EfficientRemapping/src/WyssTemporalStabilityLoss.py at main · KietzmannLab/EfficientRemapping · GitHub

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"""

Temporal Stability Loss Implementation based on Wyss, König, Verschure (2006).

Three-term objective function for hierarchical visual processing networks.

Mathematical formulation:

ω_l = -∑_i ⟨(A_l^i(t) - A_l^i(t - s_l'))²⟩_t / var_t(A_l^i)

- β ∑_{i≠j} (ρ_{ij}^t)²

- C ∑_i ⟨A_l^i⟩_t

Where:

- A_l^i(t): Activity of unit i at level l, time t

- s_l' = 2^(l-1): Time delay (increases with hierarchy level)

- ρ_{ij}^t: Temporal correlation between units i,j

- β = 5/N_l, C = 20/N_l: Level-specific weights

"""

import torch

import torch.nn as nn

import torch.nn.functional as F

from collections import deque

import numpy as np

class RunningStats:

"""

Running statistics tracker for temporal correlations, means, and variances.

Uses exponential decay with τ = 1000 time steps as in the paper.

"""

def __init__(self, num_units, device='cpu', decay_rate=0.001):

"""

Args:

num_units: Number of units in the layer

device: PyTorch device

decay_rate: 1/τ where τ = 1000 time steps

"""

self.num_units = num_units

self.device = device

self.decay_rate = decay_rate

self.alpha = 1 - decay_rate # Exponential decay factor

# Running statistics

self.mean = torch.zeros(num_units, device=device)

self.var = torch.ones(num_units, device=device) # Initialize to 1 to avoid division by zero

# Correlation matrix for all unit pairs

self.correlation_matrix = torch.zeros(num_units, num_units, device=device)

self.covariance_matrix = torch.zeros(num_units, num_units, device=device)

# Keep track of updates

self.num_updates = 0

def update(self, activity):

"""

Update running statistics with new activity vector.

Args:

activity: [batch_size, num_units] or [num_units]

"""

if len(activity.shape) == 2:

# Average over batch dimension

activity = activity.mean(dim=0)

# Update count

self.num_updates += 1

# Update running mean

self.mean = self.alpha * self.mean + self.decay_rate * activity

# Update running variance

centered_activity = activity - self.mean

self.var = self.alpha * self.var + self.decay_rate * (centered_activity ** 2)

# Update covariance matrix for correlations

# Cov(i,j) = E[(X_i - μ_i)(X_j - μ_j)]

outer_product = torch.outer(centered_activity, centered_activity)

self.covariance_matrix = self.alpha * self.covariance_matrix + self.decay_rate * outer_product

# Update correlation matrix: ρ_ij = Cov(i,j) / (σ_i * σ_j)

std_outer = torch.outer(torch.sqrt(self.var + 1e-8), torch.sqrt(self.var + 1e-8))

self.correlation_matrix = self.covariance_matrix / (std_outer + 1e-8)

def get_correlations_squared(self, exclude_diagonal=True):

"""

Get sum of squared correlations for decorrelation term.

Args:

exclude_diagonal: Whether to exclude self-correlations (always 1.0)

Returns:

Sum of squared correlations

"""

if exclude_diagonal:

# Create mask to exclude diagonal

mask = ~torch.eye(self.num_units, device=self.device).bool()

return (self.correlation_matrix[mask] ** 2).sum()

else:

return (self.correlation_matrix ** 2).sum()

class WyssTemporalStabilityLoss(nn.Module):

"""

Wyss et al. (2006) temporal stability loss with three terms:

1. Temporal stability: minimize activity differences over time

2. Decorrelation: minimize correlations between units

3. Sparsity: minimize average activity

"""

def __init__(self, level_idx=0, num_units=512, device='cpu',

statistics_decay=0.001, history_length=None):

"""

Args:

level_idx: Hierarchy level (0-based), affects time constants

num_units: Number of units in the layer

device: PyTorch device

statistics_decay: Decay rate for running statistics (1/τ)

history_length: Length of activity history buffer (default: 2^level_idx)

"""

super(WyssTemporalStabilityLoss, self).__init__()

self.level_idx = level_idx

self.num_units = num_units

self.device = device

# Time constants from paper

self.time_delay = max(1, 2 ** (level_idx - 1)) # s_l' = 2^(l-1), min 1

self.time_constant = 2 ** level_idx # s_l = 2^l

# Coefficients from paper

self.beta = 5.0 / num_units # β = 5/N_l

self.c = 20.0 / num_units # C = 20/N_l

# Activity history buffer

if history_length is None:

history_length = max(10, self.time_delay + 5) # Buffer extra for safety

self.activity_history = deque(maxlen=history_length)

# Running statistics tracker

self.running_stats = RunningStats(num_units, device, statistics_decay)

# Previous output for leaky integration

self.prev_output = torch.zeros(num_units, device=device)

print(f"WyssTemporalStabilityLoss Level {level_idx}:")

print(f" Time delay: {self.time_delay}")

print(f" Beta (decorrelation): {self.beta:.6f}")

print(f" C (sparsity): {self.c:.6f}")

print(f" History length: {history_length}")

def reset_sequence(self):

"""Reset for new sequence (clear history)"""

self.activity_history.clear()

self.prev_output.zero_()

def compute_unit_activity(self, hidden_states):

"""

Compute unit activity with saturating activation f(x) = 1 - e^(-x²)

Args:

hidden_states: [batch_size, hidden_dim] raw neural activations

Returns:

activity: [batch_size, num_units] unit activities

"""

# Apply saturating nonlinearity from paper

energy_squared = hidden_states ** 2

activity = 1.0 - torch.exp(-energy_squared)

return activity

def compute_level_output(self, activity):

"""

Leaky integration with mean-correction and normalization.

Args:

activity: [batch_size, num_units] current activity

Returns:

output: [batch_size, num_units] integrated output

"""

# Average over batch for single output

if len(activity.shape) == 2:

activity_mean = activity.mean(dim=0)

else:

activity_mean = activity

# Normalize activity: A'(t) = (A(t) - ⟨A⟩_t) / √var_t(A)

activity_centered = activity_mean - self.running_stats.mean

activity_normalized = activity_centered / (torch.sqrt(self.running_stats.var) + 1e-8)

# Leaky integration: τ = 1/s_l

tau = 1.0 / self.time_constant

output = tau * activity_normalized + (1 - tau) * self.prev_output

# Update previous output

self.prev_output = output.detach()

return output.unsqueeze(0) if len(activity.shape) == 2 else output

def temporal_stability_term(self, current_activity, past_activity):

"""

Term 1: Temporal stability

Minimize ∑_i ⟨(A_l^i(t) - A_l^i(t - s_l'))²⟩_t / var_t(A_l^i)

Args:

current_activity: [batch_size, num_units] current activity

past_activity: [batch_size, num_units] past activity

Returns:

stability_loss: scalar tensor

"""

# Compute squared differences

diff_squared = (current_activity - past_activity) ** 2

# Average over batch and units

diff_mean = diff_squared.mean(dim=0) # [num_units]

# Normalize by variance to account for different unit scales

normalized_diff = diff_mean / (self.running_stats.var + 1e-8)

# Sum over units

stability_loss = normalized_diff.sum()

return stability_loss

def decorrelation_term(self):

"""

Term 2: Decorrelation

Minimize β ∑_{i≠j} (ρ_{ij}^t)²

Returns:

decorrelation_loss: scalar tensor

"""

correlations_squared_sum = self.running_stats.get_correlations_squared(exclude_diagonal=True)

return self.beta * correlations_squared_sum

def sparsity_term(self):

"""

Term 3: Sparsity regularization

Minimize C ∑_i ⟨A_l^i⟩_t

Returns:

sparsity_loss: scalar tensor

"""

mean_activity_sum = self.running_stats.mean.sum()

return self.c * mean_activity_sum

def forward(self, hidden_states):

"""

Compute complete three-term temporal stability loss.

Args:

hidden_states: [batch_size, hidden_dim] raw neural states

Returns:

total_loss: scalar tensor (note: we minimize -ω_l to maximize ω_l)

"""

# Convert hidden states to unit activities

activity = self.compute_unit_activity(hidden_states)

# Apply leaky integration

integrated_output = self.compute_level_output(activity)

# Update running statistics (detach to prevent accumulating gradients)

self.running_stats.update(integrated_output.detach())

# Store in history (keep gradients for temporal comparison)

self.activity_history.append(integrated_output)

# Check if we have enough history for temporal comparison

if len(self.activity_history) < self.time_delay + 1:

# Return small loss to avoid affecting early training

return torch.tensor(0.0, device=self.device, requires_grad=True)

# Get past activity at appropriate time delay

past_activity = self.activity_history[-(self.time_delay + 1)]

current_activity = integrated_output

# Compute three loss terms

stability_loss = self.temporal_stability_term(current_activity, past_activity)

decorrelation_loss = self.decorrelation_term()

sparsity_loss = self.sparsity_term()

# Total loss (we minimize -ω_l to maximize ω_l from the paper)

total_loss = -stability_loss + decorrelation_loss + sparsity_loss

return total_loss

def get_loss_components(self, hidden_states):

"""

Get individual loss components for debugging/monitoring.

Args:

hidden_states: [batch_size, hidden_dim] raw neural states

Returns:

dict with individual loss components

"""

if len(self.activity_history) < self.time_delay + 1:

return {

'total_loss': 0.0,

'stability': 0.0,

'decorrelation': 0.0,

'sparsity': 0.0

}

# Get current and past activities

activity = self.compute_unit_activity(hidden_states)

integrated_output = self.compute_level_output(activity)

past_activity = self.activity_history[-(self.time_delay + 1)]

# Compute individual terms

stability = self.temporal_stability_term(integrated_output, past_activity)

decorrelation = self.decorrelation_term()

sparsity = self.sparsity_term()

total = stability + decorrelation + sparsity

return {

'total_loss': total.item(),

'stability': stability.item(),

'decorrelation': decorrelation.item(),

'sparsity': sparsity.item(),

'beta': self.beta,

'c': self.c,

'mean_activity': self.running_stats.mean.mean().item(),

'mean_variance': self.running_stats.var.mean().item()

}

def create_hierarchical_losses(hidden_sizes, device='cpu'):

"""

Create hierarchical temporal stability losses for multi-level network.

Args:

hidden_sizes: List of hidden sizes for each level

device: PyTorch device

Returns:

List of WyssTemporalStabilityLoss instances

"""

losses = []

for level_idx, hidden_size in enumerate(hidden_sizes):

loss_fn = WyssTemporalStabilityLoss(

level_idx=level_idx,

num_units=hidden_size,

device=device

)

losses.append(loss_fn)

return losses

EfficientRemapping/src/WyssTemporalStabilityLoss.py at main · KietzmannLab/EfficientRemapping · GitHub

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