---
name: model-extraction-relu-logits
description: Guidance for extracting weight matrices from black-box ReLU neural networks using only input-output queries. This skill applies when tasked with recovering internal parameters (weights, biases) of a neural network that can only be queried for outputs, particularly two-layer ReLU networks. Use this skill for model extraction, model stealing, or neural network reverse engineering tasks.
---

# Model Extraction for ReLU Networks

This skill provides guidance for extracting internal weight matrices from black-box ReLU neural networks using only input-output access.

## Problem Understanding

Model extraction tasks typically involve:
- A black-box neural network that accepts inputs and returns outputs (logits)
- The goal of recovering internal parameters (weight matrices, biases)
- No direct access to the network's implementation or internal state

### Critical Principle: True Black-Box Treatment

**Treat the target network as a genuine black-box.** Never rely on implementation details that may change during evaluation:
- Do not hardcode hidden layer dimensions from example code
- Do not assume specific random seeds or initialization schemes
- Do not directly compare extracted weights to "true" weights read from source files
- The test environment may use completely different parameters than any provided examples

## Approach Selection

### Understanding ReLU Network Structure

A two-layer ReLU network computes: `output = A2 @ ReLU(A1 @ x + b1) + b2`

Key properties to exploit:
1. **Piecewise linearity**: ReLU networks are piecewise linear functions
2. **Activation boundaries**: Each hidden neuron creates a hyperplane boundary where its output transitions from zero to active
3. **Gradient structure**: In each linear region, the gradient reveals information about active neurons

### Recommended Extraction Strategies

#### Strategy 1: Critical Point Analysis

ReLU networks have critical points where neurons transition between active/inactive states:

1. Probe the network systematically to identify transition boundaries
2. At each boundary, a hyperplane normal corresponds to a row of A1
3. Collect enough boundaries to reconstruct A1

#### Strategy 2: Gradient-Based Extraction

For networks where gradients are accessible or can be approximated:

1. Query gradients at multiple random points
2. Gradients in a linear region reveal which neurons are active
3. Use gradient information to identify weight matrix rows

#### Strategy 3: Activation Pattern Enumeration

Systematically identify which neurons are active in different input regions:

1. Start from a known point and identify its activation pattern
2. Search for inputs that cause different neurons to activate
3. Use the transition points to extract hyperplane parameters

#### Strategy 4: Optimization-Based Fitting (Fallback)

When mathematically principled methods are insufficient:

1. Generate diverse input-output pairs from the black-box
2. Train a surrogate network to match outputs
3. **Critical**: Make network capacity adaptive (try multiple hidden dimensions)
4. Validate by output matching, not parameter comparison

## Hidden Dimension Discovery

Since the hidden dimension is unknown, employ detection strategies:

1. **Rank analysis**: The output dimension and response complexity bound hidden size
2. **Binary search**: Try different hidden sizes and measure reconstruction error
3. **Overcomplete fitting**: Use larger hidden dimension than necessary, then identify redundant neurons
4. **Gradient counting**: In a fixed input region, count distinct gradient patterns

## Verification Strategy

### Correct Verification (Functional Equivalence)

```python
# Generate test inputs NOT used during extraction
test_inputs = generate_diverse_inputs(n=1000)

# Compare outputs
original_outputs = [black_box_query(x) for x in test_inputs]
extracted_outputs = [extracted_model(x) for x in test_inputs]

# Check functional equivalence
max_error = max(|original - extracted| for all test points)
assert max_error < tolerance
```

### Incorrect Verification (Avoid These)

- Comparing extracted weights directly to weights read from source files
- Using the same inputs for extraction and verification
- Relying on cosine similarity to "true" parameters
- Checking only a small number of test points

## Common Pitfalls

### 1. Peeking at Implementation Details

**Problem**: Reading source code to get the "true" weights or hidden dimension, then validating against them.

**Why it fails**: Test environments often use different parameters (different seeds, dimensions, scales).

**Solution**: Treat extraction as if source code doesn't exist. Validate only through output comparison.

### 2. Hardcoding Network Architecture

**Problem**: Assuming hidden dimension is fixed (e.g., `n_neurons=20`).

**Why it fails**: The actual network may have a different architecture.

**Solution**: Either detect hidden dimension empirically or design extraction to work with unknown dimensions.

### 3. Non-Unique Solutions

**Problem**: Many weight configurations produce identical input-output behavior.

**Why it fails**: Optimization may find a valid equivalent representation, not the original weights.

**Solution**: If the task requires recovering *specific* original weights (not just functional equivalents), use mathematically principled extraction that exploits ReLU structure.

### 4. Insufficient Test Coverage

**Problem**: Verifying on a few hand-picked inputs.

**Why it fails**: The extracted model may fail on untested input regions.

**Solution**: Use comprehensive random testing across the input domain, including edge cases.

### 5. Numerical Precision Issues

**Problem**: Accumulated floating-point errors cause extraction to fail.

**Solution**: Use numerically stable algorithms, appropriate tolerances, and verify with realistic precision expectations.

## Implementation Checklist

Before declaring success, verify:

- [ ] No implementation details (seeds, dimensions) were read from source files
- [ ] Hidden dimension was detected or handled adaptively
- [ ] Verification uses only input-output comparisons
- [ ] Verification inputs are independent from extraction inputs
- [ ] Sufficient test coverage (hundreds to thousands of points)
- [ ] Error tolerance is appropriate for the task requirements
- [ ] The extracted model works as a functional replacement

## When Standard Approaches Fail

If initial extraction attempts fail:

1. **Increase probe density**: More input-output pairs may be needed
2. **Try multiple hidden dimensions**: The assumed size may be wrong
3. **Check for numerical issues**: Scaling, precision, or conditioning problems
4. **Verify the network structure**: Ensure assumptions about architecture (two-layer, ReLU) are correct
5. **Consider alternative representations**: Some equivalent parameterizations may be easier to extract