rotation matrix
DartQuant: Efficient Rotational Distribution Calibration for LLMQuantization
Quantization plays a crucial role in accelerating the inference of large-scale models, and rotational matrices have been shown to effectively improve quantization performance by smoothing outliers. However, end-to-end fine-tuning of rotational optimization algorithms incurs high computational costs and is prone to overfitting. To address this challenge, we propose an efficient distribution-aware rotational calibration method, DartQuant, which reduces the complexity of rotational optimization by constraining the distribution of the activations after rotation. This approach also effectively reduces reliance on task-specific losses, thereby mitigating the risk of overfitting. Additionally, we introduce the QR-Orth optimization scheme, which replaces expensive alternating optimization with a more efficient solution. In a variety of model quantization experiments, DartQuant demonstrates superior performance. Compared to existing methods, it achieves 47 acceleration and 10 memory savings for rotational optimization on a 70B model. Furthermore, it is the first to successfully complete rotational calibration for a 70B model on a single 3090 GPU, making quantization of large language models feasible in resource-constrained environments.
RMLR: Extending Multinomial Logistic Regression into General Geometries
Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean multinomial logistic regression (MLR) into Riemannian manifolds. However, existing approaches suffer from limited applicability due to their strong reliance on specific geometric properties. This paper proposes a framework for designing Riemannian MLR over general geometries, referred to as RMLR. Our framework only requires minimal geometric properties, thus exhibiting broad applicability and enabling its use with a wide range of geometries.