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A unified theory for the origin of grid cells through the lens of pattern formation
Ben Sorscher*, Gabriel C. Mel*, Surya Ganguli, Sam Ocko
Grid cells
Krupic et al. (2012), Derdikman (2014)
A unified theory for the origin of grid cells through the lens of - - PowerPoint PPT Presentation
A unified theory for the origin of grid cells through the lens of - - PowerPoint PPT Presentation
A unified theory for the origin of grid cells through the lens of pattern formation Ben Sorscher*, Gabriel C. Mel*, Surya Ganguli, Sam Ocko Grid cells Krupic et al. (2012), Derdikman (2014) Trained neural networks learn grid patterns Banino et
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unconstrained nonnegative Dordek et al. (2016) Stachenfeld et al. (2014) Banino et al. (2018) Cueva & Wei (2018)
Trained neural networks learn grid patterns
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Trained neural networks learn grid patterns
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- 1. Why are the optimal maps grids?
- 2. What determines the optimal grid type - square,
amorphous, or hexagonal?
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Gradient descent as a pattern forming dynamics
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Gradient descent as a pattern forming dynamics
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Gradient descent as a pattern forming dynamics
1. Why are the optimal maps grids?
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Gradient descent as a pattern forming dynamics
1. Why are the optimal maps grids?
Translation invariance => Fourier modes
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- 1. Why are the optimal maps grids?
- 2. What determines the optimal grid type - square,
amorphous, or hexagonal?
Translation invariance => Fourier modes
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- 1. Why are the optimal maps grids?
- 2. What determines the optimal grid type - square,
amorphous, or hexagonal?
Translation invariance => Fourier modes
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Nonnegativity yields hexagonal grids
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Nonnegativity yields hexagonal grids
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Taylor expand constraint
Nonnegativity yields hexagonal grids
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Taylor expand constraint
Nonnegativity yields hexagonal grids
“Three-body interaction” between stripes 60o apart
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Taylor expand constraint
Nonnegativity yields hexagonal grids
“Three-body interaction” between stripes 60o apart
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Unifying mechanistic and normative models
Normative encoding models
Banino et al. (2018) Cueva & Wei (2018) Dordek et al. (2016) Stachenfeld et al. (2014)
Grid cell model RNNs
Skaggs et al. (1995) Zhang (1996) Fuhs and Touretzky (2006) Burak and Fiete (2009)
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Unifying mechanistic and normative models
Normative encoding models
Activity dynamics Gradient descent Pattern forming dynamics
Banino et al. (2018) Cueva & Wei (2018) Dordek et al. (2016) Stachenfeld et al. (2014)
Grid cell model RNNs
Skaggs et al. (1995) Zhang (1996) Fuhs and Touretzky (2006) Burak and Fiete (2009)
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Unifying mechanistic and normative models
Normative encoding models
Activity dynamics Gradient descent
Banino et al. (2018) Cueva & Wei (2018) Dordek et al. (2016) Stachenfeld et al. (2014)
Grid cell model RNNs =
Skaggs et al. (1995) Zhang (1996) Fuhs and Touretzky (2006) Burak and Fiete (2009)