Large language models (LLMs) have shown impressive performance on language tasks but face challenges when deployed on resource-constrained devices due to their extensive parameters and reliance on dense multiplications, resulting in high memory demands and latency bottlenecks. Shift-and-add reparameterization offers a promising solution by replacing costly multiplications with hardware-friendly primitives in both the attention and multi-layer perceptron (MLP) layers of an LLM. However, current reparameterization techniques require training from scratch or full parameter fine-tuning to restore accuracy, which is resource-intensive for LLMs. To address this, we propose accelerating pretrained LLMs through post-training shift-and-add reparameterization, creating efficient multiplication-free models, dubbed ShiftAddLLM. Specifically, we quantize each weight matrix into binary matrices paired with group-wise scaling factors. The associated multiplications are reparameterized into (1) shifts between activations and scaling factors and (2) queries and adds according to the binary matrices. To reduce accuracy loss, we present a multi-objective optimization method to minimize both weight and output activation reparameterization errors. Additionally, based on varying sensitivity across layers to reparameterization, we develop an automated bit allocation strategy to further reduce memory usage and latency. Experiments on five LLM families and eight tasks consistently validate the effectiveness of ShiftAddLLM, achieving average perplexity reductions of 5.6 and 22.7 points at comparable or lower latency compared to the most competitive quantized LLMs at 3- and 2-bit precision, respectively, and more than 80% memory and energy reductions over the original LLMs. Codes and models are available at https://github.com/GATECH-EIC/ShiftAddLLM.

Vision Transformers (ViTs) have shown impressive performance and have become a unified backbone for multiple vision tasks. However, both the attention mechanism and multi-layer perceptrons (MLPs) in ViTs are not sufficiently efficient due to dense multiplications, leading to costly training and inference. To this end, we propose to reparameterize pre-trained ViTs with a mixture of multiplication primitives, e.g., bitwise shifts and additions, towards a new type of multiplication-reduced model, dubbed $\textbf{ShiftAddViT}$, which aims to achieve end-to-end inference speedups on GPUs without requiring training from scratch. Specifically, all $\texttt{MatMuls}$ among queries, keys, and values are reparameterized using additive kernels, after mapping queries and keys to binary codes in Hamming space. The remaining MLPs or linear layers are then reparameterized with shift kernels. We utilize TVM to implement and optimize those customized kernels for practical hardware deployment on GPUs. We find that such a reparameterization on (quadratic or linear) attention maintains model accuracy, while inevitably leading to accuracy drops when being applied to MLPs. To marry the best of both worlds, we further propose a new mixture of experts (MoE) framework to reparameterize MLPs by taking multiplication or its primitives as experts, e.g., multiplication and shift, and designing a new latency-aware load-balancing loss. Such a loss helps to train a generic router for assigning a dynamic amount of input tokens to different experts according to their latency. In principle, the faster the experts run, the more input tokens they are assigned. Extensive experiments on various 2D/3D Transformer-based vision tasks consistently validate the effectiveness of our proposed ShiftAddViT, achieving up to $\textbf{5.18$\times$}$ latency reductions on GPUs and $\textbf{42.9}$% energy savings, while maintaining a comparable accuracy as original or efficient ViTs. Codes and models are available at https://github.com/GATECH-EIC/ShiftAddViT.