# CascadeFormer: Depth-Tapered Transformers Motivated by Gradient Fan-in Asymmetry

arXiv: https://arxiv.org/abs/2606.26538 · HTML: https://mlsanity.com/paper/2606.26538/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 30 of 31)

- [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)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Reducing Transformer Depth on Demand with Structured Dropout](https://mlsanity.com/paper/1909.11556/) (2019)
- [Sheared LLaMA: Accelerating Language Model Pre-training via Structured Pruning](https://mlsanity.com/paper/2310.06694/) (2023)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [FastBERT: a Self-distilling BERT with Adaptive Inference Time](https://mlsanity.com/paper/2004.02178/) (2020)
- [The Unreasonable Ineffectiveness of the Deeper Layers](https://mlsanity.com/paper/2403.17887/) (2024)
- [DeepNet: Scaling Transformers to 1,000 Layers](https://mlsanity.com/paper/2203.00555/) (2022)
- [LaCo: Large Language Model Pruning via Layer Collapse](https://mlsanity.com/paper/2402.11187/) (2024)
- [GSPMD: General and Scalable Parallelization for ML Computation Graphs](https://mlsanity.com/paper/2105.04663/) (2021)
- [SLEB: Streamlining LLMs through Redundancy Verification and Elimination of Transformer Blocks](https://mlsanity.com/paper/2402.09025/) (2024)
- [What Matters in Transformers? Not All Attention is Needed](https://mlsanity.com/paper/2406.15786/) (2024)
- [NormFormer: Improved Transformer Pretraining with Extra Normalization](https://mlsanity.com/paper/2110.09456/) (2021)
- [The Curse of Depth in Large Language Models](https://mlsanity.com/paper/2502.05795/) (2025)
- [LoRAShear: Efficient Large Language Model Structured Pruning and Knowledge Recovery](https://mlsanity.com/paper/2310.18356/) (2023)
- [Mix-LN: Unleashing the Power of Deeper Layers by Combining Pre-LN and Post-LN](https://mlsanity.com/paper/2412.13795/) (2024)
- [Tracing Representation Progression: Analyzing and Enhancing Layer-Wise Similarity](https://mlsanity.com/paper/2406.14479/) (2024)
- [B2T Connection: Serving Stability and Performance in Deep Transformers](https://mlsanity.com/paper/2206.00330/) (2022)

## Abstract (arXiv)

Deep Transformers are composed of uniformly stacked residual blocks, yet their deepest layers often add little value. We present two efficiency methods that exploit this asymmetry. CascadeFormer tapers width with depth to match the uneven information flow across layers, achieving comparable perplexity to a uniform baseline at the same training budget while reducing latency by 8.6% and increasing throughput by 9.4%. CascadeFlow Pruning removes layers using accumulated training gradients, with no post hoc analysis. It outperforms standard heuristics on perplexity and rank-stability and stays competitive on downstream accuracy. To motivate these methods, we propose Gradient Fan-in Asymmetry (GFA) as a structural account of why deeper layers contribute less. In Pre-LayerNorm residual stacks, the gradient at a layer is the sum of an identity path and all downstream functional paths, producing a gradient fan-in that decays linearly with depth (and quadratically under deep supervision), yielding richer gradients for early layers and sparser ones for later layers. We provide correlational and interventional evidence for GFA on models trained from scratch up to 1.2B parameters. Across Transformers and ResNets, accumulated training gradients follow the theoretical fan-in and are associated with post hoc layer importance. Two interventions point to structure rather than magnitude as the bottleneck: equalizing per-layer gradient norms does not restore late-layer value, while increasing downstream path counts via parameter-shared repetition restores and elevates it. Whether gradient magnitude proxies fan-in beyond high-rank regimes, and how these dynamics behave at the 100B+ scale, remain open questions.