Bayesian Speech Snn

---
name: bayesian-speech-snn
description: "Bayesian inference methodology for Spiking Neural Networks in speech processing. Uses IVON (Improved Variational Online Newton) to smooth the angular predictive landscape caused by threshold-based spike generation. Demonstrates improved NLL and Brier scores on Heidelberg Digits and Speech Commands datasets. Activation: bayesian SNN, speech SNN, surrogate gradient, IVON, loss landscape smoothing, uncertainty quantification, variational inference."
---

# Bayesian Inference for Speech Spiking Neural Networks

Methodology for applying Bayesian learning to Spiking Neural Networks (SNNs) to address the irregular predictive landscape caused by threshold-based spike generation, specifically for speech processing tasks.

## Problem Statement

SNNs are naturally suited for speech processing due to their temporal dynamics, but their threshold-based spike generation creates an **angular, irregular predictive landscape** that hampers optimization and generalization.

### Core Challenge
- Deterministic SNN training produces jagged loss landscapes
- Sharp thresholds create non-smooth gradients
- Poor uncertainty quantification in predictions

## Methodology: Bayesian SNN with IVON

### IVON (Improved Variational Online Newton)
Efficient variational Bayesian approach that:
1. **Smooths the predictive landscape** via weight posterior distributions
2. **Provides uncertainty quantification** through predictive variance
3. **Maintains computational efficiency** via online updates

### Key Insight
Bayesian weight distributions average over multiple smooth approximations of the threshold function, producing a globally smoother predictive landscape than deterministic point estimates.

## Implementation

### Step 1: Define Bayesian SNN Architecture

```python
import torch
import torch.nn as nn
from torch.distributions import Normal

class BayesianSNN(nn.Module):
    """Bayesian Spiking Neural Network for speech processing."""
    
    def __init__(self, input_dim, hidden_dim, output_dim, num_steps):
        super().__init__()
        self.num_steps = num_steps
        
        # Bayesian weights (mean + log-variance)
        self.w_mean = nn.Parameter(torch.randn(hidden_dim, input_dim) * 0.1)
        self.w_logvar = nn.Parameter(torch.zeros(hidden_dim, input_dim))
        self.b_mean = nn.Parameter(torch.zeros(hidden_dim))
        self.b_logvar = nn.Parameter(torch.zeros(hidden_dim))
        
        self.w_out_mean = nn.Parameter(torch.randn(output_dim, hidden_dim) * 0.1)
        self.w_out_logvar = nn.Parameter(torch.zeros(output_dim, hidden_dim))
        
        # Surrogate gradient function
        self.surrogate = torch.nn.Sigmoid()
        self.spike_threshold = 1.0
        self.membrane_decay = 0.9
        
    def reparameterize(self, mean, logvar):
        """Reparameterization trick for Bayesian sampling."""
        std = torch.exp(0.5 * logvar)
        eps = torch.randn_like(std)
        return mean + eps * std
    
    def forward(self, x, training=True):
        """Forward pass with spiking dynamics."""
        batch_size = x.size(0)
        hidden = torch.zeros(batch_size, self.hidden_dim)
        membrane = torch.zeros(batch_size, self.hidden_dim)
        
        all_spikes = []
        
        for t in range(self.num_steps):
            # Sample Bayesian weights during training
            if training:
                w = self.reparameterize(self.w_mean, self.w_logvar)
                b = self.reparameterize(self.b_mean, self.b_logvar)
            else:
                w = self.w_mean
                b = self.b_mean
            
            # Update membrane potential
            input_current = torch.matmul(hidden, w.t()) + b
            membrane = self.membrane_decay * membrane + input_current
            
            # Generate spikes with surrogate gradient
            spike_prob = self.surrogate(membrane - self.spike_threshold)
            spikes = (membrane > self.spike_threshold).float()
            membrane = membrane * (1 - spikes)  # Reset after spike
            
            all_spikes.append(spikes)
        
        # Output layer
        spike_sum = sum(all_spikes)
        if training:
            w_out = self.reparameterize(self.w_out_mean, self.w_out_logvar)
        else:
            w_out = self.w_out_mean
            
        output = torch.matmul(spike_sum, w_out.t())
        return output
```

### Step 2: IVON Training Loop

```python
def train_bayesian_snn(model, dataloader, optimizer, num_epochs, alpha=0.1):
    """Train Bayesian SNN with IVON."""
    
    for epoch in range(num_epochs):
        model.train()
        total_loss = 0
        
        for batch_x, batch_y in dataloader:
            # Forward pass with Bayesian sampling
            output = model(batch_x, training=True)
            
            # Negative log-likelihood loss
            nll_loss = F.cross_entropy(output, batch_y)
            
            # KL divergence for Bayesian regularization
            kl_loss = compute_kl_divergence(model)
            
            # Combined loss
            loss = nll_loss + alpha * kl_loss
            
            optimizer.zero_grad()
            loss.backward()
            optimizer.step()
            
            total_loss += loss.item()
        
        print(f"Epoch {epoch}: NLL Loss = {nll_loss:.4f}, KL Loss = {kl_loss:.4f}")

def compute_kl_divergence(model):
    """Compute KL divergence between posterior and prior."""
    kl = 0
    for param_name, param in model.named_parameters():
        if 'logvar' in param_name:
            mean_param = param_name.replace('logvar', 'mean')
            mean = getattr(model, mean_param)
            logvar = param
            kl += 0.5 * torch.sum(torch.exp(logvar) + mean**2 - 1 - logvar)
    return kl
```

### Step 3: Evaluation with Uncertainty

```python
def evaluate_with_uncertainty(model, dataloader):
    """Evaluate with Bayesian uncertainty quantification."""
    model.eval()
    correct = 0
    total = 0
    brier_scores = []
    
    with torch.no_grad():
        for batch_x, batch_y in dataloader:
            # Multiple forward passes for uncertainty
            outputs = []
            for _ in range(10):  # Monte Carlo samples
                outputs.append(model(batch_x, training=False))
            
            # Average prediction
            avg_output = torch.stack(outputs).mean(dim=0)
            pred = avg_output.argmax(dim=1)
            
            correct += (pred == batch_y).sum().item()
            total += batch_y.size(0)
            
            # Brier score for probabilistic predictions
            probs = F.softmax(avg_output, dim=1)
            one_hot = F.one_hot(batch_y, num_classes=avg_output.size(1)).float()
            brier = ((probs - one_hot) ** 2).mean().item()
            brier_scores.append(brier)
    
    accuracy = correct / total
    avg_brier = sum(brier_scores) / len(brier_scores)
    
    return accuracy, avg_brier
```

## Key Results

| Metric | Deterministic SNN | Bayesian SNN (IVON) |
|--------|-------------------|---------------------|
| NLL (Heidelberg Digits) | Higher | **Lower** |
| Brier Score | Higher | **Lower** |
| Loss Landscape | Angular, irregular | **Smooth, regular** |

## Activation Keywords

- bayesian SNN
- speech SNN
- surrogate gradient
- IVON
- loss landscape smoothing
- uncertainty quantification
- variational inference
- Heidelberg Digits
- Speech Commands
- predictive landscape

## Related Papers

- **arXiv:2604.08624**: "Practical Bayesian Inference for Speech SNNs: Uncertainty and Loss-Landscape Smoothing" by Yesmine Abdennadher, Philip N. Garner

## Pitfalls

1. **Computational overhead**: Bayesian sampling increases training time - use MC dropout as approximation
2. **Prior sensitivity**: Choice of prior significantly affects results - use empirical Bayes for hyperparameter tuning
3. **Surrogate gradient compatibility**: Ensure surrogate function is differentiable and smooth

## Tools Used

- `execute_code`: For running SNN training and evaluation experiments
- `write_file`: For saving trained models and results
- `read_file`: For loading speech datasets and configurations