# Data-Aware Random Feature Kernel for Transformers

arXiv: https://arxiv.org/abs/2603.04127 · HTML: https://mlsanity.com/paper/2603.04127/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 33 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [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)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions](https://mlsanity.com/paper/1502.06800/) (2015)
- [Orthogonal Random Features](https://mlsanity.com/paper/1610.09072/) (2016)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [Fastfood: Approximate Kernel Expansions in Loglinear Time](https://mlsanity.com/paper/1408.3060/) (2014)
- [Skyformer: Remodel Self-Attention with Gaussian Kernel and Nystr"om Method](https://mlsanity.com/paper/2111.00035/) (2021)
- [Anisotropy Is Inherent to Self-Attention in Transformers](https://mlsanity.com/paper/2401.12143/) (2024)
- [The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings](https://mlsanity.com/paper/1703.00864/) (2017)
- [PolySketchFormer: Fast Transformers via Sketching Polynomial Kernels](https://mlsanity.com/paper/2310.01655/) (2023)
- [DISTFLASHATTN: Distributed Memory-efficient Attention for Long-context LLMs Training](https://mlsanity.com/paper/2310.03294/) (2023)
- [Efficient Attention via Control Variates](https://mlsanity.com/paper/2302.04542/) (2023)
- [FAVOR#: Sharp Attention Kernel Approximations via New Classes of Positive Random Features](https://mlsanity.com/paper/2302.00787/) (2023)
- [Kernel Approximation Methods for Speech Recognition](https://mlsanity.com/paper/1701.03577/) (2017)
- [All Random Features Representations are Equivalent](https://mlsanity.com/paper/2406.18802/) (2024)

## Abstract (arXiv)

Transformers excel across domains, yet their quadratic attention complexity poses a barrier to scaling. Random-feature attention, as in Performers, can reduce this cost to linear in the sequence length by approximating the softmax kernel with positive random features drawn from an isotropic distribution. In pretrained models, however, queries and keys are typically anisotropic. This induces high Monte Carlo variance in isotropic sampling schemes unless one retrains the model or uses a large feature budget. Importance sampling can address this by adapting the sampling distribution to the input geometry, but complex data-dependent proposal distributions are often intractable. We show that by data aligning the softmax kernel, we obtain an attention mechanism which can both admit a tractable minimal-variance proposal distribution for importance sampling, and exhibits better training stability. Motivated by this finding, we introduce DARKFormer, a Data-Aware Random-feature Kernel transformer that features a data-aligned kernel geometry. DARKFormer learns the random-projection covariance, efficiently realizing an importance-sampled positive random-feature estimator for its data-aligned kernel. Empirically, DARKFormer narrows the performance gap with exact softmax attention, particularly in finetuning regimes where pretrained representations are anisotropic. By combining random-feature efficiency with data-aware kernels, DARKFormer advances kernel-based attention in resource-constrained settings.