A sub-Riemannian model of neural states in the primary motor cortex
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914323601817600 |
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| author | Mazzetti, Caterina Ali, Jawad Sarti, Alessandro Citti, Giovanna |
| author_facet | Mazzetti, Caterina Ali, Jawad Sarti, Alessandro Citti, Giovanna |
| contents | We develop a neurogeometric model for the arm area of motor cortex, which encodes complex motor primitives, ranging from simple movement features like movement direction, to short hand trajectories, termed fragments, and ultimately to more complex patterns known as neural states (Georgopoulos, Hatsopoulos, Kadmon-Harpaz et al). Based on the sub-riemannian framework introduced in 2023, we model the space of fragments as a set of short curves defined by kinematic parameters. We then introduce a geometric kernel that serves as a model for cortical connectivity and use it in a differential equation to describe cortical activity. By applying a grouping algorithm to this cortical activity model, we successfully recover the neural states observed in Kadmon-Harpaz et al, which were based on measured cortical activity. This confirms that the choice of kinematic variables and the distance metric used here are sufficient to explain the phenomena of neural state formation. The modularity of our model reflects the brain's hierarchical structure, where initial groupings in the kinematic space $\mathcal{M}$ lead to more abstract representations. This approach mimics how the brain processes stimuli at different scales, extracting both local and global properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03247 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sub-Riemannian model of neural states in the primary motor cortex Mazzetti, Caterina Ali, Jawad Sarti, Alessandro Citti, Giovanna Neurons and Cognition We develop a neurogeometric model for the arm area of motor cortex, which encodes complex motor primitives, ranging from simple movement features like movement direction, to short hand trajectories, termed fragments, and ultimately to more complex patterns known as neural states (Georgopoulos, Hatsopoulos, Kadmon-Harpaz et al). Based on the sub-riemannian framework introduced in 2023, we model the space of fragments as a set of short curves defined by kinematic parameters. We then introduce a geometric kernel that serves as a model for cortical connectivity and use it in a differential equation to describe cortical activity. By applying a grouping algorithm to this cortical activity model, we successfully recover the neural states observed in Kadmon-Harpaz et al, which were based on measured cortical activity. This confirms that the choice of kinematic variables and the distance metric used here are sufficient to explain the phenomena of neural state formation. The modularity of our model reflects the brain's hierarchical structure, where initial groupings in the kinematic space $\mathcal{M}$ lead to more abstract representations. This approach mimics how the brain processes stimuli at different scales, extracting both local and global properties. |
| title | A sub-Riemannian model of neural states in the primary motor cortex |
| topic | Neurons and Cognition |
| url | https://arxiv.org/abs/2501.03247 |