geometric-phase-transition-hippocampal-memory

name	geometric-phase-transition-hippocampal-memory
arxiv_id	2605.17199
published	2026-05-16
authors	Prashant C. Raju
description	Geometric phase transition methodology for hippocampal memory — extreme spatial memory emerges from a discrete stiffening of hippocampal population geometry from disorganized (mist) to crystalline code. Use when researching: hippocampal memory capacity, neural manifold geometry, topological phase transitions in neural codes, food-caching birds and spatial memory, geometric stability of neural representations, Valiant's Stable Memory Allocator, representational redundancy (geometric tax), excitatory-inhibitory circuit dynamics for high-capacity storage. Keywords: hippocampal memory, geometric phase transition, crystalline code, neural manifold, food-caching birds, geometric tax, spatial memory, topological rigidity.

Geometric Phase Transition Enables Extreme Hippocampal Memory Capacity

Overview

This methodology shows that superior spatial memory emerges from a topological phase transition in how neural activity is collectively organized. Comparing food-caching chickadees (high-capacity memory) to non-caching zebra finches (standard memory), the caching hippocampus maintains a topologically rigid "crystalline" code while the non-caching hippocampus resembles a disorganized "mist."

Key Findings

1. >100x capacity advantage: Crystalline codes sustain high-fidelity readout beyond M=1,000 locations while mist codes fail below M=10
2. Geometric stability (Shesha): Chickadee hippocampus shows 0.245 vs 0.166 for finch — significantly higher geometric stability
3. Temporal coherence: Nearly two-fold greater in caching birds (Shesha: 0.393 vs 0.209)
4. Geometric tax: 169-fold representational redundancy required to stabilize crystalline manifold against biological noise
5. Double dissociation with Valiant's model: Caching networks exhibit near-zero split-half allocation reliability despite geometric superiority

Core Mechanisms

The Phase Transition

• Below critical threshold (mist code): Networks suffer catastrophic interference, fail at moderate loads
• Above critical threshold (crystalline code): Reliable recall extends orders of magnitude larger
• Transition governed by topological rigidity of the neural manifold

Excitatory-Inhibitory Synergy

• Excitatory neurons: Form the spatial scaffold
• Inhibitory populations: Contribute orthogonal decorrelation
• Circuit motif: Excitatory and inhibitory populations occupy largely non-overlapping representational subspaces
• Combined effect: Expands representational dimensionality beyond what either cell class achieves alone

Crystalline Code Properties

• Population vectors at nearby spatial locations are highly similar (low-distance diagonal)
• Distant locations sharply distinct (high-distance off-diagonal blocks)
• Strict correspondence between neural geometry and physical layout (Mantel test, p<0.001)
• High geometric fidelity and temporal coherence across sessions

Methodology

Species Comparison

• Black-capped chickadees: Cache and retrieve thousands of spatial locations
• Zebra finches: No caching behavior, no comparable spatial memory demands
• Both species possess hippocampal neurons with spatial tuning

Computational Modeling

• 10,000 network configurations tested
• Topological rigidity identified as mathematical prerequisite for scale
• Valiant's Stable Memory Allocator model as baseline comparison

Key Metrics

• Shesha: Geometric stability measure of neural manifold
• Split-half allocation reliability: Tests discrete vs continuous organization
• Mantel test: Correspondence between neural geometry and physical space

Implications

For Neuroscience

• Evolution achieves extreme memory capacity by engineering geometry of the neural code, not proliferating neurons
• Geometric stability is a candidate organizing principle of biological memory
• May generalize beyond avian system to hippocampal memory across species

For AI / Machine Learning

• Novel objective: engineer crystalline neural manifolds for continual learning without catastrophic forgetting
• Geometric tax concept: redundancy-efficiency tradeoff in memory systems
• Excitatory-inhibitory subspace decomposition as architectural principle

Activation Keywords

• hippocampal geometric phase transition
• crystalline neural code
• geometric tax memory
• food-caching birds spatial memory
• topological rigidity neural manifold
• geometric stability Shesha
• mist code vs crystalline code

References

• Raju, P.C. (2026). Geometric Phase Transition Enables Extreme Hippocampal Memory Capacity. arXiv:2605.17199
• Valiant (2005). Memorization and association on a realistic neural model
• Benna & Fusi (2021). Place cells may simply be memory cells
• Payne, Lynch & Aronov (2021). Neural representations of space in the hippocampus of food-caching birds