Suwon Lee

Ungsik Kim, Suwon Lee

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.

Minjae Lee, Sang-Min Choi, Gun-Woo Kim et al.

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.