# Beyond Uniform Scaling: Exploring Depth Heterogeneity in Neural Architectures

arXiv: https://arxiv.org/abs/2402.12418 · HTML: https://mlsanity.com/paper/2402.12418/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 22 references that are in the map.
- First posted on arXiv 19 Feb 2024.

## Builds on (most cited first, 18 of 18)

- [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)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Net2Net: Accelerating Learning via Knowledge Transfer](https://mlsanity.com/paper/1511.05641/) (2015)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [Learning to Grow Pretrained Models for Efficient Transformer Training](https://mlsanity.com/paper/2303.00980/) (2023)
- [bert2BERT: Towards Reusable Pretrained Language Models](https://mlsanity.com/paper/2110.07143/) (2021)
- [GradMax: Growing Neural Networks using Gradient Information](https://mlsanity.com/paper/2201.05125/) (2022)
- [Splitting Steepest Descent for Growing Neural Architectures](https://mlsanity.com/paper/1910.02366/) (2019)
- [Firefly Neural Architecture Descent: a General Approach for Growing Neural Networks](https://mlsanity.com/paper/2102.08574/) (2021)
- [A Loss Curvature Perspective on Training Instability in Deep Learning](https://mlsanity.com/paper/2110.04369/) (2021)
- [Energy-Aware Neural Architecture Optimization with Fast Splitting Steepest Descent](https://mlsanity.com/paper/1910.03103/) (2019)
- [Steepest Descent Neural Architecture Optimization: Escaping Local Optimum with Signed Neural Splitting](https://mlsanity.com/paper/2003.10392/) (2020)

## Abstract (arXiv)

Conventional scaling of neural networks typically involves designing a base network and growing different dimensions like width, depth, etc. of the same by some predefined scaling factors. We introduce an automated scaling approach leveraging second-order loss landscape information. Our method is flexible towards skip connections a mainstay in modern vision transformers. Our training-aware method jointly scales and trains transformers without additional training iterations. Motivated by the hypothesis that not all neurons need uniform depth complexity, our approach embraces depth heterogeneity. Extensive evaluations on DeiT-S with ImageNet100 show a 2.5% accuracy gain and 10% parameter efficiency improvement over conventional scaling. Scaled networks demonstrate superior performance upon training small scale datasets from scratch. We introduce the first intact scaling mechanism for vision transformers, a step towards efficient model scaling.