# AlgoFormer: An Efficient Transformer Framework with Algorithmic Structures

arXiv: https://arxiv.org/abs/2402.13572 · HTML: https://mlsanity.com/paper/2402.13572/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 36 references that are in the map.
- First posted on arXiv 21 Feb 2024.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Sheared LLaMA: Accelerating Language Model Pre-training via Structured Pruning](https://mlsanity.com/paper/2310.06694/) (2023)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Transformers learn to implement preconditioned gradient descent for in-context learning](https://mlsanity.com/paper/2306.00297/) (2023)
- [Looped Transformers as Programmable Computers](https://mlsanity.com/paper/2301.13196/) (2023)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [One Step of Gradient Descent is Provably the Optimal In-Context Learner with One Layer of Linear Self-Attention](https://mlsanity.com/paper/2307.03576/) (2023)
- [Looped Transformers are Better at Learning Learning Algorithms](https://mlsanity.com/paper/2311.12424/) (2023)
- [In-Context Convergence of Transformers](https://mlsanity.com/paper/2310.05249/) (2023)
- [How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representations](https://mlsanity.com/paper/2310.10616/) (2023)
- [Making Transformers Solve Compositional Tasks](https://mlsanity.com/paper/2108.04378/) (2021)

## Built on by (most cited first, 11 of 11)

- [A Survey on Latent Reasoning](https://mlsanity.com/paper/2507.06203/) (2025)
- [Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence](https://mlsanity.com/paper/2511.07384/) (2025)
- [Enabling Agents to Communicate Entirely in Latent Space](https://mlsanity.com/paper/2511.09149/) (2025)
- [Enhancing Auto-regressive Chain-of-Thought through Loop-Aligned Reasoning](https://mlsanity.com/paper/2502.08482/) (2025)
- [Training-Free Looped Transformers](https://mlsanity.com/paper/2605.23872/) (2026)
- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)
- [Exact Conversion of In-Context Learning to Model Weights in Linearized-Attention Transformers](https://mlsanity.com/paper/2406.02847/) (2024)
- [Advancing the Understanding of Fixed Point Iterations in Deep Neural Networks: A Detailed Analytical Study](https://mlsanity.com/paper/2410.11279/) (2024)
- [How Transparent is DiffusionGemma?](https://mlsanity.com/paper/2606.20560/) (2026)
- [Selection, Reflection and Self-Refinement: Revisit Reasoning Tasks via a Causal Lens](https://mlsanity.com/paper/2510.08222/) (2025)
- [Think Deep, Speak Once: Relit, A Recursive Latent Implicit Transformer Framework](https://mlsanity.com/paper/2608.08113/) (2026)

## Abstract (arXiv)

Besides natural language processing, transformers exhibit extraordinary performance in solving broader applications, including scientific computing and computer vision. Previous works try to explain this from the expressive power and capability perspectives that standard transformers are capable of performing some algorithms. To empower transformers with algorithmic capabilities and motivated by the recently proposed looped transformer, we design a novel transformer framework, dubbed Algorithm Transformer (abbreviated as AlgoFormer). We provide an insight that efficient transformer architectures can be designed by leveraging prior knowledge of tasks and the underlying structure of potential algorithms. Compared with the standard transformer and vanilla looped transformer, the proposed AlgoFormer can perform efficiently in algorithm representation in some specific tasks. In particular, inspired by the structure of human-designed learning algorithms, our transformer framework consists of a pre-transformer that is responsible for task preprocessing, a looped transformer for iterative optimization algorithms, and a post-transformer for producing the desired results after post-processing. We provide theoretical evidence of the expressive power of the AlgoFormer in solving some challenging problems, mirroring human-designed algorithms. Furthermore, some theoretical and empirical results are presented to show that the designed transformer has the potential to perform algorithm representation and learning. Experimental results demonstrate the empirical superiority of the proposed transformer in that it outperforms the standard transformer and vanilla looped transformer in some specific tasks. An extensive experiment on real language tasks (e.g., neural machine translation of German and English, and text classification) further validates the expressiveness and effectiveness of AlgoFormer.