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As datasets used in scientific applications become more complex, studying the geometry and topology of data has become an increasingly prevalent part of the data analysis process. This can be seen for example with the growing interest in…

Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…

Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack principled guarantees on coverage…

We present a detailed account of a recently proposed phenomenological theory for noncatenated ring polymer melts (Phys. Rev. Lett. 106, 167802 (2011)). A basic assumption lies in the implementation of the noncatenation constraint via the…

Supervised classification approaches can predict labels for unknown data because of the supervised training process. The success of classification is heavily dependent on the labeled training data. Differently, clustering is effective in…

Sampling one or more effective solutions from large search spaces is a recurring idea in machine learning, and sequential optimization has become a popular solution. Typical examples include data summarization, sample mining for predictive…

The recent rise of unsupervised and self-supervised learning has dramatically reduced the dependency on labeled data, providing effective image representations for transfer to downstream vision tasks. Furthermore, recent works employed…

Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…

Aiming at improving performance of visual classification in a cost-effective manner, this paper proposes an incremental semi-supervised learning paradigm called Deep Co-Space (DCS). Unlike many conventional semi-supervised learning methods…

We present a methodology for using unlabeled data to design semi-supervised learning (SSL) methods that improve the predictive performance of supervised learning for regression tasks. The main idea is to design different mechanisms for…

Despite significant advances, the performance of state-of-the-art continual learning approaches hinges on the unrealistic scenario of fully labeled data. In this paper, we tackle this challenge and propose an approach for continual…

While deep learning strategies achieve outstanding results in computer vision tasks, one issue remains: The current strategies rely heavily on a huge amount of labeled data. In many real-world problems, it is not feasible to create such an…

Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph…

The ultimate goal of a supervised learning algorithm is to produce models constructed on the training data that can generalize well to new examples. In classification, functional margin maximization -- correctly classifying as many training…

In this work, we propose a novel convolutional autoencoder based architecture to generate subspace specific feature representations that are best suited for classification task. The class-specific data is assumed to lie in low dimensional…

Computer vision tasks are traditionally defined and evaluated using semantic categories. However, it is known to the field that semantic classes do not necessarily correspond to a unique visual class (e.g. inside and outside of a car).…

The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space $\mathbb{R}^3$ are easier to feel by human's intuition. We give the maximum order of finite group actions on $(\mathbb{R}^3, \Sigma)$…

Statistically correcting measured cross sections for detector effects is an important step across many applications. In particle physics, this inverse problem is known as unfolding. In cases with complex instruments, the distortions they…

Unsupervised machine learning is a cornerstone of artificial intelligence as it provides algorithms capable of learning tasks, such as classification of data, without explicit human assistance. We present an unsupervised deep learning…

Embedding tables are used by machine learning systems to work with categorical features. In modern Recommendation Systems, these tables can be very large, necessitating the development of new methods for fitting them in memory, even during…