# Research Papers — 2025-12 · bundle page 175 of 175

> Full-text markdown of papers #8701–8703 of 8703 published in 2025-12, newest first. AI-readable mirrors of the full 8703-paper 2025-12 archive (50 papers per file).

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### Open-Set Domain Adaptation Under Background Distribution Shift: Challenges and A Provably Efficient Solution

Authors: Shravan Chaudhari, Yoav Wald, Suchi Saria
Published: 2025-12-01
Categories: cs.LG, cs.AI, cs.CV
arXiv: https://arxiv.org/abs/2512.01152v5

As we deploy machine learning systems in the real world, a core challenge is to maintain a model that is performant even as the data shifts. Such shifts can take many forms: new classes may emerge that were absent during training, a problem known as open-set recognition, and the distribution of known categories may change. Guarantees on open-set recognition are mostly derived under the assumption that the distribution of known classes, which we call the background distribution, is fixed. In this paper we develop CoLOR, a method that is guaranteed to solve open-set recognition even in the challenging case where the background distribution shifts. We prove that the method works under benign assumptions that the novel class is separable from the non-novel classes, and provide theoretical guarantees that it outperforms a representative baseline in a simplified overparameterized setting. We develop techniques to make CoLOR scalable and robust, and perform comprehensive empirical evaluations on image and text data. The results show that CoLOR significantly outperforms existing open-set recognition methods under background shift. Moreover, we provide new insights into how factors such as the size of the novel class influences performance, an aspect that has not been extensively explored in prior work.

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### Fiber Bundle Networks: A Geometric Machine Learning Paradigm

Authors: Dong Liu
Published: 2025-12-01
Categories: cs.LG, math.DG
arXiv: https://arxiv.org/abs/2512.01151v1

We propose Fiber Bundle Networks (FiberNet), a novel machine learning framework integrating differential geometry with machine learning. Unlike traditional deep neural networks relying on black-box function fitting, we reformulate classification as interpretable geometric optimization on fiber bundles, where categories form the base space and wavelet-transformed features lie in the fibers above each category. We introduce two innovations: (1) learnable Riemannian metrics identifying important frequency feature components, (2) variational prototype optimization through energy function minimization. Classification is performed via Voronoi tessellation under the learned Riemannian metric, where each prototype defines a decision region and test samples are assigned to the nearest prototype, providing clear geometric interpretability. This work demonstrates that the integration of fiber bundle with machine learning provides interpretability and efficiency, which are difficult to obtain simultaneously in conventional deep learning.

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### Dynamic Algorithm for Explainable k-medians Clustering under lp Norm

Authors: Konstantin Makarychev, Ilias Papanikolaou, Liren Shan
Published: 2025-12-01
Categories: cs.LG, cs.DS
arXiv: https://arxiv.org/abs/2512.01150v1

We study the problem of explainable k-medians clustering introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian (2020). In this problem, the goal is to construct a threshold decision tree that partitions data into k clusters while minimizing the k-medians objective. These trees are interpretable because each internal node makes a simple decision by thresholding a single feature, allowing users to trace and understand how each point is assigned to a cluster. We present the first algorithm for explainable k-medians under lp norm for every finite p >= 1. Our algorithm achieves an O(p(log k)^{1 + 1/p - 1/p^2}) approximation to the optimal k-medians cost for any p >= 1. Previously, algorithms were known only for p = 1 and p = 2. For p = 2, our algorithm improves upon the existing bound of O(log^{3/2}k), and for p = 1, it matches the tight bound of log k + O(1) up to a multiplicative O(log log k) factor. We show how to implement our algorithm in a dynamic setting. The dynamic algorithm maintains an explainable clustering under a sequence of insertions and deletions, with amortized update time O(d log^3 k) and O(log k) recourse, making it suitable for large-scale and evolving datasets.

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