Usingalgebraic geometry,weestablish that UPCA is a well-defined algebraic problem in the sense that the only matrices of minimal rank that agree with the given data are row-permutations of the ground-truth matrix, arising as the unique solutions of a polynomial system of equations.

Recent foundation models for tabular data achieve strong task-specific performance via in-context learning. Nevertheless, they focus on direct prediction by encapsulating both representation learning and task-specific inference inside a single, resource-intensive network. This work specifically focuses on representation learning, i.e., on transferable, task-agnostic embeddings. We systematically evaluate task-agnostic representations from tabular foundation models (TabPFN and TabICL) alongside with classical feature engineering (TableVectorizer) across a variety of application tasks as outlier detection (ADBench) and supervised learning (TabArena Lite). We find that simple TableVectorizer features achieve comparable or superior performance while being up to three orders of magnitude faster than tabular foundation models. The code is available at https://github.com/ContactSoftwareAI/TabEmbedBench.

Correspondences in point cloud registration are prone to outliers, significantly reducing registration accuracy and highlighting the need for precise inlier identification.

The rapid deployment of Large Language Models (LLMs) highlights the need for efficient low-bit post-training quantization (PTQ), due to their high memory costs. A key challenge in weight quantization is the presence of outliers, which inflate quantization ranges and lead to large errors. While a number of outlier suppression techniques have been proposed, they either: fail to effectively shrink the quantization range, or incur (relatively) high bit overhead. In this paper, we present ICQuant, a novel framework that leverages outlier statistics to design an efficient index coding scheme for outlier-aware weight-only quantization. Compared to existing outlier suppression techniques requiring $\approx 1$ bit overhead to halve the quantization range, ICQuant requires only $\approx 0.3$ bits; a significant saving in extreme compression regimes (e.g., 2-3 bits per weight). ICQuant can be used on top of any existing quantizers to eliminate outliers, improving the quantization quality. Using just 2.3 bits per weight and simple scalar quantizers, ICQuant improves the zero-shot accuracy of the 2-bit Llama3-70B model by up to 130% and 150% relative to QTIP and QuIP#; and it achieves comparable performance to the best-known fine-tuned quantizer (PV-tuning) without fine-tuning.

Point cloud registration based on correspondences computes the rigid transformation that maximizes the number of inliers constrained within the noise threshold. Current state-of-the-art (SOTA) methods employing spatial compatibility graphs or branch-and-bound (BnB) search mainly focus on registration under high outlier ratios. However, graph-based methods require at least quadratic space and time complexity for graph construction, while multi-stage BnB search methods often suffer from inaccuracy due to local optima between decomposed stages. This paper proposes a geometric maximum overlapping registration framework via rotation-only BnB search. The rigid transformation is decomposed using Chasles' theorem into a translation along rotation axis and a 2D rigid transformation. The optimal rotation axis and angle are searched via BnB, with residual parameters formulated as range maximum query (RMQ) problems. Firstly, the top-k candidate rotation axes are searched within a hemisphere parameterized by cube mapping, and the translation along each axis is estimated through interval stabbing of the correspondences projected onto that axis. Secondly, the 2D registration is relaxed to 1D rotation angle search with 2D RMQ of geometric overlapping for axis-aligned rectangles, which is solved deterministically in polynomial time using sweep line algorithm with segment tree. Experimental results on 3DMatch, 3DLoMatch, and KITTI datasets demonstrate superior accuracy and efficiency over SOTA methods, while the time complexity is polynomial and the space complexity increases linearly with the number of points, even in the worst case.

Rejecting outliers before applying classical robust methods is a common approach to increase the success rate of estimation, particularly when the outlier ratio is extremely high (e.g. 90%). However, this method often relies on sensor- or task-specific characteristics, which may not be easily transferable across different scenarios. In this paper, we focus on the problem of rejecting 2D-3D point correspondence outliers from 2D forward-looking sonar (2D FLS) observations, which is one of the most popular perception device in the underwater field but has a significantly different imaging mechanism compared to widely used perspective cameras and LiDAR. We fully leverage the narrow field of view in the elevation of 2D FLS and develop two compatibility tests for different 3D point configurations: (1) In general cases, we design a pairwise length in-range test to filter out overly long or short edges formed from point sets; (2) In coplanar cases, we design a coplanarity test to check if any four correspondences are compatible under a coplanar setting. Both tests are integrated into outlier rejection pipelines, where they are followed by maximum clique searching to identify the largest consistent measurement set as inliers. Extensive simulations demonstrate that the proposed methods for general and coplanar cases perform effectively under outlier ratios of 80% and 90%, respectively.

This is the arxiv version for our paper submitted to IEEE/RSJ IROS 2025. We propose a scene-agnostic and light-weight visual relocalization framework that leverages semantically labeled 3D lines as a compact map representation. In our framework, the robot localizes itself by capturing a single image, extracting 2D lines, associating them with semantically similar 3D lines in the map, and solving a robust perspective-n-line problem. To address the extremely high outlier ratios~(exceeding 99.5\%) caused by one-to-many ambiguities in semantic matching, we introduce the Saturated Consensus Maximization~(Sat-CM) formulation, which enables accurate pose estimation when the classic Consensus Maximization framework fails. We further propose a fast global solver to the formulated Sat-CM problems, leveraging rigorous interval analysis results to ensure both accuracy and computational efficiency. Additionally, we develop a pipeline for constructing semantic 3D line maps using posed depth images. To validate the effectiveness of our framework, which integrates our innovations in robust estimation and practical engineering insights, we conduct extensive experiments on the ScanNet++ dataset.

Correspondence-based point cloud registration (PCR) plays a key role in robotics and computer vision. However, challenges like sensor noises, object occlusions, and descriptor limitations inevitably result in numerous outliers. RANSAC family is the most popular outlier removal solution. However, the requisite iterations escalate exponentially with the outlier ratio, rendering it far inferior to existing methods (SC2PCR [1], MAC [2], etc.) in terms of accuracy or speed. Thus, we propose a two-stage consensus filtering (TCF) that elevates RANSAC to state-of-the-art (SOTA) speed and accuracy. Firstly, one-point RANSAC obtains a consensus set based on length consistency. Subsequently, two-point RANSAC refines the set via angle consistency. Then, three-point RANSAC computes a coarse pose and removes outliers based on transformed correspondence's distances. Drawing on optimizations from one-point and two-point RANSAC, three-point RANSAC requires only a few iterations. Eventually, an iterative reweighted least squares (IRLS) is applied to yield the optimal pose. Experiments on the large-scale KITTI and ETH datasets demonstrate our method achieves up to three-orders-of-magnitude speedup compared to MAC while maintaining registration accuracy and recall. Our code is available at https://github.com/ShiPC-AI/TCF.