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Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear…

Balancing performance trade-off on long-tail (LT) data distributions remains a long-standing challenge. In this paper, we posit that this dilemma stems from a phenomenon called "tail performance degradation" (the model tends to severely…

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep…

The standard approach to representation learning on attributed graphs -- i.e., simultaneously reconstructing node attributes and graph structure -- is geometrically flawed, as it merges two potentially incompatible metric spaces. This…

Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

Real-time stereo matching methods primarily focus on enhancing in-domain performance but often overlook the critical importance of generalization in real-world applications. In contrast, recent stereo foundation models leverage monocular…

In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…

Grokking -- the abrupt transition from memorization to generalization long after near-zero training loss -- has been studied mainly in single-task settings. We extend geometric analysis to multi-task modular arithmetic, training…

Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood. In encoder-decoder arithmetic models, we…

Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex…

Text-to-optimization requires two separable capabilities: modeling -- choosing the right optimization structure -- and binding -- grounding every coefficient, index, and parameter in the concrete problem data. We study this via…

Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…

An open secret in contemporary machine learning is that many models work beautifully on standard benchmarks but fail to generalize outside the lab. This has been attributed to biased training data, which provide poor coverage over real…

A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…

The trade-off between clean accuracy and adversarial robustness is a pervasive phenomenon in deep learning, yet its geometric origin remains elusive. In this work, we utilize Symmetry-Breaking Dimensional Expansion (SBDE) as a controlled…

Accurate prediction of ionic conductivity in electrolyte systems is crucial for advancing numerous scientific and technological applications. While significant progress has been made, current research faces two fundamental challenges: (1)…

To address the challenges of long-tailed classification, researchers have proposed several approaches to reduce model bias, most of which assume that classes with few samples are weak classes. However, recent studies have shown that tail…

Neural visual decoding is a central problem in brain computer interface research, aiming to reconstruct human visual perception and to elucidate the structure of neural representations. However, existing approaches overlook a fundamental…