# Dissecting Linear Recurrent Models: How Different Gating Strategies Drive Selectivity and Generalization

arXiv: https://arxiv.org/abs/2601.12598 · HTML: https://mlsanity.com/paper/2601.12598/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 50 references that are in the map.
- First posted on arXiv 18 Jan 2026.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [Memory Networks](https://mlsanity.com/paper/1410.3916/) (2014)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models](https://mlsanity.com/paper/2402.19427/) (2024)
- [Zoology: Measuring and Improving Recall in Efficient Language Models](https://mlsanity.com/paper/2312.04927/) (2023)
- [HGRN2: Gated Linear RNNs with State Expansion](https://mlsanity.com/paper/2404.07904/) (2024)
- [In-Context Language Learning: Architectures and Algorithms](https://mlsanity.com/paper/2401.12973/) (2024)
- [Transformers Can Achieve Length Generalization But Not Robustly](https://mlsanity.com/paper/2402.09371/) (2024)
- [ATLAS: Learning to Optimally Memorize the Context at Test Time](https://mlsanity.com/paper/2505.23735/) (2025)
- [Just read twice: closing the recall gap for recurrent language models](https://mlsanity.com/paper/2407.05483/) (2024)
- [Learning Associative Inference Using Fast Weight Memory](https://mlsanity.com/paper/2011.07831/) (2020)
- [MesaNet: Sequence Modeling by Locally Optimal Test-Time Training](https://mlsanity.com/paper/2506.05233/) (2025)

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

- [Non-Commutative State Tracking with Input-Dependent Low-Rank Updates in Mamba-3](https://mlsanity.com/paper/2609.28273/) (2026)

## Abstract (arXiv)

Linear recurrent neural networks have emerged as efficient alternatives to the original Transformer's softmax attention mechanism, thanks to their highly parallelizable training and constant memory and computation requirements at inference. Iterative refinements of these models have introduced an increasing number of architectural mechanisms, leading to increased complexity and computational costs. Nevertheless, systematic direct comparisons among these models remain limited. Existing benchmark tasks are either too simplistic to reveal substantial differences or excessively resource-intensive for experimentation. In this work, we propose a refined taxonomy of linear recurrent models and introduce SelectivBench, a set of lightweight and customizable synthetic benchmark tasks for systematically evaluating sequence models. SelectivBench specifically evaluates selectivity in sequence models at small to medium scale, such as the capacity to focus on relevant inputs while ignoring context-based distractors. It employs rule-based grammars to generate sequences with adjustable complexity, incorporating irregular gaps that intentionally violate transition rules. Evaluations of linear recurrent models on SelectivBench reveal performance patterns consistent with results from large-scale language tasks. Our analysis clarifies the roles of essential architectural features: gating and rapid forgetting mechanisms facilitate recall, in-state channel mixing is unnecessary for selectivity, but critical for generalization, and softmax attention remains dominant due to its memory capacity scaling with sequence length. Our benchmark enables targeted, efficient exploration of linear recurrent models and provides a controlled setting for studying behaviors observed in large-scale evaluations. Code is available at https://github.com/symseqbench/selectivbench