# Vertical LoRA: Dense Expectation-Maximization Interpretation of Transformers

arXiv: https://arxiv.org/abs/2406.09315 · HTML: https://mlsanity.com/paper/2406.09315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 31 references that are in the map.
- First posted on arXiv 13 Jun 2024.

## Builds on (most cited first, 26 of 26)

- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [P-Tuning v2: Prompt Tuning Can Be Comparable to Fine-tuning Universally Across Scales and Tasks](https://mlsanity.com/paper/2110.07602/) (2021)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications](https://mlsanity.com/paper/1511.06530/) (2015)
- [Accelerating Very Deep Convolutional Networks for Classification and Detection](https://mlsanity.com/paper/1505.06798/) (2015)
- [LoRA Dropout as a Sparsity Regularizer for Overfitting Control](https://mlsanity.com/paper/2404.09610/) (2024)
- [PeriodicLoRA: Breaking the Low-Rank Bottleneck in LoRA Optimization](https://mlsanity.com/paper/2402.16141/) (2024)
- [LORS: Low-rank Residual Structure for Parameter-Efficient Network Stacking](https://mlsanity.com/paper/2403.04303/) (2024)

## Abstract (arXiv)

In this paper, we show how Transformers can be interpreted as dense Expectation-Maximization algorithms performed on Bayesian Nets. Based on the above interpretation, we propose a new model design paradigm, namely Vertical LoRA (VLoRA), which reduces the parameter count dramatically while preserving performance. In VLoRA, a model consists of layers, each of which recursively learns an increment based on the previous layer. We then apply LoRA decomposition to the increments. VLoRA works on the base model, which is orthogonal to LoRA, meaning they can be used together. We do experiments on various tasks and models. The results show that 1) with VLoRA, the Transformer model parameter count can be reduced dramatically and 2) the performance of the original model is preserved. The source code is available at urlhttps://github.com/neverUseThisName/vlora