Jakob Stubenrauch
@jakobstubenrauch.bsky.social
(3/3)
- Linearizing around the nearest fixed point captures roughly the true velocity...
- ...but linearizing around the second-nearest is only slightly worse.
-> Fixed points collectively attract and lur the dynamics
For detailed analytical and numerical analysis check doi.org/10.1103/Phys...
- Linearizing around the nearest fixed point captures roughly the true velocity...
- ...but linearizing around the second-nearest is only slightly worse.
-> Fixed points collectively attract and lur the dynamics
For detailed analytical and numerical analysis check doi.org/10.1103/Phys...
Fixed point geometry in chaotic neural networks
Understanding the high-dimensional chaotic dynamics occurring in complex biological systems such as recurrent neural networks or ecosystems remains a conceptual challenge. For low-dimensional dynamics...
doi.org
June 4, 2025 at 9:47 AM
(3/3)
- Linearizing around the nearest fixed point captures roughly the true velocity...
- ...but linearizing around the second-nearest is only slightly worse.
-> Fixed points collectively attract and lur the dynamics
For detailed analytical and numerical analysis check doi.org/10.1103/Phys...
- Linearizing around the nearest fixed point captures roughly the true velocity...
- ...but linearizing around the second-nearest is only slightly worse.
-> Fixed points collectively attract and lur the dynamics
For detailed analytical and numerical analysis check doi.org/10.1103/Phys...
(2/3) Key findings:
- The number of fixed points is exponential in number of neurons
- Fixed points concentrate on a shell withing the shell where the dynamics concentrates -> radial separation
- Yet, dynamics and fixed points live near the same low-dimensional manifold
- The number of fixed points is exponential in number of neurons
- Fixed points concentrate on a shell withing the shell where the dynamics concentrates -> radial separation
- Yet, dynamics and fixed points live near the same low-dimensional manifold
June 4, 2025 at 9:46 AM
(2/3) Key findings:
- The number of fixed points is exponential in number of neurons
- Fixed points concentrate on a shell withing the shell where the dynamics concentrates -> radial separation
- Yet, dynamics and fixed points live near the same low-dimensional manifold
- The number of fixed points is exponential in number of neurons
- Fixed points concentrate on a shell withing the shell where the dynamics concentrates -> radial separation
- Yet, dynamics and fixed points live near the same low-dimensional manifold