# Cubit: Token Mixer with Kernel Ridge Regression

arXiv: https://arxiv.org/abs/2605.06501 · HTML: https://mlsanity.com/paper/2605.06501/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 58 of its 95 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 30 of 58)

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- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
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- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [CogView: Mastering Text-to-Image Generation via Transformers](https://mlsanity.com/paper/2105.13290/) (2021)

## Abstract (arXiv)

Since its introduction in 2017, the Transformer has become one of the most widely adopted architectures in modern deep learning. Despite extensive efforts to improve positional encoding, attention mechanisms, and feed-forward networks, the core token-mixing mechanism in Transformers remains attention. In this work, we show that the attention module in Transformers can be interpreted as performing Nadaraya-Watson regression, where it computes similarities between tokens and aggregates the corresponding values accordingly. Motivated by this perspective, we propose Cubit, a potential next-generation architecture that leverages Kernel Ridge Regression (KRR), while the vanilla Transformer relies on Nadaraya-Watson regression. Specifically, Cubit modifies the classical attention computation by incorporating the closed-form solution of KRR, combining value aggregation through kernel similarities with normalization via the inverse of the kernel matrix. To improve the training stability, we further propose the Limited-Range Rescale (LRR), which rescales the value layer within a controlled range. We argue that Cubit, as a KRR-based architecture, provides a stronger mathematical foundation than the vanilla Transformer, whose attention mechanism corresponds to Nadaraya-Watson regression. We validate this claim through comprehensive experiments. The experimental results suggest that Cubit may exhibit stronger long-sequence modeling capability. In particular, its performance gain over the Transformer appears to increase as the training sequence length grows.