Q. Jiang
Publications
The Hidden Power of Scaling Factor in LoRA Optimization
In Low-Rank Adaptation (LoRA), the scaling factor $α$ is often treated as a mere complement to the learning rate, yet its role in optimization remains poorly understood. In this paper, we reveal that the scaling factor $α$ and the learning rate function differently, with $α$ emerging as the dominant driver of effective optimization, delivering gains that cannot be replicated by learning rate scaling alone. Through the synergy of extensive empirical analysis and a theoretical Signal-Drift framework, we uncover three findings into LoRA's scaling mechanism: First, LoRA's spectral suppression smooths the optimization landscape, rendering standard hyperparameters overly conservative and creating an optimization gap. Second, when leveraging this smoothness to accelerate convergence, $α$ outperforms the learning rate by amplifying the task signal without increasing the drift ratio. Third, the optimal scaling factor follows a sublinear relationship with the rank, well characterized by a square-root law with an unexpectedly large coefficient, revealing the insufficient scaling of existing rank-tied heuristics. Based on these insights, we propose LoRA-$α$, a minimalist framework that restores $α$ to its principled regime, making LoRA compatible with standard small learning rates. Extensive evaluations across diverse tasks demonstrate that LoRA-$α$ consistently improves performance while streamlining hyperparameter search, unleashing the learning potential of LoRA.
Spectral Disentanglement and Enhancement: A Dual-domain Contrastive Framework for Representation Learning
Large-scale multimodal contrastive learning has recently achieved impressive success in learning rich and transferable representations, yet it remains fundamentally limited by the uniform treatment of feature dimensions and the neglect of the intrinsic spectral structure of the learned features. Empirical evidence indicates that high-dimensional embeddings tend to collapse into narrow cones, concentrating task-relevant semantics in a small subspace, while the majority of dimensions remain occupied by noise and spurious correlations. Such spectral imbalance and entanglement undermine model generalization. We propose Spectral Disentanglement and Enhancement (SDE), a novel framework that bridges the gap between the geometry of the embedded spaces and their spectral properties. Our approach leverages singular value decomposition to adaptively partition feature dimensions into strong signals that capture task-critical semantics, weak signals that reflect ancillary correlations, and noise representing irrelevant perturbations. A curriculum-based spectral enhancement strategy is then applied, selectively amplifying informative components with theoretical guarantees on training stability. Building upon the enhanced features, we further introduce a dual-domain contrastive loss that jointly optimizes alignment in both the feature and spectral spaces, effectively integrating spectral regularization into the training process and encouraging richer, more robust representations. Extensive experiments on large-scale multimodal benchmarks demonstrate that SDE consistently improves representation robustness and generalization, outperforming state-of-the-art methods. SDE integrates seamlessly with existing contrastive pipelines, offering an effective solution for multimodal representation learning.