Repetitive Contrastive Learning Enhances Mamba's Selectivity in Time Series Prediction

Long sequence prediction is a key challenge in time series forecasting. While Mamba-based models have shown strong performance due to their sequence selection capabilities, they still struggle with insufficient focus on critical time steps and incomplete noise suppression, caused by limited selective abilities. To address this, we introduce Repetitive Contrastive Learning (RCL), a token-level contrastive pretraining framework aimed at enhancing Mamba's selective capabilities. RCL pretrains a single Mamba block to strengthen its selective abilities and then transfers these pretrained parameters to initialize Mamba blocks in various backbone models, improving their temporal prediction performance. RCL uses sequence augmentation with Gaussian noise and applies inter-sequence and intra-sequence contrastive learning to help the Mamba module prioritize information-rich time steps while ignoring noisy ones. Extensive experiments show that RCL consistently boosts the performance of backbone models, surpassing existing methods and achieving state-of-the-art results. Additionally, we propose two metrics to quantify Mamba's selective capabilities, providing theoretical, qualitative, and quantitative evidence for the improvements brought by RCL.

Gradient Based Method for the Fusion of Lattice Quantizers

In practical applications, lattice quantizers leverage discrete lattice points to approximate arbitrary points in the lattice. An effective lattice quantizer significantly enhances both the accuracy and efficiency of these approximations. In the context of high-dimensional lattice quantization, previous work proposed utilizing low-dimensional optimal lattice quantizers and addressed the challenge of determining the optimal length ratio in orthogonal splicing. Notably, it was demonstrated that fixed length ratios and orthogonality yield suboptimal results when combining low-dimensional lattices. Building on this foundation, another approach employed gradient descent to identify optimal lattices, which inspired us to explore the use of neural networks to discover matrices that outperform those obtained from orthogonal splicing methods. We propose two novel approaches to tackle this problem: the Household Algorithm and the Matrix Exp Algorithm. Our results indicate that both the Household Algorithm and the Matrix Exp Algorithm achieve improvements in lattice quantizers across dimensions 13, 15, 17 to 19, 21, and 22. Moreover, the Matrix Exp Algorithm demonstrates superior efficacy in high-dimensional settings.