# Position-Aware Depth Decay Decoding (D3): Boosting Large Language Model Inference Efficiency

arXiv: https://arxiv.org/abs/2503.08524 · HTML: https://mlsanity.com/paper/2503.08524/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 32 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 25 of 25)

- [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 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Efficient Large-Scale Language Model Training on GPU Clusters Using Megatron-LM](https://mlsanity.com/paper/2104.04473/) (2021)
- [BranchyNet: Fast Inference via Early Exiting from Deep Neural Networks](https://mlsanity.com/paper/1709.01686/) (2017)
- [SkipNet: Learning Dynamic Routing in Convolutional Networks](https://mlsanity.com/paper/1711.09485/) (2017)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [Depth-Adaptive Transformer](https://mlsanity.com/paper/1910.10073/) (2019)
- [FastBERT: a Self-distilling BERT with Adaptive Inference Time](https://mlsanity.com/paper/2004.02178/) (2020)
- [Adaptive Neural Networks for Efficient Inference](https://mlsanity.com/paper/1702.07811/) (2017)
- [LaCo: Large Language Model Pruning via Layer Collapse](https://mlsanity.com/paper/2402.11187/) (2024)
- [The Efficiency Misnomer](https://mlsanity.com/paper/2110.12894/) (2021)
- [SLEB: Streamlining LLMs through Redundancy Verification and Elimination of Transformer Blocks](https://mlsanity.com/paper/2402.09025/) (2024)
- [SkipDecode: Autoregressive Skip Decoding with Batching and Caching for Efficient LLM Inference](https://mlsanity.com/paper/2307.02628/) (2023)
- [CascadeBERT: Accelerating Inference of Pre-trained Language Models via Calibrated Complete Models Cascade](https://mlsanity.com/paper/2012.14682/) (2020)
- [Accelerating BERT Inference for Sequence Labeling via Early-Exit](https://mlsanity.com/paper/2105.13878/) (2021)
- [Learning to Skip for Language Modeling](https://mlsanity.com/paper/2311.15436/) (2023)

## Built on by (most cited first, 2 of 2)

- [SimLens for Early Exit in Large Language Models: Eliciting Accurate Latent Predictions with One More Token](https://mlsanity.com/paper/2507.17618/) (2025)
- [Depth Adaptive Efficient Visual Autoregressive Modeling](https://mlsanity.com/paper/2604.17286/) (2026)

## Abstract (arXiv)

Due to the large number of parameters, the inference phase of Large Language Models (LLMs) is resource-intensive. Unlike traditional model compression, which needs retraining, recent dynamic computation methods show that not all components are required for inference, enabling a training-free pipeline. In this paper, we focus on the dynamic depth of LLM generation. A token-position aware layer skipping framework is proposed to save 1.5x times operations efficiently while maintaining performance. We first observed that tokens predicted later have lower perplexity and thus require less computation. Then, we propose a training-free algorithm called Position-Aware Depth Decay Decoding (D3), which leverages a power-law decay function, leftlfloor L × (αi) rightrfloor, to determine the number of layers to retain when generating token Ti. Remarkably, without any retraining, the D3 achieves success across a wide range of generation tasks for the first time. Experiments on large language models (ie the Llama) with 7 ~ 70 billion parameters show that D3 can achieve an average 1.5x speedup compared with the full-inference pipeline while maintaining comparable performance with nearly no performance drop (<1%) on the GSM8K and BBH benchmarks.