HBRB-BoW: A Retrained Bag-of-Words Vocabulary for ORB-SLAM via Hierarchical BRB-KMeans

In visual simultaneous localization and mapping (SLAM), the quality of the visual vocabulary is fundamental to the system's ability to represent environments and recognize locations. While ORB-SLAM is a widely used framework, its binary vocabulary, trained through the k-majority-based bag-of-words (BoW) approach, suffers from inherent precision loss. The inability of conventional binary clustering to represent subtle feature distributions leads to the degradation of visual words, a problem that is compounded as errors accumulate and propagate through the hierarchical tree structure. To address these structural deficiencies, this paper proposes hierarchical binary-to-real-and-back (HBRB)-BoW, a refined hierarchical binary vocabulary training algorithm. By integrating a global real-valued flow within the hierarchical clustering process, our method preserves high-fidelity descriptor information until the final binarization at the leaf nodes. Experimental results demonstrate that the proposed approach yields a more discriminative and well-structured vocabulary than traditional methods, significantly enhancing the representational integrity of the visual dictionary in complex environments. Furthermore, replacing the default ORB-SLAM vocabulary file with our HBRB-BoW file is expected to improve performance in loop closing and relocalization tasks.

TT-FSI: Scalable Faithful Shapley Interactions via Tensor-Train

The Faithful Shapley Interaction (FSI) index uniquely satisfies the faithfulness axiom among Shapley interaction indices, but computing FSI requires $O(d^\ell \cdot 2^d)$ time and existing implementations use $O(4^d)$ memory. We present TT-FSI, which exploits FSI's algebraic structure via Matrix Product Operators (MPO). Our main theoretical contribution is proving that the linear operator $v \mapsto \text{FSI}(v)$ admits an MPO representation with TT-rank $O(\ell d)$, enabling an efficient sweep algorithm with $O(\ell^2 d^3 \cdot 2^d)$ time and $O(\ell d^2)$ core storage an exponential improvement over existing methods. Experiments on six datasets ($d=8$ to $d=20$) demonstrate up to 280$\times$ speedup over baseline, 85$\times$ over SHAP-IQ, and 290$\times$ memory reduction. TT-FSI scales to $d=20$ (1M coalitions) where all competing methods fail.