Indeed, it is so fundamental that it lends its name to one of the most successful ML frameworks. The core object in the ML pipeline is the vector, or, alternatively, its multidimensional generalization, the tensor. However, geometry is far more pervasive and fundamental than these particular properties. At the same time, these geometric notions are typically thought of as specific properties of some aspects of ML. For example, we often study the convexity landscapes of functions, dimensionality and projections are critical to data representations, and we frequently produce visualizations to understand our data and training processes. Geometry is certainly not an unfamiliar field for the ML community geometric ideas play an important role in many parts of ML. One important such choice has to do with geometry, and it is the subject of this blog post. While this approach has produced a robust field, it has also led to several key notions to be de-facto adopted into the machine learning ecosystem for reasons of convenience or tradition, rather than by design. Their rise to fame and fortune has occurred via evolution: a gradual grafting of ideas and approaches contributed by many thinkers and spanning many fields onto the overall structure. Machine learning (ML) methods have become enormously successful and popular.
Non euclidean geometry examples code#
We review some of these exciting ideas, describe some of our contributions, and provide a vision into the future of non-Euclidean space (the final frontier?).Ĭheck out our papers: ICML '18, ICLR '19, NeurIPS '19, GR Learning '19 (fresh off the presses!), and our code on GitHub! Starting with the notion of hyperbolic representations for hierarchical data two years ago, a major push has resulted in new ideas for representations in non-Euclidean spaces, new algorithms and models with non-Euclidean data and operations, and new perspectives on the underlying functionality of non-Euclidean ML. Is our comfortable and familiar Euclidean space and its linear structure always the right place for machine learning? Recent research argues otherwise: it is not always needed and sometimes harmful, as demonstrated by a wave of exciting work. Into the Wild: Machine Learning In Non-Euclidean Spaces by Fred Sala, Ines Chami, Adva Wolf, Albert Gu, Beliz Gunel and Chris Ré
0 kommentar(er)
