# Length Generalization with Log-Depth Recurrent Units

arXiv: https://arxiv.org/abs/2605.26035 · HTML: https://mlsanity.com/paper/2605.26035/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 79 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 30 of 53)

- [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)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks](https://mlsanity.com/paper/1503.00075/) (2015)
- [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)
- [Neural Networks and the Chomsky Hierarchy](https://mlsanity.com/paper/2207.02098/) (2022)
- [Exploring Length Generalization in Large Language Models](https://mlsanity.com/paper/2207.04901/) (2022)
- [What Algorithms can Transformers Learn? A Study in Length Generalization](https://mlsanity.com/paper/2310.16028/) (2023)
- [ListOps: A Diagnostic Dataset for Latent Tree Learning](https://mlsanity.com/paper/1804.06028/) (2018)
- [Parallelizing Linear Recurrent Neural Nets Over Sequence Length](https://mlsanity.com/paper/1709.04057/) (2017)
- [What Formal Languages Can Transformers Express? A Survey](https://mlsanity.com/paper/2311.00208/) (2023)
- [Randomized Positional Encodings Boost Length Generalization of Transformers](https://mlsanity.com/paper/2305.16843/) (2023)
- [Overcoming a Theoretical Limitation of Self-Attention](https://mlsanity.com/paper/2202.12172/) (2022)
- [Structured State Space Models for In-Context Reinforcement Learning](https://mlsanity.com/paper/2303.03982/) (2023)
- [Unlocking State-Tracking in Linear RNNs Through Negative Eigenvalues](https://mlsanity.com/paper/2411.12537/) (2024)
- [Looped Transformers for Length Generalization](https://mlsanity.com/paper/2409.15647/) (2024)
- [Transformers Can Achieve Length Generalization But Not Robustly](https://mlsanity.com/paper/2402.09371/) (2024)

## Built on by (most cited first, 1 of 1)

- [Log-Depth Recurrent Language Modeling](https://mlsanity.com/paper/2609.28212/) (2026)

## Abstract (arXiv)

Length generalization remains a persistent challenge for neural networks: recurrent models tend to suffer from positional biases, while transformers are constrained by fixed computational depth. Regular languages provide a frequently used testbed for evaluating length generalization, as label prediction can be checked for any sequence length. We propose MLP-LDRU, a type of Log-Depth Recurrent Unit, which captures a class of associativity-biased operators designed to approximate recurrence through parallel reduction. We evaluate MLP-LDRU on 21 regular-language tasks, consisting of standard benchmarks and new prefix languages, where it achieves 100% out-of-distribution accuracy on 18 tasks and at least 99.9% on the remaining 3 when increasing max training length, outperforming comparable recurrent and attention-based models. We further evaluate MLP-LDRU beyond regular languages on ListOps and NLP classification benchmarks, where it performs competitively.