Towards LLM-guided Efficient and Interpretable Multi-linear Tensor Network Rank Selection

We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs, our approach offers enhanced interpretability of the rank choices and can effectively optimise the objective function. This framework enables users without specialised domain expertise to utilise tensor network decompositions and understand the underlying rationale within the rank selection process. Experimental results validate our method on financial higher-order datasets, demonstrating interpretable reasoning, strong generalisation to unseen test data, and its potential for self-enhancement over successive iterations. This work is placed at the intersection of large language models and higher-order data analysis.

EasyTrack: Efficient and Compact One-stream 3D Point Clouds Tracker

Most of 3D single object trackers (SOT) in point clouds follow the two-stream multi-stage 3D Siamese or motion tracking paradigms, which process the template and search area point clouds with two parallel branches, built on supervised point cloud backbones. In this work, beyond typical 3D Siamese or motion tracking, we propose a neat and compact one-stream transformer 3D SOT paradigm from the novel perspective, termed as \textbf{EasyTrack}, which consists of three special designs: 1) A 3D point clouds tracking feature pre-training module is developed to exploit the masked autoencoding for learning 3D point clouds tracking representations. 2) A unified 3D tracking feature learning and fusion network is proposed to simultaneously learns target-aware 3D features, and extensively captures mutual correlation through the flexible self-attention mechanism. 3) A target location network in the dense bird's eye view (BEV) feature space is constructed for target classification and regression. Moreover, we develop an enhanced version named EasyTrack++, which designs the center points interaction (CPI) strategy to reduce the ambiguous targets caused by the noise point cloud background information. The proposed EasyTrack and EasyTrack++ set a new state-of-the-art performance ($\textbf{18\%}$, $\textbf{40\%}$ and $\textbf{3\%}$ success gains) in KITTI, NuScenes, and Waymo while runing at \textbf{52.6fps} with few parameters (\textbf{1.3M}). The code will be available at https://github.com/KnightApple427/Easytrack.

Tensor Star Decomposition

A novel tensor decomposition framework, termed Tensor Star (TS) decomposition, is proposed which represents a new type of tensor network decomposition based on tensor contractions. This is achieved by connecting the core tensors in a ring shape, whereby the core tensors act as skip connections between the factor tensors and allow for direct correlation characterisation between any two arbitrary dimensions. Uniquely, this makes it possible to decompose an order-$N$ tensor into $N$ order-$3$ factor tensors $\{\mathcal{G}_{k}\}_{k=1}^{N}$ and $N$ order-$4$ core tensors $\{\mathcal{C}_{k}\}_{k=1}^{N}$, which are arranged in a star shape. Unlike the class of Tensor Train (TT) decompositions, these factor tensors are not directly connected to one another. The so obtained core tensors also enable consecutive factor tensors to have different latent ranks. In this way, the TS decomposition alleviates the "curse of dimensionality" and controls the "curse of ranks", exhibiting a storage complexity which scales linearly with the number of dimensions and as the fourth power of the ranks.