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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,051 papers · 148 categories

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0111 · Oct 201819922001200920182026
4 results for “self-position”
On Path Integration of Grid Cells: Group Representation and Isotropic Scalingq-bio.NC

The paper analyzes how grid cells perform path integration and learns hexagon grid patterns.

problem Understanding how grid cells perform path integration calculations.
method Theoretical analysis of a general representation model of path integration by grid cells, identifying group representation and isotropic scaling conditions.
result The learned model of hexagon grid patterns is capable of accurate long distance path integration.
grid cellspath integrationhexagon patternsgroup representationisotropic scaling
2020-06-18abs ↗pdf ↗
Learning Grid Cells as Vector Representation of Self-Position Coupled with Matrix Representation of Self-Motionstat.ML

A model for grid cells using vectors and matrices for position and motion.

problem Representing self-position and motion in a high-dimensional space.
method Vector-matrix multiplication, magnified local isometry, and global adjacency kernel.
result The model can learn hexagon patterns and correct errors.
grid cellsvector representationmatrix representationself-positionself-motion
2018-10-12abs ↗pdf ↗
Conformal Isometry of Lie Group Representation in Recurrent Network of Grid Cellsq-bio.NC

Hexagon grid patterns emerge from conformal isometry in grid cell neural networks.

problem Understanding the algebraic, geometric, and topological properties of grid cells.
method Investigating recurrent neural network models of grid cells, focusing on Lie group and Lie algebra representations, conformal isometry, and hexagon periodic patterns.
result Conformal isometry leads to hexagon periodic patterns in grid cell responses and accurate path integration.
grid cellsrecurrent networksLie groupconformal isometryhexagon patterns
2022-10-06abs ↗pdf ↗
Emergence of Grid-like Representations by Training Recurrent Networks with Conformal Normalizationq-bio.NC

The paper studies how grid cell patterns emerge in neural networks.

problem Understanding how grid cells in the brain form hexagonal firing patterns.
method Training recurrent neural networks with conformal normalization of velocity inputs.
result Conformal normalization is crucial for the emergence of hexagonal grid patterns in neural networks.
grid cellsneural networkshexagonal patternsconformal normalization2D navigation
2023-10-29abs ↗pdf ↗