# HAARES Half-Split Residual Basis Routing for Deep Transformers

arXiv: https://arxiv.org/abs/2606.06564 · HTML: https://mlsanity.com/paper/2606.06564/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 27 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Going deeper with Image Transformers](https://mlsanity.com/paper/2103.17239/) (2021)
- [CodeSearchNet Challenge: Evaluating the State of Semantic Code Search](https://mlsanity.com/paper/1909.09436/) (2019)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Using the Output Embedding to Improve Language Models](https://mlsanity.com/paper/1608.05859/) (2016)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [DeepNet: Scaling Transformers to 1,000 Layers](https://mlsanity.com/paper/2203.00555/) (2022)
- [Attention Residuals](https://mlsanity.com/paper/2603.15031/) (2026)
- [DenseFormer: Enhancing Information Flow in Transformers via Depth Weighted Averaging](https://mlsanity.com/paper/2402.02622/) (2024)
- [Training Deeper Neural Machine Translation Models with Transparent Attention](https://mlsanity.com/paper/1808.07561/) (2018)
- [MUDDFormer: Breaking Residual Bottlenecks in Transformers via Multiway Dynamic Dense Connections](https://mlsanity.com/paper/2502.12170/) (2025)
- [Delta Attention Residuals](https://mlsanity.com/paper/2605.18855/) (2026)

## Abstract (arXiv)

Block-level residual routing makes learned residual aggregation practical by routing over block summaries, but each summary compresses an ordered sequence of attention and MLP updates into one cumulative vector. We propose method, a lightweight residual basis router that keeps the cumulative block source and adds one half-split detail basis, computed as the difference between first-half and second-half residual updates. The detail basis is RMS-matched and updated online, exposing coarse intra-block trajectory information without dense sublayer-level routing. Across OpenWebText, cross-domain character-level benchmarks, and BPE-tokenized OpenWebText, the empirical pattern is depth-dependent: gains are small or mixed at shallow depth and most reliable in 48-layer models. In the 201M 48-layer setting, method improves over Block AttnRes across all three seeds, while a 453M two-seed probe shows the same direction. Ablations rule out source duplication, random signed details, fixed detail-source biases, or block-count changes alone. Cost analysis shows that the method is FLOP-light but not wall-clock-free: it adds memory and routing overhead, yet its relative arithmetic cost is amortized as width grows and earlier convergence can reduce time-to-target.