Complex KDA: Understanding and Enhancing the Expressivity of Kimi Delta Attention

2026-09-21

AI Summary

本文通过扩展KDA参数范围，提出Complex KDA(CKDA)模型，以增强线性RNN的表达能力，同时保持其稳定性和效率。

Abstract

Linear RNNs based on the delta-rule enable efficient sequence modeling, but their linear updates with a low-rank correction constrain their expressivity. Prior work has shown that composing two delta-rule transitions in a single recurrent update can model a 2D rotation, but this increases the rank and the cost of the updates compared to a single transition. We show that Kimi Delta Attention (KDA) can realize 2D rotations by combining a single delta-rule transformation with a second reflection supplied by its channel-wise gate. This requires extending the parameter ranges of KDA by combining two existing range extensions: allowing gates in $[-1,1]$ and the delta-rule coefficient $β$ in $[0,2]$. We call the resulting model Complex KDA (CKDA). It preserves KDA's stability and efficiency, with transitions that remain diagonal-plus-rank-one and non-expansive, while reaching the state-tracking expressivity of DeltaProduct$_2$. We characterize the expressivity of CKDA and prove that every orthogonal diagonal-plus-rank-one matrix is exactly a CKDA transition matrix. A single CKDA layer can track every finite group isomorphic to a subgroup of $\mathrm{SO}(3)$, and many state-tracking results use one fewer layer for CKDA compared to other diagonal-plus-rank-one Linear RNNs. Empirically, combining both extensions yields the strongest length extrapolation among tested KDA range settings on $S_3$, $S_4$, and periodic audio continuation. In language modeling, CKDA outperforms Transformers and other linear RNNs, obtains similar results to a KDA baseline, and shows promising scaling behavior. Our code is open source at https://github.com/OpenEuroLLM/ComplexKDA and our models are available at https://huggingface.co/collections/openeurollm/complexkda.

Problem

• Linear RNNs
• delta-rule
• expressivity
• Kimi Delta Attention
• 2D rotations

Innovation

• Complex KDA
• 2D Rotations
• Expressivity Enhancement
• Parameter Range Extension
• Efficient Sequence Modeling