Function-Counting Theory for Low-Dimensional Data Structures
The success of deep learning models in classification and regression is widely attributed to the low-dimensional structure that real-world data tend to exhibit, despite their high-dimensional representation. This work attempts to provide a mathematical framework for binary classification on low-dimensional data, building on Cover's (1965) function-counting theory. With our framework, we aim to address the question of how the low-dimensional structure of the data affects the classification capabilities of learning models. Cover's theory relies on a general position assumption that blinds it to the underlying data structure. We refine this assumption to account for the low-dimensionality of...
| Authors | Konstantin Häberle, Helmut Bölcskei |
|---|---|
| Primary category | stat.ML |
| Published | 1 July 2026 |
| Last updated at source | 1 July 2026 |
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