bottlenecks, we propose xHC (Expanded Hyper-Connections), the first HC-family method to achieve meaningful expansion beyond N=4. xHC combines temporal feature augmentation for richer write-back with a sparse residual-stream architecture that updates only k=4 of the N=16 streams while retaining dense access to the full residual state. Across 18B and 28B MoE models, xHC delivers strong and consistent downstream improvements. On an 18B MoE model, xHC improves the average downstream score by 4.0 points over mHC, while adding only modest training FLOPs over the vanilla baseline. Scaling-law experiments show that the vanilla and mHC require 1.50× and 1.19× the compute of xHC, respectively, to reach the same loss. Practical large-N training also requires controlling memory traffic from the expanded residual state. We therefore introduce xHC-Flash, which reduces the per-sublayer memory traffic from 73.5C to 40C, comparable to the 34C required by mHC at N=4, while retaining the gains of full xHC. Together, xHC and xHC-Flash make large-N residual-stream expansion effective and practical for LLM pre-training.
Hyper-Connections (HC) replace the single Transformer residual stream with multiple streams, introducing a permutation symmetry over stream indices. We study how this symmetry is resolved in practice: whether streams specialize in a balanced way or exhibit dominant-stream usage. Using fine-grained diagnostics for HC-based language models, we trace how multi-stream representations are actually used. We find that after an early seeding stage, residual mixing often remains close to identity, limiting a core HC mechanism for exchanging information between streams. Moreover, both signal and interpretable features concentrate in a dominant stream, and the nominally multi-stream residual connection can underutilize its capacity, behaving closer to a single-stream residual pathway. Finally, we show that breaking symmetry at stream initialization reduces dominant behavior and improves performance across \textit{m}HC variants. Our code is publicly available.
Ekaterina Alimaskina, Gleb Molodtsov, Aleksandr Beznosikov
Scaling Large Language Models (LLMs) has been driven mainly by enlarging the Transformer backbone, but for an already-strong model this requires another round of costly pretraining. We study whether an existing backbone can keep improving by allocating more computation to each token while leaving the Transformer backbone fixed. Depth-recurrent (looped) Transformers pursue this goal but are hard to scale, because looped computation does not fit naturally with the pipeline parallelism used to train the largest models. We add computation along the sequence-length dimension, where the extra computation is simply a longer input and stays compatible with standard large-model training. We propose Hidden Decoding, a sequence-length scaling method applied during continued pretraining (CPT). It expands each token into n streams with independent embedding tables and keeps the intermediate streams' key-value cache as context, so each token performs more internal computation without adding or widening Transformer layers. To keep this affordable at scale, we introduce Stream-Factorized Attention, in which most layers attend only within each stream and only a few layers mix across streams, reducing the attention cost from quadratic to roughly linear in n. Experiments support two scaling results. At frontier scale, we train WeLM-HD4-80B and WeLM-HD4-617B at n=4 and improve their matched non-HD baselines, making Hidden Decoding the first demonstrated sequence-length scaling method at the 100B+ MoE scale. Across expansion factors, the gains grow as n increases, showing that sequence-length expansion is a practical fixed-backbone scaling path for frontier-scale LLMs.
Most parameter-efficient finetuning (PEFT) methods adapt weights or activations, thus leaving one of the key Transformer components unchanged: residual connections. This paper investigates Manifold-Constrained Hyper-Connections (mHC), a generalisation of residual connections, as a novel PEFT approach, wrapping frozen OLMo-2 backbones with learned residual routing modules. We find that mHC can finetune frozen Transformers, but that its role differs fundamentally from the original pre-training setting: in finetuning, fixing the residual mixing matrix to identity often improves performance. As a standalone PEFT method, mHC does not consistently outperform LoRA. However, at matched trainable parameter budgets, mHC+LoRA combinations improve language-modelling loss and show task-dependent benchmark gains at both 1B and 7B scale. Overall, our results identify residual routing as a distinct and promising novel PEFT axis.
Valentijn Oldenburg, Floris de Kam, Bente Zuijdam +4