# Pause Tokens Strictly Increase the Expressivity of Constant-Depth Transformers

arXiv: https://arxiv.org/abs/2505.21024 · HTML: https://mlsanity.com/paper/2505.21024/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 42 references that are in the map.
- First posted on arXiv 27 May 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Theoretical Limitations of Self-Attention in Neural Sequence Models](https://mlsanity.com/paper/1906.06755/) (2019)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [Neural Networks and the Chomsky Hierarchy](https://mlsanity.com/paper/2207.02098/) (2022)
- [The Parallelism Tradeoff: Limitations of Log-Precision Transformers](https://mlsanity.com/paper/2207.00729/) (2022)
- [Let's Think Dot by Dot: Hidden Computation in Transformer Language Models](https://mlsanity.com/paper/2404.15758/) (2024)
- [Representational Strengths and Limitations of Transformers](https://mlsanity.com/paper/2306.02896/) (2023)
- [On the Turing Completeness of Modern Neural Network Architectures](https://mlsanity.com/paper/1901.03429/) (2019)
- [What Formal Languages Can Transformers Express? A Survey](https://mlsanity.com/paper/2311.00208/) (2023)
- [Formal Language Recognition by Hard Attention Transformers: Perspectives from Circuit Complexity](https://mlsanity.com/paper/2204.06618/) (2022)
- [Memory Transformer](https://mlsanity.com/paper/2006.11527/) (2020)
- [On Limitations of the Transformer Architecture](https://mlsanity.com/paper/2402.08164/) (2024)
- [Theoretical limitations of multi-layer Transformer](https://mlsanity.com/paper/2412.02975/) (2024)
- [Separations in the Representational Capabilities of Transformers and Recurrent Architectures](https://mlsanity.com/paper/2406.09347/) (2024)
- [Transformers in Uniform TC0](https://mlsanity.com/paper/2409.13629/) (2024)
- [Super-Linear Gate and Super-Quadratic Wire Lower Bounds for Depth-Two and Depth-Three Threshold Circuits](https://mlsanity.com/paper/1511.07860/) (2015)
- [Understanding Hidden Computations in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2412.04537/) (2024)

## Built on by (most cited first, 8 of 8)

- [Emergence of Superposition: Unveiling the Training Dynamics of Chain of Continuous Thought](https://mlsanity.com/paper/2509.23365/) (2025)
- [Meaningless Tokens, Meaningful Gains: How Activation Shifts Enhance LLM Reasoning](https://mlsanity.com/paper/2510.01032/) (2025)
- [On the Reasoning Abilities of Masked Diffusion Language Models](https://mlsanity.com/paper/2510.13117/) (2025)
- [Thoughtbubbles: an Unsupervised Method for Parallel Thinking in Latent Space](https://mlsanity.com/paper/2510.00219/) (2025)
- [Internalizing LLM Reasoning via Discovery and Replay of Latent Actions](https://mlsanity.com/paper/2602.04925/) (2026)
- [Catch Your Breath: Adaptive Computation for Self-Paced Sequence Production](https://mlsanity.com/paper/2510.13879/) (2025)
- [Transformers Provably Learn to Internalize Chain-of-Thought](https://mlsanity.com/paper/2605.28600/) (2026)
- [Revisiting Padded Transformer Expressivity: Which Architectural Choices Matter and Which Don't](https://mlsanity.com/paper/2605.30523/) (2026)

## Abstract (arXiv)

Pause tokens, simple filler symbols such as "...", consistently improve Transformer performance on both language and mathematical tasks, yet their theoretical effect remains unexplained. We provide the first formal separation result, proving that adding pause tokens to constant-depth, logarithmic-width Transformers strictly increases their computational expressivity. With bounded-precision activations, Transformers without pause tokens compute only a strict subset of mathsfAC0 functions, while adding a polynomial number of pause tokens allows them to express the entire class. For logarithmic-precision Transformers, we show that adding pause tokens achieves expressivity equivalent to mathsfTC0, matching known upper bounds. Empirically, we demonstrate that two-layer causally masked Transformers can learn parity when supplied with pause tokens, a function that they appear unable to learn without them. Our results provide a rigorous theoretical explanation for prior empirical findings, clarify how pause tokens interact with width, depth, and numeric precision, and position them as a distinct mechanism, complementary to chain-of-thought prompting, for enhancing Transformer reasoning.