Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

Visual-spatial understanding, the ability to infer object relationships and layouts from visual input, is fundamental to downstream tasks such as robotic navigation and embodied interaction. However, existing methods face spatial uncertainty and data scarcity, limiting the 3D spatial reasoning capability of pre-trained visionlanguage models (VLMs). To address these challenges, we present a unified framework for enhancing 3D spatial reasoning in pre-trained VLMs without modifying their architecture. This framework combines SpatialMind, a structured prompting strategy that decomposes complex scenes and questions into interpretable reasoning steps, with ScanForgeQA, a scalable question-answering dataset built from diverse 3D simulation scenes through an automated construction process designed for fine-tuning. Extensive experiments across multiple benchmarks demonstrate the individual and combined effectiveness of our prompting and fine-tuning strategies, and yield insights that may inspire future research on visual-spatial understanding.

Progress in the field of machine learning has been fueled by the introduction of benchmark datasets pushing the limits of existing algorithms. Enabling the design of datasets to test specific properties and failure modes of learning algorithms is thus a problem of high interest, as it has a direct impact on innovation in the field. In this sense, we introduce Synbols -- Synthetic Symbols -- a tool for rapidly generating new datasets with a rich composition of latent features rendered in low resolution images. Synbols leverages the large amount of symbols available in the Unicode standard and the wide range of artistic font provided by the open font community. Our tool's high-level interface provides a language for rapidly generating new distributions on the latent features, including various types of textures and occlusions. To showcase the versatility of Synbols, we use it to dissect the limitations and flaws in standard learning algorithms in various learning setups including supervised learning, active learning, out of distribution generalization, unsupervised representation learning, and object counting.

Clustering is a fundamental task in data science with wide-ranging applications. In k-medoids clustering, cluster centers must be actual datapoints and arbitrary distance metrics may be used; these features allow for greater interpretability of the cluster centers and the clustering of exotic objects in k-medoids clustering, respectively.

Clustering is a fundamental task in data science with wide-ranging applications. In k-medoids clustering, cluster centers must be actual datapoints and arbitrary distance metrics may be used; these features allow for greater interpretability of the cluster centers and the clustering of exotic objects in k-medoids clustering, respectively.

Private data analysis suffers a costly curse of dimensionality. However, the data1 often has an underlying low-dimensional structure. For example, when optimizing2 via gradient descent, the gradients often lie in or near a low-dimensional subspace.3 If that low-dimensional structure can be identified, then we can avoid paying (in4 terms of privacy or accuracy) for the high ambient dimension.5 We present differentially private algorithms that take input data sampled from6 a low-dimensional linear subspace (possibly with a small amount of error) and7 output that subspace (or an approximation to it). These algorithms can serve as a8 pre-processing step for other procedures.9

A novel approach to rank estimation, called geometric order learning (GOL), is proposed in this paper. First, we construct an embedding space, in which the direction and distance between objects represent order and metric relations between their ranks, by enforcing two geometric constraints: the order constraint compels objects to be sorted according to their ranks, while the metric constraint makes the distance between objects reflect their rank difference. Then, we perform the simple knearest neighbor (k-NN) search in the embedding space to estimate the rank of a test object. Moreover, to assess the quality of embedding spaces for rank estimation, we propose a metric called discriminative ratio for ranking (DRR). Extensive experiments on facial age estimation, historical color image (HCI) classification, and aesthetic score regression demonstrate that GOL constructs effective embedding spaces and thus yields excellent rank estimation performances. The source codes are available at https://github.com/seon92/GOL

Enabling deep models to generalize in non-stationary environments is vital for real-world machine learning, as data distributions are often found to continually change. Recently, evolving domain generalization (EDG) has emerged to tackle the domain generalization in a time-varying system, where the domain gradually evolves over time in an underlying continuous structure. Nevertheless, it typically assumes multiple source domains simultaneously ready. It still remains an open problem to address EDG in the domain-incremental setting, where source domains are non-static and arrive sequentially to mimic the evolution of training domains. To this end, we propose Weight Diffusion (W-Diff), a novel framework that utilizes the conditional diffusion model in the parameter space to learn the evolving pattern of classifiers during the domain-incremental training process. Specifically, the diffusion model is conditioned on the classifier weights of different historical domain (regarded as a reference point) and the prototypes of current domain, to learn the evolution from the reference point to the classifier weights of current domain (regarded as the anchor point). In addition, a domain-shared feature encoder is learned by enforcing prediction consistency among multiple classifiers, so as to mitigate the overfitting problem and restrict the evolving pattern to be reflected in the classifier as much as possible. During inference, we adopt the ensemble manner based on a great number of target domain-customized classifiers, which are cheaply obtained via the conditional diffusion model, for robust prediction. Comprehensive experiments on both synthetic and real-world datasets show the superior generalization performance of W-Diff on unseen domains in the future.