FurkanNar/Spatial_Context_Networks

Spatial Context Networks (SCN)

Geometric Semantic Routing in Neural Architectures
Furkan Nar — Independent Researcher
February 2026

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Overview

Spatial Context Networks (SCN) is a novel neural architecture that treats neurons as geometric entities in a learned semantic space. Rather than relying on weighted linear combinations, each neuron operates as a point-mass with a learnable centroid — activating based on its distance to the input in that space.

This repository contains the reference PyTorch implementation accompanying the paper.

📄 Paper: https://doi.org/10.5281/zenodo.18599303

Key Ideas

• Geometric Activation — activation inversely proportional to normalized Euclidean distance from a learnable centroid
• Semantic Routing — binary hard-routing that only activates neurons geometrically close to the input
• Connection Density Weighting — adaptive normalization that stabilizes signal magnitude across sparsity regimes
• Pattern Distribution — a Bayesian prior over output patterns via learnable softmax weights

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Architecture

Input x ∈ ℝ^d
     │
     ▼
┌─────────────────────────┐
│  Semantic Routing Layer  │  ← Geometric activations + binary mask
│  f(v) = 1 / (‖v−μ‖/√d + ε)│
└─────────────────────────┘
     │ activations, mask
     ▼
┌─────────────────────────┐
│ Connection Density Layer │  ← Adaptive normalization + explosion control
│  C = Σ w_i / (α/z)      │
└─────────────────────────┘
     │ context score
     ▼
┌─────────────────────────┐
│   Linear Projection      │
└─────────────────────────┘
     │
     ▼
┌─────────────────────────┐
│  Pattern Distribution    │  ← h ⊙ softmax(w_p)
└─────────────────────────┘
     │
     ▼
Output o ∈ ℝ^dout

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Installation

git clone https://github.com/TheOfficialFurkanNar/spatial-context-networks.git
cd spatial-context-networks
pip install -e .

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Quick Start

import torch
from model.py import SpatialContextNetwork

# Instantiate the model
model = SpatialContextNetwork(
    input_dim=10,
    n_neurons=32,
    output_dim=4,
    routing_threshold=0.5,
    stability_factor=10.0,
    explosion_threshold=2.0,
)

# Forward pass
x = torch.randn(8, 10)
output = model(x)          # shape: (8, 4)

# Diagnostic stats
stats = model.get_network_stats(x)
print(f"Network efficiency: {stats['network_efficiency']:.1%}")
print(f"Mean active neurons: {stats['mean_active_neurons']:.1f} / 32")

---

Training

python train.py \
    --input_dim 10 \
    --n_neurons 32 \
    --output_dim 4 \
    --epochs 50 \
    --batch_size 8 \
    --lr 1e-3 \
    --save_path scn_model.pt

---

Inference

python inference.py --checkpoint scn_model.pt --batch_size 8

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Hyperparameters

Parameter	Default	Description
input_dim	10	Input feature dimensionality
n_neurons	32	Number of geometric hidden neurons
output_dim	4	Output dimensionality
routing_threshold τ	0.5	Minimum activation to route through a neuron
stability_factor SF	10.0	ε = 1/SF; prevents division by zero at centroid
explosion_threshold τ_exp	2.0	Context scores above this get √ damped

---

Results (Proof-of-Concept)

Metric	Value
Mean active neurons	29.1 / 32
Network efficiency	91%
Mean context score	0.444
Total parameters	~500
Hardware	Consumer gaming laptop (RTX)

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Citation

If you use this work, please cite:

@article{nar2026scn,
  title   = {Spatial Context Networks: Geometric Semantic Routing in Neural Architectures},
  author  = {Nar, Furkan},
  year    = {2026},
  month   = {February},
  doi     = {10.5281/zenodo.18599303},
  url     = {https://doi.org/10.5281/zenodo.18599303},
  note    = {Independent research. Published on Zenodo and Academia.edu}
}

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License

MIT © 2026 Furkan Nar