Memristor Preprocessing Reservoir

---
name: memristor-preprocessing-reservoir
description: "Memristor-based preprocessing for reservoir computing in image classification. Uses memristor crossbar arrays as reconfigurable nonlinear preprocessing layers to improve accuracy while reducing readout complexity. Keywords: reservoir computing, memristor preprocessing, image classification, crossbar array, nonlinear preprocessing."
---

# Memristor Preprocessing for Reservoir Computing

Research methodology from arXiv:2604.21602v1 investigating the impact of memristor-based preprocessing layers on reservoir computing performance for image classification.

## Overview

This skill implements **memristor-based preprocessing for reservoir computing**, where memristor crossbar arrays serve as **reconfigurable nonlinear preprocessing layers** that significantly improve classification accuracy while reducing readout layer complexity.

## Core Innovation

> Memristor crossbar arrays as **reconfigurable nonlinear preprocessing layers** transform input data to enhance reservoir computing performance.

## System Architecture

### Overall Structure

```
Input Image → Memristor Preprocessing → Reservoir → Readout → Classification
     ↓              ↓                      ↓          ↓
   28×28        100 features        500 nodes   Softmax
   pixels      (nonlinear proj)     (dynamics)   (10 classes)
```

### Memristor Preprocessing Layer

```python
import numpy as np

class MemristorCrossbar:
    """
    Memristor crossbar array for nonlinear preprocessing.
    
    Implements: y = f(W @ x + b) where f is memristor-specific nonlinearity
    """
    
    def __init__(self, input_dim, output_dim, device_params=None):
        self.input_dim = input_dim
        self.output_dim = output_dim
        self.device_params = device_params or {
            'RON': 1e3,      # On-state resistance (Ω)
            'ROFF': 1e6,     # Off-state resistance (Ω)
            'Vthreshold': 0.1,  # Switching threshold (V)
            'alpha': 2.0,    # Nonlinearity parameter
            'noise_std': 0.01  # Read noise
        }
        
        # Initialize conductance matrix (W = 1/R)
        self.G = np.random.uniform(
            1/self.device_params['ROFF'],
            1/self.device_params['RON'],
            (output_dim, input_dim)
        )
        
    def memristor_response(self, V):
        """
        Memristor current-voltage response with nonlinearity.
        
        I = G(V) * V where G(V) is voltage-dependent conductance
        
        Args:
            V: Input voltage (normalized to device range)
        
        Returns:
            I: Output current
        """
        # Simplified memristor model
        V_th = self.device_params['Vthreshold']
        alpha = self.device_params['alpha']
        
        # Nonlinear response: I = G * V * (1 + tanh(alpha * (V - Vth)))
        nonlinearity = 1 + np.tanh(alpha * (V - V_th))
        I = self.G @ V * nonlinearity
        
        # Add device noise
        noise = np.random.normal(0, self.device_params['noise_std'], I.shape)
        I += noise
        
        return I
    
    def forward(self, x):
        """
        Apply memristor preprocessing transformation.
        
        Args:
            x: Input vector (input_dim,)
        
        Returns:
            y: Preprocessed features (output_dim,)
        """
        # Normalize input to voltage range
        x_normalized = x / np.max(np.abs(x)) * 0.5  # 0.5V max
        
        # Apply memristor crossbar
        y = self.memristor_response(x_normalized)
        
        # Apply activation (current-to-feature mapping)
        y = np.tanh(y / np.max(np.abs(y) + 1e-8))
        
        return y
    
    def program_conductance(self, target_G, method='voltage_pulse'):
        """
        Program crossbar to target conductance values.
        
        Args:
            target_G: Target conductance matrix
            method: Programming method
        """
        if method == 'voltage_pulse':
            # Simulate voltage pulse programming
            delta_G = target_G - self.G
            
            # Programming pulses (simplified)
            pulses = np.sign(delta_G) * np.sqrt(np.abs(delta_G)) * 0.1
            
            # Update with programming nonlinearity
            self.G += pulses * (1 - 0.1 * np.random.rand(*self.G.shape))
            
            # Clip to device limits
            self.G = np.clip(self.G, 
                           1/self.device_params['ROFF'],
                           1/self.device_params['RON'])
        
        elif method == 'gradient_descent':
            # Direct update (simulation)
            self.G = target_G
            self.G = np.clip(self.G,
                           1/self.device_params['ROFF'],
                           1/self.device_params['RON'])
    
    def get_memory_capacity(self):
        """
        Estimate effective memory capacity of the preprocessing layer.
        
        Returns:
            capacity: Information capacity in bits
        """
        # Based on conductance levels
        G_levels = (self.device_params['RON'] / self.device_params['ROFF'])
        bits_per_device = np.log2(G_levels)
        total_bits = bits_per_device * self.input_dim * self.output_dim
        
        return total_bits


class MemristorPreprocessing:
    """
    Complete preprocessing pipeline with memristor crossbar.
    """
    
    def __init__(self, input_shape, n_features, n_layers=1):
        self.input_shape = input_shape
        self.n_features = n_features
        self.n_layers = n_layers
        
        input_dim = np.prod(input_shape)
        
        # Stack of memristor crossbars
        self.layers = []
        for i in range(n_layers):
            if i == 0:
                dim = input_dim
            else:
                dim = n_features
            
            self.layers.append(MemristorCrossbar(dim, n_features))
    
    def preprocess(self, x):
        """
        Preprocess input through memristor layers.
        
        Args:
            x: Input (flattened or batched)
        
        Returns:
            features: Preprocessed features
        """
        # Flatten if needed
        if x.ndim > 1:
            x = x.flatten()
        
        # Apply layers
        for layer in self.layers:
            x = layer.forward(x)
        
        return x
    
    def preprocess_batch(self, X):
        """
        Preprocess batch of inputs.
        
        Args:
            X: Input batch (n_samples, ...)
        
        Returns:
            features: Preprocessed features (n_samples, n_features)
        """
        n_samples = X.shape[0]
        features = np.zeros((n_samples, self.n_features))
        
        for i in range(n_samples):
            features[i] = self.preprocess(X[i])
        
        return features
```

## Reservoir Computing with Preprocessing

### Echo State Network with Memristor Input

```python
class MemristorReservoirESN:
    """
    Echo State Network with memristor-based preprocessing.
    """
    
    def __init__(self, 
                 input_shape,
                 preprocessing_features=100,
                 reservoir_size=500,
                 spectral_radius=0.9,
                 leaking_rate=0.3):
        
        self.input_shape = input_shape
        self.preprocessing = MemristorPreprocessing(input_shape, preprocessing_features)
        self.reservoir_size = reservoir_size
        self.leaking_rate = leaking_rate
        
        # Initialize reservoir weights
        self.Win = np.random.randn(reservoir_size, preprocessing_features) * 0.1
        
        # Reservoir weights (sparse, random)
        density = 0.1
        W = np.random.randn(reservoir_size, reservoir_size)
        mask = np.random.rand(reservoir_size, reservoir_size) < density
        W = W * mask
        
        # Scale to spectral radius
        eigenvalues = np.linalg.eigvals(W)
        max_eigenval = np.max(np.abs(eigenvalues))
        self.W = W * spectral_radius / max_eigenval
        
        # State
        self.x = np.zeros(reservoir_size)
        self.readout = None
    
    def reset_state(self):
        """Reset reservoir state."""
        self.x = np.zeros(self.reservoir_size)
    
    def step(self, u):
        """
        Single reservoir step with preprocessed input.
        
        Args:
            u: Raw input
        
        Returns:
            x: New reservoir state
        """
        # Preprocess input
        u_pre = self.preprocessing.preprocess(u)
        
        # Reservoir update (leaky integrator)
        x_new = np.tanh(self.Win @ u_pre + self.W @ self.x)
        self.x = (1 - self.leaking_rate) * self.x + self.leaking_rate * x_new
        
        return self.x.copy()
    
    def run(self, sequence, initial_state=None):
        """
        Run reservoir on input sequence.
        
        Args:
            sequence: Input sequence (time_steps, ...)
            initial_state: Optional initial state
        
        Returns:
            states: Reservoir states (time_steps, reservoir_size)
        """
        if initial_state is not None:
            self.x = initial_state
        else:
            self.reset_state()
        
        states = []
        for u in sequence:
            x = self.step(u)
            states.append(x)
        
        return np.array(states)
    
    def train_readout(self, X_train, y_train, alpha=1.0):
        """
        Train linear readout using ridge regression.
        
        Args:
            X_train: Training inputs (n_samples, ...)
            y_train: Training targets (n_samples, n_classes)
            alpha: Ridge regularization
        """
        # Collect reservoir states
        states_list = []
        for x in X_train:
            # For images, treat as single timestep
            if x.ndim == 2 or x.ndim == 3:
                self.reset_state()
                u_pre = self.preprocessing.preprocess(x)
                state = np.tanh(self.Win @ u_pre)
                states_list.append(state)
            else:
                states = self.run(x)
                states_list.append(states[-1])  # Final state
        
        states_matrix = np.array(states_list)
        
        # Ridge regression
        I = np.eye(states_matrix.shape[1])
        self.readout = np.linalg.solve(
            states_matrix.T @ states_matrix + alpha * I,
            states_matrix.T @ y_train
        )
    
    def predict(self, X):
        """
        Make predictions on new data.
        
        Args:
            X: Input data
        
        Returns:
            predictions: Class probabilities
        """
        states_list = []
        for x in X:
            if x.ndim == 2 or x.ndim == 3:
                self.reset_state()
                u_pre = self.preprocessing.preprocess(x)
                state = np.tanh(self.Win @ u_pre)
                states_list.append(state)
            else:
                states = self.run(x)
                states_list.append(states[-1])
        
        states_matrix = np.array(states_list)
        logits = states_matrix @ self.readout
        
        # Softmax
        exp_logits = np.exp(logits - np.max(logits, axis=1, keepdims=True))
        probabilities = exp_logits / np.sum(exp_logits, axis=1, keepdims=True)
        
        return probabilities
```

## Training Pipeline

```python
class MemristorReservoirTrainer:
    """
    Training pipeline for memristor reservoir classifier.
    """
    
    def __init__(self, model, batch_size=32):
        self.model = model
        self.batch_size = batch_size
    
    def train(self, X_train, y_train, X_val, y_val, epochs=100):
        """
        Train the model with early stopping.
        
        Args:
            X_train, y_train: Training data
            X_val, y_val: Validation data
            epochs: Maximum epochs
        
        Returns:
            history: Training history
        """
        history = {'train_acc': [], 'val_acc': []}
        best_val_acc = 0
        best_weights = None
        patience = 10
        patience_counter = 0
        
        # Encode labels
        n_classes = len(np.unique(y_train))
        y_train_onehot = np.eye(n_classes)[y_train]
        y_val_onehot = np.eye(n_classes)[y_val]
        
        for epoch in range(epochs):
            # Train readout
            self.model.train_readout(X_train, y_train_onehot)
            
            # Evaluate
            train_pred = self.model.predict(X_train)
            train_acc = np.mean(np.argmax(train_pred, axis=1) == y_train)
            
            val_pred = self.model.predict(X_val)
            val_acc = np.mean(np.argmax(val_pred, axis=1) == y_val)
            
            history['train_acc'].append(train_acc)
            history['val_acc'].append(val_acc)
            
            print(f"Epoch {epoch+1}/{epochs}: Train Acc = {train_acc:.4f}, Val Acc = {val_acc:.4f}")
            
            # Early stopping
            if val_acc > best_val_acc:
                best_val_acc = val_acc
                best_weights = self.model.readout.copy()
                patience_counter = 0
            else:
                patience_counter += 1
                if patience_counter >= patience:
                    print(f"Early stopping at epoch {epoch+1}")
                    break
        
        # Restore best weights
        self.model.readout = best_weights
        
        return history
```

## Memristor Dynamics Analysis

```python
def analyze_memristor_dynamics(preprocessing_layer, test_inputs):
    """
    Analyze memristor switching dynamics impact on performance.
    
    Args:
        preprocessing_layer: MemristorPreprocessing instance
        test_inputs: Test input samples
    
    Returns:
        analysis: Dynamics metrics
    """
    # Test different programming states
    n_states = 5
    programming_levels = np.linspace(0.1, 0.9, n_states)
    
    responses = []
    for level in programming_levels:
        # Program to level
        target_G = np.ones_like(preprocessing_layer.layers[0].G) * level
        preprocessing_layer.layers[0].program_conductance(target_G)
        
        # Get responses
        layer_responses = []
        for inp in test_inputs[:100]:
            out = preprocessing_layer.preprocess(inp)
            layer_responses.append(out)
        
        responses.append(np.array(layer_responses))
    
    # Analyze
    analysis = {
        'mean_response': [np.mean(r) for r in responses],
        'response_variance': [np.var(r) for r in responses],
        'separation_capacity': [],
        'memory_effects': []
    }
    
    # Calculate class separation
    for r in responses:
        # Simplified: variance between vs within classes
        between_class_var = np.var(np.mean(r, axis=0))
        within_class_var = np.mean(np.var(r, axis=0))
        separation = between_class_var / (within_class_var + 1e-8)
        analysis['separation_capacity'].append(separation)
    
    return analysis


def compare_with_without_preprocessing(X_train, y_train, X_test, y_test):
    """
    Compare performance with and without memristor preprocessing.
    
    Args:
        X_train, y_train, X_test, y_test: Data
    
    Returns:
        comparison: Performance comparison
    """
    input_shape = X_train[0].shape
    n_classes = len(np.unique(y_train))
    
    # With preprocessing
    model_with = MemristorReservoirESN(
        input_shape=input_shape,
        preprocessing_features=100,
        reservoir_size=500
    )
    trainer_with = MemristorReservoirTrainer(model_with)
    history_with = trainer_with.train(X_train, y_train, X_test, y_test)
    pred_with = model_with.predict(X_test)
    acc_with = np.mean(np.argmax(pred_with, axis=1) == y_test)
    
    # Without preprocessing (identity)
    class IdentityPreprocessing:
        def preprocess(self, x):
            return x.flatten()[:100]  # Truncate/pad to 100
    
    model_without = MemristorReservoirESN(
        input_shape=input_shape,
        preprocessing_features=np.prod(input_shape),
        reservoir_size=500
    )
    model_without.preprocessing = IdentityPreprocessing()
    trainer_without = MemristorReservoirTrainer(model_without)
    history_without = trainer_without.train(X_train, y_train, X_test, y_test)
    pred_without = model_without.predict(X_test)
    acc_without = np.mean(np.argmax(pred_without, axis=1) == y_test)
    
    return {
        'accuracy_with_preprocessing': acc_with,
        'accuracy_without_preprocessing': acc_without,
        'improvement': acc_with - acc_without,
        'improvement_percent': (acc_with - acc_without) / acc_without * 100,
        'history_with': history_with,
        'history_without': history_without
    }
```

## Applications

### 1. Image Classification

```python
def classify_mnist_with_memristor_reservoir():
    """
    MNIST classification using memristor reservoir computing.
    """
    from sklearn.datasets import fetch_openml
    from sklearn.model_selection import train_test_split
    from sklearn.preprocessing import StandardScaler
    
    # Load MNIST
    mnist = fetch_openml('mnist_784', version=1)
    X, y = mnist.data[:10000] / 255.0, mnist.target[:10000].astype(int)
    
    # Reshape to 28x28
    X = X.reshape(-1, 28, 28)
    
    # Split
    X_train, X_test, y_train, y_test = train_test_split(
        X, y, test_size=0.2, random_state=42
    )
    
    # Create model
    model = MemristorReservoirESN(
        input_shape=(28, 28),
        preprocessing_features=100,
        reservoir_size=500,
        spectral_radius=0.95,
        leaking_rate=0.3
    )
    
    # Train
    trainer = MemristorReservoirTrainer(model)
    history = trainer.train(X_train, y_train, X_test, y_test)
    
    return model, history
```

### 2. Memory Capacity Optimization

```python
def optimize_preprocessing_for_memory(preprocessing_layer, sequence_data):
    """
    Optimize preprocessing layer for maximum memory capacity.
    
    Args:
        preprocessing_layer: MemristorPreprocessing instance
        sequence_data: Sequential input data
    
    Returns:
        optimized_params: Optimized parameters
    """
    from scipy.optimize import minimize
    
    def objective(params):
        # Set conductance based on params
        G_base = params[0]
        G_var = params[1]
        
        target_G = np.random.normal(G_base, G_var, 
                                   preprocessing_layer.layers[0].G.shape)
        target_G = np.clip(target_G, 
                          preprocessing_layer.layers[0].device_params['ROFF']**-1,
                          preprocessing_layer.layers[0].device_params['RON']**-1)
        
        preprocessing_layer.layers[0].program_conductance(target_G)
        
        # Measure memory capacity on sequence
        capacity = 0
        for seq in sequence_data[:50]:
            preprocessed = preprocessing_layer.preprocess_batch(seq)
            
            # Simple memory test: correlation with delayed versions
            for delay in range(1, min(10, len(seq))):
                corr = np.corrcoef(
                    preprocessed[:-delay].flatten(),
                    preprocessed[delay:].flatten()
                )[0, 1]
                capacity += abs(corr)
        
        return -capacity  # Minimize negative capacity
    
    # Optimize
    result = minimize(objective, [0.5e-3, 0.1e-3], method='Nelder-Mead')
    
    return {
        'optimal_base_conductance': result.x[0],
        'optimal_variance': result.x[1],
        'max_capacity': -result.fun
    }
```

## Key Findings

1. **Accuracy Improvement**: Memristor preprocessing improves classification accuracy by 5-15%
2. **Readout Simplification**: Enables simpler readout layers (linear vs. nonlinear)
3. **Memory Enhancement**: Increases reservoir memory capacity through nonlinear projection
4. **Separation Property**: Improves separation of different input classes
5. **Device Nonlinearity**: Memristor switching dynamics contribute beneficial nonlinearity

## Design Guidelines

| Parameter | Recommendation |
|-----------|---------------|
| Preprocessing features | 100-200 for images |
| Reservoir size | 500-1000 nodes |
| Spectral radius | 0.9-0.99 |
| Leaking rate | 0.1-0.5 |
| RON/ROFF ratio | 10:1 to 100:1 |
| Programming precision | 4-6 bits sufficient |

## References

- Daniels, R., et al. (2026). On the Role of Preprocessing and Memristor Dynamics in Reservoir Computing for Image Classification. arXiv:2604.21602v1
- Strukov, D.B., et al. (2008). The missing memristor found
- Jaeger, H. (2001). The "echo state" approach to analysing and training recurrent neural networks
- Lukoševičius, M., & Jaeger, H. (2009). Reservoir computing approaches to recurrent neural network training

## Related Skills

- `reservoir-computing`: General reservoir computing methods
- `memristive-neuromorphic`: Memristor-based neuromorphic systems
- `snn-learning-survey`: SNN learning approaches
- `neuromorphic-hardware-optimization`: Hardware optimization for neuromorphic systems

## Activation Keywords

- memristor preprocessing
- reservoir computing crossbar
- image classification reservoir
- memristor dynamics analysis
- nonlinear preprocessing reservoir
- crossbar array reservoir