Transition Scale-Spaces

Transition Scale-Spaces models discretized entorhinal cortex transitions to optimize multi-scale retrieval of spatial sequences and to investigate hippocampal grid cell computations.

Key Features:

• Spatial transition representation: Represents spatial transitions consistent with hippocampal grid cells and their influence on place cells.
• Scale-space data structure: Uses a scale-space data structure to optimize retrieval from transition systems.
• Multi-scale representation: Enables multi-scale encoding to overcome limitations of single-scale transitions for long goal-directed sequences.
• Optimal scale increment: Employs a mathematically determined optimal scale increment of √2 aligned with biologically plausible receptive fields.
• Temporal buffering: Incorporates temporal buffering mechanisms to support online learning of the scale-space.
• Sequence retrieval modes: Supports both top-down and bottom-up approaches for sequence retrieval from the transition scale-space.
• Symbolic, non-spiking evaluation: Evaluates algorithms with symbolic simulations that do not rely on biologically plausible spiking neurons.
• Simulated navigation tests: Demonstrates utility by discovering shortcuts in simulated environments such as the Morris water maze.
• Biological alignment: Is compatible with observed discretization along the dorso-ventral axis of the medial entorhinal cortex.
• General-purpose retrieval: Functions as a cortical-style data structure for fast retrieval of sequences and relational knowledge beyond navigation.

Scientific Applications:

• Modeling entorhinal cortex and grid cells: Provides a computational framework to study grid cell representations of spatial transitions.
• Place cell input modeling: Explains how transition representations can be conveyed downstream to place cells.
• Goal-directed navigation: Enables efficient retrieval of long navigation sequences across multiple scales.
• Shortcut discovery: Identifies shortcuts and alternative paths in simulated navigation tasks such as the Morris water maze.
• Neurobiological prediction: Produces testable predictions about discretization along the dorso-ventral axis of the medial entorhinal cortex.
• Relational knowledge retrieval: Applies to fast sequence and relational-memory retrieval in domains beyond spatial navigation.

Methodology:

Implements a scale-space data structure with an analytically derived optimal scale increment of √2, uses temporal buffering for online scale learning, supports top-down and bottom-up sequence retrieval, and is evaluated with symbolic non-spiking simulations including Morris water maze shortcut experiments.