# DepthBench: Measuring How Residual Connections Enable More Computational Depth

arXiv: https://arxiv.org/abs/2609.32534 · HTML: https://mlsanity.com/paper/2609.32534/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 55 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 50)

- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [CogView: Mastering Text-to-Image Generation via Transformers](https://mlsanity.com/paper/2105.13290/) (2021)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [Adaptive Input Representations for Neural Language Modeling](https://mlsanity.com/paper/1809.10853/) (2018)
- [MobileLLM: Optimizing Sub-billion Parameter Language Models for On-Device Use Cases](https://mlsanity.com/paper/2402.14905/) (2024)
- [DeepNet: Scaling Transformers to 1,000 Layers](https://mlsanity.com/paper/2203.00555/) (2022)
- [Kimi K3: Open Frontier Intelligence](https://mlsanity.com/paper/2607.24653/) (2026)
- [Scale Efficiently: Insights from Pre-training and Fine-tuning Transformers](https://mlsanity.com/paper/2109.10686/) (2021)
- [Resolving Discrepancies in Compute-Optimal Scaling of Language Models](https://mlsanity.com/paper/2406.19146/) (2024)

## Built on by (most cited first, 1 of 1)

- [Depth Memory](https://mlsanity.com/paper/2610.18809/) (2026)

## Abstract (arXiv)

Depth is a natural way to increase the computational capacity in Transformers, yet the contribution of deeper layers can diminish as depth grows larger. Recent approaches enhance normalization (e.g., LayerNorm Scaling) or residual connections (e.g., mHC, AttnRes) to enable better information flow and depth utilization. However, it remains unclear whether they truly translate increased architectural depth into effective computational depth, and whether their reported gains stem from better access to information across depth, or unaccounted-for confounding factors. In this paper, we introduce DepthBench, a controlled benchmark for studying computational depth across various architectures. We systematically vary the width--depth aspect ratio (dmodel/nlayer) from shallow--wide to deep--narrow shapes, while keeping the model size and pre-training recipe fixed. Across 10 representative architectures, we find that the benefit of allocating more capacity to depth is strongly architecture-dependent. Standard Pre-LN and most of its norm- and scaling-based variants provide little benefit and can even degrade performance as models become deeper and narrower, whereas HC and Full AttnRes improve consistently even at extreme deep shapes. These gains extend beyond pre-training loss and consistently translate into improved domain-specific performance and effective computation. Controlled layer-level analyses further show that the gains of HC and Full AttnRes are associated with more effective utilization of additional layers, revealing distinct mechanisms of computational depth across architectures. Overall, our results identify residual connection design as a key determinant of whether depth can serve as a meaningful scaling axis by enabling additional architectural depth to translate into effective computation.