neural-receptive-fields-hyperbolic-geometry

name	neural-receptive-fields-hyperbolic-geometry
description	Neural Receptive Fields via Hyperbolic Geometry

Neural Receptive Fields via Hyperbolic Geometry

Source: arXiv:2509.25453v2 (January 2026) Utility: 0.90 Authors: Yuri A. Dabaghian

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Description

This skill implements a physiologically grounded framework where neural receptive fields arise naturally from the effective hyperbolic geometry of scale-free networks - without synaptic fine-tuning. By embedding stimulus space at the boundary of hyperbolic geometry, localized activity patterns reflect stimulus structure.

Core Insight: Receptive field size depends on neuron's connectivity degree, following experimentally observed statistics. Generalizes across modalities (orientation, place selectivity).

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Tools Used

• scale_free_network - Network structure modeling
• hyperbolic_embedding - Geometric representation
• rate_based_model - Neural dynamics simulation
• spiking_model - Spiking neuron dynamics
• stimulus_space - Boundary embedding
• place_field_data - Hippocampal recordings

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Instructions for Agents

1. Construct scale-free network - Connectivity structure
2. Hyperbolic embedding - Embed network in hyperbolic space
3. Associate stimulus space - Map to hyperbolic boundary
4. Simulate neural dynamics - Rate-based or spiking models
5. Observe receptive fields - Localized activity patterns
6. Validate statistics - Compare with experimental data
7. Analyze degree-dependence - RF size vs connectivity degree

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Examples

Example 1: Orientation Selectivity

User: 如何理解方向选择性感受野的形成？

Agent: 双曲几何框架：

1. 网络结构 - 无标度网络
2. 双曲嵌入 - 有效几何表示
3. 刺激空间 - 方向空间映射到边界
4. 神经动力学 - 模拟产生局部活动
5. 感受野 - 自然形成方向选择性

优势： 无需精细调整突触连接！

Example 2: Place Fields (Hippocampus)

User: 海马位置场如何从网络几何产生？

Agent: 实验验证支持：

发现	描述
感受野大小	依赖神经元连接度
统计特性	符合实验观察
线性轨道	海马位置场验证
模态推广	方向 + 位置选择性

核心原理： 刺激空间边界 → 局部活动模式 → 感受野形成

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Activation Keywords

• 感受野、receptive field
• 双曲几何、hyperbolic geometry
• 无标度网络、scale-free network
• 刺激空间嵌入、stimulus space embedding
• 方向选择性、orientation selectivity
• 位置场、place field、hippocampal

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Key Concepts

1. Scale-Free Network Geometry

Structure: Power-law degree distribution

Effective geometry: Hyperbolic space naturally represents scale-free networks

Key property: High-degree neurons → smaller receptive fields

2. Hyperbolic Embedding

Purpose: Map network to hyperbolic space

Stimulus space: Associated with hyperbolic boundary

Result: Localized activity patterns reflect stimulus structure

3. Receptive Field Statistics

Property	Observation
Size vs degree	Degree-dependent (high degree = small RF)
Statistics	Match experimental data
Modality	Orientation, place selectivity
Fine-tuning	Not required

4. Organizing Principle

Scale-Free Network → Hyperbolic Geometry
    ↓
Stimulus Space Boundary → Neural Dynamics
    ↓
Localized Activity → Receptive Fields

Novel insight: Network structure → Stimulus encoding → Neural dynamics linkage without fine-tuning

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Architecture

Scale-Free Network → Hyperbolic Embedding
    ↓
Stimulus Space (Boundary)
    ↓
Neural Dynamics (Rate/Spiking) → Receptive Fields
    ↓
Experimental Validation (Place Fields)

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Results (Paper)

Metric	Result
RF formation	Natural emergence ✅
Synaptic fine-tuning	Not required ✅
RF statistics	Match experiments ✅
Degree-dependence	Validated ✅
Modality generalization	Orientation + Place ✅
Hippocampal validation	Linear track place fields ✅

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When to Use

1. Receptive field modeling - RF formation without fine-tuning
2. Network-encoding coupling - Structure-function relationship
3. Hippocampal place fields - Spatial navigation research
4. Orientation selectivity - Visual cortex modeling
5. Scale-free network analysis - Brain network geometry

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Advantages over Fine-Tuning Approach

Fine-Tuning	This Framework
Synaptic adjustment required	✅ No fine-tuning
Limited biological plausibility	✅ Physiologically grounded
RF statistics artificial	✅ Match experiments
Single modality	✅ Generalizes across modalities

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Biological Plausibility

Why no fine-tuning needed?

1. Effective geometry - Hyperbolic structure inherent in scale-free networks
2. Stimulus boundary - Natural encoding at hyperbolic boundary
3. Degree-dependence - Connectivity determines RF properties
4. Population attractors - Dynamics arise from geometry

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Limitations

1. Assumes scale-free network structure
2. Hyperbolic embedding computational complexity
3. Validation limited to hippocampal place fields
4. Extension to other brain areas needs testing

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Related Skills

• brain-network-joint-embedding - Network embedding methods
• hyperbolic-brain-network-neurodegeneration - Hyperbolic brain networks
• mesoscale-brain-organization - Brain organization principles
• neutral-theory-neural-dynamics - Neural dynamics theory