Related papers: Provable Accuracy Collapse in Embedding-Based Repr…
Effective representation of data is crucial in various machine learning tasks, as it captures the underlying structure and context of the data. Embeddings have emerged as a powerful technique for data representation, but evaluating their…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…
Universal Domain Adaptation (UniDA) addresses unsupervised domain adaptation where target classes may differ arbitrarily from source ones, except for a shared subset. A widely used approach, partial domain matching (PDM), aligns only shared…
Multimodal contrastive learning (MCL) aims to embed data from different modalities in a shared embedding space. However, empirical evidence shows that representations from different modalities occupy completely separate regions of embedding…
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…
Why does the low dimensionality of representations, typically $d\approx 1000$, not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of data points? To answer this question, we study maximal-margin…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
Deep metric learning (DML) is a popular approach for images retrieval, solving verification (same or not) problems and addressing open set classification. Arguably, the most common DML approach is with triplet loss, despite significant…
Recent advances in foundation models have led to a promising trend of developing large recommendation models to leverage vast amounts of available data. Still, mainstream models remain embarrassingly small in size and na\"ive enlarging does…
Dimensionality Reduction (DR) methods are widely used to visualize high-dimensional data. One key task in DR-based analysis is discovering neighborhoods, which relies on analyzing the fine-grained local structure of a projection. However,…
The key challenge in learning dense correspondences lies in the lack of ground-truth matches for real image pairs. While photometric consistency losses provide unsupervised alternatives, they struggle with large appearance changes, which…
Oblivious low-distortion subspace embeddings are a crucial building block for numerical linear algebra problems. We show for any real $p, 1 \leq p < \infty$, given a matrix $M \in \mathbb{R}^{n \times d}$ with $n \gg d$, with constant…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
Proximities are at the heart of almost all machine learning methods. If the input data are given as numerical vectors of equal lengths, euclidean distance, or a Hilbertian inner product is frequently used in modeling algorithms. In a more…
Large Deep Learning models are often compressed before being deployed in a resource-constrained environment. Can we trust the prediction of compressed models just as we trust the prediction of the original large model? Existing work has…
Predictions made by deep neural networks were shown to be highly sensitive to small changes made in the input space where such maliciously crafted data points containing small perturbations are being referred to as adversarial examples. On…
Given an arbitrary set of high dimensional points in $\ell_1$, there are known negative results that preclude the possibility of always mapping them to a low dimensional $\ell_1$ space while preserving distances with small multiplicative…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in evaluation metrics such as the pixel-wise relative error, most methods neglect the geometric…
Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can…