# StackTrans: From Large Language Model to Large Pushdown Automata Model

arXiv: https://arxiv.org/abs/2507.15343 · HTML: https://mlsanity.com/paper/2507.15343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 46 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [Theoretical Limitations of Self-Attention in Neural Sequence Models](https://mlsanity.com/paper/1906.06755/) (2019)
- [Neural Networks and the Chomsky Hierarchy](https://mlsanity.com/paper/2207.02098/) (2022)
- [Hyper-Connections](https://mlsanity.com/paper/2409.19606/) (2024)
- [Inferring Algorithmic Patterns with Stack-Augmented Recurrent Nets](https://mlsanity.com/paper/1503.01007/) (2015)
- [Learning to Transduce with Unbounded Memory](https://mlsanity.com/paper/1506.02516/) (2015)
- [Transformer Grammars: Augmenting Transformer Language Models with Syntactic Inductive Biases at Scale](https://mlsanity.com/paper/2203.00633/) (2022)
- [Stack Attention: Improving the Ability of Transformers to Model Hierarchical Patterns](https://mlsanity.com/paper/2310.01749/) (2023)
- [A Transformer with Stack Attention](https://mlsanity.com/paper/2405.04515/) (2024)

## Abstract (arXiv)

The Transformer architecture has emerged as a landmark advancement within the broad field of artificial intelligence, effectively catalyzing the advent of large language models (LLMs). However, despite its remarkable capabilities and the substantial progress it has facilitated, the Transformer architecture still has some limitations. One such intrinsic limitation is its inability to effectively capture the Chomsky hierarchy, such as regular expressions or deterministic context-free grammars. Drawing inspiration from pushdown automata, which efficiently resolve deterministic context-free grammars using stacks, we propose StackTrans to address the aforementioned issue within LLMs. Unlike previous approaches that modify the attention computation, StackTrans explicitly incorporates hidden state stacks between Transformer layers. This design maintains compatibility with existing frameworks like flash-attention. Specifically, our design features stack operations -- such as pushing and popping hidden states -- that are differentiable and can be learned in an end-to-end manner. Our comprehensive evaluation spans benchmarks for both Chomsky hierarchies and large-scale natural languages. Across these diverse tasks, StackTrans consistently outperforms standard Transformer models and other baselines. We have successfully scaled StackTrans up from 360M to 7B parameters. In particular, our from-scratch pretrained model StackTrans-360M outperforms several larger open-source LLMs with 2-3x more parameters, showcasing its superior efficiency and reasoning capability.