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Spatial Context Networks (SCN)
Geometric Semantic Routing in Neural Architectures
Author: Furkan Nar
"""
import torch
import torch.nn as nn
import torch.nn.functional as F
import math
class GeometricActivation(nn.Module):
"""
Geometric activation function based on normalized Euclidean distance.
Each neuron acts as a point-mass with a learnable centroid in d-dimensional space.
Activation is inversely proportional to the normalized distance from the centroid:
f(v) = 1 / (||v - mu||_2 / sqrt(d) + epsilon)
Args:
n_neurons (int): Number of neurons (centroids) in this layer.
dim (int): Dimensionality of the input semantic space.
stability_factor (float): SF in the paper; epsilon = 1/SF. Default: 10.0
"""
def __init__(self, n_neurons: int, dim: int, stability_factor: float = 10.0):
super().__init__()
self.n_neurons = n_neurons
self.dim = dim
self.epsilon = 1.0 / stability_factor
# Learnable centroids: shape (n_neurons, dim)
self.centroids = nn.Parameter(torch.randn(n_neurons, dim))
def forward(self, x: torch.Tensor) -> torch.Tensor:
"""
Args:
x: Input tensor of shape (batch_size, dim)
Returns:
activations: Tensor of shape (batch_size, n_neurons)
"""
# x: (B, dim) -> (B, 1, dim)
# centroids: (n_neurons, dim) -> (1, n_neurons, dim)
diff = x.unsqueeze(1) - self.centroids.unsqueeze(0) # (B, n_neurons, dim)
dist = torch.norm(diff, dim=-1) # (B, n_neurons)
normalized_dist = dist / math.sqrt(self.dim)
activations = 1.0 / (normalized_dist + self.epsilon)
return activations
class SemanticRoutingLayer(nn.Module):
"""
Semantic routing layer that selectively activates neurons based on
geometric affinity to the input.
Active set: S = { n_i | f_i(q) > tau }
Binary mask: M_ij = I[ f_j(v_i) > tau ]
Args:
n_neurons (int): Number of neurons.
dim (int): Input dimensionality.
routing_threshold (float): Activation threshold tau. Default: 0.5
stability_factor (float): Passed to GeometricActivation. Default: 10.0
"""
def __init__(
self,
n_neurons: int,
dim: int,
routing_threshold: float = 0.5,
stability_factor: float = 10.0,
):
super().__init__()
self.routing_threshold = routing_threshold
self.geo_activation = GeometricActivation(n_neurons, dim, stability_factor)
def forward(self, x: torch.Tensor):
"""
Args:
x: Input tensor of shape (batch_size, dim)
Returns:
activations: Raw activations, shape (batch_size, n_neurons)
mask: Binary routing mask, shape (batch_size, n_neurons)
"""
activations = self.geo_activation(x)
mask = (activations > self.routing_threshold).float()
return activations, mask
class ConnectionDensityLayer(nn.Module):
"""
Connection density weighting with adaptive scaling and explosion control.
C = sum_{i in S} w_i / (alpha / z)
where alpha = total neurons, z = |S| (active neurons).
When C > tau_exp, square-root damping is applied: C_stable = sqrt(C).
Args:
n_neurons (int): Total number of neurons (alpha).
explosion_threshold (float): tau_exp. Default: 2.0
"""
def __init__(self, n_neurons: int, explosion_threshold: float = 2.0):
super().__init__()
self.n_neurons = n_neurons
self.explosion_threshold = explosion_threshold
# Learnable per-neuron connection weights
self.connection_weights = nn.Parameter(torch.randn(n_neurons))
def forward(self, activations: torch.Tensor, mask: torch.Tensor) -> torch.Tensor:
"""
Args:
activations: Shape (batch_size, n_neurons)
mask: Binary mask, shape (batch_size, n_neurons)
Returns:
context: Scalar context score per sample, shape (batch_size, 1)
"""
z = mask.sum(dim=-1, keepdim=True).clamp(min=1.0) # (B, 1)
alpha = float(self.n_neurons)
# Weighted masked activations
weighted = activations * mask * self.connection_weights.unsqueeze(0) # (B, n)
context = weighted.sum(dim=-1, keepdim=True) / (alpha / z) # (B, 1)
# Explosion control: sqrt damping
context = torch.where(
context > self.explosion_threshold,
torch.sqrt(context.abs() + 1e-8) * context.sign(),
context,
)
return context
class SpatialContextNetwork(nn.Module):
"""
Spatial Context Network (SCN).
Full architecture:
1. SemanticRoutingLayer — geometric activation + binary routing mask
2. ConnectionDensityLayer — adaptive normalization + explosion control
3. Linear projection — map context score to output space
4. Pattern distribution — element-wise multiply by softmax(pattern_weights)
Args:
input_dim (int): Dimensionality of input features.
n_neurons (int): Number of hidden geometric neurons. Default: 32
output_dim (int): Number of output classes/dimensions. Default: 4
routing_threshold (float): Routing threshold tau. Default: 0.5
stability_factor (float): Controls epsilon = 1/SF. Default: 10.0
explosion_threshold (float): Threshold for sqrt damping. Default: 2.0
Example::
model = SpatialContextNetwork(input_dim=10, n_neurons=32, output_dim=4)
x = torch.randn(8, 10)
output = model(x) # (8, 4)
"""
def __init__(
self,
input_dim: int = 10,
n_neurons: int = 32,
output_dim: int = 4,
routing_threshold: float = 0.5,
stability_factor: float = 10.0,
explosion_threshold: float = 2.0,
):
super().__init__()
self.input_dim = input_dim
self.n_neurons = n_neurons
self.output_dim = output_dim
self.routing = SemanticRoutingLayer(
n_neurons, input_dim, routing_threshold, stability_factor
)
self.density = ConnectionDensityLayer(n_neurons, explosion_threshold)
self.projection = nn.Linear(1, output_dim)
# Pattern prior weights (learnable)
self.pattern_weights = nn.Parameter(torch.zeros(output_dim))
# Initialise pattern weights to approximate the priors from the paper
# [Mathematics=0.38, Language=0.25, Vision=0.22, Reasoning=0.15]
with torch.no_grad():
prior = torch.tensor([0.38, 0.25, 0.22, 0.15])
if output_dim == 4:
self.pattern_weights.copy_(torch.log(prior + 1e-8))
def forward(self, x: torch.Tensor) -> torch.Tensor:
"""
Args:
x: Input tensor of shape (batch_size, input_dim)
Returns:
output: Tensor of shape (batch_size, output_dim)
"""
activations, mask = self.routing(x)
context = self.density(activations, mask)
hidden = self.projection(context) # (B, output_dim)
output = hidden * F.softmax(self.pattern_weights, dim=-1)
return output
def get_network_stats(self, x: torch.Tensor) -> dict:
"""
Returns diagnostic statistics for a batch of inputs.
Returns:
dict with keys: mean_active_neurons, network_efficiency,
mean_context_score, activations, mask
"""
with torch.no_grad():
activations, mask = self.routing(x)
context = self.density(activations, mask)
active = mask.sum(dim=-1)
return {
"mean_active_neurons": active.mean().item(),
"network_efficiency": (active / self.n_neurons).mean().item(),
"mean_context_score": context.mean().item(),
"activations": activations,
"mask": mask,
} |