Top-Theta Attention: Sparsifying Transformers by Compensated Thresholding

Abstract: The attention mechanism is essential for the impressive capabilities of transformer-based LLMs. However, calculating attention is computationally intensive due to its quadratic dependency on the sequence length. We introduce a novel approach called Top-Theta Attention, or simply Top-$\theta$, which selectively prunes less essential attention elements by comparing them against carefully calibrated thresholds. This method greatly improves the efficiency of self-attention matrix multiplication while preserving model accuracy, reducing the number of required V cache rows by 3x during generative decoding and the number of attention elements by 10x during the prefill phase. Our method does not require model retraining; instead, it requires only a brief calibration phase to be resilient to distribution shifts, thus not requiring the thresholds for different datasets to be recalibrated. Unlike top-k attention, Top-$\theta$ eliminates full-vector dependency, making it suitable for tiling and scale-out and avoiding costly top-k search. A key innovation of our approach is the development of efficient numerical compensation techniques, which help preserve model accuracy even under aggressive pruning of attention scores.