Integrate-and-Fire from a Mathematical and Signal Processing Perspective
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909462636265472 |
|---|---|
| author | Moser, Bernhard A. Werzi, Anna Lunglmayr, Michael |
| author_facet | Moser, Bernhard A. Werzi, Anna Lunglmayr, Michael |
| contents | Integrate-and-Fire (IF) is an idealized model of the spike-triggering mechanism of a biological neuron. It is used to realize the bio-inspired event-based principle of information processing in neuromorphic computing. We show that IF is closely related to the concept of Send-on-Delta (SOD) as used in threshold-based sampling. It turns out that the IF model can be adjusted in a way that SOD can be understood as differential version of IF. As a result, we gain insight into the underlying metric structure based on the Alexiewicz norm with consequences for clarifying the underlying signal space including bounded integrable signals with superpositions of finitely many Dirac impulses, the identification of a maximum sparsity property, error bounds for signal reconstruction and a characterization in terms of sparse regularization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrate-and-Fire from a Mathematical and Signal Processing Perspective Moser, Bernhard A. Werzi, Anna Lunglmayr, Michael Signal Processing Neural and Evolutionary Computing 94A20 Integrate-and-Fire (IF) is an idealized model of the spike-triggering mechanism of a biological neuron. It is used to realize the bio-inspired event-based principle of information processing in neuromorphic computing. We show that IF is closely related to the concept of Send-on-Delta (SOD) as used in threshold-based sampling. It turns out that the IF model can be adjusted in a way that SOD can be understood as differential version of IF. As a result, we gain insight into the underlying metric structure based on the Alexiewicz norm with consequences for clarifying the underlying signal space including bounded integrable signals with superpositions of finitely many Dirac impulses, the identification of a maximum sparsity property, error bounds for signal reconstruction and a characterization in terms of sparse regularization. |
| title | Integrate-and-Fire from a Mathematical and Signal Processing Perspective |
| topic | Signal Processing Neural and Evolutionary Computing 94A20 |
| url | https://arxiv.org/abs/2501.11453 |