Orthogonal Quadratic Complements for Vision Transformer Feed-Forward Networks

Vision Transformers (ViTs) achieve strong performance on image recognition and mobile vision applications, but their high-dimensional linear projections and attention computations still impose substantial storage and inference costs. Extremely low-bit quantization is a promising solution, yet ViTs often suffer severe accuracy degradation because conventional real-valued scalar codebooks are poorly matched to the directional geometry of Transformer projections. We present RPFQ-ViT, a Rotated Phase-Frame Quantization method that quantizes paired channels in two-dimensional phase planes, enabling low-bit codes to better preserve projection directions while recovering magnitude with lightweight scaling. RPFQ-ViT serves as a drop-in QAT replacement for nn.Linear and does not modify the standard real-valued attention, normalization, or activation computation graph. On ImageNet-1K, RPFQ-ViT-B/16 reaches 79.33% Top-1 / 94.48% Top-5 under W2/A4, Swin-T reaches 79.30% Top-1 / 94.79% Top-5 under W2/A8, and DeiT-S reaches 77.41% Top-1 / 93.11% Top-5 under W2/A8. Ablations, phase-geometry analysis, and direction-preservation metrics show that channel pairing, learnable rotation, phase-anchor learning, and residual phase refinement each improve quantization quality. We further deploy RPFQ-ViT image-classification models on native iOS and Android runtime stacks; with 2-bit packed weights, model size shrinks by roughly $5.4$-$7.1\times$ relative to FP32 and end-to-end on-device latency drops by $1.4$-$1.6\times$. All ImageNet results trained in our codebase use a matched 300-epoch recipe and are reported as mean accuracies over three independent runs. These results show that RPFQ-ViT provides a favorable trade-off among accuracy, compression, and practical mobile deployment for extremely low-bit ViTs.

Vision Transformers (ViTs) are essential in computer vision but are computationally intensive, too. Model quantization, particularly to low bit-widths like 4-bit, aims to alleviate this difficulty, yet existing Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT) methods exhibit significant limitations. PTQ often incurs substantial accuracy drop, while QAT achieves high accuracy but suffers from prohibitive computational costs, limited generalization to downstream tasks, training instability, and lacking of open-source codebase. To address these challenges, this paper introduces General, Practical, and Lightning Quantization (GPLQ), a novel framework designed for efficient and effective ViT quantization. GPLQ is founded on two key empirical insights: the paramount importance of activation quantization and the necessity of preserving the model's original optimization basin'' to maintain generalization. Consequently, GPLQ employs a sequential activation-first, weights-later'' strategy. Stage 1 keeps weights in FP32 while quantizing activations with a feature mimicking loss in only 1 epoch to keep it stay in the same ``basin'', thereby preserving generalization. Stage 2 quantizes weights using a PTQ method. As a result, GPLQ is 100x faster than existing QAT methods, lowers memory footprint to levels even below FP32 training, and achieves 4-bit model performance that is highly competitive with FP32 models in terms of both accuracy on ImageNet and generalization to diverse downstream tasks, including fine-grained visual classification and object detection. We will release an easy-to-use open-source toolkit supporting multiple vision tasks.

Post-training quantization (PTQ) efficiently compresses Vision Transformers (ViTs) without retraining, yet suffers severe accuracy degradation at low bit-widths. Existing optimization-based PTQ methods guide block reconstruction via either soft logits or second-order Hessian proxies. Logit supervision is prone to overfitting on limited calibration data, while Hessian approximations incur structural truncation errors. To address these limitations, we propose GLF-Q, a novel PTQ framework guided by Global-Local Feature alignment. GLF-Q propagates quantized block outputs through downstream full-precision layers to align penultimate-layer representations under local output regularization, providing downstream feature supervision without explicitly approximating the Hessian or using a Taylor expansion. Furthermore, offline Hadamard transformations are introduced with zero runtime overhead to disperse activation outliers across channels, effectively contracting dynamic ranges and reducing quantization errors. Meanwhile, optimizing this loss via a Straight-Through Estimator (STE) achieves rapid convergence, bypassing continuous relaxation rounding formulations such as AdaRound. Extensive experiments across representative ViT architectures demonstrate that GLF-Q with standard uniform quantizers substantially outperforms state-of-the-art methods under 3-bit quantization on image classification. In addition, GLF-Q exhibits strong out-of-domain calibration robustness and achieves speedups under 8-bit GPU deployment.