SciPost Submission Page
High-dimensional random landscapes: from typical to large deviations
by Valentina Ros
Submission summary
| Authors (as registered SciPost users): | Valentina Ros |
| Submission information | |
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| Preprint Link: | scipost_202502_00002v1 (pdf) |
| Date submitted: | 2025-02-03 12:24 |
| Submitted by: | Ros, Valentina |
| Submitted to: | SciPost Physics Lecture Notes |
| for consideration in Collection: | |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an example, we con- sider a high-dimensional inference problem in two forms: matrix denoising (Case 1) and tensor denoising (Case 2). We show how to map the inference problem onto the opti- mization problem of a high-dimensional landscape, which exhibits distinct geometrical properties in the two Cases. We discuss methods for characterizing typical realizations of these landscapes and their optimization through local dynamics. We conclude by highlighting connections between the landscape problem and Large Deviation Theory.
Current status:
In refereeing