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Spatial reasoning focuses on locating target objects based on spatial relations in 3D scenes, which plays a crucial role in developing intelligent embodied agents. Due to the limited availability of 3D scene-language paired data, it is…
We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…
In the context of pose-invariant object recognition and retrieval, we demonstrate that it is possible to achieve significant improvements in performance if both the category-based and the object-identity-based embeddings are learned…
Manifold learning techniques, such as Locally linear embedding (LLE), are designed to preserve the local neighborhood structures of high-dimensional data during dimensionality reduction. Traditional LLE employs Euclidean distance to define…
With distributed machine learning being a prominent technique for large-scale machine learning tasks, communication complexity has become a major bottleneck for speeding up training and scaling up machine numbers. In this paper, we propose…
Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric…
Positional embeddings (PE) play a crucial role in Vision Transformers (ViTs) by providing spatial information otherwise lost due to the permutation invariant nature of self attention. While absolute positional embeddings (APE) have shown…
Semantic text representation is a fundamental task in the field of natural language processing. Existing text embedding (e.g., SimCSE and LLM2Vec) have demonstrated excellent performance, but the values of each dimension are difficult to…
We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the…
To investigate objects without a describable notion of distance, one can gather ordinal information by asking triplet comparisons of the form "Is object $x$ closer to $y$ or is $x$ closer to $z$?" In order to learn from such data, the…
There is a recent surge of interest in cross-modal representation learning corresponding to images and text. The main challenge lies in mapping images and text to a shared latent space where the embeddings corresponding to a similar…
Text-to-Image Retrieval (T2IR) is a highly valuable task that aims to match a given textual query to images in a gallery. Existing benchmarks primarily focus on textual queries describing overall image semantics or foreground salient…
Embedding a web-scale information network into a low-dimensional vector space facilitates tasks such as link prediction, classification, and visualization. Past research has addressed the problem of extracting such embeddings by adopting…
We introduce Locally Linear Embedding (LLE) to the astronomical community as a new classification technique, using SDSS spectra as an example data set. LLE is a nonlinear dimensionality reduction technique which has been studied in the…
Low-dimensional embeddings (LDEs) of high-dimensional data are ubiquitous in science and engineering. They allow us to quickly understand the main properties of the data, identify outliers and processing errors, and inform the next steps of…
Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…
Olfaction lies at the intersection of chemical structure, neural encoding, and linguistic perception, yet existing representation methods fail to fully capture this pathway. Current approaches typically model only isolated segments of the…
Text-driven image editing enables users to flexibly modify visual content through natural language instructions, and is widely applied to tasks such as semantic object replacement, insertion, and removal. While recent inversion-based…
Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…