LUNA: Linear Universal Neural Attention with Generalization Guarantees

• URL: http://arxiv.org/abs/2512.08061v1
• Date: Mon, 08 Dec 2025 21:49:55 GMT
• Title: LUNA: Linear Universal Neural Attention with Generalization Guarantees
• Authors: Ashkan Shahbazi, Ping He, Ali Abbasi, Yikun Bai, Xinran Liu, Elaheh Akbari, Darian Salehi, Navid NaderiAlizadeh, Soheil Kolouri,
• Abstract summary: textscLuna achieves state-of-the-art average accuracy among efficient Transformers under compute parity.<n>textscLuna also excels at post-hoc conversion: replacing softmax in fine-tuned BERT and ViT-B/16 checkpoints.
• Score: 27.74721677870656
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Scaling attention faces a critical bottleneck: the $\mathcal{O}(n^2)$ quadratic computational cost of softmax attention, which limits its application in long-sequence domains. While linear attention mechanisms reduce this cost to $\mathcal{O}(n)$, they typically rely on fixed random feature maps, such as random Fourier features or hand-crafted functions. This reliance on static, data-agnostic kernels creates a fundamental trade-off, forcing practitioners to sacrifice significant model accuracy for computational efficiency. We introduce \textsc{LUNA}, a kernelized linear attention mechanism that eliminates this trade-off, retaining linear cost while matching and surpassing the accuracy of quadratic attention. \textsc{LUNA} is built on the key insight that the kernel feature map itself should be learned rather than fixed a priori. By parameterizing the kernel, \textsc{LUNA} learns a feature basis tailored to the specific data and task, overcoming the expressive limitations of fixed-feature methods. \textsc{Luna} implements this with a learnable feature map that induces a positive-definite kernel and admits a streaming form, yielding linear time and memory scaling in the sequence length. Empirical evaluations validate our approach across diverse settings. On the Long Range Arena (LRA), \textsc{Luna} achieves state-of-the-art average accuracy among efficient Transformers under compute parity, using the same parameter count, training steps, and approximate FLOPs. \textsc{Luna} also excels at post-hoc conversion: replacing softmax in fine-tuned BERT and ViT-B/16 checkpoints and briefly fine-tuning recovers most of the original performance, substantially outperforming fixed linearizations.

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