# Amortized-Precision Quantization for Early-Exit Vision Transformers

arXiv: https://arxiv.org/abs/2605.07317 · HTML: https://mlsanity.com/paper/2605.07317/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Token pruning and merging for ViTs, one of 12 directions in Efficient LLM inference and serving.
- Builds on 39 of its 49 references that are in the map.
- First posted on arXiv 8 May 2026.

## Placed in

- Efficient LLM inference and serving / [Token pruning and merging for ViTs](https://mlsanity.com/inference/token-pruning-and-merging-for-vits/)

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification](https://mlsanity.com/paper/2103.14899/) (2021)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [BranchyNet: Fast Inference via Early Exiting from Deep Neural Networks](https://mlsanity.com/paper/1709.01686/) (2017)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2106.14156/) (2021)
- [Tutel: Adaptive Mixture-of-Experts at Scale](https://mlsanity.com/paper/2206.03382/) (2022)
- [You Only Look at One Sequence: Rethinking Transformer in Vision through Object Detection](https://mlsanity.com/paper/2106.00666/) (2021)
- [Quantization Networks](https://mlsanity.com/paper/1911.09464/) (2019)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [Overcoming Oscillations in Quantization-Aware Training](https://mlsanity.com/paper/2203.11086/) (2022)
- [UTNet: A Hybrid Transformer Architecture for Medical Image Segmentation](https://mlsanity.com/paper/2107.00781/) (2021)
- [Q-ViT: Accurate and Fully Quantized Low-bit Vision Transformer](https://mlsanity.com/paper/2210.06707/) (2022)
- [Adaptive Inference through Early-Exit Networks: Design, Challenges and Directions](https://mlsanity.com/paper/2106.05022/) (2021)
- [Towards Accurate Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2303.14341/) (2023)
- [MoEQuant: Enhancing Quantization for Mixture-of-Experts Large Language Models via Expert-Balanced Sampling and Affinity Guidance](https://mlsanity.com/paper/2505.03804/) (2025)

## Abstract (arXiv)

Vision Transformers (ViTs) achieve strong performance across vision tasks, yet their deployment with low-precision early exiting remains fragile. Existing quantization methods assume static full-depth execution, making them unstable when exit decisions are perturbed by quantization noise, which can amplify errors along dynamic inference paths. In this paper, we introduce Amortized-Precision Quantization (APQ), a utilization-aware formulation that accounts for layer-wise stochastic exposure to quantization noise and reveals depth-precision trade-offs. Building on APQ, we propose Mutual Adaptive Quantization with Early Exiting (MAQEE), a bi-level framework that jointly optimizes exit thresholds and bit-widths under explicit risk control to improve inference stability. MAQEE establishes a superior Pareto frontier in the accuracy-efficiency trade-off, reducing BOPs by up to 95% while maintaining accuracy and outperforming strong baselines by up to 20% across classification, detection, and segmentation tasks.