Linear Log-Normal Attention with Unbiased Concentration

Transformer models have achieved remarkable results in a wide range of applications. However, their scalability is hampered by the quadratic time and memory complexity of the self-attention mechanism concerning the sequence length. This limitation poses a substantial obstacle when dealing with long documents or high-resolution images. In this work, we study the self-attention mechanism by analyzing the distribution of the attention matrix and its concentration ability. Furthermore, we propose instruments to measure these quantities and introduce a novel self-attention mechanism, Linear Log-Normal Attention, designed to emulate the distribution and concentration behavior of the original self-attention. Our experimental results on popular natural language benchmarks reveal that our proposed Linear Log-Normal Attention outperforms other linearized attention alternatives, offering a promising avenue for enhancing the scalability of transformer models. Our code is available in supplementary materials.

Rotation Invariant Quantization for Model Compression

Post-training Neural Network (NN) model compression is an attractive approach for deploying large, memory-consuming models on devices with limited memory resources. In this study, we investigate the rate-distortion tradeoff for NN model compression. First, we suggest a Rotation-Invariant Quantization (RIQ) technique that utilizes a single parameter to quantize the entire NN model, yielding a different rate at each layer, i.e., mixed-precision quantization. Then, we prove that our rotation-invariant approach is optimal in terms of compression. We rigorously evaluate RIQ and demonstrate its capabilities on various models and tasks. For example, RIQ facilitates $\times 19.4$ and $\times 52.9$ compression ratios on pre-trained VGG dense and pruned models, respectively, with $<0.4\%$ accuracy degradation. Code: \url{https://github.com/ehaleva/RIQ}.