# HubRouter: A Pluggable Sub-Quadratic Routing Primitive for Hybrid Sequence Models

arXiv: https://arxiv.org/abs/2604.22442 · HTML: https://mlsanity.com/paper/2604.22442/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 24 Apr 2026.

## Builds on (most cited first, 23 of 23)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [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)
- [Zamba: A Compact 7B SSM Hybrid Model](https://mlsanity.com/paper/2405.16712/) (2024)
- [Mamba-3: Improved Sequence Modeling using State Space Principles](https://mlsanity.com/paper/2603.15569/) (2026)
- [When Does Content-Based Routing Work? Representation Requirements for Selective Attention in Hybrid Sequence Models](https://mlsanity.com/paper/2603.20997/) (2026)

## Abstract (arXiv)

We introduce HubRouter, a pluggable module that replaces O(n^2) attention layers with O(nM) hub-mediated routing, where M << n is a small number of learned hub tokens. We demonstrate it in two from-scratch architectures: a Jamba-style hybrid and a 12-layer Transformer; retrofit into pretrained models is a tested negative case. HubRouter implements an encode-decode-score-council pipeline: M learned hubs cross-attend to all tokens, tokens project against hubs for routing fingerprints, a score head selects top-k tokens, and a sparse council attends only to the selected subset. We validate HubRouter in three settings. (1) Hub-Jamba yields a nominal 4.2% PPL improvement (200.2 vs 209.0, single seed; possibly within seed noise) and up to ~90x training throughput at sequence length 1024 in matched PyTorch-native baselines; an optimised baseline would narrow this to ~10-15x. (2) Graduated replacement of 25% of Transformer attention layers gives the best perplexity in our matched-budget sweep (268.0 vs 282.4 pure Transformer). (3) Hub-GPT provides strictly causal routing, achieving PPL 211.5 +/- 0.4 over 3 seeds (post council-causal fix); approximately 3 PPL worse than Jamba's 208.5 +/- 0.7, a measurable quality cost for avoiding O(n^2) computation. Post-fix, chunk size C has little effect; the pre-fix chunk-size benefit was an artifact of a bidirectional-council leak we found in adversarial review. A multi-seed hub-count sweep (~105 runs across M=1-32) reveals M=8-14 as the reliably-converging sub-band (4-5/5 seeds); M=6 is rescued to 5/5 by orthogonal regularization, while M>=20 shows increasing seed sensitivity. Companion paper arXiv:2603.20997 (Basu, 2026) defines the routing diagnostic task. Code and scripts will be released.