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TinyTorch/modules/16_compression/compression.py
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# %% [markdown]
"""
# Module 16: Compression - Pruning and Model Compression
Welcome to Module 16! You're about to build model compression techniques that make neural networks smaller and more efficient while preserving their intelligence.
## 🔗 Prerequisites & Progress
**You've Built**: Complete optimization pipeline with profiling (14) and quantization (15)
**You'll Build**: Pruning (magnitude & structured), knowledge distillation, and low-rank approximation
**You'll Enable**: Compressed models that maintain accuracy while using dramatically less storage and memory
**Connection Map**:
```
Profiling (14) → Quantization (15) → Compression (16) → Memoization (17) → Acceleration (18)
(measure size) (reduce precision) (remove weights) (cache compute) (speed up compute)
```
## Learning Objectives
By the end of this module, you will:
1. Implement magnitude-based and structured pruning
2. Build knowledge distillation for model compression
3. Create low-rank approximations of weight matrices
4. Measure compression ratios and sparsity levels
5. Understand structured vs unstructured sparsity trade-offs
Let's get started!
## 📦 Where This Code Lives in the Final Package
**Learning Side:** You work in `modules/17_compression/compression_dev.py`
**Building Side:** Code exports to `tinytorch.optimization.compression`
```python
# How to use this module:
from tinytorch.optimization.compression import magnitude_prune, structured_prune, measure_sparsity
```
**Why this matters:**
- **Learning:** Complete compression system in one focused module for deep understanding
- **Production:** Proper organization like real compression libraries with all techniques together
- **Consistency:** All compression operations and sparsity management in optimization.compression
- **Integration:** Works seamlessly with models and quantization for complete optimization pipeline
"""
# %% nbgrader={"grade": false, "grade_id": "imports", "solution": true}
#| default_exp optimization.compression
#| export
import numpy as np
import copy
from typing import List, Dict, Any, Tuple, Optional
import time
# Import from TinyTorch package (previous modules must be completed and exported)
from tinytorch.core.tensor import Tensor
from tinytorch.core.layers import Linear
from tinytorch.core.activations import ReLU
# Constants for memory calculations
BYTES_PER_FLOAT32 = 4 # Standard float32 size in bytes
MB_TO_BYTES = 1024 * 1024 # Megabytes to bytes conversion
# %% [markdown]
"""
### 🚨 CRITICAL: Why No Sequential Container in TinyTorch
**TinyTorch teaches ATOMIC COMPONENTS, not compositions!**
**FORBIDDEN Pattern:**
```python
model = Sequential([Linear(10, 20), ReLU(), Linear(20, 10)])
y = model(x) # Student can't see what's happening!
```
**CORRECT Pattern:**
```python
# Explicit composition - students see every step
layer1 = Linear(10, 20)
activation = ReLU()
layer2 = Linear(20, 10)
# Forward pass - nothing hidden
x = layer1.forward(input)
x = activation.forward(x)
output = layer2.forward(x)
```
**Why This Matters:**
- Students MUST see explicit forward passes to understand data flow
- Hidden abstractions prevent learning
- Sequential belongs in helper utilities, NOT core modules
- Educational value comes from seeing layer interactions explicitly
"""
# %%
# Helper class for testing only - demonstrates explicit composition pattern
class SimpleModel:
"""
Simple model container for testing - demonstrates explicit composition.
EDUCATIONAL NOTE: This is a TEST HELPER, not a core module component!
In real code, students should write explicit forward passes.
"""
def __init__(self, *layers):
self.layers = list(layers)
def forward(self, x):
"""Explicit forward pass through layers."""
for layer in self.layers:
x = layer.forward(x)
return x
def __call__(self, x):
return self.forward(x)
def parameters(self):
"""Collect parameters from all layers."""
params = []
for layer in self.layers:
params.extend(layer.parameters())
return params
# %% [markdown]
"""
## 🔬 Motivation: Why Compression Matters
Before we learn compression, let's profile a model to analyze its weight
distribution. We'll discover that many weights are tiny and might not matter much!
"""
# %%
# Profile weight distribution to discover pruning opportunities
# Module 14 (Profiling) must be completed before Module 16
from tinytorch.profiling.profiler import Profiler, analyze_weight_distribution
profiler = Profiler()
# Create a model and analyze its weights
model = Linear(512, 512)
input_data = Tensor(np.random.randn(1, 512))
# Profile basic characteristics
profile = profiler.profile_forward_pass(model, input_data)
print("🔬 Profiling Parameter Distribution:\n")
print(f" Total parameters: {profile['parameters']:,}")
print(f" Model memory: {profile['parameters'] * BYTES_PER_FLOAT32 / MB_TO_BYTES:.1f} MB (FP32)")
# Analyze weight distribution
weights = model.weight.data.flatten()
abs_weights = np.abs(weights)
print("\n Weight Statistics:")
print(f" Mean: {np.mean(abs_weights):.4f}")
print(f" Std: {np.std(abs_weights):.4f}")
print(f" Min: {np.min(abs_weights):.4f}")
print(f" Max: {np.max(abs_weights):.4f}")
# Check how many weights are small
thresholds = [0.001, 0.01, 0.1, 0.5]
print("\n Weights Below Threshold:")
print(" Threshold | Percentage")
print(" -----------|--------------")
for threshold in thresholds:
percentage = np.sum(abs_weights < threshold) / len(weights) * 100
print(f" < {threshold:<6} | {percentage:5.1f}%")
print("\n💡 Key Observations:")
print(" • Many weights are very small (close to zero)")
print(" • Weight distribution typically: mean ≈ 0, concentrated near zero")
print(" • Small weights contribute little to final predictions")
print(" • Typical finding: 50-90% of weights can be removed!")
print("\n🎯 The Problem:")
print(" Why store and compute with weights that barely matter?")
print(" • They take memory")
print(" • They require computation")
print(" • They slow down inference")
print(" • But removing them has minimal accuracy impact!")
print("\n✨ The Solution:")
print(" Prune (remove) small weights:")
print(" • Magnitude pruning: Set small weights to zero")
print(" • Structured pruning: Remove entire neurons/channels")
print(" • Typical: 80-90% sparsity with <1% accuracy loss")
print(" • Benefit: Smaller models, faster inference, less memory\n")
# %% [markdown]
"""
## 1. Introduction: What is Model Compression?
Imagine you have a massive library with millions of books, but you only reference 10% of them regularly. Model compression is like creating a curated collection that keeps the essential knowledge while dramatically reducing storage space.
Model compression reduces the size and computational requirements of neural networks while preserving their intelligence. It's the bridge between powerful research models and practical deployment.
### Why Compression Matters in ML Systems
**The Storage Challenge:**
- Modern language models: 100GB+ (GPT-3 scale)
- Mobile devices: <1GB available for models
- Edge devices: <100MB realistic limits
- Network bandwidth: Slow downloads kill user experience
**The Speed Challenge:**
- Research models: Designed for accuracy, not efficiency
- Production needs: Sub-second response times
- Battery life: Energy consumption matters for mobile
- Cost scaling: Inference costs grow with model size
### The Compression Landscape
```
Neural Network Compression Techniques:
┌─────────────────────────────────────────────────────────────┐
│ COMPRESSION METHODS │
├─────────────────────────────────────────────────────────────┤
│ WEIGHT-BASED │ ARCHITECTURE-BASED │
│ ┌─────────────────────────────┐ │ ┌─────────────────────┐ │
│ │ Magnitude Pruning │ │ │ Knowledge Distillation│ │
│ │ • Remove small weights │ │ │ • Teacher → Student │ │
│ │ • 90% sparsity achievable │ │ │ • 10x size reduction │ │
│ │ │ │ │ │ │
│ │ Structured Pruning │ │ │ Neural Architecture │ │
│ │ • Remove entire channels │ │ │ Search (NAS) │ │
│ │ • Hardware-friendly │ │ │ • Automated design │ │
│ │ │ │ │ │ │
│ │ Low-Rank Approximation │ │ │ Early Exit │ │
│ │ • Matrix factorization │ │ │ • Adaptive compute │ │
│ │ • SVD decomposition │ │ │ │ │
│ └─────────────────────────────┘ │ └─────────────────────┘ │
└─────────────────────────────────────────────────────────────┘
```
Think of compression like optimizing a recipe - you want to keep the essential ingredients that create the flavor while removing anything that doesn't contribute to the final dish.
"""
# %% [markdown]
"""
## 2. Foundations: Mathematical Background
Understanding the mathematics behind compression helps us choose the right technique for each situation and predict their effects on model performance.
### Magnitude-Based Pruning: The Simple Approach
The core insight: small weights contribute little to the final prediction. Magnitude pruning removes weights based on their absolute values.
```
Mathematical Foundation:
For weight w_ij in layer l:
If |w_ij| < threshold_l → w_ij = 0
Threshold Selection:
- Global: One threshold for entire model
- Layer-wise: Different threshold per layer
- Percentile-based: Remove bottom k% of weights
Sparsity Calculation:
Sparsity = (Zero weights / Total weights) × 100%
```
### Structured Pruning: Hardware-Friendly Compression
Unlike magnitude pruning which creates scattered zeros, structured pruning removes entire computational units (neurons, channels, attention heads).
```
Channel Importance Metrics:
Method 1: L2 Norm
Importance(channel_i) = ||W[:,i]||₂ = √(Σⱼ W²ⱼᵢ)
Method 2: Gradient-based
Importance(channel_i) = |∂Loss/∂W[:,i]|
Method 3: Activation-based
Importance(channel_i) = E[|activations_i|]
Pruning Decision:
Remove bottom k% of channels based on importance ranking
```
### Knowledge Distillation: Learning from Teachers
Knowledge distillation transfers knowledge from a large "teacher" model to a smaller "student" model. The student learns not just the correct answers, but the teacher's reasoning process.
```
Distillation Loss Function:
L_total = α × L_soft + (1-α) × L_hard
Where:
L_soft = KL_divergence(σ(z_s/T), σ(z_t/T)) # Soft targets
L_hard = CrossEntropy(σ(z_s), y_true) # Hard targets
σ(z/T) = Softmax with temperature T
z_s = Student logits, z_t = Teacher logits
α = Balance parameter (typically 0.7)
T = Temperature parameter (typically 3-5)
Temperature Effect:
T=1: Standard softmax (sharp probabilities)
T>1: Softer distributions (reveals teacher's uncertainty)
```
### Low-Rank Approximation: Matrix Compression
Large weight matrices often have redundancy that can be captured with lower-rank approximations using Singular Value Decomposition (SVD).
```
SVD Decomposition:
W_{m×n} = U_{m×k} × Σ_{k×k} × V^T_{k×n}
Parameter Reduction:
Original: m × n parameters
Compressed: (m × k) + k + (k × n) = k(m + n + 1) parameters
Compression achieved when: k < mn/(m+n+1)
Reconstruction Error:
||W - W_approx||_F = √(Σᵢ₌ₖ₊₁ʳ σᵢ²)
Where σᵢ are singular values, r = rank(W)
```
"""
# %% [markdown]
"""
## 3. Sparsity Measurement: Understanding Model Density
Before we can compress models, we need to understand how dense they are. Sparsity measurement tells us what percentage of weights are zero (or effectively zero).
### Understanding Sparsity
Sparsity is like measuring how much of a parking lot is empty. A 90% sparse model means 90% of its weights are zero - only 10% of the "parking spaces" are occupied.
```
Sparsity Visualization:
Dense Matrix (0% sparse): Sparse Matrix (75% sparse):
┌─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─┐ ┌─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─┐
│ 2.1 1.3 0.8 1.9 2.4 1.1 0.7 │ │ 2.1 0.0 0.0 1.9 0.0 0.0 0.0 │
│ 1.5 2.8 1.2 0.9 1.6 2.2 1.4 │ │ 0.0 2.8 0.0 0.0 0.0 2.2 0.0 │
│ 0.6 1.7 2.5 1.1 0.8 1.3 2.0 │ │ 0.0 0.0 2.5 0.0 0.0 0.0 2.0 │
│ 1.9 1.0 1.6 2.3 1.8 0.9 1.2 │ │ 1.9 0.0 0.0 2.3 0.0 0.0 0.0 │
└─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─┘ └─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─┘
All weights active Only 7/28 weights active
Storage: 28 values Storage: 7 values + indices
```
Why this matters: Sparsity directly relates to memory savings, but achieving speedup requires special sparse computation libraries.
"""
# %% nbgrader={"grade": false, "grade_id": "measure-sparsity", "solution": true, "schema_version": 3}
def measure_sparsity(model) -> float:
"""
Calculate the percentage of zero weights in a model.
TODO: Count zero weights and total weights across all layers
APPROACH:
1. Iterate through all model parameters
2. Count zeros using np.sum(weights == 0)
3. Count total parameters
4. Return percentage: zeros / total * 100
Args:
model: Model with .parameters() method
Returns:
Sparsity percentage (0.0-100.0)
EXAMPLE:
>>> # Create test model with explicit composition
>>> layer1 = Linear(10, 5)
>>> layer2 = Linear(5, 2)
>>> model = SimpleModel(layer1, layer2)
>>> sparsity = measure_sparsity(model)
>>> print(f"Model sparsity: {sparsity:.1f}%")
Model sparsity: 0.0% # Before pruning
HINT: Use np.sum() to count zeros efficiently
"""
### BEGIN SOLUTION
total_params = 0
zero_params = 0
for param in model.parameters():
# Only count weight matrices (2D), not biases (1D)
# Biases are often initialized to zero, which would skew sparsity
if len(param.shape) > 1:
total_params += param.size
zero_params += np.sum(param.data == 0)
if total_params == 0:
return 0.0
return (zero_params / total_params) * 100.0
### END SOLUTION
# %% nbgrader={"grade": true, "grade_id": "test-measure-sparsity", "locked": true, "points": 5, "solution": false, "schema_version": 3}
def test_unit_measure_sparsity():
"""🔬 Test sparsity measurement functionality."""
print("🔬 Unit Test: Measure Sparsity...")
# Test with dense model - explicit composition shows structure
layer1 = Linear(4, 3)
layer2 = Linear(3, 2)
model = SimpleModel(layer1, layer2) # Test helper for parameter collection
initial_sparsity = measure_sparsity(model)
assert initial_sparsity == 0.0, f"Expected 0% sparsity, got {initial_sparsity}%"
# Test with manually sparse model - students see which weights are zeroed
layer1.weight.data[0, 0] = 0 # Zero out specific weight
layer1.weight.data[1, 1] = 0 # Zero out another weight
sparse_sparsity = measure_sparsity(model)
assert sparse_sparsity > 0, f"Expected >0% sparsity, got {sparse_sparsity}%"
print("✅ measure_sparsity works correctly!")
if __name__ == "__main__":
test_unit_measure_sparsity()
# %% [markdown]
"""
## 4. Magnitude-Based Pruning: Removing Small Weights
Magnitude pruning is the simplest and most intuitive compression technique. It's based on the observation that weights with small magnitudes contribute little to the model's output.
### How Magnitude Pruning Works
Think of magnitude pruning like editing a document - you remove words that don't significantly change the meaning. In neural networks, we remove weights that don't significantly affect predictions.
```
Magnitude Pruning Process:
Step 1: Collect All Weights
┌──────────────────────────────────────────────────┐
│ Layer 1: [2.1, 0.1, -1.8, 0.05, 3.2, -0.02] │
│ Layer 2: [1.5, -0.03, 2.8, 0.08, -2.1, 0.01] │
│ Layer 3: [0.7, 2.4, -0.06, 1.9, 0.04, -1.3] │
└──────────────────────────────────────────────────┘
Step 2: Calculate Magnitudes
┌──────────────────────────────────────────────────┐
│ Magnitudes: [2.1, 0.1, 1.8, 0.05, 3.2, 0.02, │
│ 1.5, 0.03, 2.8, 0.08, 2.1, 0.01, │
│ 0.7, 2.4, 0.06, 1.9, 0.04, 1.3] │
└──────────────────────────────────────────────────┘
Step 3: Find Threshold (e.g., 70th percentile)
┌──────────────────────────────────────────────────┐
│ Sorted: [0.01, 0.02, 0.03, 0.04, 0.05, 0.06, │
│ 0.08, 0.1, 0.7, 1.3, 1.5, 1.8, │ Threshold: 0.1
│ 1.9, 2.1, 2.1, 2.4, 2.8, 3.2] │ (70% of weights removed)
└──────────────────────────────────────────────────┘
Step 4: Apply Pruning Mask
┌──────────────────────────────────────────────────┐
│ Layer 1: [2.1, 0.0, -1.8, 0.0, 3.2, 0.0] │
│ Layer 2: [1.5, 0.0, 2.8, 0.0, -2.1, 0.0] │ 70% weights → 0
│ Layer 3: [0.7, 2.4, 0.0, 1.9, 0.0, -1.3] │ 30% preserved
└──────────────────────────────────────────────────┘
Memory Impact:
- Dense storage: 18 values
- Sparse storage: 6 values + 6 indices = 12 values (33% savings)
- Theoretical limit: 70% savings with perfect sparse format
```
### Why Global Thresholding Works
Global thresholding treats the entire model as one big collection of weights, finding a single threshold that achieves the target sparsity across all layers.
**Advantages:**
- Simple to implement and understand
- Preserves overall model capacity
- Works well for uniform network architectures
**Disadvantages:**
- May over-prune some layers, under-prune others
- Doesn't account for layer-specific importance
- Can hurt performance if layers have very different weight distributions
"""
# %% nbgrader={"grade": false, "grade_id": "magnitude-prune", "solution": true, "schema_version": 3}
#| export
def magnitude_prune(model, sparsity=0.9):
"""
Remove weights with smallest magnitudes to achieve target sparsity.
TODO: Implement global magnitude-based pruning
APPROACH:
1. Collect all weights from the model
2. Calculate absolute values to get magnitudes
3. Find threshold at desired sparsity percentile
4. Set weights below threshold to zero (in-place)
EXAMPLE:
>>> # Create model with explicit layer composition
>>> layer1 = Linear(100, 50)
>>> layer2 = Linear(50, 10)
>>> model = SimpleModel(layer1, layer2)
>>> original_params = sum(p.size for p in model.parameters())
>>> magnitude_prune(model, sparsity=0.8)
>>> final_sparsity = measure_sparsity(model)
>>> print(f"Achieved {final_sparsity:.1f}% sparsity")
Achieved 80.0% sparsity
HINTS:
- Use np.percentile() to find threshold
- Modify model parameters in-place
- Consider only weight matrices, not biases
"""
### BEGIN SOLUTION
# Collect all weights (excluding biases)
all_weights = []
weight_params = []
for param in model.parameters():
# Skip biases (typically 1D)
if len(param.shape) > 1:
all_weights.extend(param.data.flatten())
weight_params.append(param)
if not all_weights:
return model
# Calculate magnitude threshold
magnitudes = np.abs(all_weights)
threshold = np.percentile(magnitudes, sparsity * 100)
# Apply pruning to each weight parameter
for param in weight_params:
mask = np.abs(param.data) >= threshold
param.data = param.data * mask
return model
### END SOLUTION
# %% nbgrader={"grade": true, "grade_id": "test-magnitude-prune", "locked": true, "points": 10, "solution": false, "schema_version": 3}
def test_unit_magnitude_prune():
"""🔬 Test magnitude-based pruning functionality."""
print("🔬 Unit Test: Magnitude Prune...")
# Create test model with explicit composition - students see structure
layer1 = Linear(4, 3)
layer2 = Linear(3, 2)
model = SimpleModel(layer1, layer2)
# Set specific weight values for predictable testing
# Students can see exactly which weights we're testing
layer1.weight.data = np.array([
[1.0, 2.0, 3.0], # Large weights - should survive pruning
[0.1, 0.2, 0.3], # Medium weights
[4.0, 5.0, 6.0], # Large weights - should survive pruning
[0.01, 0.02, 0.03] # Tiny weights - will be pruned
])
initial_sparsity = measure_sparsity(model)
assert initial_sparsity == 0.0, "Model should start with no sparsity"
# Apply 50% pruning - removes smallest 50% of weights
magnitude_prune(model, sparsity=0.5)
final_sparsity = measure_sparsity(model)
# Should achieve approximately 50% sparsity
assert 40 <= final_sparsity <= 60, f"Expected ~50% sparsity, got {final_sparsity}%"
# Verify largest weights survived - students understand pruning criteria
remaining_weights = layer1.weight.data[layer1.weight.data != 0]
assert len(remaining_weights) > 0, "Some weights should remain"
assert np.all(np.abs(remaining_weights) >= 0.1), "Large weights should survive"
print("✅ magnitude_prune works correctly!")
if __name__ == "__main__":
test_unit_magnitude_prune()
# %% [markdown]
"""
## 5. Structured Pruning: Hardware-Friendly Compression
While magnitude pruning creates scattered zeros throughout the network, structured pruning removes entire computational units (channels, neurons, heads). This creates sparsity patterns that modern hardware can actually accelerate.
### Why Structured Pruning Matters
Think of the difference between removing random words from a paragraph versus removing entire sentences. Structured pruning removes entire "sentences" (channels) rather than random "words" (individual weights).
```
Unstructured vs Structured Sparsity:
UNSTRUCTURED (Magnitude Pruning):
┌─────────────────────────────────────────────┐
│ Channel 0: [2.1, 0.0, 1.8, 0.0, 3.2] │ ← Sparse weights
│ Channel 1: [0.0, 2.8, 0.0, 2.1, 0.0] │ ← Sparse weights
│ Channel 2: [1.5, 0.0, 2.4, 0.0, 1.9] │ ← Sparse weights
│ Channel 3: [0.0, 1.7, 0.0, 2.0, 0.0] │ ← Sparse weights
└─────────────────────────────────────────────┘
Issues: Irregular memory access, no hardware speedup
STRUCTURED (Channel Pruning):
┌─────────────────────────────────────────────┐
│ Channel 0: [2.1, 1.3, 1.8, 0.9, 3.2] │ ← Fully preserved
│ Channel 1: [0.0, 0.0, 0.0, 0.0, 0.0] │ ← Fully removed
│ Channel 2: [1.5, 2.2, 2.4, 1.1, 1.9] │ ← Fully preserved
│ Channel 3: [0.0, 0.0, 0.0, 0.0, 0.0] │ ← Fully removed
└─────────────────────────────────────────────┘
Benefits: Regular patterns, hardware acceleration possible
```
### Channel Importance Ranking
How do we decide which channels to remove? We rank them by importance using various metrics:
```
Channel Importance Metrics:
Method 1: L2 Norm (Most Common)
For each output channel i:
Importance_i = ||W[:, i]||_2 = √(Σⱼ w²ⱼᵢ)
Intuition: Channels with larger weights have bigger impact
Method 2: Activation-Based
Importance_i = E[|activation_i|] over dataset
Intuition: Channels that activate more are more important
Method 3: Gradient-Based
Importance_i = |∂Loss/∂W[:, i]|
Intuition: Channels with larger gradients affect loss more
Ranking Process:
1. Calculate importance for all channels
2. Sort channels by importance (ascending)
3. Remove bottom k% (least important)
4. Zero out entire channels, not individual weights
```
### Hardware Benefits of Structured Sparsity
Structured sparsity enables real hardware acceleration because:
1. **Memory Coalescing**: Accessing contiguous memory chunks is faster
2. **SIMD Operations**: Can process multiple remaining channels in parallel
3. **No Indexing Overhead**: Don't need to track locations of sparse weights
4. **Cache Efficiency**: Better spatial locality of memory access
"""
# %% nbgrader={"grade": false, "grade_id": "structured-prune", "solution": true, "schema_version": 3}
#| export
def structured_prune(model, prune_ratio=0.5):
"""
Remove entire channels/neurons based on L2 norm importance.
TODO: Implement structured pruning for Linear layers
APPROACH:
1. For each Linear layer, calculate L2 norm of each output channel
2. Rank channels by importance (L2 norm)
3. Remove lowest importance channels by setting to zero
4. This creates block sparsity that's hardware-friendly
EXAMPLE:
>>> # Create model with explicit layers
>>> layer1 = Linear(100, 50)
>>> layer2 = Linear(50, 10)
>>> model = SimpleModel(layer1, layer2)
>>> original_shape = layer1.weight.shape
>>> structured_prune(model, prune_ratio=0.3)
>>> # 30% of channels are now completely zero
>>> final_sparsity = measure_sparsity(model)
>>> print(f"Structured sparsity: {final_sparsity:.1f}%")
Structured sparsity: 30.0%
HINTS:
- Calculate L2 norm along input dimension for each output channel
- Use np.linalg.norm(weights[:, channel]) for channel importance
- Set entire channels to zero (not just individual weights)
"""
### BEGIN SOLUTION
# All Linear layers have .weight attribute
for layer in model.layers:
if isinstance(layer, Linear):
weight = layer.weight.data
# Calculate L2 norm for each output channel (column)
channel_norms = np.linalg.norm(weight, axis=0)
# Find channels to prune (lowest importance)
num_channels = weight.shape[1]
num_to_prune = int(num_channels * prune_ratio)
if num_to_prune > 0:
# Get indices of channels to prune (smallest norms)
prune_indices = np.argpartition(channel_norms, num_to_prune)[:num_to_prune]
# Zero out entire channels
weight[:, prune_indices] = 0
# Also zero corresponding bias elements if bias exists
if layer.bias is not None:
layer.bias.data[prune_indices] = 0
return model
### END SOLUTION
# %% nbgrader={"grade": true, "grade_id": "test-structured-prune", "locked": true, "points": 10, "solution": false, "schema_version": 3}
def test_unit_structured_prune():
"""🔬 Test structured pruning functionality."""
print("🔬 Unit Test: Structured Prune...")
# Create test model with explicit layers - students see the architecture
layer1 = Linear(4, 6)
layer2 = Linear(6, 2)
model = SimpleModel(layer1, layer2)
# Set predictable weights for testing
# Students can see channel importance: col 0,2,4 = large, col 1,3,5 = small
layer1.weight.data = np.array([
[1.0, 0.1, 2.0, 0.05, 3.0, 0.01], # Channels with varying importance
[1.1, 0.11, 2.1, 0.06, 3.1, 0.02], # Large values in columns 0,2,4
[1.2, 0.12, 2.2, 0.07, 3.2, 0.03], # Small values in columns 1,3,5
[1.3, 0.13, 2.3, 0.08, 3.3, 0.04] # Pruning removes small channels
])
initial_sparsity = measure_sparsity(model)
assert initial_sparsity == 0.0, "Model should start with no sparsity"
# Apply 33% structured pruning (2 out of 6 channels)
# This removes entire channels, not scattered weights
structured_prune(model, prune_ratio=0.33)
final_sparsity = measure_sparsity(model)
# Check that some channels are completely zero
weight = layer1.weight.data
zero_channels = np.sum(np.all(weight == 0, axis=0))
assert zero_channels >= 1, f"Expected at least 1 zero channel, got {zero_channels}"
# Check that non-zero channels are completely preserved
# This is structured pruning - entire channels are zero or non-zero
for col in range(weight.shape[1]):
channel = weight[:, col]
assert np.all(channel == 0) or np.all(channel != 0), "Channels should be fully zero or fully non-zero"
print("✅ structured_prune works correctly!")
if __name__ == "__main__":
test_unit_structured_prune()
# %% [markdown]
"""
## 6. Low-Rank Approximation: Matrix Compression Through Factorization
Low-rank approximation discovers that large weight matrices often contain redundant information that can be captured with much smaller matrices through mathematical decomposition.
### The Intuition Behind Low-Rank Approximation
Imagine you're storing a massive spreadsheet where many columns are highly correlated. Instead of storing all columns separately, you could store a few "basis" columns and coefficients for how to combine them to recreate the original data.
```
Low-Rank Decomposition Visualization:
Original Matrix W (large): Factorized Form (smaller):
┌─────────────────────────┐ ┌──────┐ ┌──────────────┐
│ 2.1 1.3 0.8 1.9 2.4 │ │ 1.1 │ │ 1.9 1.2 0.7│
│ 1.5 2.8 1.2 0.9 1.6 │ ≈ │ 2.4 │ @ │ 0.6 1.2 0.5│
│ 0.6 1.7 2.5 1.1 0.8 │ │ 0.8 │ │ 1.4 2.1 0.9│
│ 1.9 1.0 1.6 2.3 1.8 │ │ 1.6 │ │ 0.5 0.6 1.1│
└─────────────────────────┘ └──────┘ └──────────────┘
W (4×5) = 20 params U (4×2)=8 + V (2×5)=10 = 18 params
Parameter Reduction:
- Original: 4 × 5 = 20 parameters
- Compressed: (4 × 2) + (2 × 5) = 18 parameters
- Compression ratio: 18/20 = 0.9 (10% savings)
For larger matrices, savings become dramatic:
- W (1000×1000): 1M parameters → U (1000×100) + V (100×1000): 200K parameters
- Compression ratio: 0.2 (80% savings)
```
### SVD: The Mathematical Foundation
Singular Value Decomposition (SVD) finds the optimal low-rank approximation by identifying the most important "directions" in the data:
```
SVD Decomposition:
W = U × Σ × V^T
Where:
U: Left singular vectors (input patterns)
Σ: Singular values (importance weights)
V^T: Right singular vectors (output patterns)
Truncated SVD (Rank-k approximation):
W ≈ U[:,:k] × Σ[:k] × V^T[:k,:]
Quality vs Compression Trade-off:
Higher k → Better approximation, less compression
Lower k → More compression, worse approximation
Choosing Optimal Rank:
Method 1: Fixed ratio (k = ratio × min(m,n))
Method 2: Energy threshold (keep 90% of singular value energy)
Method 3: Error threshold (reconstruction error < threshold)
```
### When Low-Rank Works Best
Low-rank approximation works well when:
- **Matrices are large**: Compression benefits scale with size
- **Data has structure**: Correlated patterns enable compression
- **Moderate accuracy loss acceptable**: Some precision traded for efficiency
It works poorly when:
- **Matrices are already small**: Overhead exceeds benefits
- **Data is random**: No patterns to exploit
- **High precision required**: SVD introduces approximation error
"""
# %% nbgrader={"grade": false, "grade_id": "low-rank-approx", "solution": true, "schema_version": 3}
def low_rank_approximate(weight_matrix, rank_ratio=0.5):
"""
Approximate weight matrix using low-rank decomposition (SVD).
TODO: Implement SVD-based low-rank approximation
APPROACH:
1. Perform SVD: W = U @ S @ V^T
2. Keep only top k singular values where k = rank_ratio * min(dimensions)
3. Reconstruct: W_approx = U[:,:k] @ diag(S[:k]) @ V[:k,:]
4. Return decomposed matrices for memory savings
EXAMPLE:
>>> weight = np.random.randn(100, 50)
>>> U, S, V = low_rank_approximate(weight, rank_ratio=0.3)
>>> # Original: 100*50 = 5000 params
>>> # Compressed: 100*15 + 15*50 = 2250 params (55% reduction)
HINTS:
- Use np.linalg.svd() for decomposition
- Choose k = int(rank_ratio * min(m, n))
- Return U[:,:k], S[:k], V[:k,:] for reconstruction
"""
### BEGIN SOLUTION
m, n = weight_matrix.shape
# Perform SVD
U, S, V = np.linalg.svd(weight_matrix, full_matrices=False)
# Determine target rank
max_rank = min(m, n)
target_rank = max(1, int(rank_ratio * max_rank))
# Truncate to target rank
U_truncated = U[:, :target_rank]
S_truncated = S[:target_rank]
V_truncated = V[:target_rank, :]
return U_truncated, S_truncated, V_truncated
### END SOLUTION
# %% nbgrader={"grade": true, "grade_id": "test-low-rank", "locked": true, "points": 10, "solution": false, "schema_version": 3}
def test_unit_low_rank_approximate():
"""🔬 Test low-rank approximation functionality."""
print("🔬 Unit Test: Low-Rank Approximate...")
# Create test weight matrix
original_weight = np.random.randn(20, 15)
original_params = original_weight.size
# Apply low-rank approximation
U, S, V = low_rank_approximate(original_weight, rank_ratio=0.4)
# Check dimensions
target_rank = int(0.4 * min(20, 15)) # min(20,15) = 15, so 0.4*15 = 6
assert U.shape == (20, target_rank), f"Expected U shape (20, {target_rank}), got {U.shape}"
assert S.shape == (target_rank,), f"Expected S shape ({target_rank},), got {S.shape}"
assert V.shape == (target_rank, 15), f"Expected V shape ({target_rank}, 15), got {V.shape}"
# Check parameter reduction
compressed_params = U.size + S.size + V.size
compression_ratio = compressed_params / original_params
assert compression_ratio < 1.0, f"Should compress, but ratio is {compression_ratio}"
# Check reconstruction quality
reconstructed = U @ np.diag(S) @ V
reconstruction_error = np.linalg.norm(original_weight - reconstructed)
relative_error = reconstruction_error / np.linalg.norm(original_weight)
# Low-rank approximation trades accuracy for compression - error is expected
assert relative_error < 0.7, f"Reconstruction error too high: {relative_error}"
print("✅ low_rank_approximate works correctly!")
if __name__ == "__main__":
test_unit_low_rank_approximate()
# %% [markdown]
"""
## 7. Knowledge Distillation: Learning from Teacher Models
Knowledge distillation is like having an expert teacher simplify complex concepts for a student. The large "teacher" model shares its knowledge with a smaller "student" model, achieving similar performance with far fewer parameters.
### The Teacher-Student Learning Process
Unlike traditional training where models learn from hard labels (cat/dog), knowledge distillation uses "soft" targets that contain richer information about the teacher's decision-making process.
```
Knowledge Distillation Process:
TEACHER MODEL (Large)
┌─────────────────────┐
Input Data ────────→│ 100M parameters │
│ 95% accuracy │
│ 500ms inference │
└─────────────────────┘
↓ Soft Targets
┌─────────────────────┐
│ Logits: [2.1, 0.3, │
│ 0.8, 4.2] │ ← Rich information
└─────────────────────┘
↓ Distillation Loss
┌─────────────────────┐
Input Data ────────→│ STUDENT MODEL │
Hard Labels ───────→│ 10M parameters │ ← 10x smaller
│ 93% accuracy │ ← 2% loss
│ 50ms inference │ ← 10x faster
└─────────────────────┘
Benefits:
• Size: 10x smaller models
• Speed: 10x faster inference
• Accuracy: Only 2-5% degradation
• Knowledge transfer: Student learns teacher's "reasoning"
```
### Temperature Scaling: Softening Decisions
Temperature scaling is a key innovation that makes knowledge distillation effective. It "softens" the teacher's confidence, revealing uncertainty that helps the student learn.
```
Temperature Effect on Probability Distributions:
Without Temperature (T=1): With Temperature (T=3):
Teacher Logits: [1.0, 2.0, 0.5] Teacher Logits: [1.0, 2.0, 0.5]
↓ ↓ ÷ 3
Softmax: [0.09, 0.67, 0.24] Logits/T: [0.33, 0.67, 0.17]
^ ^ ^ ↓
Low High Med Softmax: [0.21, 0.42, 0.17]
^ ^ ^
Sharp decisions (hard to learn) Soft decisions (easier to learn)
Why Soft Targets Help:
1. Reveal teacher's uncertainty about similar classes
2. Provide richer gradients for student learning
3. Transfer knowledge about class relationships
4. Reduce overfitting to hard labels
```
### Loss Function Design
The distillation loss balances learning from both the teacher's soft knowledge and the ground truth hard labels:
```
Combined Loss Function:
L_total = α × L_soft + (1-α) × L_hard
Where:
L_soft = KL_divergence(Student_soft, Teacher_soft)
└─ Measures how well student mimics teacher
L_hard = CrossEntropy(Student_predictions, True_labels)
└─ Ensures student still learns correct answers
Balance Parameter α:
α = 0.7: Focus mainly on teacher (typical)
α = 0.9: Almost pure distillation
α = 0.3: Balance teacher and ground truth
α = 0.0: Ignore teacher (regular training)
Temperature T:
• T = 1: No softening (standard softmax)
• T = 3-5: Good balance (typical range)
• T = 10+: Very soft (may lose information)
```
"""
# %% nbgrader={"grade": false, "grade_id": "distillation", "solution": true, "schema_version": 3}
#| export
class KnowledgeDistillation:
"""
Knowledge distillation for model compression.
Train a smaller student model to mimic a larger teacher model.
"""
def __init__(self, teacher_model, student_model, temperature=3.0, alpha=0.7):
"""
Initialize knowledge distillation.
TODO: Set up teacher and student models with distillation parameters
APPROACH:
1. Store teacher and student models
2. Set temperature for softening probability distributions
3. Set alpha for balancing hard vs soft targets
EXAMPLE:
>>> # Create teacher with more capacity (explicit layers)
>>> teacher_l1 = Linear(100, 200)
>>> teacher_l2 = Linear(200, 50)
>>> teacher = SimpleModel(teacher_l1, teacher_l2)
>>>
>>> # Create smaller student (explicit layer)
>>> student = SimpleModel(Linear(100, 50))
>>>
>>> kd = KnowledgeDistillation(teacher, student, temperature=4.0, alpha=0.8)
>>> print(f"Temperature: {kd.temperature}, Alpha: {kd.alpha}")
Temperature: 4.0, Alpha: 0.8
HINTS:
- Simply assign the parameters to instance variables
- Temperature typically ranges from 3-5 for effective softening
- Alpha of 0.7 means 70% soft targets, 30% hard targets
Args:
teacher_model: Large, pre-trained model
student_model: Smaller model to train
temperature: Softening parameter for distributions
alpha: Weight for soft target loss (1-alpha for hard targets)
"""
### BEGIN SOLUTION
self.teacher_model = teacher_model
self.student_model = student_model
self.temperature = temperature
self.alpha = alpha
### END SOLUTION
def distillation_loss(self, student_logits, teacher_logits, true_labels):
"""
Calculate combined distillation loss.
TODO: Implement knowledge distillation loss function
APPROACH:
1. Calculate hard target loss (student vs true labels)
2. Calculate soft target loss (student vs teacher, with temperature)
3. Combine losses: alpha * soft_loss + (1-alpha) * hard_loss
EXAMPLE:
>>> kd = KnowledgeDistillation(teacher, student)
>>> loss = kd.distillation_loss(student_out, teacher_out, labels)
>>> print(f"Distillation loss: {loss:.4f}")
HINTS:
- Use temperature to soften distributions: logits/temperature
- Soft targets use KL divergence or cross-entropy
- Hard targets use standard classification loss
"""
### BEGIN SOLUTION
# Extract numpy arrays from Tensors
# student_logits and teacher_logits are always Tensors from forward passes
student_logits = student_logits.data
teacher_logits = teacher_logits.data
# true_labels might be numpy array or Tensor
if isinstance(true_labels, Tensor):
true_labels = true_labels.data
# Soften distributions with temperature
student_soft = self._softmax(student_logits / self.temperature)
teacher_soft = self._softmax(teacher_logits / self.temperature)
# Soft target loss (KL divergence)
soft_loss = self._kl_divergence(student_soft, teacher_soft)
# Hard target loss (cross-entropy)
student_hard = self._softmax(student_logits)
hard_loss = self._cross_entropy(student_hard, true_labels)
# Combined loss
total_loss = self.alpha * soft_loss + (1 - self.alpha) * hard_loss
return total_loss
### END SOLUTION
def _softmax(self, logits):
"""Compute softmax with numerical stability."""
exp_logits = np.exp(logits - np.max(logits, axis=-1, keepdims=True))
return exp_logits / np.sum(exp_logits, axis=-1, keepdims=True)
def _kl_divergence(self, p, q):
"""Compute KL divergence between distributions."""
return np.sum(p * np.log(p / (q + 1e-8) + 1e-8))
def _cross_entropy(self, predictions, labels):
"""Compute cross-entropy loss."""
# Simple implementation for integer labels
if labels.ndim == 1:
return -np.mean(np.log(predictions[np.arange(len(labels)), labels] + 1e-8))
else:
return -np.mean(np.sum(labels * np.log(predictions + 1e-8), axis=1))
# %% nbgrader={"grade": true, "grade_id": "test-distillation", "locked": true, "points": 15, "solution": false, "schema_version": 3}
def test_unit_knowledge_distillation():
"""🔬 Test knowledge distillation functionality."""
print("🔬 Unit Test: Knowledge Distillation...")
# Create teacher model with more capacity - explicit composition
teacher_l1 = Linear(10, 20)
teacher_l2 = Linear(20, 5)
teacher = SimpleModel(teacher_l1, teacher_l2)
# Create smaller student model - explicit composition shows size difference
student_l1 = Linear(10, 5)
student = SimpleModel(student_l1) # Direct connection, no hidden layer
# Initialize knowledge distillation with temperature scaling
kd = KnowledgeDistillation(teacher, student, temperature=3.0, alpha=0.7)
# Create dummy data for testing
input_data = Tensor(np.random.randn(8, 10)) # Batch of 8 samples
true_labels = np.array([0, 1, 2, 3, 4, 0, 1, 2]) # Class labels
# Forward passes - students see explicit data flow through each model
teacher_output = teacher.forward(input_data) # Large model predictions
student_output = student.forward(input_data) # Small model predictions
# Calculate distillation loss - combines soft and hard targets
loss = kd.distillation_loss(student_output, teacher_output, true_labels)
# Verify loss is reasonable
assert isinstance(loss, (float, np.floating)), f"Loss should be float, got {type(loss)}"
assert loss > 0, f"Loss should be positive, got {loss}"
assert not np.isnan(loss), "Loss should not be NaN"
print("✅ knowledge_distillation works correctly!")
if __name__ == "__main__":
test_unit_knowledge_distillation()
# %% [markdown]
"""
## 8. Integration: Complete Compression Pipeline
Now let's combine all our compression techniques into a unified system that can apply multiple methods and track their cumulative effects.
### Compression Strategy Design
Real-world compression often combines multiple techniques in sequence, each targeting different types of redundancy:
```
Multi-Stage Compression Pipeline:
Original Model (100MB, 100% accuracy)
↓ Stage 1: Magnitude Pruning (remove 80% of small weights)
Sparse Model (20MB, 98% accuracy)
↓ Stage 2: Structured Pruning (remove 30% of channels)
Compact Model (14MB, 96% accuracy)
↓ Stage 3: Low-Rank Approximation (compress large layers)
Factorized Model (10MB, 95% accuracy)
↓ Stage 4: Knowledge Distillation (train smaller architecture)
Student Model (5MB, 93% accuracy)
Final Result: 20x size reduction, 7% accuracy loss
```
### Compression Configuration
Different deployment scenarios require different compression strategies:
```
Deployment Scenarios and Strategies:
MOBILE APP (Aggressive compression needed):
┌─────────────────────────────────────────┐
│ Target: <10MB, <100ms inference │
│ Strategy: │
│ • Magnitude pruning: 95% sparsity │
│ • Structured pruning: 50% channels │
│ • Knowledge distillation: 10x reduction │
│ • Quantization: 8-bit weights │
└─────────────────────────────────────────┘
EDGE DEVICE (Balanced compression):
┌─────────────────────────────────────────┐
│ Target: <50MB, <200ms inference │
│ Strategy: │
│ • Magnitude pruning: 80% sparsity │
│ • Structured pruning: 30% channels │
│ • Low-rank: 50% rank reduction │
│ • Quantization: 16-bit weights │
└─────────────────────────────────────────┘
CLOUD SERVICE (Minimal compression):
┌─────────────────────────────────────────┐
│ Target: Maintain accuracy, reduce cost │
│ Strategy: │
│ • Magnitude pruning: 50% sparsity │
│ • Structured pruning: 10% channels │
│ • Dynamic batching optimization │
│ • Mixed precision inference │
└─────────────────────────────────────────┘
```
"""
# %% nbgrader={"grade": false, "grade_id": "compress-model-comprehensive", "solution": true, "schema_version": 3}
def compress_model(model, compression_config):
"""
Apply comprehensive model compression based on configuration.
TODO: Implement complete compression pipeline
APPROACH:
1. Apply magnitude pruning if specified
2. Apply structured pruning if specified
3. Apply low-rank approximation if specified
4. Return compression statistics
EXAMPLE:
>>> config = {
... 'magnitude_prune': 0.8,
... 'structured_prune': 0.3,
... 'low_rank': 0.5
... }
>>> stats = compress_model(model, config)
>>> print(f"Final sparsity: {stats['sparsity']:.1f}%")
Final sparsity: 85.0%
HINT: Apply techniques sequentially and measure results
"""
### BEGIN SOLUTION
original_params = sum(p.size for p in model.parameters())
original_sparsity = measure_sparsity(model)
stats = {
'original_params': original_params,
'original_sparsity': original_sparsity,
'applied_techniques': []
}
# Apply magnitude pruning
if 'magnitude_prune' in compression_config:
sparsity = compression_config['magnitude_prune']
magnitude_prune(model, sparsity=sparsity)
stats['applied_techniques'].append(f'magnitude_prune_{sparsity}')
# Apply structured pruning
if 'structured_prune' in compression_config:
ratio = compression_config['structured_prune']
structured_prune(model, prune_ratio=ratio)
stats['applied_techniques'].append(f'structured_prune_{ratio}')
# Apply low-rank approximation (conceptually - would need architecture changes)
if 'low_rank' in compression_config:
ratio = compression_config['low_rank']
# For demo, we'll just record that it would be applied
stats['applied_techniques'].append(f'low_rank_{ratio}')
# Final measurements
final_sparsity = measure_sparsity(model)
stats['final_sparsity'] = final_sparsity
stats['sparsity_increase'] = final_sparsity - original_sparsity
return stats
### END SOLUTION
# %% nbgrader={"grade": true, "grade_id": "test-compression-integration", "locked": true, "points": 20, "solution": false, "schema_version": 3}
def test_unit_compress_model():
"""🔬 Test comprehensive model compression."""
print("🔬 Unit Test: Compress Model...")
# Create test model with explicit layers - students see the full architecture
layer1 = Linear(20, 15)
layer2 = Linear(15, 10)
layer3 = Linear(10, 5)
model = SimpleModel(layer1, layer2, layer3)
# Define compression configuration
# Students understand what each technique does
config = {
'magnitude_prune': 0.7, # Remove 70% of smallest weights
'structured_prune': 0.2 # Remove 20% of least important channels
}
# Apply compression pipeline - multiple techniques sequentially
stats = compress_model(model, config)
# Verify statistics - students understand what was measured
assert 'original_params' in stats, "Should track original parameter count"
assert 'final_sparsity' in stats, "Should track final sparsity"
assert 'applied_techniques' in stats, "Should track applied techniques"
# Verify compression was applied successfully
assert stats['final_sparsity'] > stats['original_sparsity'], "Sparsity should increase"
assert len(stats['applied_techniques']) == 2, "Should apply both techniques"
# Verify model still has reasonable structure after compression
remaining_params = sum(np.count_nonzero(p.data) for p in model.parameters())
assert remaining_params > 0, "Model should retain some parameters"
print("✅ compress_model works correctly!")
if __name__ == "__main__":
test_unit_compress_model()
# %% [markdown]
"""
## 5. Verification: Proving Pruning Works
Before analyzing compression in production, let's verify that our pruning actually achieves sparsity using real measurements.
"""
# %% nbgrader={"grade": false, "grade_id": "verify_pruning", "solution": false}
def verify_pruning_works(model, target_sparsity=0.8):
"""
Verify pruning actually creates zeros using real zero-counting.
This is NOT a theoretical calculation - we count actual zero values
in parameter arrays and honestly report memory footprint (unchanged with dense storage).
Args:
model: Model with pruned parameters
target_sparsity: Expected sparsity ratio (default 0.8 = 80%)
Returns:
dict: Verification results with sparsity, zeros, total, verified
Example:
>>> model = SimpleModel(Linear(100, 50))
>>> magnitude_prune(model, sparsity=0.8)
>>> results = verify_pruning_works(model, target_sparsity=0.8)
>>> assert results['verified'] # Pruning actually works!
"""
print("🔬 Verifying pruning sparsity with actual zero-counting...")
# Count actual zeros in model parameters
zeros = sum(np.sum(p.data == 0) for p in model.parameters())
total = sum(p.data.size for p in model.parameters())
sparsity = zeros / total
memory_bytes = sum(p.data.nbytes for p in model.parameters())
# Display results
print(f" Total parameters: {total:,}")
print(f" Zero parameters: {zeros:,}")
print(f" Active parameters: {total - zeros:,}")
print(f" Sparsity achieved: {sparsity*100:.1f}%")
print(f" Memory footprint: {memory_bytes / MB_TO_BYTES:.2f} MB (unchanged - dense storage)")
# Verify target met (allow 15% tolerance for structured pruning variations)
verified = abs(sparsity - target_sparsity) < 0.15
status = '' if verified else ''
print(f" {status} Meets {target_sparsity*100:.0f}% sparsity target")
assert verified, f"Sparsity target not met: {sparsity:.2f} vs {target_sparsity:.2f}"
print(f"\n✅ VERIFIED: {sparsity*100:.1f}% sparsity achieved")
print(f"⚠️ Memory saved: 0 MB (dense numpy arrays)")
print(f"💡 LEARNING: Compute savings ~{sparsity*100:.1f}% (skip zero multiplications)")
print(f" In production: Use sparse formats (scipy.sparse.csr_matrix) for memory savings")
return {
'sparsity': sparsity,
'zeros': zeros,
'total': total,
'active': total - zeros,
'memory_mb': memory_bytes / MB_TO_BYTES,
'verified': verified
}
# Run verification example when developing
if __name__ == "__main__":
# Create and prune test model
test_model = SimpleModel(Linear(100, 50), Linear(50, 25))
magnitude_prune(test_model, sparsity=0.8)
verify_pruning_works(test_model, target_sparsity=0.8)
# %% [markdown]
"""
## 6. Systems Analysis: Compression Techniques
Understanding the real-world effectiveness of different compression techniques through systematic measurement and comparison.
### Accuracy vs Compression Trade-offs
The fundamental challenge in model compression is balancing three competing objectives: model size, inference speed, and prediction accuracy.
"""
# %% [markdown]
"""
## 8.5 Measuring Compression Impact with Profiler
Now let's use the **Profiler** tool from Module 14 to measure the actual parameter reduction from pruning. This demonstrates the complete workflow: profile baseline (M14) → apply compression (M16) → measure impact (M14+M16).
This is the production workflow: measure → prune → validate → deploy.
"""
# %% nbgrader={"grade": false, "grade_id": "demo-profiler-compression", "solution": true}
# Import Profiler from Module 14 (already imported above)
def demo_compression_with_profiler():
"""📊 Demonstrate parameter reduction using Profiler from Module 14."""
print("📊 Measuring Compression Impact with Profiler")
print("=" * 70)
profiler = Profiler()
# Create a simple model (Linear already imported above)
model = Linear(512, 256)
model.name = "baseline_model"
print("\n🏋️ BEFORE: Dense Model")
print("-" * 70)
# Measure baseline
param_count_before = profiler.count_parameters(model)
sparsity_before = measure_sparsity(model)
input_shape = (32, 512)
memory_before = profiler.measure_memory(model, input_shape)
print(f" Parameters: {param_count_before:,}")
print(f" Sparsity: {sparsity_before*100:.1f}% (zeros)")
print(f" Memory: {memory_before['parameter_memory_mb']:.2f} MB")
print(f" Active parameters: {int(param_count_before * (1 - sparsity_before)):,}")
# Apply magnitude pruning
target_sparsity = 0.7 # Remove 70% of parameters
print(f"\n✂️ Applying {target_sparsity*100:.0f}% Magnitude Pruning...")
pruned_model = magnitude_prune(model, sparsity=target_sparsity)
pruned_model.name = "pruned_model"
print("\n🪶 AFTER: Pruned Model")
print("-" * 70)
# Measure after pruning
param_count_after = profiler.count_parameters(pruned_model)
sparsity_after = measure_sparsity(pruned_model)
memory_after = profiler.measure_memory(pruned_model, input_shape)
print(f" Parameters: {param_count_after:,} (same, but many are zero)")
print(f" Sparsity: {sparsity_after*100:.1f}% (zeros)")
print(f" Memory: {memory_after['parameter_memory_mb']:.2f} MB (same storage)")
print(f" Active parameters: {int(param_count_after * (1 - sparsity_after)):,}")
print("\n📈 COMPRESSION RESULTS")
print("=" * 70)
sparsity_gain = (sparsity_after - sparsity_before) * 100
active_before = int(param_count_before * (1 - sparsity_before))
active_after = int(param_count_after * (1 - sparsity_after))
reduction_ratio = active_before / active_after if active_after > 0 else 1
params_removed = active_before - active_after
print(f" Sparsity increased: {sparsity_before*100:.1f}% → {sparsity_after*100:.1f}%")
print(f" Active params reduced: {active_before:,}{active_after:,}")
print(f" Parameters removed: {params_removed:,} ({sparsity_gain:.1f}% of total)")
print(f" Compression ratio: {reduction_ratio:.1f}x fewer active parameters")
print("\n💡 Key Insight:")
print(f" Magnitude pruning removes {sparsity_gain:.0f}% of parameters")
print(f" With sparse storage formats, this means {reduction_ratio:.1f}x less memory!")
print(f" Critical for: edge devices, mobile apps, energy efficiency")
print("\n✅ This is the power of compression: remove what doesn't matter!")
demo_compression_with_profiler()
# %% [markdown]
"""
## 8.6 Systems Analysis - Compression Techniques
Understanding the real-world effectiveness of different compression techniques.
"""
# %%
def analyze_compression_techniques():
"""📊 Compare compression ratios across different techniques."""
print("📊 Analyzing Compression Techniques")
print("=" * 60)
# Create baseline model (Linear already imported above)
model_configs = [
("Small MLP", [Linear(128, 64), Linear(64, 32)]),
("Medium MLP", [Linear(512, 256), Linear(256, 128)]),
("Large MLP", [Linear(1024, 512), Linear(512, 256)])
]
print(f"\n{'Model':<15} {'Technique':<20} {'Sparsity':<12} {'Compression':<12}")
print("-" * 60)
for model_name, layers in model_configs:
# Create model with explicit composition
model = SimpleModel(*layers)
baseline_params = sum(p.size for p in model.parameters())
# Test magnitude pruning on copy of model
# Create fresh layers for magnitude pruning test
mag_layers = [Linear(l.weight.shape[0], l.weight.shape[1]) for l in layers]
for i, layer in enumerate(mag_layers):
layer.weight = layers[i].weight
# Linear layers always have bias (may be None)
layer.bias = layers[i].bias
mag_model = SimpleModel(*mag_layers)
magnitude_prune(mag_model, sparsity=0.8)
mag_sparsity = measure_sparsity(mag_model)
mag_ratio = 1.0 / (1.0 - mag_sparsity / 100) if mag_sparsity < 100 else float('inf')
print(f"{model_name:<15} {'Magnitude (80%)':<20} {mag_sparsity:>10.1f}% {mag_ratio:>10.1f}x")
# Test structured pruning on separate copy
# Create fresh layers for structured pruning test
struct_layers = [Linear(l.weight.shape[0], l.weight.shape[1]) for l in layers]
for i, layer in enumerate(struct_layers):
layer.weight = layers[i].weight
# Linear layers always have bias (may be None)
layer.bias = layers[i].bias
struct_model = SimpleModel(*struct_layers)
structured_prune(struct_model, prune_ratio=0.5)
struct_sparsity = measure_sparsity(struct_model)
struct_ratio = 1.0 / (1.0 - struct_sparsity / 100) if struct_sparsity < 100 else float('inf')
print(f"{'':<15} {'Structured (50%)':<20} {struct_sparsity:>10.1f}% {struct_ratio:>10.1f}x")
print()
print("💡 Key Insights:")
print(" • Magnitude pruning achieves higher sparsity (80%+)")
print(" • Structured pruning creates hardware-friendly patterns")
print(" • Larger models compress more effectively")
print(" • Compression ratio = 1 / (1 - sparsity)")
analyze_compression_techniques()
# %% [markdown]
"""
### Knowledge Distillation Analysis
Now let's analyze how knowledge distillation compares to other compression techniques for different compression ratios and accuracy preservation goals.
"""
# %%
def analyze_distillation_effectiveness():
"""📊 Analyze knowledge distillation compression and accuracy trade-offs."""
print("\n📊 Analyzing Knowledge Distillation Effectiveness")
print("=" * 60)
# Simulate teacher-student scenarios
scenarios = [
("Large→Small", 100_000, 10_000, 0.95, 0.90, 10.0),
("Medium→Tiny", 50_000, 5_000, 0.92, 0.87, 10.0),
("Small→Micro", 10_000, 1_000, 0.88, 0.83, 10.0),
]
print(f"\n{'Scenario':<15} {'Teacher':<12} {'Student':<12} {'Ratio':<10} {'Acc Loss':<10}")
print("-" * 60)
for name, teacher_params, student_params, teacher_acc, student_acc, compression in scenarios:
acc_retention = (student_acc / teacher_acc) * 100
acc_loss = teacher_acc - student_acc
print(f"{name:<15} {teacher_params:>10,}p {student_params:>10,}p {compression:>8.1f}x {acc_loss*100:>8.1f}%")
print("\n💡 Knowledge Distillation Insights:")
print(" • Achieves 10x+ compression with 5-10% accuracy loss")
print(" • Student learns teacher's 'soft' predictions")
print(" • More effective than naive pruning for large reductions")
print(" • Requires retraining (unlike pruning/quantization)")
print("\n🚀 Best Use Case:")
print(" Deploy small student models on edge devices")
print(" Train expensive teacher once, distill many students")
analyze_distillation_effectiveness()
# %% [markdown]
"""
## 9. Module Integration Test
Final validation that all compression techniques work together correctly.
"""
# %%
def test_module():
"""🧪 Module Test: Complete Integration
Comprehensive test of entire compression module functionality.
This final test runs before module summary to ensure:
- All unit tests pass
- Functions work together correctly
- Module is ready for integration with TinyTorch
"""
print("🧪 RUNNING MODULE INTEGRATION TEST")
print("=" * 50)
# Run all unit tests
print("Running unit tests...")
test_unit_measure_sparsity()
test_unit_magnitude_prune()
test_unit_structured_prune()
test_unit_low_rank_approximate()
test_unit_knowledge_distillation()
test_unit_compress_model()
print("\nRunning integration scenarios...")
# Test 1: Complete compression pipeline
print("🔬 Integration Test: Complete compression pipeline...")
# Create a realistic model with explicit layers - students see the architecture
input_layer = Linear(784, 512) # Input layer (like MNIST)
hidden1 = Linear(512, 256) # Hidden layer 1
hidden2 = Linear(256, 128) # Hidden layer 2
output_layer = Linear(128, 10) # Output layer
model = SimpleModel(input_layer, hidden1, hidden2, output_layer)
original_params = sum(p.size for p in model.parameters())
print(f"Original model: {original_params:,} parameters")
# Apply comprehensive compression - students see each technique
compression_config = {
'magnitude_prune': 0.8, # Remove 80% of smallest weights
'structured_prune': 0.3 # Remove 30% of channels
}
stats = compress_model(model, compression_config)
final_sparsity = measure_sparsity(model)
# Validate compression results
assert final_sparsity > 70, f"Expected >70% sparsity, got {final_sparsity:.1f}%"
assert stats['sparsity_increase'] > 70, "Should achieve significant compression"
assert len(stats['applied_techniques']) == 2, "Should apply both techniques"
print(f"✅ Achieved {final_sparsity:.1f}% sparsity with {len(stats['applied_techniques'])} techniques")
# Test 2: Knowledge distillation setup
print("🔬 Integration Test: Knowledge distillation...")
# Create teacher with more capacity - explicit layers show architecture
teacher_l1 = Linear(100, 200)
teacher_l2 = Linear(200, 50)
teacher = SimpleModel(teacher_l1, teacher_l2)
# Create smaller student - explicit shows size difference
student_l1 = Linear(100, 50)
student = SimpleModel(student_l1) # 3x fewer parameters
kd = KnowledgeDistillation(teacher, student, temperature=4.0, alpha=0.8)
# Verify setup
teacher_params = sum(p.size for p in teacher.parameters())
student_params = sum(p.size for p in student.parameters())
compression_ratio = student_params / teacher_params
assert compression_ratio < 0.5, f"Student should be <50% of teacher size, got {compression_ratio:.2f}"
assert kd.temperature == 4.0, "Temperature should be set correctly"
assert kd.alpha == 0.8, "Alpha should be set correctly"
print(f"✅ Knowledge distillation: {compression_ratio:.2f}x size reduction")
# Test 3: Low-rank approximation
print("🔬 Integration Test: Low-rank approximation...")
large_matrix = np.random.randn(200, 150)
U, S, V = low_rank_approximate(large_matrix, rank_ratio=0.3)
original_size = large_matrix.size
compressed_size = U.size + S.size + V.size
compression_ratio = compressed_size / original_size
assert compression_ratio < 0.7, f"Should achieve compression, got ratio {compression_ratio:.2f}"
# Test reconstruction
reconstructed = U @ np.diag(S) @ V
error = np.linalg.norm(large_matrix - reconstructed) / np.linalg.norm(large_matrix)
# Low-rank approximation trades accuracy for compression - some error is expected
assert error < 0.7, f"Reconstruction error too high: {error:.3f}"
print(f"✅ Low-rank: {compression_ratio:.2f}x compression, {error:.3f} error")
# Verify pruning actually works
print()
target_sparsity = compression_config['magnitude_prune']
verification_results = verify_pruning_works(model, target_sparsity=target_sparsity)
print("\n" + "=" * 50)
print("🎉 ALL TESTS PASSED! Module ready for export.")
print("📈 Compression system provides:")
print(f"{verification_results['sparsity']*100:.1f}% sparsity")
print(f" • ✓ VERIFIED: {verification_results['zeros']:,} actual zeros counted")
print(f" • Honest: Dense storage = no memory savings (educational limitation)")
print("Run: tito module complete 16")
# Call the integration test
test_module()
# %%
if __name__ == "__main__":
print("🚀 Running Compression module...")
test_module()
print("✅ Module validation complete!")
# %% [markdown]
"""
## 🏁 Consolidated Compression Classes for Export
Now that we've implemented all compression techniques, let's create a consolidated class
for export to the tinytorch package. This allows milestones to use the complete compression system.
"""
# %% nbgrader={"grade": false, "grade_id": "compression_export", "solution": false}
#| export
class CompressionComplete:
"""
Complete compression system for milestone use.
Provides pruning, distillation, and low-rank approximation techniques.
"""
@staticmethod
def measure_sparsity(model) -> float:
"""Measure the sparsity of a model (fraction of zero weights)."""
# SimpleModel has .layers, each layer has .parameters() method
total_params = 0
zero_params = 0
for layer in model.layers:
for param in layer.parameters():
total_params += param.size
zero_params += np.sum(param.data == 0)
return zero_params / total_params if total_params > 0 else 0.0
@staticmethod
def magnitude_prune(model, sparsity=0.5):
"""
Prune model weights by magnitude (smallest weights set to zero).
Args:
model: SimpleModel with .layers attribute
sparsity: Fraction of weights to prune (0-1)
"""
# SimpleModel has .layers, each layer has .parameters() method
for layer in model.layers:
for param in layer.parameters():
threshold = np.percentile(np.abs(param.data), sparsity * 100)
param.data[np.abs(param.data) < threshold] = 0
return model
@staticmethod
def structured_prune(model, prune_ratio=0.5):
"""
Prune entire neurons/channels (structured pruning).
Args:
model: SimpleModel with .layers attribute
prune_ratio: Fraction of structures to prune (0-1)
"""
# SimpleModel has .layers, process Linear layers
for layer in model.layers:
if isinstance(layer, Linear):
# Linear layers have .weight attribute with .data
weight = layer.weight
if len(weight.shape) == 2: # Linear layer
# Prune output neurons
neuron_norms = np.linalg.norm(weight.data, axis=0)
threshold = np.percentile(neuron_norms, prune_ratio * 100)
mask = neuron_norms >= threshold
weight.data[:, ~mask] = 0
return model
@staticmethod
def compress_model(model, compression_config: Dict[str, Any]):
"""
Apply complete compression pipeline to a model.
Args:
model: Model to compress
compression_config: Dictionary with compression settings
- 'magnitude_sparsity': float (0-1)
- 'structured_prune_ratio': float (0-1)
Returns:
Compressed model with sparsity stats
"""
stats = {
'original_sparsity': CompressionComplete.measure_sparsity(model)
}
# Apply magnitude pruning
if 'magnitude_sparsity' in compression_config:
model = CompressionComplete.magnitude_prune(
model, compression_config['magnitude_sparsity']
)
# Apply structured pruning
if 'structured_prune_ratio' in compression_config:
model = CompressionComplete.structured_prune(
model, compression_config['structured_prune_ratio']
)
stats['final_sparsity'] = CompressionComplete.measure_sparsity(model)
stats['compression_ratio'] = 1.0 / (1.0 - stats['final_sparsity']) if stats['final_sparsity'] < 1.0 else float('inf')
return model, stats
# Convenience functions for backward compatibility
def measure_sparsity(model) -> float:
"""Measure model sparsity."""
return CompressionComplete.measure_sparsity(model)
def magnitude_prune(model, sparsity=0.5):
"""Apply magnitude-based pruning."""
return CompressionComplete.magnitude_prune(model, sparsity)
def structured_prune(model, prune_ratio=0.5):
"""Apply structured pruning."""
return CompressionComplete.structured_prune(model, prune_ratio)
def compress_model(model, compression_config: Dict[str, Any]):
"""Apply complete compression pipeline."""
return CompressionComplete.compress_model(model, compression_config)
# %% [markdown]
"""
## 🤔 ML Systems Thinking: Compression Foundations
### Question 1: Compression Trade-offs
You implemented magnitude pruning that removes 90% of weights from a 10M parameter model.
- How many parameters remain active? _____ M parameters
- If the original model was 40MB, what's the theoretical minimum storage? _____ MB
- Why might actual speedup be less than 10x? _____________
### Question 2: Structured vs Unstructured Sparsity
Your structured pruning removes entire channels, while magnitude pruning creates scattered zeros.
- Which enables better hardware acceleration? _____________
- Which preserves accuracy better at high sparsity? _____________
- Which creates more predictable memory access patterns? _____________
### Question 3: Knowledge Distillation Efficiency
A teacher model has 100M parameters, student has 10M parameters, both achieve 85% accuracy.
- What's the compression ratio? _____x
- If teacher inference takes 100ms, student takes 15ms, what's the speedup? _____x
- Why is the speedup greater than the compression ratio? _____________
### Question 4: Low-Rank Decomposition
You approximate a (512, 256) weight matrix with rank 64 using SVD.
- Original parameter count: _____ parameters
- Decomposed parameter count: _____ parameters
- Compression ratio: _____x
- At what rank does compression become ineffective? rank > _____
### Question 5: Pruning Strategy Selection
For deploying on a mobile device with 50MB model limit and 100ms latency requirement:
- Which pruning strategy optimizes for memory? [magnitude/structured/both]
- Which pruning strategy optimizes for speed? [magnitude/structured/both]
- What order should you apply compression techniques? _____________
"""
# %% [markdown]
"""
## 🎯 MODULE SUMMARY: Compression
Congratulations! You've built a comprehensive model compression system that can dramatically reduce model size while preserving intelligence!
### Key Accomplishments
- Built magnitude-based and structured pruning techniques with clear sparsity patterns
- Implemented knowledge distillation for teacher-student compression with temperature scaling
- Created low-rank approximation using SVD decomposition for matrix factorization
- Developed sparsity measurement and comprehensive compression pipeline
- Analyzed compression trade-offs between size, speed, and accuracy with real measurements
- All tests pass ✅ (validated by `test_module()`)
### Systems Insights Gained
- **Structured vs Unstructured**: Hardware-friendly sparsity patterns vs maximum compression ratios
- **Compression Cascading**: Multiple techniques compound benefits but require careful sequencing
- **Accuracy Preservation**: Knowledge distillation maintains performance better than pruning alone
- **Memory vs Speed**: Parameter reduction doesn't guarantee proportional speedup without sparse libraries
- **Deployment Strategy**: Different scenarios (mobile, edge, cloud) require different compression approaches
### Technical Mastery
- **Sparsity Measurement**: Calculate and track zero weight percentages across models
- **Magnitude Pruning**: Global thresholding based on weight importance ranking
- **Structured Pruning**: Channel-wise removal using L2 norm importance metrics
- **Knowledge Distillation**: Teacher-student training with temperature-scaled soft targets
- **Low-Rank Approximation**: SVD-based matrix factorization for parameter reduction
- **Pipeline Integration**: Sequential application of multiple compression techniques
### Ready for Next Steps
Your compression implementation enables efficient model deployment across diverse hardware constraints!
Export with: `tito module complete 18`
**Next**: Module 19 will add comprehensive benchmarking to evaluate all optimization techniques together, measuring the cumulative effects of quantization, acceleration, and compression!
"""