Data-Aware Random Feature Kernel for Transformers
This work addresses the problem of high variance in random-feature attention for Transformers, particularly for finetuning pretrained models with anisotropic representations, which is a problem for researchers and practitioners working with large-scale Transformers in resource-constrained settings.
Transformers suffer from quadratic attention complexity, which random-feature attention (e.g., Performers) reduces to linear. However, existing random-feature methods struggle with anisotropic query/key distributions in pretrained models, leading to high variance. This paper introduces DARKFormer, which uses a data-aligned softmax kernel and an importance-sampled positive random-feature estimator to address this, narrowing the performance gap with exact softmax attention, especially in finetuning.
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.