mirror of
https://github.com/MLSysBook/TinyTorch.git
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3dfaca0f19
- Added Section 8.5: Measuring Compression Impact with Profiler - Demonstrates 70% magnitude pruning parameter reduction - Shows sparsity measurements and active parameter counts - Uses Profiler from Module 15 for measurements - Educates students on compression workflow: measure prune validate deploy
1544 lines
60 KiB
Python
1544 lines
60 KiB
Python
# ---
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# jupyter:
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# extension: .py
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# format_version: '1.3'
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# language: python
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# name: python3
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# ---
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# %% [markdown]
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"""
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# Module 18: Compression - Making Models Smaller
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Welcome to Module 18! You're about to build model compression techniques that make neural networks smaller and more efficient while preserving their intelligence.
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## 🔗 Prerequisites & Progress
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**You've Built**: Full TinyGPT pipeline with profiling, acceleration, and quantization
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**You'll Build**: Pruning (magnitude & structured), knowledge distillation, and low-rank approximation
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**You'll Enable**: Compressed models that maintain accuracy while using dramatically less storage and memory
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**Connection Map**:
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```
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Quantization → Compression → Benchmarking
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(precision) (sparsity) (evaluation)
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```
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## Learning Objectives
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By the end of this module, you will:
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1. Implement magnitude-based and structured pruning
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2. Build knowledge distillation for model compression
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3. Create low-rank approximations of weight matrices
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4. Measure compression ratios and sparsity levels
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5. Understand structured vs unstructured sparsity trade-offs
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Let's get started!
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## 📦 Where This Code Lives in the Final Package
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**Learning Side:** You work in `modules/18_compression/compression_dev.py`
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**Building Side:** Code exports to `tinytorch.optimization.compression`
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```python
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# How to use this module:
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from tinytorch.optimization.compression import magnitude_prune, structured_prune, measure_sparsity
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```
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**Why this matters:**
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- **Learning:** Complete compression system in one focused module for deep understanding
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- **Production:** Proper organization like real compression libraries with all techniques together
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- **Consistency:** All compression operations and sparsity management in optimization.compression
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- **Integration:** Works seamlessly with models and quantization for complete optimization pipeline
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"""
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# %% nbgrader={"grade": false, "grade_id": "imports", "solution": true}
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#| default_exp optimization.compression
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#| export
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import numpy as np
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import copy
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from typing import List, Dict, Any, Tuple, Optional
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import time
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# Import from TinyTorch modules
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from tinytorch.core.tensor import Tensor
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from tinytorch.core.layers import Linear
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# Sequential container for model compression
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class Sequential:
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"""Sequential container for compression (not exported from core layers)."""
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def __init__(self, *layers):
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self.layers = list(layers)
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def forward(self, x):
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for layer in self.layers:
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x = layer.forward(x) if hasattr(layer, 'forward') else layer(x)
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return x
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def __call__(self, x):
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return self.forward(x)
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def parameters(self):
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params = []
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for layer in self.layers:
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if hasattr(layer, 'parameters'):
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params.extend(layer.parameters())
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return params
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# %% [markdown]
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"""
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## 1. Introduction: What is Model Compression?
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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.
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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.
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### Why Compression Matters in ML Systems
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**The Storage Challenge:**
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- Modern language models: 100GB+ (GPT-3 scale)
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- Mobile devices: <1GB available for models
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- Edge devices: <100MB realistic limits
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- Network bandwidth: Slow downloads kill user experience
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**The Speed Challenge:**
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- Research models: Designed for accuracy, not efficiency
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- Production needs: Sub-second response times
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- Battery life: Energy consumption matters for mobile
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- Cost scaling: Inference costs grow with model size
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### The Compression Landscape
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```
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Neural Network Compression Techniques:
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┌─────────────────────────────────────────────────────────────┐
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│ COMPRESSION METHODS │
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├─────────────────────────────────────────────────────────────┤
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│ WEIGHT-BASED │ ARCHITECTURE-BASED │
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│ ┌─────────────────────────────┐ │ ┌─────────────────────┐ │
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│ │ Magnitude Pruning │ │ │ Knowledge Distillation│ │
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│ │ • Remove small weights │ │ │ • Teacher → Student │ │
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│ │ • 90% sparsity achievable │ │ │ • 10x size reduction │ │
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│ │ │ │ │ │ │
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│ │ Structured Pruning │ │ │ Neural Architecture │ │
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│ │ • Remove entire channels │ │ │ Search (NAS) │ │
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│ │ • Hardware-friendly │ │ │ • Automated design │ │
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│ │ │ │ │ │ │
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│ │ Low-Rank Approximation │ │ │ Early Exit │ │
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│ │ • Matrix factorization │ │ │ • Adaptive compute │ │
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│ │ • SVD decomposition │ │ │ │ │
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│ └─────────────────────────────┘ │ └─────────────────────┘ │
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└─────────────────────────────────────────────────────────────┘
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```
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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.
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"""
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# %% [markdown]
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"""
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## 2. Foundations: Mathematical Background
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Understanding the mathematics behind compression helps us choose the right technique for each situation and predict their effects on model performance.
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### Magnitude-Based Pruning: The Simple Approach
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The core insight: small weights contribute little to the final prediction. Magnitude pruning removes weights based on their absolute values.
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```
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Mathematical Foundation:
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For weight w_ij in layer l:
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If |w_ij| < threshold_l → w_ij = 0
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Threshold Selection:
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- Global: One threshold for entire model
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- Layer-wise: Different threshold per layer
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- Percentile-based: Remove bottom k% of weights
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Sparsity Calculation:
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Sparsity = (Zero weights / Total weights) × 100%
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```
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### Structured Pruning: Hardware-Friendly Compression
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Unlike magnitude pruning which creates scattered zeros, structured pruning removes entire computational units (neurons, channels, attention heads).
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```
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Channel Importance Metrics:
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Method 1: L2 Norm
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Importance(channel_i) = ||W[:,i]||₂ = √(Σⱼ W²ⱼᵢ)
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Method 2: Gradient-based
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Importance(channel_i) = |∂Loss/∂W[:,i]|
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Method 3: Activation-based
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Importance(channel_i) = E[|activations_i|]
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Pruning Decision:
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Remove bottom k% of channels based on importance ranking
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```
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### Knowledge Distillation: Learning from Teachers
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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.
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```
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Distillation Loss Function:
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L_total = α × L_soft + (1-α) × L_hard
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Where:
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L_soft = KL_divergence(σ(z_s/T), σ(z_t/T)) # Soft targets
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L_hard = CrossEntropy(σ(z_s), y_true) # Hard targets
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σ(z/T) = Softmax with temperature T
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z_s = Student logits, z_t = Teacher logits
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α = Balance parameter (typically 0.7)
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T = Temperature parameter (typically 3-5)
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Temperature Effect:
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T=1: Standard softmax (sharp probabilities)
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T>1: Softer distributions (reveals teacher's uncertainty)
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```
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### Low-Rank Approximation: Matrix Compression
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Large weight matrices often have redundancy that can be captured with lower-rank approximations using Singular Value Decomposition (SVD).
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```
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SVD Decomposition:
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W_{m×n} = U_{m×k} × Σ_{k×k} × V^T_{k×n}
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Parameter Reduction:
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Original: m × n parameters
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Compressed: (m × k) + k + (k × n) = k(m + n + 1) parameters
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Compression achieved when: k < mn/(m+n+1)
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Reconstruction Error:
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||W - W_approx||_F = √(Σᵢ₌ₖ₊₁ʳ σᵢ²)
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Where σᵢ are singular values, r = rank(W)
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```
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"""
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# %% [markdown]
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"""
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## 3. Sparsity Measurement - Understanding Model Density
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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).
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### Understanding Sparsity
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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.
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```
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Sparsity Visualization:
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Dense Matrix (0% sparse): Sparse Matrix (75% sparse):
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┌─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─┐ ┌─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─┐
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│ 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 │
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│ 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 │
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│ 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 │
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│ 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 │
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└─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─┘ └─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─┘
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All weights active Only 7/28 weights active
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Storage: 28 values Storage: 7 values + indices
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```
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Why this matters: Sparsity directly relates to memory savings, but achieving speedup requires special sparse computation libraries.
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"""
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# %%
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def measure_sparsity(model) -> float:
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"""
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Calculate the percentage of zero weights in a model.
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TODO: Count zero weights and total weights across all layers
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APPROACH:
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1. Iterate through all model parameters
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2. Count zeros using np.sum(weights == 0)
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3. Count total parameters
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4. Return percentage: zeros / total * 100
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EXAMPLE:
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>>> model = Sequential(Linear(10, 5), Linear(5, 2))
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>>> sparsity = measure_sparsity(model)
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>>> print(f"Model sparsity: {sparsity:.1f}%")
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Model sparsity: 0.0% # Before pruning
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HINT: Use np.sum() to count zeros efficiently
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"""
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### BEGIN SOLUTION
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total_params = 0
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zero_params = 0
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for param in model.parameters():
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total_params += param.size
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zero_params += np.sum(param.data == 0)
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if total_params == 0:
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return 0.0
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return (zero_params / total_params) * 100.0
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### END SOLUTION
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def test_unit_measure_sparsity():
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"""🔬 Test sparsity measurement functionality."""
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print("🔬 Unit Test: Measure Sparsity...")
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# Test with dense model
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model = Sequential(Linear(4, 3), Linear(3, 2))
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initial_sparsity = measure_sparsity(model)
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assert initial_sparsity == 0.0, f"Expected 0% sparsity, got {initial_sparsity}%"
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# Test with manually sparse model
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model.layers[0].weight.data[0, 0] = 0
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model.layers[0].weight.data[1, 1] = 0
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sparse_sparsity = measure_sparsity(model)
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assert sparse_sparsity > 0, f"Expected >0% sparsity, got {sparse_sparsity}%"
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print("✅ measure_sparsity works correctly!")
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test_unit_measure_sparsity()
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# %% [markdown]
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"""
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## 4. Magnitude-Based Pruning - Removing Small Weights
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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.
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### How Magnitude Pruning Works
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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.
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```
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Magnitude Pruning Process:
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Step 1: Collect All Weights
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┌──────────────────────────────────────────────────┐
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│ Layer 1: [2.1, 0.1, -1.8, 0.05, 3.2, -0.02] │
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│ Layer 2: [1.5, -0.03, 2.8, 0.08, -2.1, 0.01] │
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│ Layer 3: [0.7, 2.4, -0.06, 1.9, 0.04, -1.3] │
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└──────────────────────────────────────────────────┘
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↓
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Step 2: Calculate Magnitudes
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┌──────────────────────────────────────────────────┐
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│ Magnitudes: [2.1, 0.1, 1.8, 0.05, 3.2, 0.02, │
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│ 1.5, 0.03, 2.8, 0.08, 2.1, 0.01, │
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│ 0.7, 2.4, 0.06, 1.9, 0.04, 1.3] │
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└──────────────────────────────────────────────────┘
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↓
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Step 3: Find Threshold (e.g., 70th percentile)
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┌──────────────────────────────────────────────────┐
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│ Sorted: [0.01, 0.02, 0.03, 0.04, 0.05, 0.06, │
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│ 0.08, 0.1, 0.7, 1.3, 1.5, 1.8, │ Threshold: 0.1
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│ 1.9, 2.1, 2.1, 2.4, 2.8, 3.2] │ (70% of weights removed)
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└──────────────────────────────────────────────────┘
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↓
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Step 4: Apply Pruning Mask
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┌──────────────────────────────────────────────────┐
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│ Layer 1: [2.1, 0.0, -1.8, 0.0, 3.2, 0.0] │
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│ Layer 2: [1.5, 0.0, 2.8, 0.0, -2.1, 0.0] │ 70% weights → 0
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│ Layer 3: [0.7, 2.4, 0.0, 1.9, 0.0, -1.3] │ 30% preserved
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└──────────────────────────────────────────────────┘
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Memory Impact:
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- Dense storage: 18 values
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- Sparse storage: 6 values + 6 indices = 12 values (33% savings)
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- Theoretical limit: 70% savings with perfect sparse format
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```
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### Why Global Thresholding Works
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Global thresholding treats the entire model as one big collection of weights, finding a single threshold that achieves the target sparsity across all layers.
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**Advantages:**
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- Simple to implement and understand
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- Preserves overall model capacity
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- Works well for uniform network architectures
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**Disadvantages:**
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- May over-prune some layers, under-prune others
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- Doesn't account for layer-specific importance
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- Can hurt performance if layers have very different weight distributions
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"""
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# %%
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def magnitude_prune(model, sparsity=0.9):
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"""
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Remove weights with smallest magnitudes to achieve target sparsity.
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TODO: Implement global magnitude-based pruning
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APPROACH:
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1. Collect all weights from the model
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2. Calculate absolute values to get magnitudes
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3. Find threshold at desired sparsity percentile
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4. Set weights below threshold to zero (in-place)
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EXAMPLE:
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>>> model = Sequential(Linear(100, 50), Linear(50, 10))
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>>> original_params = sum(p.size for p in model.parameters())
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>>> magnitude_prune(model, sparsity=0.8)
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>>> final_sparsity = measure_sparsity(model)
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>>> print(f"Achieved {final_sparsity:.1f}% sparsity")
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Achieved 80.0% sparsity
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HINTS:
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- Use np.percentile() to find threshold
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- Modify model parameters in-place
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- Consider only weight matrices, not biases
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"""
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### BEGIN SOLUTION
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# Collect all weights (excluding biases)
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all_weights = []
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weight_params = []
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for param in model.parameters():
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# Skip biases (typically 1D)
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if len(param.shape) > 1:
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all_weights.extend(param.data.flatten())
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weight_params.append(param)
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if not all_weights:
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return
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# Calculate magnitude threshold
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magnitudes = np.abs(all_weights)
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threshold = np.percentile(magnitudes, sparsity * 100)
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# Apply pruning to each weight parameter
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for param in weight_params:
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mask = np.abs(param.data) >= threshold
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param.data = param.data * mask
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### END SOLUTION
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def test_unit_magnitude_prune():
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"""🔬 Test magnitude-based pruning functionality."""
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print("🔬 Unit Test: Magnitude Prune...")
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||
|
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# Create test model with known weights
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model = Sequential(Linear(4, 3), Linear(3, 2))
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# Set specific weight values for predictable testing
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model.layers[0].weight.data = np.array([
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[1.0, 2.0, 3.0],
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[0.1, 0.2, 0.3],
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[4.0, 5.0, 6.0],
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[0.01, 0.02, 0.03]
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])
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initial_sparsity = measure_sparsity(model)
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assert initial_sparsity == 0.0, "Model should start with no sparsity"
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# Apply 50% pruning
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magnitude_prune(model, sparsity=0.5)
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final_sparsity = measure_sparsity(model)
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# Should achieve approximately 50% sparsity
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assert 40 <= final_sparsity <= 60, f"Expected ~50% sparsity, got {final_sparsity}%"
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# Verify largest weights survived
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remaining_weights = model.layers[0].weight.data[model.layers[0].weight.data != 0]
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assert len(remaining_weights) > 0, "Some weights should remain"
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assert np.all(np.abs(remaining_weights) >= 0.1), "Large weights should survive"
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print("✅ magnitude_prune works correctly!")
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test_unit_magnitude_prune()
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# %% [markdown]
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||
"""
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## 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.
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||
|
||
### 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).
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||
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```
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Unstructured vs Structured Sparsity:
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UNSTRUCTURED (Magnitude Pruning):
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||
┌─────────────────────────────────────────────┐
|
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│ Channel 0: [2.1, 0.0, 1.8, 0.0, 3.2] │ ← Sparse weights
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│ Channel 1: [0.0, 2.8, 0.0, 2.1, 0.0] │ ← Sparse weights
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│ 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
|
||
"""
|
||
|
||
# %%
|
||
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:
|
||
>>> model = Sequential(Linear(100, 50), Linear(50, 10))
|
||
>>> original_shape = model.layers[0].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
|
||
for layer in model.layers:
|
||
if isinstance(layer, Linear) and hasattr(layer, 'weight'):
|
||
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
|
||
### END SOLUTION
|
||
|
||
def test_unit_structured_prune():
|
||
"""🔬 Test structured pruning functionality."""
|
||
print("🔬 Unit Test: Structured Prune...")
|
||
|
||
# Create test model
|
||
model = Sequential(Linear(4, 6), Linear(6, 2))
|
||
|
||
# Set predictable weights for testing
|
||
model.layers[0].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],
|
||
[1.2, 0.12, 2.2, 0.07, 3.2, 0.03],
|
||
[1.3, 0.13, 2.3, 0.08, 3.3, 0.04]
|
||
])
|
||
|
||
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)
|
||
structured_prune(model, prune_ratio=0.33)
|
||
final_sparsity = measure_sparsity(model)
|
||
|
||
# Check that some channels are completely zero
|
||
weight = model.layers[0].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
|
||
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!")
|
||
|
||
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
|
||
"""
|
||
|
||
# %%
|
||
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
|
||
|
||
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)
|
||
assert relative_error < 0.5, f"Reconstruction error too high: {relative_error}"
|
||
|
||
print("✅ low_rank_approximate works correctly!")
|
||
|
||
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)
|
||
```
|
||
"""
|
||
|
||
# %%
|
||
#| 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:
|
||
>>> teacher = Sequential(Linear(100, 200), Linear(200, 50))
|
||
>>> student = Sequential(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
|
||
# Convert to numpy for this implementation
|
||
if hasattr(student_logits, 'data'):
|
||
student_logits = student_logits.data
|
||
if hasattr(teacher_logits, 'data'):
|
||
teacher_logits = teacher_logits.data
|
||
if hasattr(true_labels, 'data'):
|
||
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))
|
||
|
||
def test_unit_knowledge_distillation():
|
||
"""🔬 Test knowledge distillation functionality."""
|
||
print("🔬 Unit Test: Knowledge Distillation...")
|
||
|
||
# Create teacher and student models
|
||
teacher = Sequential(Linear(10, 20), Linear(20, 5))
|
||
student = Sequential(Linear(10, 5)) # Smaller model
|
||
|
||
# Initialize knowledge distillation
|
||
kd = KnowledgeDistillation(teacher, student, temperature=3.0, alpha=0.7)
|
||
|
||
# Create dummy data
|
||
input_data = Tensor(np.random.randn(8, 10)) # Batch of 8
|
||
true_labels = np.array([0, 1, 2, 3, 4, 0, 1, 2]) # Class labels
|
||
|
||
# Forward passes
|
||
teacher_output = teacher.forward(input_data)
|
||
student_output = student.forward(input_data)
|
||
|
||
# Calculate distillation loss
|
||
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!")
|
||
|
||
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 │
|
||
└─────────────────────────────────────────┘
|
||
```
|
||
"""
|
||
|
||
# %%
|
||
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
|
||
|
||
def test_unit_compress_model():
|
||
"""🔬 Test comprehensive model compression."""
|
||
print("🔬 Unit Test: Compress Model...")
|
||
|
||
# Create test model
|
||
model = Sequential(Linear(20, 15), Linear(15, 10), Linear(10, 5))
|
||
|
||
# Define compression configuration
|
||
config = {
|
||
'magnitude_prune': 0.7,
|
||
'structured_prune': 0.2
|
||
}
|
||
|
||
# Apply compression
|
||
stats = compress_model(model, config)
|
||
|
||
# Verify statistics
|
||
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
|
||
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
|
||
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!")
|
||
|
||
test_unit_compress_model()
|
||
|
||
# %% [markdown]
|
||
"""
|
||
|
||
Understanding the real-world implications of compression choices and how to design compression strategies for different deployment scenarios.
|
||
|
||
### 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 15 to measure the actual parameter reduction from pruning. This demonstrates the complete workflow: profile baseline (M15) → apply compression (M18) → measure impact (M15+M18).
|
||
|
||
This is the production workflow: measure → prune → validate → deploy.
|
||
"""
|
||
|
||
# %% nbgrader={"grade": false, "grade_id": "demo-profiler-compression", "solution": true}
|
||
# Import Profiler from Module 15
|
||
from tinytorch.profiling.profiler import Profiler
|
||
|
||
def demo_compression_with_profiler():
|
||
"""📊 Demonstrate parameter reduction using Profiler from Module 15."""
|
||
print("📊 Measuring Compression Impact with Profiler")
|
||
print("=" * 70)
|
||
|
||
profiler = Profiler()
|
||
|
||
# Create a simple model
|
||
from tinytorch.core.layers import Linear
|
||
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]
|
||
"""
|
||
## 9. Module Integration Test
|
||
|
||
Final validation that all compression techniques work together correctly.
|
||
"""
|
||
|
||
# %%
|
||
def test_module():
|
||
"""
|
||
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
|
||
model = Sequential(
|
||
Linear(784, 512), # Input layer (like MNIST)
|
||
Linear(512, 256), # Hidden layer 1
|
||
Linear(256, 128), # Hidden layer 2
|
||
Linear(128, 10) # Output layer
|
||
)
|
||
|
||
original_params = sum(p.size for p in model.parameters())
|
||
print(f"Original model: {original_params:,} parameters")
|
||
|
||
# Apply comprehensive compression
|
||
compression_config = {
|
||
'magnitude_prune': 0.8,
|
||
'structured_prune': 0.3
|
||
}
|
||
|
||
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...")
|
||
|
||
teacher = Sequential(Linear(100, 200), Linear(200, 50))
|
||
student = Sequential(Linear(100, 50)) # 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)
|
||
assert error < 0.5, f"Reconstruction error too high: {error:.3f}"
|
||
|
||
print(f"✅ Low-rank: {compression_ratio:.2f}x compression, {error:.3f} error")
|
||
|
||
print("\n" + "=" * 50)
|
||
print("🎉 ALL TESTS PASSED! Module ready for export.")
|
||
print("Run: tito module complete 18")
|
||
|
||
# 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)."""
|
||
total_params = 0
|
||
zero_params = 0
|
||
|
||
if hasattr(model, 'parameters'):
|
||
for param in model.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: Model with parameters() method
|
||
sparsity: Fraction of weights to prune (0-1)
|
||
"""
|
||
if hasattr(model, 'parameters'):
|
||
for param in model.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: Model to prune
|
||
prune_ratio: Fraction of structures to prune (0-1)
|
||
"""
|
||
if hasattr(model, 'parameters'):
|
||
params = list(model.parameters())
|
||
if len(params) > 0 and hasattr(params[0], 'data'):
|
||
weight = params[0]
|
||
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 > _____
|
||
"""
|
||
|
||
# %% [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!
|
||
""" |