HOT: Hadamard-based Optimized Training

It has become increasingly important to optimize backpropagation to reduce memory usage and computational overhead. Achieving this goal is highly challenging, as multiple objectives must be considered jointly while maintaining training quality. In this paper, we focus on matrix multiplication, which accounts for the largest portion of training costs, and analyze its backpropagation in detail to identify lightweight techniques that offer the best benefits. Based on this analysis, we introduce a novel method, Hadamard-based Optimized Training (HOT). In this approach, we apply Hadamard-based optimizations, such as Hadamard quantization and Hadamard low-rank approximation, selectively and with awareness of the suitability of each optimization for different backward paths. Additionally, we introduce two enhancements: activation buffer compression and layer-wise quantizer selection. Our extensive analysis shows that HOT achieves up to 75% memory savings and a 2.6 times acceleration on real GPUs, with negligible accuracy loss compared to FP32 precision.

PTQ4VM: Post-Training Quantization for Visual Mamba

Visual Mamba is an approach that extends the selective space state model, Mamba, to vision tasks. It processes image tokens sequentially in a fixed order, accumulating information to generate outputs. Despite its growing popularity for delivering high-quality outputs at a low computational cost across various tasks, Visual Mamba is highly susceptible to quantization, which makes further performance improvements challenging. Our analysis reveals that the fixed token access order in Visual Mamba introduces unique quantization challenges, which we categorize into three main issues: 1) token-wise variance, 2) channel-wise outliers, and 3) a long tail of activations. To address these challenges, we propose Post-Training Quantization for Visual Mamba (PTQ4VM), which introduces two key strategies: Per-Token Static (PTS) quantization and Joint Learning of Smoothing Scale and Step Size (JLSS). To the our best knowledge, this is the first quantization study on Visual Mamba. PTQ4VM can be applied to various Visual Mamba backbones, converting the pretrained model to a quantized format in under 15 minutes without notable quality degradation. Extensive experiments on large-scale classification and regression tasks demonstrate its effectiveness, achieving up to 1.83x speedup on GPUs with negligible accuracy loss compared to FP16. Our code is available at https://github.com/YoungHyun197/ptq4vm.

HLQ: Fast and Efficient Backpropagation via Hadamard Low-rank Quantization

With the rapid increase in model size and the growing importance of various fine-tuning applications, lightweight training has become crucial. Since the backward pass is twice as expensive as the forward pass, optimizing backpropagation is particularly important. However, modifications to this process can lead to suboptimal convergence, so training optimization should minimize perturbations, which is a highly challenging task. In this study, we introduce a novel optimization strategy called Hadamard Low-rank Quantization (HLQ), focusing on reducing the cost of backpropagation in convolutional and linear layers. We first analyze the sensitivity of gradient computation with respect to activation and weight, and judiciously design the HLQ pipeline to apply 4-bit Hadamard quantization to the activation gradient and Hadamard low-rank approximation to the weight gradient. This combination was found to be the best for maximizing benefits, and our extensive experiments demonstrate the outstanding performance of HLQ in both training from scratch and fine-tuning, achieving significant memory savings and acceleration on real GPUs with negligible quality degradation.