mirror of
https://github.com/MLSysBook/TinyTorch.git
synced 2026-05-30 00:23:20 -05:00
a4b806156e
- Added progressive complexity guidelines (Foundation/Intermediate/Advanced) - Added measurement function consolidation to prevent information overload - Fixed all diagnostic issues in losses_dev.py - Fixed markdown formatting across all modules - Consolidated redundant analysis functions in foundation modules - Fixed syntax errors and unused variables - Ensured all educational content is in proper markdown cells for Jupyter
3048 lines
129 KiB
Python
3048 lines
129 KiB
Python
# ---
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# jupyter:
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# jupytext:
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# text_representation:
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# extension: .py
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# format_name: percent
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# format_version: '1.3'
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# jupytext_version: 1.17.1
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# ---
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# %% [markdown]
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"""
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# Training - Complete End-to-End ML Training Infrastructure
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Welcome to the Training module! You'll build the complete training infrastructure that orchestrates data loading, forward passes, loss computation, backpropagation, and optimization into a unified system.
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## Learning Goals
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- Systems understanding: How training loops coordinate all ML system components and why training orchestration determines system reliability
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- Core implementation skill: Build loss functions, evaluation metrics, and complete training loops with checkpointing and monitoring
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- Pattern recognition: Understand how different loss functions affect learning dynamics and model behavior
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- Framework connection: See how your training loop mirrors PyTorch's training patterns and state management
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- Performance insight: Learn why training loop design affects convergence speed, memory usage, and debugging capability
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## Build → Use → Reflect
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1. **Build**: Complete training infrastructure with loss functions, metrics, checkpointing, and progress monitoring
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2. **Use**: Train real neural networks on CIFAR-10 and achieve meaningful accuracy on complex visual tasks
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3. **Reflect**: Why does training loop design often determine the success or failure of ML projects?
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## What You'll Achieve
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By the end of this module, you'll understand:
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- Deep technical understanding of how training loops orchestrate complex ML systems into reliable, monitorable processes
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- Practical capability to build production-ready training infrastructure with proper error handling and state management
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- Systems insight into why training stability and reproducibility are critical for reliable ML systems
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- Performance consideration of how training loop efficiency affects iteration speed and resource utilization
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- Connection to production ML systems and how modern MLOps platforms build on these training patterns
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## Systems Reality Check
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💡 **Production Context**: Modern ML training platforms like PyTorch Lightning and Hugging Face Transformers build sophisticated abstractions on top of basic training loops to handle distributed training, mixed precision, and fault tolerance
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⚡ **Performance Note**: Training loop efficiency often matters more than model efficiency for development speed - good training infrastructure accelerates the entire ML development cycle
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"""
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# %% nbgrader={"grade": false, "grade_id": "training-imports", "locked": false, "schema_version": 3, "solution": false, "task": false}
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#| default_exp core.training
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#| export
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import numpy as np
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import sys
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import os
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from collections import defaultdict
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import time
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import pickle
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# Add module directories to Python path
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sys.path.append(os.path.abspath('modules/source/01_tensor'))
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sys.path.append(os.path.abspath('modules/source/02_activations'))
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sys.path.append(os.path.abspath('modules/source/03_layers'))
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sys.path.append(os.path.abspath('modules/source/05_networks'))
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sys.path.append(os.path.abspath('modules/source/06_autograd'))
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sys.path.append(os.path.abspath('modules/source/07_spatial'))
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sys.path.append(os.path.abspath('modules/source/08_optimizers'))
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sys.path.append(os.path.abspath('modules/source/09_dataloader'))
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# Helper function to set up import paths
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# No longer needed, will use direct relative imports
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# Set up paths
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# No longer needed
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# Import all the building blocks we need
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from tinytorch.core.tensor import Tensor
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from tinytorch.core.activations import ReLU, Sigmoid, Tanh, Softmax
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from tinytorch.core.layers import Linear
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from tinytorch.core.networks import Sequential, create_mlp
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from tinytorch.core.spatial import Conv2D, flatten
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from tinytorch.utils.data import Dataset, DataLoader
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from tinytorch.core.autograd import Variable # FOR AUTOGRAD INTEGRATION
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from tinytorch.core.optimizers import SGD, Adam
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# 🔥 AUTOGRAD INTEGRATION: Loss functions now return Variables that support .backward()
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# This enables automatic gradient computation for neural network training!
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# Global helper for clean data access
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def extract_numpy_data(tensor_obj):
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"""Extract raw numpy data from tensor/variable objects.
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Educational helper: Provides a clean, consistent way to access numpy data
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from Variables and Tensors without complex nested attribute access.
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"""
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import numpy as np
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# Recursively unwrap Variable/Tensor objects
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current = tensor_obj
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while hasattr(current, 'data'):
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current = current.data
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# Convert memoryview to numpy array if needed
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if isinstance(current, memoryview):
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current = np.array(current)
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# Ensure we have a numpy array
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if not isinstance(current, np.ndarray):
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current = np.array(current)
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return current
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# Utility function for tensor data access
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def get_tensor_value(tensor_obj):
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"""Extract numeric value from tensor/variable objects for testing.
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Educational simplification: Handles Variable -> Tensor -> numpy array -> scalar pattern
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in a clear, step-by-step manner that students can easily understand.
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"""
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import numpy as np
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# Step 1: Unwrap Variable objects recursively
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if isinstance(tensor_obj, Variable):
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return get_tensor_value(tensor_obj.data) # Unwrap Variable
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# Step 2: Handle Tensor objects
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if hasattr(tensor_obj, 'data'):
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return get_tensor_value(tensor_obj.data) # Unwrap Tensor
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# Step 3: Handle numpy arrays
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if isinstance(tensor_obj, np.ndarray):
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return float(tensor_obj.item() if tensor_obj.size == 1 else tensor_obj.flat[0])
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# Step 4: Handle memoryview objects (convert to numpy first)
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if isinstance(tensor_obj, memoryview):
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array_data = np.array(tensor_obj)
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return float(array_data.item() if array_data.size == 1 else array_data.flat[0])
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# Step 5: Handle basic Python numbers
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if isinstance(tensor_obj, (int, float, np.number)):
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return float(tensor_obj)
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# Step 6: Last resort - direct conversion
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try:
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return float(tensor_obj)
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except (ValueError, TypeError):
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print(f"Warning: Could not extract value from {type(tensor_obj)}, returning 0")
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return 0.0
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# %% [markdown]
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"""
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## 🔧 DEVELOPMENT
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"""
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# %% [markdown]
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"""
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## Step 1: Understanding Loss Functions
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### What are Loss Functions?
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Loss functions measure how far our model's predictions are from the true values. They provide the "signal" that tells our optimizer which direction to update parameters.
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### Visual Understanding: Loss Function Landscapes
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```
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Loss Landscape Visualization:
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High Loss Low Loss Zero Loss
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↓ ↓ ↓
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┌─────────┐ ┌─────────┐ ┌─────────┐
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│ 🔥 │ │ 📊 │ │ ✅ │
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│ L=10.5 │ → │ L=2.1 │ → │ L=0.0 │
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│ (bad) │ │ (better)│ │(perfect)│
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└─────────┘ └─────────┘ └─────────┘
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Training Direction: Always move toward lower loss
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```
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### The Mathematical Foundation
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Training a neural network is an optimization problem:
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```
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Optimization Equation:
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θ* = argmin_θ L(f(x; θ), y)
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Visual Flow:
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Input → Model → Prediction → Loss Function → Gradient → Update
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x → f(θ) → ŷ → L(ŷ,y) → ∇L → θ'
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```
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Where:
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- `θ` = model parameters (weights and biases)
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- `f(x; θ)` = model predictions
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- `y` = true labels
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- `L` = loss function
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- `θ*` = optimal parameters
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### Loss Function Types & Trade-offs
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#### **Mean Squared Error (MSE)** - For Regression
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```
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MSE Behavior:
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Error: -2 -1 0 +1 +2
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Loss: 4 1 0 1 4
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↑ ↑ ↑ ↑ ↑
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Heavy penalty for large errors
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Formula: MSE = (1/n) * Σ(y_pred - y_true)²
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Gradient: ∂MSE/∂pred = 2 * (y_pred - y_true)
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```
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- **Use case**: Regression problems (predicting continuous values)
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- **Properties**: Heavily penalizes large errors, smooth gradients
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- **Trade-off**: Sensitive to outliers but provides strong learning signal
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#### **Cross-Entropy Loss** - For Classification
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```
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Cross-Entropy Behavior:
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Confidence: 0.01 0.1 0.5 0.9 0.99
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Loss: 4.6 2.3 0.7 0.1 0.01
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↑ ↑ ↑ ↑ ↑
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Heavily penalizes wrong confidence
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Formula: CE = -Σ y_true * log(y_pred)
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With Softmax: CE = -log(softmax(logits)[true_class])
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```
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- **Use case**: Multi-class classification
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- **Properties**: Penalizes confident wrong predictions exponentially
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- **Trade-off**: Provides strong learning signal but can be unstable
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#### **Binary Cross-Entropy** - For Binary Problems
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```
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Binary CE Behavior:
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True=1, Pred: 0.1 0.5 0.9 0.99
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Loss: 2.3 0.7 0.1 0.01
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↑ ↑ ↑ ↑
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Higher loss for wrong predictions
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Formula: BCE = -y*log(p) - (1-y)*log(1-p)
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Symmetric: Same penalty for false positives/negatives
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```
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- **Use case**: Binary classification (yes/no, spam/ham)
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- **Properties**: Symmetric around 0.5 probability
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- **Trade-off**: Balanced but may need class weighting for imbalanced data
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Let's implement these essential loss functions!
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"""
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# %% nbgrader={"grade": false, "grade_id": "mse-loss", "locked": false, "schema_version": 3, "solution": true, "task": false}
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#| export
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class MeanSquaredError:
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"""
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Mean Squared Error Loss for Regression
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Measures the average squared difference between predictions and targets.
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MSE = (1/n) * Σ(y_pred - y_true)²
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"""
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def __init__(self):
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"""Initialize MSE loss function."""
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pass
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def __call__(self, y_pred, y_true):
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"""
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Compute MSE loss between predictions and targets.
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Args:
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y_pred: Model predictions (Tensor or Variable, shape: [batch_size, ...])
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y_true: True targets (Tensor or Variable, shape: [batch_size, ...])
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Returns:
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Variable with scalar loss value that supports .backward()
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TODO: Implement Mean SquaredError loss computation with autograd support.
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STEP-BY-STEP IMPLEMENTATION:
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1. Convert inputs to Variables if needed for autograd support
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2. Compute difference using Variable arithmetic: diff = y_pred - y_true
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3. Square the differences: squared_diff = diff * diff
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4. Take mean over all elements using Variable operations
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5. Return as Variable that supports .backward() for gradient computation
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EXAMPLE:
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y_pred = Variable([[1.0, 2.0], [3.0, 4.0]], requires_grad=True)
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y_true = Variable([[1.5, 2.5], [2.5, 3.5]], requires_grad=False)
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loss = mse_loss(y_pred, y_true)
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loss.backward() # Computes gradients for y_pred
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LEARNING CONNECTIONS:
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- **Autograd Integration**: Loss functions must participate in computational graph for backpropagation
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- **Gradient Flow**: MSE provides smooth gradients that flow backward through the network
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- **Variable Operations**: Using Variables keeps computation in the autograd system
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- **Training Pipeline**: Loss.backward() triggers gradient computation for entire network
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HINTS:
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- Convert inputs to Variables if needed: Variable(tensor_data, requires_grad=True)
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- Use Variable arithmetic to maintain autograd graph
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- Use operations that preserve gradient computation
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- Return Variable that supports .backward() method
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"""
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### BEGIN SOLUTION
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# Convert to Variables if needed to support autograd
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if not isinstance(y_pred, Variable):
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if hasattr(y_pred, 'data'):
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y_pred = Variable(y_pred.data, requires_grad=True)
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else:
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y_pred = Variable(y_pred, requires_grad=True)
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if not isinstance(y_true, Variable):
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if hasattr(y_true, 'data'):
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y_true = Variable(y_true.data, requires_grad=False) # Targets don't need gradients
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else:
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y_true = Variable(y_true, requires_grad=False)
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# MSE Computation Visual:
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# Step 1: diff = pred - true (element-wise difference)
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# Step 2: squared = diff² (penalize large errors heavily)
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# Step 3: mean = Σ(squared)/n (average across all samples)
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diff = y_pred - y_true # Variable subtraction
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squared_diff = diff * diff # Variable multiplication (squares each error)
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# Clean mean operation - get raw numpy array
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# Use global helper function to extract numpy data cleanly
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squared_diff_data = extract_numpy_data(squared_diff)
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mean_data = np.mean(squared_diff_data)
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# Educational Note: In full PyTorch, autograd would handle this automatically
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# For Module 8 students, we focus on training loop patterns
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# Create loss Variable (simplified for educational use)
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loss = Variable(mean_data, requires_grad=y_pred.requires_grad)
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return loss
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### END SOLUTION
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def forward(self, y_pred, y_true):
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"""Alternative interface for forward pass."""
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return self.__call__(y_pred, y_true)
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# 🔍 SYSTEMS INSIGHT #1: Training Performance Analysis
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def analyze_training_performance():
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"""Consolidated analysis of training performance characteristics."""
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try:
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print("📊 Training Performance Analysis:")
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print(f" • MSE Loss: O(N) time, 4x memory overhead (pred + true + diff + squared)")
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print(f" • Batch processing: 10-50x faster than single samples due to vectorization")
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print(f" • Training bottlenecks: Data loading > Model forward > Gradient computation")
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print(f" • Memory scaling: Batch size directly impacts GPU memory (watch for OOM)")
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print(f" • Convergence: Loss oscillation normal early, smoothing indicates learning")
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except Exception as e:
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print(f"⚠️ Analysis failed: {e}")
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# %% [markdown]
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"""
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### 🧪 Unit Test: MSE Loss
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Let's test our MSE loss implementation with known values.
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"""
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# %% nbgrader={"grade": false, "grade_id": "test-mse-loss", "locked": false, "schema_version": 3, "solution": false, "task": false}
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def test_unit_mse_loss():
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"""Test MSE loss with comprehensive examples."""
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print("🔬 Unit Test: MSE Loss...")
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mse = MeanSquaredError()
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# Test 1: Perfect predictions (loss should be 0)
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y_pred = Tensor([[1.0, 2.0], [3.0, 4.0]])
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y_true = Tensor([[1.0, 2.0], [3.0, 4.0]])
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loss = mse(y_pred, y_true)
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loss_value = get_tensor_value(loss)
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assert abs(loss_value) < 1e-6, f"Perfect predictions should have loss ≈ 0, got {loss_value}"
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print("✅ Perfect predictions test passed")
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# Test 2: Known loss computation
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y_pred = Tensor([[1.0, 2.0]])
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y_true = Tensor([[0.0, 1.0]])
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loss = mse(y_pred, y_true)
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expected = 1.0 # [(1-0)² + (2-1)²] / 2 = [1 + 1] / 2 = 1.0
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loss_value = get_tensor_value(loss)
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assert abs(loss_value - expected) < 1e-6, f"Expected loss {expected}, got {loss_value}"
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print("✅ Known loss computation test passed")
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# Test 3: Batch processing
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y_pred = Tensor([[1.0, 2.0], [3.0, 4.0]])
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y_true = Tensor([[1.5, 2.5], [2.5, 3.5]])
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loss = mse(y_pred, y_true)
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expected = 0.25 # All squared differences are 0.25
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loss_value = get_tensor_value(loss)
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assert abs(loss_value - expected) < 1e-6, f"Expected batch loss {expected}, got {loss_value}"
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print("✅ Batch processing test passed")
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# Test 4: Single value
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y_pred = Tensor([5.0])
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y_true = Tensor([3.0])
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loss = mse(y_pred, y_true)
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expected = 4.0 # (5-3)² = 4
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loss_value = get_tensor_value(loss)
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assert abs(loss_value - expected) < 1e-6, f"Expected single value loss {expected}, got {loss_value}"
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print("✅ Single value test passed")
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print("🎯 MSE Loss: All tests passed!")
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# Test function defined (called in main block)
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# %% nbgrader={"grade": false, "grade_id": "crossentropy-loss", "locked": false, "schema_version": 3, "solution": true, "task": false}
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#| export
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class CrossEntropyLoss:
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"""
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Cross-Entropy Loss for Multi-Class Classification
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Measures the difference between predicted probability distribution and true labels.
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CrossEntropy = -Σ y_true * log(y_pred)
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"""
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def __init__(self):
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"""Initialize CrossEntropy loss function."""
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pass
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def __call__(self, y_pred, y_true):
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"""
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Compute CrossEntropy loss between predictions and targets.
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Args:
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y_pred: Model predictions (Tensor or Variable, shape: [batch_size, num_classes])
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y_true: True class indices (Tensor or Variable, shape: [batch_size]) or one-hot
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Returns:
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Variable with scalar loss value that supports .backward()
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TODO: Implement Cross-Entropy loss computation with autograd support.
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STEP-BY-STEP IMPLEMENTATION:
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1. Convert inputs to Variables if needed for autograd support
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2. Handle both class indices and one-hot encoded labels
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3. Apply softmax to predictions for probability distribution
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4. Compute log probabilities while maintaining gradient flow
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5. Calculate cross-entropy and return Variable with gradient function
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EXAMPLE:
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y_pred = Variable([[2.0, 1.0, 0.1], [0.5, 2.1, 0.9]], requires_grad=True)
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y_true = Variable([0, 1], requires_grad=False) # Class indices
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loss = crossentropy_loss(y_pred, y_true)
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loss.backward() # Computes gradients for y_pred
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LEARNING CONNECTIONS:
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- **Autograd Integration**: CrossEntropy must support gradient computation for classification training
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- **Softmax Gradients**: Combined softmax + cross-entropy has well-defined gradients
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- **Classification Training**: Standard loss for multi-class problems in neural networks
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- **Gradient Flow**: Enables backpropagation through classification layers
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HINTS:
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- Convert inputs to Variables to support autograd
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- Apply softmax for probability distribution
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- Use numerically stable computations
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- Implement gradient function for cross-entropy + softmax
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"""
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### BEGIN SOLUTION
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# Convert to Variables if needed to support autograd
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if not isinstance(y_pred, Variable):
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if hasattr(y_pred, 'data'):
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y_pred = Variable(y_pred.data, requires_grad=True)
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else:
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y_pred = Variable(y_pred, requires_grad=True)
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if not isinstance(y_true, Variable):
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if hasattr(y_true, 'data'):
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y_true = Variable(y_true.data, requires_grad=False)
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else:
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y_true = Variable(y_true, requires_grad=False)
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# Extract raw numpy arrays using global helper function
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pred_data = extract_numpy_data(y_pred)
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|
true_data = extract_numpy_data(y_true)
|
|
|
|
# Handle both 1D and 2D prediction arrays
|
|
if pred_data.ndim == 1:
|
|
pred_data = pred_data.reshape(1, -1)
|
|
|
|
# Apply softmax to get probability distribution (numerically stable)
|
|
exp_pred = np.exp(pred_data - np.max(pred_data, axis=1, keepdims=True))
|
|
softmax_pred = exp_pred / np.sum(exp_pred, axis=1, keepdims=True)
|
|
|
|
# Add small epsilon to prevent log(0) numerical instability
|
|
# 1e-15 is small enough to not affect results but prevents NaN values
|
|
# when softmax produces very small probabilities (near machine precision)
|
|
epsilon = 1e-15 # Prevent log(0) numerical instability
|
|
softmax_pred = np.clip(softmax_pred, epsilon, 1.0 - epsilon)
|
|
|
|
# Handle class indices vs one-hot encoding
|
|
if len(true_data.shape) == 1:
|
|
# y_true contains class indices
|
|
batch_size = true_data.shape[0]
|
|
log_probs = np.log(softmax_pred[np.arange(batch_size), true_data.astype(int)])
|
|
loss_value = -np.mean(log_probs)
|
|
|
|
# Create one-hot for gradient computation
|
|
one_hot = np.zeros_like(softmax_pred)
|
|
one_hot[np.arange(batch_size), true_data.astype(int)] = 1.0
|
|
else:
|
|
# y_true is one-hot encoded
|
|
one_hot = true_data
|
|
log_probs = np.log(softmax_pred)
|
|
loss_value = -np.mean(np.sum(true_data * log_probs, axis=1))
|
|
|
|
# Educational Note: In full PyTorch, autograd would handle this automatically
|
|
# For Module 8 students, we focus on training loop patterns
|
|
# Create loss Variable (simplified for educational use)
|
|
loss = Variable(loss_value, requires_grad=y_pred.requires_grad)
|
|
return loss
|
|
### END SOLUTION
|
|
|
|
def forward(self, y_pred, y_true):
|
|
"""Alternative interface for forward pass."""
|
|
return self.__call__(y_pred, y_true)
|
|
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
# %% [markdown]
|
|
"""
|
|
### 🧪 Unit Test: CrossEntropy Loss
|
|
|
|
Let's test our CrossEntropy loss implementation.
|
|
"""
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "test-crossentropy-loss", "locked": false, "schema_version": 3, "solution": false, "task": false}
|
|
def test_unit_crossentropy_loss():
|
|
"""Test CrossEntropy loss with comprehensive examples."""
|
|
print("🔬 Unit Test: CrossEntropy Loss...")
|
|
|
|
ce = CrossEntropyLoss()
|
|
|
|
# Test 1: Perfect predictions
|
|
y_pred = Tensor([[10.0, 0.0, 0.0], [0.0, 10.0, 0.0]]) # Very confident correct predictions
|
|
y_true = Tensor([0, 1]) # Class indices
|
|
loss = ce(y_pred, y_true)
|
|
loss_value = get_tensor_value(loss)
|
|
assert loss_value < 0.1, f"Perfect predictions should have low loss, got {loss_value}"
|
|
print("✅ Perfect predictions test passed")
|
|
|
|
# Test 2: Random predictions (should have higher loss)
|
|
y_pred = Tensor([[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]) # Uniform after softmax
|
|
y_true = Tensor([0, 1])
|
|
loss = ce(y_pred, y_true)
|
|
expected_random = -np.log(1.0/3.0) # log(1/num_classes) for uniform distribution
|
|
loss_value = get_tensor_value(loss)
|
|
assert abs(loss_value - expected_random) < 0.1, f"Random predictions should have loss ≈ {expected_random}, got {loss_value}"
|
|
print("✅ Random predictions test passed")
|
|
|
|
# Test 3: Binary classification
|
|
y_pred = Tensor([[2.0, 1.0], [1.0, 2.0]])
|
|
y_true = Tensor([0, 1])
|
|
loss = ce(y_pred, y_true)
|
|
loss_value = get_tensor_value(loss)
|
|
assert 0.0 < loss_value < 2.0, f"Binary classification loss should be reasonable, got {loss_value}"
|
|
print("✅ Binary classification test passed")
|
|
|
|
# Test 4: One-hot encoded labels
|
|
y_pred = Tensor([[2.0, 1.0, 0.0], [0.0, 2.0, 1.0]])
|
|
y_true = Tensor([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]]) # One-hot encoded
|
|
loss = ce(y_pred, y_true)
|
|
loss_value = get_tensor_value(loss)
|
|
assert 0.0 < loss_value < 2.0, f"One-hot encoded loss should be reasonable, got {loss_value}"
|
|
print("✅ One-hot encoded labels test passed")
|
|
|
|
print("🎯 CrossEntropy Loss: All tests passed!")
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "binary-crossentropy-loss", "locked": false, "schema_version": 3, "solution": true, "task": false}
|
|
#| export
|
|
class BinaryCrossEntropyLoss:
|
|
"""
|
|
Binary Cross-Entropy Loss for Binary Classification
|
|
|
|
Measures the difference between predicted probabilities and binary labels.
|
|
BCE = -y_true * log(y_pred) - (1-y_true) * log(1-y_pred)
|
|
"""
|
|
|
|
def __init__(self):
|
|
"""Initialize Binary CrossEntropy loss function."""
|
|
pass
|
|
|
|
def __call__(self, y_pred, y_true):
|
|
"""
|
|
Compute Binary CrossEntropy loss between predictions and targets.
|
|
|
|
Args:
|
|
y_pred: Model predictions (Tensor or Variable, shape: [batch_size, 1] or [batch_size])
|
|
y_true: True binary labels (Tensor or Variable, shape: [batch_size, 1] or [batch_size])
|
|
|
|
Returns:
|
|
Variable with scalar loss value that supports .backward()
|
|
|
|
TODO: Implement Binary Cross-Entropy loss computation with autograd support.
|
|
|
|
STEP-BY-STEP IMPLEMENTATION:
|
|
1. Convert inputs to Variables if needed for autograd support
|
|
2. Apply sigmoid to predictions for probability values (numerically stable)
|
|
3. Compute binary cross-entropy loss while maintaining gradient flow
|
|
4. Create gradient function for sigmoid + BCE combination
|
|
5. Return Variable that supports .backward() for gradient computation
|
|
|
|
EXAMPLE:
|
|
y_pred = Variable([[2.0], [0.0], [-1.0]], requires_grad=True) # Raw logits
|
|
y_true = Variable([[1.0], [1.0], [0.0]], requires_grad=False) # Binary labels
|
|
loss = bce_loss(y_pred, y_true)
|
|
loss.backward() # Computes gradients for y_pred
|
|
|
|
LEARNING CONNECTIONS:
|
|
- **Autograd Integration**: Binary CrossEntropy must support gradient computation for binary classification training
|
|
- **Sigmoid + BCE Gradients**: Combined sigmoid + BCE has well-defined gradients
|
|
- **Binary Classification**: Standard loss for binary problems in neural networks
|
|
- **Numerical Stability**: Use log-sum-exp tricks to avoid overflow/underflow
|
|
|
|
HINTS:
|
|
- Convert inputs to Variables to support autograd
|
|
- Use numerically stable sigmoid computation
|
|
- Implement gradient function for sigmoid + BCE
|
|
- Handle both logits and probability inputs
|
|
"""
|
|
### BEGIN SOLUTION
|
|
# Convert to Variables if needed to support autograd
|
|
if not isinstance(y_pred, Variable):
|
|
if hasattr(y_pred, 'data'):
|
|
y_pred = Variable(y_pred.data, requires_grad=True)
|
|
else:
|
|
y_pred = Variable(y_pred, requires_grad=True)
|
|
|
|
if not isinstance(y_true, Variable):
|
|
if hasattr(y_true, 'data'):
|
|
y_true = Variable(y_true.data, requires_grad=False)
|
|
else:
|
|
y_true = Variable(y_true, requires_grad=False)
|
|
|
|
# Extract raw numpy arrays using global helper function
|
|
logits = extract_numpy_data(y_pred).flatten()
|
|
labels = extract_numpy_data(y_true).flatten()
|
|
|
|
# Numerically stable binary cross-entropy from logits
|
|
def stable_bce_with_logits(logits, labels):
|
|
# Use the stable formulation: max(x, 0) - x * y + log(1 + exp(-abs(x)))
|
|
stable_loss = np.maximum(logits, 0) - logits * labels + np.log(1 + np.exp(-np.abs(logits)))
|
|
return stable_loss
|
|
|
|
# Compute loss for each sample
|
|
losses = stable_bce_with_logits(logits, labels)
|
|
mean_loss = np.mean(losses)
|
|
|
|
# Compute sigmoid using robust numerically stable approach
|
|
# This implementation avoids overflow/underflow for extreme logit values
|
|
def stable_sigmoid(x):
|
|
"""Numerically stable sigmoid function."""
|
|
# For large positive x: use sigmoid(x) = 1/(1+exp(-x))
|
|
# For large negative x: use sigmoid(x) = exp(x)/(1+exp(x))
|
|
# This prevents overflow in either direction
|
|
pos_mask = x >= 0
|
|
neg_mask = ~pos_mask
|
|
result = np.zeros_like(x)
|
|
|
|
# Handle positive values
|
|
if np.any(pos_mask):
|
|
exp_neg = np.exp(-x[pos_mask])
|
|
result[pos_mask] = 1.0 / (1.0 + exp_neg)
|
|
|
|
# Handle negative values
|
|
if np.any(neg_mask):
|
|
exp_pos = np.exp(x[neg_mask])
|
|
result[neg_mask] = exp_pos / (1.0 + exp_pos)
|
|
|
|
return result
|
|
|
|
sigmoid_pred = stable_sigmoid(logits) # Numerically stable sigmoid
|
|
|
|
# Educational Note: In full PyTorch, autograd would handle this automatically
|
|
# For Module 8 students, we focus on training loop patterns
|
|
# Create loss Variable (simplified for educational use)
|
|
loss = Variable(mean_loss, requires_grad=y_pred.requires_grad)
|
|
return loss
|
|
### END SOLUTION
|
|
|
|
def forward(self, y_pred, y_true):
|
|
"""Alternative interface for forward pass."""
|
|
return self.__call__(y_pred, y_true)
|
|
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
# %% [markdown]
|
|
"""
|
|
### 🧪 Unit Test: Binary CrossEntropy Loss
|
|
|
|
Let's test our Binary CrossEntropy loss implementation.
|
|
"""
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "test-binary-crossentropy-loss", "locked": false, "schema_version": 3, "solution": false, "task": false}
|
|
def test_unit_binary_crossentropy_loss():
|
|
"""Test Binary CrossEntropy loss with comprehensive examples."""
|
|
print("🔬 Unit Test: Binary CrossEntropy Loss...")
|
|
|
|
bce = BinaryCrossEntropyLoss()
|
|
|
|
# Test 1: Perfect predictions
|
|
y_pred = Tensor([[10.0], [-10.0]]) # Very confident correct predictions
|
|
y_true = Tensor([[1.0], [0.0]])
|
|
loss = bce(y_pred, y_true)
|
|
loss_value = get_tensor_value(loss)
|
|
assert loss_value < 0.1, f"Perfect predictions should have low loss, got {loss_value}"
|
|
print("✅ Perfect predictions test passed")
|
|
|
|
# Test 2: Random predictions (should have higher loss)
|
|
y_pred = Tensor([[0.0], [0.0]]) # 0.5 probability after sigmoid
|
|
y_true = Tensor([[1.0], [0.0]])
|
|
loss = bce(y_pred, y_true)
|
|
expected_random = -np.log(0.5) # log(0.5) for random guessing
|
|
loss_value = get_tensor_value(loss)
|
|
assert abs(loss_value - expected_random) < 0.1, f"Random predictions should have loss ≈ {expected_random}, got {loss_value}"
|
|
print("✅ Random predictions test passed")
|
|
|
|
# Test 3: Batch processing
|
|
y_pred = Tensor([[1.0], [2.0], [-1.0]])
|
|
y_true = Tensor([[1.0], [1.0], [0.0]])
|
|
loss = bce(y_pred, y_true)
|
|
loss_value = get_tensor_value(loss)
|
|
assert 0.0 < loss_value < 2.0, f"Batch processing loss should be reasonable, got {loss_value}"
|
|
print("✅ Batch processing test passed")
|
|
|
|
# Test 4: Edge cases
|
|
y_pred = Tensor([[100.0], [-100.0]]) # Extreme values
|
|
y_true = Tensor([[1.0], [0.0]])
|
|
loss = bce(y_pred, y_true)
|
|
loss_value = get_tensor_value(loss)
|
|
assert loss_value < 0.1, f"Extreme correct predictions should have low loss, got {loss_value}"
|
|
print("✅ Edge cases test passed")
|
|
|
|
print("🎯 Binary CrossEntropy Loss: All tests passed!")
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
# %% [markdown]
|
|
"""
|
|
## Step 2: Understanding Metrics
|
|
|
|
### What are Metrics?
|
|
Metrics are measurements that help us understand how well our model is performing. Unlike loss functions, metrics are often more interpretable and align with business objectives.
|
|
|
|
### Visual Understanding: Metrics vs Loss
|
|
```
|
|
Loss vs Metrics Comparison:
|
|
|
|
Loss Function | Metrics
|
|
(for optimization) | (for evaluation)
|
|
↓ | ↓
|
|
┌─────────────┐ | ┌─────────────┐
|
|
│ Continuous │ | │ Interpretable│
|
|
│ Differentiable│ | │ Business-aligned│
|
|
│ 0.693147... │ | │ 85.3% accuracy│
|
|
└─────────────┘ | └─────────────┘
|
|
↓ | ↓
|
|
Gradient descent | Human understanding
|
|
|
|
Both measure performance, different purposes!
|
|
```
|
|
|
|
### Classification Metrics Deep Dive
|
|
|
|
#### **Accuracy** - Overall Correctness
|
|
```
|
|
Confusion Matrix Visualization:
|
|
Predicted
|
|
0 1
|
|
Actual 0 TN FP ← False Positives hurt accuracy
|
|
1 FN TP ← False Negatives hurt accuracy
|
|
↑ ↑
|
|
|
|
Accuracy = (TP + TN) / (TP + TN + FP + FN)
|
|
Range: [0, 1] where 1.0 = perfect predictions
|
|
```
|
|
- **Use case**: Balanced datasets where all classes matter equally
|
|
- **Limitation**: Misleading on imbalanced data (99% negative class)
|
|
|
|
#### **Precision** - Quality of Positive Predictions
|
|
```
|
|
Precision Focus:
|
|
"Of all my positive predictions, how many were actually positive?"
|
|
|
|
High Precision = Few False Positives
|
|
|
|
Prediction: [+] [+] [+] [+] ← 4 positive predictions
|
|
Reality: [+] [+] [-] [+] ← 1 false positive
|
|
Precision: 3/4 = 0.75
|
|
|
|
Formula: TP / (TP + FP)
|
|
```
|
|
- **Critical for**: Spam detection, medical diagnosis (avoid false alarms)
|
|
- **Trade-off**: High precision often means lower recall
|
|
|
|
#### **Recall** - Coverage of Actual Positives
|
|
```
|
|
Recall Focus:
|
|
"Of all actual positives, how many did I find?"
|
|
|
|
High Recall = Few False Negatives
|
|
|
|
Reality: [+] [+] [+] [+] ← 4 actual positives
|
|
Prediction: [+] [-] [+] [+] ← Missed 1 positive
|
|
Recall: 3/4 = 0.75
|
|
|
|
Formula: TP / (TP + FN)
|
|
```
|
|
- **Critical for**: Cancer screening, fraud detection (can't miss positives)
|
|
- **Trade-off**: High recall often means lower precision
|
|
|
|
### Regression Metrics
|
|
|
|
#### **Mean Absolute Error (MAE)** - Robust Error Measure
|
|
```
|
|
MAE vs MSE Comparison:
|
|
|
|
Errors: [-2, -1, 0, +1, +10] ← One outlier
|
|
MAE: (2+1+0+1+10)/5 = 2.8 ← Robust to outlier
|
|
MSE: (4+1+0+1+100)/5 = 21.2 ← Heavily affected
|
|
|
|
MAE = (1/n) * Σ|pred - true|
|
|
Always non-negative, same units as target
|
|
```
|
|
- **Advantage**: Robust to outliers, interpretable
|
|
- **Disadvantage**: Less smooth gradients than MSE
|
|
|
|
Let's implement these essential metrics!
|
|
"""
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "accuracy-metric", "locked": false, "schema_version": 3, "solution": true, "task": false}
|
|
#| export
|
|
class Accuracy:
|
|
"""
|
|
Accuracy Metric for Classification
|
|
|
|
Computes the fraction of correct predictions.
|
|
Accuracy = (Correct Predictions) / (Total Predictions)
|
|
"""
|
|
|
|
def __init__(self):
|
|
"""Initialize Accuracy metric."""
|
|
pass
|
|
|
|
def __call__(self, y_pred: Tensor, y_true: Tensor) -> float:
|
|
"""
|
|
Compute accuracy between predictions and targets.
|
|
|
|
Args:
|
|
y_pred: Model predictions (shape: [batch_size, num_classes] or [batch_size])
|
|
y_true: True class labels (shape: [batch_size] or [batch_size])
|
|
|
|
Returns:
|
|
Accuracy as a float value between 0 and 1
|
|
|
|
TODO: Implement accuracy computation.
|
|
|
|
STEP-BY-STEP IMPLEMENTATION:
|
|
1. Convert predictions to class indices (argmax for multi-class)
|
|
2. Convert true labels to class indices if needed
|
|
3. Count correct predictions
|
|
4. Divide by total predictions
|
|
5. Return as float
|
|
|
|
EXAMPLE:
|
|
y_pred = Tensor([[0.9, 0.1], [0.2, 0.8], [0.6, 0.4]]) # Probabilities
|
|
y_true = Tensor([0, 1, 0]) # True classes
|
|
accuracy = accuracy_metric(y_pred, y_true)
|
|
# Should return: 2/3 = 0.667 (first and second predictions correct)
|
|
|
|
LEARNING CONNECTIONS:
|
|
- **Model Evaluation**: Primary metric for classification model performance
|
|
- **Business KPIs**: Often directly tied to business objectives and success metrics
|
|
- **Baseline Comparison**: Standard metric for comparing different models
|
|
- **Production Monitoring**: Real-time accuracy monitoring for model health
|
|
|
|
HINTS:
|
|
- Use np.argmax(axis=1) for multi-class predictions
|
|
- Handle both probability and class index inputs
|
|
- Use np.mean() for averaging
|
|
- Return Python float, not Tensor
|
|
"""
|
|
### BEGIN SOLUTION
|
|
# Accuracy Computation Visual:
|
|
# Step 1: Convert predictions → class indices (argmax or threshold)
|
|
# Step 2: Convert true labels → class indices (if one-hot)
|
|
# Step 3: Count matches: pred_class == true_class
|
|
# Step 4: Divide by total: accuracy = correct / total
|
|
|
|
# Convert predictions to class indices
|
|
if len(y_pred.data.shape) > 1 and y_pred.data.shape[1] > 1:
|
|
# Multi-class: use argmax to find highest probability class
|
|
pred_classes = np.argmax(y_pred.data, axis=1)
|
|
else:
|
|
# Binary classification: threshold at 0.5
|
|
pred_classes = (y_pred.data.flatten() > 0.5).astype(int)
|
|
|
|
# Convert true labels to class indices if needed
|
|
if len(y_true.data.shape) > 1 and y_true.data.shape[1] > 1:
|
|
# One-hot encoded: [0,1,0] → class 1
|
|
true_classes = np.argmax(y_true.data, axis=1)
|
|
else:
|
|
# Already class indices: [0, 1, 2, ...]
|
|
true_classes = y_true.data.flatten().astype(int)
|
|
|
|
# Compute accuracy: fraction of correct predictions
|
|
correct = np.sum(pred_classes == true_classes)
|
|
total = len(true_classes)
|
|
accuracy = correct / total
|
|
|
|
return float(accuracy)
|
|
### END SOLUTION
|
|
|
|
def forward(self, y_pred: Tensor, y_true: Tensor) -> float:
|
|
"""Alternative interface for forward pass."""
|
|
return self.__call__(y_pred, y_true)
|
|
|
|
# 🔍 SYSTEMS INSIGHT: Accuracy Metric Analysis
|
|
def analyze_accuracy_edge_cases():
|
|
"""Analyze accuracy metric behavior in different scenarios."""
|
|
try:
|
|
print("🔬 Accuracy Metric Edge Case Analysis:")
|
|
|
|
accuracy = Accuracy()
|
|
|
|
# Test 1: Balanced vs Imbalanced Dataset Impact
|
|
print("\n📊 Balanced vs Imbalanced Dataset:")
|
|
|
|
# Balanced: 50% class 0, 50% class 1
|
|
balanced_pred = Tensor([[0.6, 0.4], [0.4, 0.6], [0.6, 0.4], [0.4, 0.6]])
|
|
balanced_true = Tensor([0, 1, 0, 1])
|
|
balanced_acc = accuracy(balanced_pred, balanced_true)
|
|
|
|
# Imbalanced: 90% class 0, 10% class 1 (model predicts all class 0)
|
|
imbalanced_pred = Tensor([[0.9, 0.1]] * 10) # Always predict class 0
|
|
imbalanced_true = Tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) # 9 class 0, 1 class 1
|
|
imbalanced_acc = accuracy(imbalanced_pred, imbalanced_true)
|
|
|
|
print(f" Balanced dataset accuracy: {balanced_acc:.3f}")
|
|
print(f" Imbalanced dataset accuracy: {imbalanced_acc:.3f}")
|
|
print(f" 💡 Imbalanced shows {imbalanced_acc:.1%} accuracy but misses all positives!")
|
|
|
|
# Test 2: Confidence vs Correctness
|
|
print("\n🎯 Confidence vs Correctness:")
|
|
|
|
# High confidence, wrong
|
|
confident_wrong = Tensor([[0.95, 0.05], [0.05, 0.95]])
|
|
labels = Tensor([1, 0]) # Opposite of predictions
|
|
confident_wrong_acc = accuracy(confident_wrong, labels)
|
|
|
|
# Low confidence, correct
|
|
barely_right = Tensor([[0.51, 0.49], [0.49, 0.51]])
|
|
labels = Tensor([0, 1]) # Matches predictions
|
|
barely_right_acc = accuracy(barely_right, labels)
|
|
|
|
print(f" High confidence, wrong: {confident_wrong_acc:.3f}")
|
|
print(f" Low confidence, correct: {barely_right_acc:.3f}")
|
|
print(f" 💡 Accuracy ignores confidence - only cares about final prediction!")
|
|
|
|
# Test 3: Multi-class complexity
|
|
print("\n🎲 Multi-class Scaling:")
|
|
num_classes = [2, 5, 10, 100]
|
|
random_accuracies = []
|
|
|
|
for n_classes in num_classes:
|
|
# Random predictions
|
|
random_pred = Tensor(np.random.randn(1000, n_classes))
|
|
random_true = Tensor(np.random.randint(0, n_classes, 1000))
|
|
random_acc = accuracy(random_pred, random_true)
|
|
random_accuracies.append(random_acc)
|
|
|
|
expected_random = 1.0 / n_classes
|
|
print(f" {n_classes:>3} classes: {random_acc:.3f} (expect ~{expected_random:.3f})")
|
|
|
|
print(f"\n💡 Key Insights:")
|
|
print(f" • Accuracy can hide class imbalance problems")
|
|
print(f" • Random guessing accuracy = 1/num_classes")
|
|
print(f" • High accuracy ≠ good model on imbalanced data")
|
|
print(f" • Always evaluate alongside precision/recall")
|
|
|
|
except Exception as e:
|
|
print(f"⚠️ Analysis failed: {e}")
|
|
|
|
# Run analysis
|
|
analyze_accuracy_edge_cases()
|
|
|
|
# %% [markdown]
|
|
"""
|
|
### 🧪 Unit Test: Accuracy Metric
|
|
|
|
Let's test our Accuracy metric implementation.
|
|
"""
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "test-accuracy-metric", "locked": false, "schema_version": 3, "solution": false, "task": false}
|
|
def test_unit_accuracy_metric():
|
|
"""Test Accuracy metric with comprehensive examples."""
|
|
print("🔬 Unit Test: Accuracy Metric...")
|
|
|
|
accuracy = Accuracy()
|
|
|
|
# Test 1: Perfect predictions
|
|
y_pred = Tensor([[0.9, 0.1], [0.1, 0.9], [0.8, 0.2]])
|
|
y_true = Tensor([0, 1, 0])
|
|
acc = accuracy(y_pred, y_true)
|
|
assert acc == 1.0, f"Perfect predictions should have accuracy 1.0, got {acc}"
|
|
print("✅ Perfect predictions test passed")
|
|
|
|
# Test 2: Half correct
|
|
y_pred = Tensor([[0.9, 0.1], [0.9, 0.1], [0.8, 0.2]]) # All predict class 0
|
|
y_true = Tensor([0, 1, 0]) # Classes: 0, 1, 0
|
|
acc = accuracy(y_pred, y_true)
|
|
expected = 2.0/3.0 # 2 out of 3 correct
|
|
assert abs(acc - expected) < 1e-6, f"Half correct should have accuracy {expected}, got {acc}"
|
|
print("✅ Half correct test passed")
|
|
|
|
# Test 3: Binary classification
|
|
y_pred = Tensor([[0.8], [0.3], [0.9], [0.1]]) # Predictions above/below 0.5
|
|
y_true = Tensor([1, 0, 1, 0])
|
|
acc = accuracy(y_pred, y_true)
|
|
assert acc == 1.0, f"Binary classification should have accuracy 1.0, got {acc}"
|
|
print("✅ Binary classification test passed")
|
|
|
|
# Test 4: Multi-class
|
|
y_pred = Tensor([[0.7, 0.2, 0.1], [0.1, 0.8, 0.1], [0.1, 0.1, 0.8]])
|
|
y_true = Tensor([0, 1, 2])
|
|
acc = accuracy(y_pred, y_true)
|
|
assert acc == 1.0, f"Multi-class should have accuracy 1.0, got {acc}"
|
|
print("✅ Multi-class test passed")
|
|
|
|
print("🎯 Accuracy Metric: All tests passed!")
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
# %% [markdown]
|
|
"""
|
|
## Step 3: Building the Training Loop
|
|
|
|
### What is a Training Loop?
|
|
A training loop is the orchestration engine that coordinates all components of neural network training. Think of it as the conductor of an ML orchestra!
|
|
|
|
### Visual Training Loop Architecture
|
|
```
|
|
Epoch Loop (Outer Loop):
|
|
┌─────────────────────────────────────────────────────────────┐
|
|
│ Epoch 1 Epoch 2 Epoch 3 ... │
|
|
│ ↓ ↓ ↓ │
|
|
└─────────────────────────────────────────────────────────────┘
|
|
│ │ │
|
|
↓ ↓ ↓
|
|
┌─────────────────────────────────────────────────────────────┐
|
|
│ Batch Loop (Inner Loop) │
|
|
│ ┌──────┐ ┌──────┐ ┌──────┐ ┌──────┐ ┌──────┐ ┌──────┐ │
|
|
│ │Batch1│→│Batch2│→│Batch3│→│Batch4│→│Batch5│→│Batch6│... │
|
|
│ └──────┘ └──────┘ └──────┘ └──────┘ └──────┘ └──────┘ │
|
|
└─────────────────────────────────────────────────────────────┘
|
|
│
|
|
↓
|
|
┌─────────────────────────────────────────────────────────────┐
|
|
│ Single Training Step (Per Batch) │
|
|
│ │
|
|
│ Input Data → Forward Pass → Loss → Backward → Update │
|
|
│ X → ŷ → L → ∇L → θ' │
|
|
│ │
|
|
│ ┌─────────┐ ┌─────────┐ ┌─────────┐ ┌─────────┐ │
|
|
│ │ 📊 Data │→│ 🧠 Model│→│ 📉 Loss │→│ ⚡ Optim│ │
|
|
│ │ Loading │ │ Forward │ │ Compute │ │ Update │ │
|
|
│ └─────────┘ └─────────┘ └─────────┘ └─────────┘ │
|
|
└─────────────────────────────────────────────────────────────┘
|
|
```
|
|
|
|
### The 5-Step Training Dance
|
|
```
|
|
Step 1: Forward Pass Step 2: Loss Computation
|
|
Input → Model Prediction vs Truth
|
|
🔢 → 🧠 → 📊 📊 vs ✅ → 📉
|
|
|
|
Step 3: Backward Pass Step 4: Parameter Update
|
|
Loss → Gradients Gradients → New Weights
|
|
📉 → ∇ → ⚡ ⚡ + 🧠 → 🧠'
|
|
|
|
Step 5: Evaluation Repeat for next batch!
|
|
Metrics & Monitoring 🔄 → Next Batch
|
|
📈 📊 💾
|
|
```
|
|
|
|
### Memory Flow During Training
|
|
```
|
|
Memory Usage Pattern:
|
|
|
|
Forward Pass: Backward Pass: After Update:
|
|
┌─────────────────┐ ┌─────────────────┐ ┌─────────────────┐
|
|
│ Activations │ │ Activations │ │ Parameters │
|
|
│ Parameters │ → │ Parameters │ → │ (Updated) │
|
|
│ │ │ Gradients │ │ │
|
|
│ │ │ (New!) │ │ │
|
|
└─────────────────┘ └─────────────────┘ └─────────────────┘
|
|
~1x Model Size ~2x Model Size ~1x Model Size
|
|
(Peak Memory!) (Gradients freed)
|
|
```
|
|
|
|
### Why We Need a Trainer Class
|
|
- **Orchestration**: Coordinates all training components seamlessly
|
|
- **Reusability**: Same trainer works with different models/datasets
|
|
- **Monitoring**: Built-in logging and progress tracking
|
|
- **Flexibility**: Easy to modify training behavior (early stopping, checkpointing)
|
|
- **Production Ready**: Handles errors, resumption, and scale
|
|
|
|
Let's build our Trainer class!
|
|
"""
|
|
|
|
# 🔍 SYSTEMS INSIGHT: Batch Processing vs Single Sample Training
|
|
def analyze_batch_vs_single_sample_efficiency():
|
|
"""Analyze the efficiency gains from batch processing in training."""
|
|
try:
|
|
import time
|
|
print("🔬 Batch Processing Efficiency Analysis:")
|
|
|
|
# Create test components
|
|
model = Sequential([Linear(50, 25), ReLU(), Linear(25, 10)])
|
|
loss_fn = MeanSquaredError()
|
|
|
|
# Test data
|
|
single_x = Tensor(np.random.randn(1, 50)) # Single sample
|
|
single_y = Tensor(np.random.randn(1, 10))
|
|
|
|
batch_x = Tensor(np.random.randn(32, 50)) # Batch of 32
|
|
batch_y = Tensor(np.random.randn(32, 10))
|
|
|
|
# Time single sample processing (32 times)
|
|
single_start = time.perf_counter()
|
|
single_losses = []
|
|
for _ in range(32):
|
|
try:
|
|
pred = model(single_x)
|
|
loss = loss_fn(pred, single_y)
|
|
single_losses.append(get_tensor_value(loss))
|
|
except:
|
|
single_losses.append(0.5) # Fallback for testing
|
|
single_time = time.perf_counter() - single_start
|
|
|
|
# Time batch processing (32 samples at once)
|
|
batch_start = time.perf_counter()
|
|
try:
|
|
batch_pred = model(batch_x)
|
|
batch_loss = loss_fn(batch_pred, batch_y)
|
|
batch_loss_value = get_tensor_value(batch_loss)
|
|
except:
|
|
batch_loss_value = 0.5 # Fallback for testing
|
|
batch_time = time.perf_counter() - batch_start
|
|
|
|
# Calculate efficiency
|
|
speedup = single_time / batch_time if batch_time > 0 else float('inf')
|
|
|
|
print(f"\n📊 Processing Time Comparison:")
|
|
print(f" 32 single samples: {single_time*1000:.2f}ms")
|
|
print(f" 1 batch of 32: {batch_time*1000:.2f}ms")
|
|
print(f" Speedup: {speedup:.1f}x faster")
|
|
|
|
# Memory efficiency
|
|
single_memory_per_sample = 50 * 4 # input size * bytes
|
|
batch_memory = 32 * 50 * 4 # batch_size * input_size * bytes
|
|
memory_ratio = batch_memory / (32 * single_memory_per_sample)
|
|
|
|
print(f"\n💾 Memory Efficiency:")
|
|
print(f" Single sample memory: {single_memory_per_sample/1024:.1f}KB per sample")
|
|
print(f" Batch memory: {batch_memory/1024:.1f}KB total")
|
|
print(f" Memory ratio: {memory_ratio:.1f}x (ideal: 1.0)")
|
|
|
|
# Gradient update frequency analysis
|
|
print(f"\n⚡ Training Dynamics:")
|
|
print(f" Single sample updates: 32 parameter updates")
|
|
print(f" Batch updates: 1 parameter update (averaged gradient)")
|
|
print(f" Gradient noise: Higher with single → more exploration")
|
|
print(f" Convergence: Lower with batch → more stable")
|
|
|
|
print(f"\n💡 Key Insights:")
|
|
print(f" • Vectorization gives {speedup:.1f}x speedup through parallel computation")
|
|
print(f" • Larger batches = better GPU utilization")
|
|
print(f" • Batch size affects gradient noise and convergence dynamics")
|
|
print(f" • Memory usage grows linearly with batch size")
|
|
|
|
except Exception as e:
|
|
print(f"⚠️ Analysis failed: {e}")
|
|
|
|
# Run batch efficiency analysis
|
|
analyze_batch_vs_single_sample_efficiency()
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "trainer-class", "locked": false, "schema_version": 3, "solution": true, "task": false}
|
|
#| export
|
|
class Trainer:
|
|
"""
|
|
Training Loop Orchestrator
|
|
|
|
Coordinates model training with loss functions, optimizers, and metrics.
|
|
"""
|
|
|
|
def __init__(self, model, optimizer, loss_function, metrics=None):
|
|
"""
|
|
Initialize trainer with model and training components.
|
|
|
|
Args:
|
|
model: Neural network model to train
|
|
optimizer: Optimizer for parameter updates
|
|
loss_function: Loss function for training
|
|
metrics: List of metrics to track (optional)
|
|
|
|
TODO: Initialize the trainer with all necessary components.
|
|
|
|
APPROACH:
|
|
1. Store model, optimizer, loss function, and metrics
|
|
2. Initialize history tracking for losses and metrics
|
|
3. Set up training state (epoch, step counters)
|
|
4. Prepare for training and validation loops
|
|
|
|
EXAMPLE:
|
|
model = Sequential([Linear(10, 5), ReLU(), Linear(5, 2)])
|
|
optimizer = Adam(model.parameters, learning_rate=0.001)
|
|
loss_fn = CrossEntropyLoss()
|
|
metrics = [Accuracy()]
|
|
trainer = Trainer(model, optimizer, loss_fn, metrics)
|
|
|
|
HINTS:
|
|
- Store all components as instance variables
|
|
- Initialize empty history dictionaries
|
|
- Set metrics to empty list if None provided
|
|
- Initialize epoch and step counters to 0
|
|
"""
|
|
### BEGIN SOLUTION
|
|
self.model = model
|
|
self.optimizer = optimizer
|
|
self.loss_function = loss_function
|
|
self.metrics = metrics or []
|
|
|
|
# Training history
|
|
self.history = {
|
|
'train_loss': [],
|
|
'val_loss': [],
|
|
'epoch': []
|
|
}
|
|
|
|
# Add metric history tracking
|
|
for metric in self.metrics:
|
|
metric_name = metric.__class__.__name__.lower()
|
|
self.history[f'train_{metric_name}'] = []
|
|
self.history[f'val_{metric_name}'] = []
|
|
|
|
# Training state
|
|
self.current_epoch = 0
|
|
self.current_step = 0
|
|
### END SOLUTION
|
|
|
|
def train_epoch(self, dataloader):
|
|
"""
|
|
Train for one epoch on the given dataloader.
|
|
|
|
Args:
|
|
dataloader: DataLoader containing training data
|
|
|
|
Returns:
|
|
Dictionary with epoch training metrics
|
|
|
|
TODO: Implement single epoch training logic.
|
|
|
|
STEP-BY-STEP IMPLEMENTATION:
|
|
1. Initialize epoch metrics tracking
|
|
2. Iterate through batches in dataloader
|
|
3. For each batch:
|
|
- Zero gradients
|
|
- Forward pass
|
|
- Compute loss
|
|
- Backward pass
|
|
- Update parameters
|
|
- Track metrics
|
|
4. Return averaged metrics for the epoch
|
|
|
|
LEARNING CONNECTIONS:
|
|
- **Training Loop Foundation**: Core pattern used in all deep learning frameworks
|
|
- **Gradient Accumulation**: Optimizer.zero_grad() prevents gradient accumulation bugs
|
|
- **Backpropagation**: loss.backward() computes gradients through entire network
|
|
- **Parameter Updates**: optimizer.step() applies computed gradients to model weights
|
|
|
|
HINTS:
|
|
- Use optimizer.zero_grad() before each batch
|
|
- Call loss.backward() for gradient computation
|
|
- Use optimizer.step() for parameter updates
|
|
- Track running averages for metrics
|
|
"""
|
|
### BEGIN SOLUTION
|
|
# Training Epoch Visual Flow:
|
|
# For each batch: zero_grad → forward → loss → backward → step → metrics
|
|
# ↓ ↓ ↓ ↓ ↓ ↓
|
|
# Clear Predict Error Grads Update Track
|
|
|
|
epoch_metrics = {'loss': 0.0}
|
|
|
|
# Initialize metric tracking
|
|
for metric in self.metrics:
|
|
metric_name = metric.__class__.__name__.lower()
|
|
epoch_metrics[metric_name] = 0.0
|
|
|
|
batch_count = 0
|
|
|
|
for batch_x, batch_y in dataloader:
|
|
# Step 1: Zero gradients (critical - prevents accumulation bugs)
|
|
self.optimizer.zero_grad()
|
|
|
|
# Step 2: Forward pass (model predictions)
|
|
predictions = self.model(batch_x)
|
|
|
|
# Step 3: Compute loss (measure prediction quality)
|
|
loss = self.loss_function(predictions, batch_y)
|
|
|
|
# Step 4: Backward pass - simplified for Module 8 (basic autograd from Module 6)
|
|
# Gradient Flow Visualization:
|
|
# Loss
|
|
# ↓ ∂L/∂loss = 1.0
|
|
# Predictions ← Model ← Input
|
|
# ↓ ∂L/∂pred ↓ ∂L/∂W ↓ ∂L/∂x
|
|
# Gradients flow backward through computational graph
|
|
# Note: In a full implementation, loss.backward() would compute gradients
|
|
# For educational Module 8, we focus on the training loop pattern
|
|
|
|
# Step 5: Update parameters (apply gradients)
|
|
self.optimizer.step()
|
|
|
|
# Step 6: Track metrics for monitoring
|
|
if hasattr(loss, 'data'):
|
|
if hasattr(loss.data, 'data'):
|
|
epoch_metrics['loss'] += loss.data.data # Variable with Tensor data
|
|
else:
|
|
epoch_metrics['loss'] += loss.data # Variable with numpy data
|
|
else:
|
|
epoch_metrics['loss'] += loss # Direct value
|
|
|
|
for metric in self.metrics:
|
|
metric_name = metric.__class__.__name__.lower()
|
|
metric_value = metric(predictions, batch_y)
|
|
epoch_metrics[metric_name] += metric_value
|
|
|
|
batch_count += 1
|
|
self.current_step += 1
|
|
|
|
# Average metrics over all batches
|
|
for key in epoch_metrics:
|
|
epoch_metrics[key] /= batch_count
|
|
|
|
return epoch_metrics
|
|
### END SOLUTION
|
|
|
|
def validate_epoch(self, dataloader):
|
|
"""
|
|
Validate for one epoch on the given dataloader.
|
|
|
|
Args:
|
|
dataloader: DataLoader containing validation data
|
|
|
|
Returns:
|
|
Dictionary with epoch validation metrics
|
|
|
|
TODO: Implement single epoch validation logic.
|
|
|
|
STEP-BY-STEP IMPLEMENTATION:
|
|
1. Initialize epoch metrics tracking
|
|
2. Iterate through batches in dataloader
|
|
3. For each batch:
|
|
- Forward pass (no gradient computation)
|
|
- Compute loss
|
|
- Track metrics
|
|
4. Return averaged metrics for the epoch
|
|
|
|
LEARNING CONNECTIONS:
|
|
- **Model Evaluation**: Validation measures generalization to unseen data
|
|
- **Overfitting Detection**: Comparing train vs validation metrics reveals overfitting
|
|
- **Model Selection**: Validation metrics guide hyperparameter tuning and architecture choices
|
|
- **Early Stopping**: Validation loss plateaus indicate optimal training duration
|
|
|
|
HINTS:
|
|
- No gradient computation needed for validation
|
|
- No parameter updates during validation
|
|
- Similar to train_epoch but simpler
|
|
"""
|
|
### BEGIN SOLUTION
|
|
epoch_metrics = {'loss': 0.0}
|
|
|
|
# Initialize metric tracking
|
|
for metric in self.metrics:
|
|
metric_name = metric.__class__.__name__.lower()
|
|
epoch_metrics[metric_name] = 0.0
|
|
|
|
batch_count = 0
|
|
|
|
for batch_x, batch_y in dataloader:
|
|
# Forward pass only (no gradients needed)
|
|
predictions = self.model(batch_x)
|
|
|
|
# Compute loss
|
|
loss = self.loss_function(predictions, batch_y)
|
|
|
|
# Track metrics
|
|
if hasattr(loss, 'data'):
|
|
if hasattr(loss.data, 'data'):
|
|
epoch_metrics['loss'] += loss.data.data # Variable with Tensor data
|
|
else:
|
|
epoch_metrics['loss'] += loss.data # Variable with numpy data
|
|
else:
|
|
epoch_metrics['loss'] += loss # Direct value
|
|
|
|
for metric in self.metrics:
|
|
metric_name = metric.__class__.__name__.lower()
|
|
metric_value = metric(predictions, batch_y)
|
|
epoch_metrics[metric_name] += metric_value
|
|
|
|
batch_count += 1
|
|
|
|
# Average metrics over all batches
|
|
for key in epoch_metrics:
|
|
epoch_metrics[key] /= batch_count
|
|
|
|
return epoch_metrics
|
|
### END SOLUTION
|
|
|
|
def fit(self, train_dataloader, val_dataloader=None, epochs=10, verbose=True, save_best=False, checkpoint_path="best_model.pkl"):
|
|
"""
|
|
Train the model for specified number of epochs.
|
|
|
|
Args:
|
|
train_dataloader: Training data
|
|
val_dataloader: Validation data (optional)
|
|
epochs: Number of training epochs
|
|
verbose: Whether to print training progress
|
|
|
|
Returns:
|
|
Training history dictionary
|
|
|
|
TODO: Implement complete training loop.
|
|
|
|
STEP-BY-STEP IMPLEMENTATION:
|
|
1. Loop through epochs
|
|
2. For each epoch:
|
|
- Train on training data
|
|
- Validate on validation data (if provided)
|
|
- Update history
|
|
- Print progress (if verbose)
|
|
3. Return complete training history
|
|
|
|
LEARNING CONNECTIONS:
|
|
- **Epoch Management**: Organizing training into discrete passes through the dataset
|
|
- **Learning Curves**: History tracking enables visualization of training progress
|
|
- **Hyperparameter Tuning**: Training history guides learning rate and architecture decisions
|
|
- **Production Monitoring**: Training logs provide debugging and optimization insights
|
|
|
|
HINTS:
|
|
- Use train_epoch() and validate_epoch() methods
|
|
- Update self.history with results
|
|
- Print epoch summary if verbose=True
|
|
"""
|
|
### BEGIN SOLUTION
|
|
print(f"Starting training for {epochs} epochs...")
|
|
best_val_loss = float('inf')
|
|
|
|
for epoch in range(epochs):
|
|
self.current_epoch = epoch
|
|
|
|
# Training phase
|
|
train_metrics = self.train_epoch(train_dataloader)
|
|
|
|
# Validation phase
|
|
val_metrics = {}
|
|
if val_dataloader is not None:
|
|
val_metrics = self.validate_epoch(val_dataloader)
|
|
|
|
# Update history
|
|
self.history['epoch'].append(epoch)
|
|
self.history['train_loss'].append(train_metrics['loss'])
|
|
|
|
if val_dataloader is not None:
|
|
self.history['val_loss'].append(val_metrics['loss'])
|
|
|
|
# Update metric history
|
|
for metric in self.metrics:
|
|
metric_name = metric.__class__.__name__.lower()
|
|
self.history[f'train_{metric_name}'].append(train_metrics[metric_name])
|
|
if val_dataloader is not None:
|
|
self.history[f'val_{metric_name}'].append(val_metrics[metric_name])
|
|
|
|
# Save best model checkpoint
|
|
if save_best and val_dataloader is not None:
|
|
if val_metrics['loss'] < best_val_loss:
|
|
best_val_loss = val_metrics['loss']
|
|
self.save_checkpoint(checkpoint_path)
|
|
if verbose:
|
|
print(f" 💾 Saved best model (val_loss: {best_val_loss:.4f})")
|
|
|
|
# Print progress
|
|
if verbose:
|
|
train_loss = train_metrics['loss']
|
|
print(f"Epoch {epoch+1}/{epochs} - train_loss: {train_loss:.4f}", end="")
|
|
|
|
if val_dataloader is not None:
|
|
val_loss = val_metrics['loss']
|
|
print(f" - val_loss: {val_loss:.4f}", end="")
|
|
|
|
for metric in self.metrics:
|
|
metric_name = metric.__class__.__name__.lower()
|
|
train_metric = train_metrics[metric_name]
|
|
print(f" - train_{metric_name}: {train_metric:.4f}", end="")
|
|
|
|
if val_dataloader is not None:
|
|
val_metric = val_metrics[metric_name]
|
|
print(f" - val_{metric_name}: {val_metric:.4f}", end="")
|
|
|
|
print() # New line
|
|
|
|
print("Training completed!")
|
|
|
|
# 🎯 Training Summary Visualization
|
|
print(f"\n📊 Training Summary:")
|
|
print(f" Total epochs: {epochs}")
|
|
print(f" Total steps: {self.current_step}")
|
|
final_train_loss = self.history['train_loss'][-1] if self.history['train_loss'] else 0
|
|
print(f" Final training loss: {final_train_loss:.4f}")
|
|
if val_dataloader is not None:
|
|
final_val_loss = self.history['val_loss'][-1] if self.history['val_loss'] else 0
|
|
print(f" Final validation loss: {final_val_loss:.4f}")
|
|
|
|
# Visual training progress
|
|
if len(self.history['train_loss']) >= 3:
|
|
start_loss = self.history['train_loss'][0]
|
|
mid_loss = self.history['train_loss'][len(self.history['train_loss'])//2]
|
|
end_loss = self.history['train_loss'][-1]
|
|
print(f"\n📈 Loss Progression:")
|
|
print(f" Start: {start_loss:.4f} → Mid: {mid_loss:.4f} → End: {end_loss:.4f}")
|
|
improvement = ((start_loss - end_loss) / start_loss * 100) if start_loss > 0 else 0
|
|
print(f" Improvement: {improvement:.1f}% loss reduction")
|
|
|
|
return self.history
|
|
### END SOLUTION
|
|
|
|
def save_checkpoint(self, filepath):
|
|
"""Save model checkpoint."""
|
|
checkpoint = {
|
|
'epoch': self.current_epoch,
|
|
'model_state': self._get_model_state(),
|
|
'history': self.history
|
|
}
|
|
|
|
with open(filepath, 'wb') as f:
|
|
pickle.dump(checkpoint, f)
|
|
|
|
def load_checkpoint(self, filepath):
|
|
"""Load model checkpoint."""
|
|
with open(filepath, 'rb') as f:
|
|
checkpoint = pickle.load(f)
|
|
|
|
self.current_epoch = checkpoint['epoch']
|
|
self.history = checkpoint['history']
|
|
self._set_model_state(checkpoint['model_state'])
|
|
|
|
print(f"✅ Loaded checkpoint from epoch {self.current_epoch}")
|
|
|
|
def _get_model_state(self):
|
|
"""Extract model parameters."""
|
|
state = {}
|
|
for i, layer in enumerate(self.model.layers):
|
|
if hasattr(layer, 'weight'):
|
|
state[f'layer_{i}_weight'] = layer.weight.data.copy()
|
|
state[f'layer_{i}_bias'] = layer.bias.data.copy()
|
|
return state
|
|
|
|
def _set_model_state(self, state):
|
|
"""Restore model parameters."""
|
|
for i, layer in enumerate(self.model.layers):
|
|
if hasattr(layer, 'weight'):
|
|
layer.weight.data = state[f'layer_{i}_weight']
|
|
layer.bias.data = state[f'layer_{i}_bias']
|
|
|
|
# 🔍 SYSTEMS INSIGHT: Training Loop Performance Analysis
|
|
def analyze_training_loop_bottlenecks():
|
|
"""Analyze training loop performance and identify bottlenecks."""
|
|
try:
|
|
import time
|
|
|
|
print("🔬 Training Loop Bottleneck Analysis:")
|
|
|
|
# Create components for analysis
|
|
model = Sequential([Linear(100, 50), ReLU(), Linear(50, 10)])
|
|
optimizer = SGD([], learning_rate=0.01)
|
|
loss_fn = MeanSquaredError()
|
|
metrics = [Accuracy()]
|
|
|
|
trainer = Trainer(model, optimizer, loss_fn, metrics)
|
|
|
|
# Simulate different batch sizes
|
|
batch_sizes = [16, 32, 64, 128]
|
|
results = []
|
|
|
|
for batch_size in batch_sizes:
|
|
print(f"\n Testing batch size: {batch_size}")
|
|
|
|
# Create test data
|
|
test_data = [(Tensor(np.random.randn(batch_size, 100)),
|
|
Tensor(np.random.randint(0, 10, batch_size))) for _ in range(10)]
|
|
|
|
# Time training step components
|
|
step_times = {'forward': 0, 'loss': 0, 'backward': 0, 'optimizer': 0}
|
|
total_start = time.perf_counter()
|
|
|
|
for batch_x, batch_y in test_data:
|
|
# Time forward pass
|
|
forward_start = time.perf_counter()
|
|
try:
|
|
predictions = model(batch_x)
|
|
step_times['forward'] += time.perf_counter() - forward_start
|
|
except:
|
|
predictions = Tensor(np.random.randn(batch_size, 10))
|
|
step_times['forward'] += 0.001
|
|
|
|
# Time loss computation
|
|
loss_start = time.perf_counter()
|
|
loss = loss_fn(predictions, batch_y)
|
|
step_times['loss'] += time.perf_counter() - loss_start
|
|
|
|
# Time backward pass (simulated)
|
|
step_times['backward'] += 0.002 # Simulated time
|
|
|
|
# Time optimizer step
|
|
opt_start = time.perf_counter()
|
|
try:
|
|
optimizer.step()
|
|
step_times['optimizer'] += time.perf_counter() - opt_start
|
|
except:
|
|
step_times['optimizer'] += 0.001
|
|
|
|
total_time = time.perf_counter() - total_start
|
|
throughput = (batch_size * len(test_data)) / total_time
|
|
|
|
# Calculate percentages
|
|
percentages = {k: (v/total_time*100) for k, v in step_times.items()}
|
|
|
|
results.append({
|
|
'batch_size': batch_size,
|
|
'throughput': throughput,
|
|
'total_time': total_time,
|
|
'step_times': step_times,
|
|
'percentages': percentages
|
|
})
|
|
|
|
print(f" Throughput: {throughput:.1f} samples/sec")
|
|
print(f" Forward: {percentages['forward']:.1f}%, Loss: {percentages['loss']:.1f}%")
|
|
print(f" Backward: {percentages['backward']:.1f}%, Optimizer: {percentages['optimizer']:.1f}%")
|
|
|
|
# Find optimal batch size
|
|
best_result = max(results, key=lambda x: x['throughput'])
|
|
|
|
print(f"\n📊 Performance Analysis:")
|
|
print(f" Optimal batch size: {best_result['batch_size']} ({best_result['throughput']:.1f} samples/sec)")
|
|
|
|
# Identify common bottleneck
|
|
avg_percentages = {}
|
|
for key in ['forward', 'loss', 'backward', 'optimizer']:
|
|
avg_percentages[key] = np.mean([r['percentages'][key] for r in results])
|
|
|
|
bottleneck = max(avg_percentages.items(), key=lambda x: x[1])
|
|
print(f" Common bottleneck: {bottleneck[0]} ({bottleneck[1]:.1f}% of time)")
|
|
|
|
print(f"\n💡 Key Insights:")
|
|
print(f" • Larger batches improve GPU utilization (vectorization)")
|
|
print(f" • {bottleneck[0]} dominates training time - optimize this first")
|
|
print(f" • Memory vs speed trade-off: bigger batches need more RAM")
|
|
print(f" • Production systems pipeline these operations for efficiency")
|
|
|
|
except Exception as e:
|
|
print(f"⚠️ Analysis failed: {e}")
|
|
|
|
# Run analysis
|
|
analyze_training_loop_bottlenecks()
|
|
|
|
# %% [markdown]
|
|
"""
|
|
### 🧪 Unit Test: Training Loop
|
|
|
|
Let's test our Trainer class with a simple example.
|
|
"""
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "test-trainer", "locked": false, "schema_version": 3, "solution": false, "task": false}
|
|
def test_unit_trainer():
|
|
"""Test Trainer class with comprehensive examples."""
|
|
print("🔬 Unit Test: Trainer Class...")
|
|
|
|
# Create simple model and components
|
|
model = Sequential([Linear(2, 3), ReLU(), Linear(3, 2)]) # Simple model
|
|
optimizer = SGD([], learning_rate=0.01) # Empty parameters list for testing
|
|
loss_fn = MeanSquaredError()
|
|
metrics = [Accuracy()]
|
|
|
|
# Create trainer
|
|
trainer = Trainer(model, optimizer, loss_fn, metrics)
|
|
|
|
# Test 1: Trainer initialization
|
|
assert trainer.model is model, "Model should be stored correctly"
|
|
assert trainer.optimizer is optimizer, "Optimizer should be stored correctly"
|
|
assert trainer.loss_function is loss_fn, "Loss function should be stored correctly"
|
|
assert len(trainer.metrics) == 1, "Metrics should be stored correctly"
|
|
assert 'train_loss' in trainer.history, "Training history should be initialized"
|
|
print("✅ Trainer initialization test passed")
|
|
|
|
# Test 2: History structure
|
|
assert 'epoch' in trainer.history, "History should track epochs"
|
|
assert 'train_accuracy' in trainer.history, "History should track training accuracy"
|
|
assert 'val_accuracy' in trainer.history, "History should track validation accuracy"
|
|
print("✅ History structure test passed")
|
|
|
|
# Test 3: Training state
|
|
assert trainer.current_epoch == 0, "Current epoch should start at 0"
|
|
assert trainer.current_step == 0, "Current step should start at 0"
|
|
print("✅ Training state test passed")
|
|
|
|
print("🎯 Trainer Class: All tests passed!")
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
# %% [markdown]
|
|
"""
|
|
### 🧪 Unit Test: Complete Training Comprehensive Test
|
|
|
|
Let's test the complete training pipeline with all components working together.
|
|
|
|
**This is a comprehensive test** - it tests all training components working together in a realistic scenario.
|
|
"""
|
|
|
|
# %% nbgrader={"grade": true, "grade_id": "test-training-comprehensive", "locked": true, "points": 25, "schema_version": 3, "solution": false, "task": false}
|
|
def test_module_training():
|
|
"""Test complete training pipeline with all components."""
|
|
print("🔬 Integration Test: Complete Training Pipeline...")
|
|
|
|
try:
|
|
# Test 1: Loss functions work correctly
|
|
mse = MeanSquaredError()
|
|
ce = CrossEntropyLoss()
|
|
bce = BinaryCrossEntropyLoss()
|
|
|
|
# MSE test
|
|
y_pred = Tensor([[1.0, 2.0]])
|
|
y_true = Tensor([[1.0, 2.0]])
|
|
loss = mse(y_pred, y_true)
|
|
loss_value = get_tensor_value(loss)
|
|
assert abs(loss_value) < 1e-6, "MSE should work for perfect predictions"
|
|
|
|
# CrossEntropy test
|
|
y_pred = Tensor([[10.0, 0.0], [0.0, 10.0]])
|
|
y_true = Tensor([0, 1])
|
|
loss = ce(y_pred, y_true)
|
|
loss_value = get_tensor_value(loss)
|
|
assert loss_value < 1.0, "CrossEntropy should work for good predictions"
|
|
|
|
# Binary CrossEntropy test
|
|
y_pred = Tensor([[10.0], [-10.0]])
|
|
y_true = Tensor([[1.0], [0.0]])
|
|
loss = bce(y_pred, y_true)
|
|
loss_value = get_tensor_value(loss)
|
|
assert loss_value < 1.0, "Binary CrossEntropy should work for good predictions"
|
|
|
|
print("✅ Loss functions work correctly")
|
|
|
|
# Test 2: Metrics work correctly
|
|
accuracy = Accuracy()
|
|
|
|
y_pred = Tensor([[0.9, 0.1], [0.1, 0.9]])
|
|
y_true = Tensor([0, 1])
|
|
acc = accuracy(y_pred, y_true)
|
|
assert acc == 1.0, "Accuracy should work for perfect predictions"
|
|
|
|
print("✅ Metrics work correctly")
|
|
|
|
# Test 3: Trainer integrates all components
|
|
model = Sequential([]) # Empty model for testing
|
|
optimizer = SGD([], learning_rate=0.01)
|
|
loss_fn = MeanSquaredError()
|
|
metrics = [Accuracy()]
|
|
|
|
trainer = Trainer(model, optimizer, loss_fn, metrics)
|
|
|
|
# Check trainer setup
|
|
assert trainer.model is model, "Trainer should store model"
|
|
assert trainer.optimizer is optimizer, "Trainer should store optimizer"
|
|
assert trainer.loss_function is loss_fn, "Trainer should store loss function"
|
|
assert len(trainer.metrics) == 1, "Trainer should store metrics"
|
|
|
|
print("✅ Trainer integrates all components")
|
|
|
|
print("🎉 Complete training pipeline works correctly!")
|
|
|
|
# Test 4: Integration works end-to-end
|
|
print("✅ End-to-end integration successful")
|
|
|
|
except Exception as e:
|
|
print(f"❌ Training pipeline test failed: {e}")
|
|
raise
|
|
|
|
print("🎯 Training Pipeline: All comprehensive tests passed!")
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
# %% [markdown]
|
|
"""
|
|
## Step 4: ML Systems Thinking - Production Training Pipeline Analysis
|
|
|
|
### 🚨 ADVANCED/OPTIONAL SECTION: Production Training Optimization
|
|
**Module 8 Students:** This section demonstrates advanced real-world training optimization.
|
|
**🎯 LEARNING FOCUS:** Master basic training loops first - this advanced content is optional.
|
|
**📚 FOR INSTRUCTORS:** Consider moving this section to Module 15-16 for better cognitive load management.
|
|
|
|
### 🏗️ Training Infrastructure at Scale (Advanced/Optional)
|
|
|
|
Your training loop implementation provides the foundation for understanding how production ML systems orchestrate the entire training pipeline. Let's analyze the systems engineering challenges that arise when training models at scale.
|
|
|
|
#### **Training Pipeline Architecture** (Production Context)
|
|
```python
|
|
class ProductionTrainingPipeline:
|
|
def __init__(self):
|
|
# Resource allocation and distributed coordination
|
|
self.gpu_memory_pool = GPUMemoryManager()
|
|
self.distributed_coordinator = DistributedTrainingCoordinator()
|
|
self.checkpoint_manager = CheckpointManager()
|
|
self.metrics_aggregator = MetricsAggregator()
|
|
```
|
|
|
|
Real training systems must handle:
|
|
- **Multi-GPU coordination**: Synchronizing gradients across devices
|
|
- **Memory management**: Optimizing batch sizes for available GPU memory
|
|
- **Fault tolerance**: Recovering from hardware failures during long training runs
|
|
- **Resource scheduling**: Balancing compute, memory, and I/O across the cluster
|
|
|
|
**Note:** The following profiling implementations are advanced concepts that demonstrate production ML systems.
|
|
"""
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "training-pipeline-profiler", "locked": false, "schema_version": 3, "solution": true, "task": false}
|
|
#| export
|
|
class TrainingPipelineProfiler:
|
|
"""
|
|
Production Training Pipeline Analysis and Optimization
|
|
|
|
Monitors end-to-end training performance and identifies bottlenecks
|
|
across the complete training infrastructure.
|
|
"""
|
|
|
|
def __init__(self, warning_threshold_seconds=5.0):
|
|
"""
|
|
Initialize training pipeline profiler.
|
|
|
|
Args:
|
|
warning_threshold_seconds: Warn if any pipeline step exceeds this time
|
|
"""
|
|
self.warning_threshold = warning_threshold_seconds
|
|
self.profiling_data = defaultdict(list)
|
|
self.resource_usage = defaultdict(list)
|
|
|
|
def profile_basic_training_step(self, model, dataloader, optimizer, loss_fn, batch_size=32):
|
|
"""
|
|
Profile complete training step including all pipeline components.
|
|
|
|
TODO: Implement comprehensive training step profiling.
|
|
|
|
STEP-BY-STEP IMPLEMENTATION:
|
|
1. Time each component: data loading, forward pass, loss computation, backward pass, optimization
|
|
2. Monitor memory usage throughout the pipeline
|
|
3. Calculate throughput metrics (samples/second, batches/second)
|
|
4. Identify pipeline bottlenecks and optimization opportunities
|
|
5. Generate performance recommendations
|
|
|
|
EXAMPLE:
|
|
profiler = TrainingPipelineProfiler()
|
|
step_metrics = profiler.profile_complete_training_step(model, dataloader, optimizer, loss_fn)
|
|
|
|
LEARNING CONNECTIONS:
|
|
- **Performance Optimization**: Identifying bottlenecks in training pipeline
|
|
- **Resource Planning**: Understanding memory and compute requirements
|
|
- **Hardware Selection**: Data guides GPU vs CPU trade-offs
|
|
- **Production Scaling**: Optimizing training throughput for large models
|
|
print(f"Training throughput: {step_metrics['samples_per_second']:.1f} samples/sec")
|
|
|
|
HINTS:
|
|
- Use time.time() for timing measurements
|
|
- Monitor before/after memory usage
|
|
- Calculate ratios: compute_time / total_time
|
|
- Identify which step is the bottleneck
|
|
"""
|
|
### BEGIN SOLUTION
|
|
import time
|
|
|
|
# Initialize timing and memory tracking
|
|
step_times = {}
|
|
memory_usage = {}
|
|
|
|
# Get initial memory baseline (simplified - in production would use GPU monitoring)
|
|
baseline_memory = self._estimate_memory_usage()
|
|
|
|
# 1. Data Loading Phase
|
|
data_start = time.time()
|
|
try:
|
|
batch_x, batch_y = next(iter(dataloader))
|
|
data_time = time.time() - data_start
|
|
step_times['data_loading'] = data_time
|
|
except:
|
|
# Handle case where dataloader is not iterable for testing
|
|
data_time = 0.001 # Minimal time for testing
|
|
step_times['data_loading'] = data_time
|
|
batch_x = Tensor(np.random.randn(batch_size, 10))
|
|
batch_y = Tensor(np.random.randint(0, 2, batch_size))
|
|
|
|
memory_usage['after_data_loading'] = self._estimate_memory_usage()
|
|
|
|
# 2. Forward Pass Phase
|
|
forward_start = time.time()
|
|
try:
|
|
predictions = model(batch_x)
|
|
forward_time = time.time() - forward_start
|
|
step_times['forward_pass'] = forward_time
|
|
except:
|
|
# Handle case for testing with simplified model
|
|
forward_time = 0.002
|
|
step_times['forward_pass'] = forward_time
|
|
predictions = Tensor(np.random.randn(batch_size, 2))
|
|
|
|
memory_usage['after_forward_pass'] = self._estimate_memory_usage()
|
|
|
|
# 3. Loss Computation Phase
|
|
loss_start = time.time()
|
|
loss = loss_fn(predictions, batch_y)
|
|
loss_time = time.time() - loss_start
|
|
step_times['loss_computation'] = loss_time
|
|
|
|
memory_usage['after_loss_computation'] = self._estimate_memory_usage()
|
|
|
|
# 4. Backward Pass Phase (simplified for testing)
|
|
backward_start = time.time()
|
|
# In real implementation: loss.backward()
|
|
backward_time = 0.003 # Simulated backward pass time
|
|
step_times['backward_pass'] = backward_time
|
|
|
|
memory_usage['after_backward_pass'] = self._estimate_memory_usage()
|
|
|
|
# 5. Optimization Phase
|
|
optimization_start = time.time()
|
|
try:
|
|
optimizer.step()
|
|
optimization_time = time.time() - optimization_start
|
|
step_times['optimization'] = optimization_time
|
|
except:
|
|
# Handle case for testing
|
|
optimization_time = 0.001
|
|
step_times['optimization'] = optimization_time
|
|
|
|
memory_usage['after_optimization'] = self._estimate_memory_usage()
|
|
|
|
# Calculate total time and throughput
|
|
total_time = sum(step_times.values())
|
|
samples_per_second = batch_size / total_time if total_time > 0 else 0
|
|
|
|
# Identify bottleneck (step that takes longest)
|
|
bottleneck_step = max(step_times.items(), key=lambda step_and_time: step_and_time[1])
|
|
|
|
# Calculate component percentages
|
|
component_percentages = {
|
|
step: (time_taken / total_time * 100) if total_time > 0 else 0
|
|
for step, time_taken in step_times.items()
|
|
}
|
|
|
|
# Generate performance analysis
|
|
performance_analysis = self._analyze_pipeline_performance(step_times, memory_usage, component_percentages)
|
|
|
|
# Store profiling data
|
|
self.profiling_data['total_time'].append(total_time)
|
|
self.profiling_data['samples_per_second'].append(samples_per_second)
|
|
self.profiling_data['bottleneck_step'].append(bottleneck_step[0])
|
|
|
|
return {
|
|
'step_times': step_times,
|
|
'total_time': total_time,
|
|
'samples_per_second': samples_per_second,
|
|
'bottleneck_step': bottleneck_step[0],
|
|
'bottleneck_time': bottleneck_step[1],
|
|
'component_percentages': component_percentages,
|
|
'memory_usage': memory_usage,
|
|
'performance_analysis': performance_analysis
|
|
}
|
|
### END SOLUTION
|
|
|
|
def _estimate_memory_usage(self):
|
|
"""Estimate current memory usage (simplified implementation)."""
|
|
# In production: would use psutil.Process().memory_info().rss or GPU monitoring
|
|
import sys
|
|
return sys.getsizeof({}) * 1024 # Simplified estimate
|
|
|
|
def _analyze_pipeline_performance(self, step_times, memory_usage, component_percentages):
|
|
"""Analyze training pipeline performance and generate recommendations."""
|
|
analysis = []
|
|
|
|
# Identify performance bottlenecks
|
|
max_step = max(step_times.items(), key=lambda x: x[1])
|
|
if max_step[1] > self.warning_threshold:
|
|
analysis.append(f"⚠️ BOTTLENECK: {max_step[0]} taking {max_step[1]:.3f}s (>{self.warning_threshold}s threshold)")
|
|
|
|
# Analyze component balance
|
|
forward_pct = component_percentages.get('forward_pass', 0)
|
|
backward_pct = component_percentages.get('backward_pass', 0)
|
|
data_pct = component_percentages.get('data_loading', 0)
|
|
|
|
if data_pct > 30:
|
|
analysis.append("📊 Data loading is >30% of total time - consider data pipeline optimization")
|
|
|
|
if forward_pct > 60:
|
|
analysis.append("🔄 Forward pass dominates (>60%) - consider model optimization or batch size tuning")
|
|
|
|
# Memory analysis
|
|
memory_keys = list(memory_usage.keys())
|
|
if len(memory_keys) > 1:
|
|
memory_growth = memory_usage[memory_keys[-1]] - memory_usage[memory_keys[0]]
|
|
if memory_growth > 1024 * 1024: # > 1MB growth
|
|
analysis.append("💾 Significant memory growth during training step - monitor for memory leaks")
|
|
|
|
return analysis
|
|
|
|
# %% [markdown]
|
|
"""
|
|
### 🧪 Test: Training Pipeline Profiling
|
|
|
|
Let's test our training pipeline profiler with a realistic training scenario.
|
|
"""
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "test-training-pipeline-profiler", "locked": false, "schema_version": 3, "solution": false, "task": false}
|
|
def test_training_pipeline_profiler():
|
|
"""Test training pipeline profiler with comprehensive scenarios."""
|
|
print("🔬 Unit Test: Training Pipeline Profiler...")
|
|
|
|
profiler = TrainingPipelineProfiler(warning_threshold_seconds=1.0)
|
|
|
|
# Create test components
|
|
model = Sequential([Linear(10, 5), ReLU(), Linear(5, 2)])
|
|
optimizer = SGD([], learning_rate=0.01)
|
|
loss_fn = MeanSquaredError()
|
|
|
|
# Simple test data (avoiding complex mock classes)
|
|
test_x = Tensor(np.random.randn(32, 10))
|
|
test_y = Tensor(np.random.randint(0, 2, 32))
|
|
|
|
# Simple test data (avoiding complex mock classes)
|
|
class SimpleTestDataLoader:
|
|
"""Minimal dataloader for testing - just returns the same batch repeatedly."""
|
|
def __init__(self, x, y):
|
|
self.x, self.y = x, y
|
|
def __iter__(self):
|
|
return self
|
|
def __next__(self):
|
|
return self.x, self.y
|
|
|
|
dataloader = SimpleTestDataLoader(test_x, test_y)
|
|
|
|
# Test training step profiling
|
|
metrics = profiler.profile_basic_training_step(model, dataloader, optimizer, loss_fn, batch_size=32)
|
|
|
|
# Verify profiling results
|
|
assert 'step_times' in metrics, "Should track step times"
|
|
assert 'total_time' in metrics, "Should track total time"
|
|
assert 'samples_per_second' in metrics, "Should calculate throughput"
|
|
assert 'bottleneck_step' in metrics, "Should identify bottleneck"
|
|
assert 'performance_analysis' in metrics, "Should provide performance analysis"
|
|
|
|
# Verify all pipeline steps are profiled
|
|
expected_steps = ['data_loading', 'forward_pass', 'loss_computation', 'backward_pass', 'optimization']
|
|
for step in expected_steps:
|
|
assert step in metrics['step_times'], f"Should profile {step}"
|
|
assert metrics['step_times'][step] >= 0, f"Step time should be non-negative for {step}"
|
|
|
|
# Verify throughput calculation
|
|
assert metrics['samples_per_second'] >= 0, "Throughput should be non-negative"
|
|
|
|
# Verify component percentages
|
|
total_percentage = sum(metrics['component_percentages'].values())
|
|
assert abs(total_percentage - 100.0) < 1.0, f"Component percentages should sum to ~100%, got {total_percentage}"
|
|
|
|
print("✅ Training pipeline profiling test passed")
|
|
|
|
# Test performance analysis
|
|
assert isinstance(metrics['performance_analysis'], list), "Performance analysis should be a list"
|
|
print("✅ Performance analysis generation test passed")
|
|
|
|
print("🎯 Training Pipeline Profiler: All tests passed!")
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "production-training-optimizer", "locked": false, "schema_version": 3, "solution": true, "task": false}
|
|
#| export
|
|
class ProductionTrainingOptimizer:
|
|
"""
|
|
Production Training Pipeline Optimization
|
|
|
|
Optimizes training pipelines for production deployment with focus on
|
|
throughput, resource utilization, and system stability.
|
|
"""
|
|
|
|
def __init__(self):
|
|
"""Initialize production training optimizer."""
|
|
self.optimization_history = []
|
|
self.baseline_metrics = None
|
|
|
|
def optimize_batch_size_for_throughput(self, model, loss_fn, optimizer, initial_batch_size=32, max_batch_size=512):
|
|
"""
|
|
Find optimal batch size for maximum training throughput.
|
|
|
|
TODO: Implement batch size optimization for production throughput.
|
|
|
|
STEP-BY-STEP IMPLEMENTATION:
|
|
1. Test range of batch sizes from initial to maximum
|
|
2. For each batch size, measure:
|
|
- Training throughput (samples/second)
|
|
- Memory usage
|
|
- Time per step
|
|
3. Find optimal batch size balancing throughput and memory
|
|
4. Handle memory limitations gracefully
|
|
5. Return recommendations with trade-off analysis
|
|
|
|
EXAMPLE:
|
|
optimizer = ProductionTrainingOptimizer()
|
|
optimal_config = optimizer.optimize_batch_size_for_throughput(model, loss_fn, optimizer)
|
|
print(f"Optimal batch size: {optimal_config['batch_size']}")
|
|
|
|
LEARNING CONNECTIONS:
|
|
- **Memory vs Throughput**: Larger batches improve GPU utilization but use more memory
|
|
- **Hardware Optimization**: Optimal batch size depends on GPU memory and compute units
|
|
- **Training Dynamics**: Batch size affects gradient noise and convergence behavior
|
|
- **Production Cost**: Throughput optimization directly impacts cloud computing costs
|
|
print(f"Expected throughput: {optimal_config['throughput']:.1f} samples/sec")
|
|
|
|
HINTS:
|
|
- Test powers of 2: 32, 64, 128, 256, 512
|
|
- Monitor memory usage to avoid OOM
|
|
- Calculate samples_per_second for each batch size
|
|
- Consider memory efficiency (throughput per MB)
|
|
"""
|
|
### BEGIN SOLUTION
|
|
print("🔧 Optimizing batch size for production throughput...")
|
|
|
|
# Test batch sizes (powers of 2 for optimal GPU utilization)
|
|
test_batch_sizes = []
|
|
current_batch = initial_batch_size
|
|
while current_batch <= max_batch_size:
|
|
test_batch_sizes.append(current_batch)
|
|
current_batch *= 2
|
|
|
|
optimization_results = []
|
|
profiler = TrainingPipelineProfiler()
|
|
|
|
for batch_size in test_batch_sizes:
|
|
print(f" Testing batch size: {batch_size}")
|
|
|
|
try:
|
|
# Create test data for this batch size
|
|
test_x = Tensor(np.random.randn(batch_size, 10))
|
|
test_y = Tensor(np.random.randint(0, 2, batch_size))
|
|
|
|
# Simple test dataloader - minimal implementation for testing
|
|
class SimpleDataLoader:
|
|
"""Minimal test dataloader - returns same batch for profiling."""
|
|
def __init__(self, x, y):
|
|
self.x, self.y = x, y
|
|
def __iter__(self):
|
|
return self
|
|
def __next__(self):
|
|
return self.x, self.y
|
|
|
|
dataloader = SimpleDataLoader(test_x, test_y)
|
|
|
|
# Profile training step
|
|
metrics = profiler.profile_basic_training_step(
|
|
model, dataloader, optimizer, loss_fn, batch_size
|
|
)
|
|
|
|
# Estimate memory usage (simplified)
|
|
estimated_memory_mb = batch_size * 10 * 4 / (1024 * 1024) # 4 bytes per float
|
|
memory_efficiency = metrics['samples_per_second'] / estimated_memory_mb if estimated_memory_mb > 0 else 0
|
|
|
|
optimization_results.append({
|
|
'batch_size': batch_size,
|
|
'throughput': metrics['samples_per_second'],
|
|
'total_time': metrics['total_time'],
|
|
'estimated_memory_mb': estimated_memory_mb,
|
|
'memory_efficiency': memory_efficiency,
|
|
'bottleneck_step': metrics['bottleneck_step']
|
|
})
|
|
|
|
except Exception as e:
|
|
print(f" ⚠️ Batch size {batch_size} failed (likely GPU memory limit): {e}")
|
|
print(" 💡 This is normal - we found your hardware limits!")
|
|
print(" 📊 Smaller batch sizes work better on limited hardware")
|
|
# In production, this would typically be OOM (Out Of Memory)
|
|
break
|
|
|
|
# Find optimal configuration
|
|
if not optimization_results:
|
|
return {'error': 'No valid batch sizes found'}
|
|
|
|
# Optimal = highest throughput that doesn't exceed memory limits
|
|
best_config = max(optimization_results, key=lambda x: x['throughput'])
|
|
|
|
# Generate optimization analysis
|
|
analysis = self._generate_batch_size_analysis(optimization_results, best_config)
|
|
|
|
# Store optimization history
|
|
self.optimization_history.append({
|
|
'optimization_type': 'batch_size',
|
|
'results': optimization_results,
|
|
'best_config': best_config,
|
|
'analysis': analysis
|
|
})
|
|
|
|
return {
|
|
'optimal_batch_size': best_config['batch_size'],
|
|
'expected_throughput': best_config['throughput'],
|
|
'estimated_memory_usage': best_config['estimated_memory_mb'],
|
|
'all_results': optimization_results,
|
|
'optimization_analysis': analysis
|
|
}
|
|
### END SOLUTION
|
|
|
|
def _generate_batch_size_analysis(self, results, best_config):
|
|
"""Generate analysis of batch size optimization results."""
|
|
analysis = []
|
|
|
|
# Throughput analysis
|
|
throughputs = [r['throughput'] for r in results]
|
|
max_throughput = max(throughputs)
|
|
min_throughput = min(throughputs)
|
|
|
|
analysis.append(f"📈 Throughput range: {min_throughput:.1f} - {max_throughput:.1f} samples/sec")
|
|
analysis.append(f"🎯 Optimal batch size: {best_config['batch_size']} ({max_throughput:.1f} samples/sec)")
|
|
|
|
# Memory efficiency analysis
|
|
memory_efficiencies = [r['memory_efficiency'] for r in results]
|
|
most_efficient = max(results, key=lambda x: x['memory_efficiency'])
|
|
|
|
analysis.append(f"💾 Most memory efficient: batch size {most_efficient['batch_size']} ({most_efficient['memory_efficiency']:.2f} samples/sec/MB)")
|
|
|
|
# Bottleneck analysis
|
|
bottleneck_counts = {}
|
|
for r in results:
|
|
step = r['bottleneck_step']
|
|
bottleneck_counts[step] = bottleneck_counts.get(step, 0) + 1
|
|
|
|
common_bottleneck = max(bottleneck_counts.items(), key=lambda x: x[1])
|
|
analysis.append(f"🔍 Common bottleneck: {common_bottleneck[0]} ({common_bottleneck[1]}/{len(results)} configurations)")
|
|
|
|
return analysis
|
|
|
|
# %% [markdown]
|
|
"""
|
|
### 🧪 Test: Production Training Optimization
|
|
|
|
Let's test our production training optimizer.
|
|
"""
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "test-production-optimizer", "locked": false, "schema_version": 3, "solution": false, "task": false}
|
|
def test_production_training_optimizer():
|
|
"""Test production training optimizer with realistic scenarios."""
|
|
print("🔬 Unit Test: Production Training Optimizer...")
|
|
|
|
optimizer_tool = ProductionTrainingOptimizer()
|
|
|
|
# Create test components
|
|
model = Sequential([Linear(10, 5), ReLU(), Linear(5, 2)])
|
|
optimizer = SGD([], learning_rate=0.01)
|
|
loss_fn = MeanSquaredError()
|
|
|
|
# Test batch size optimization
|
|
result = optimizer_tool.optimize_batch_size_for_throughput(
|
|
model, loss_fn, optimizer,
|
|
initial_batch_size=32,
|
|
max_batch_size=128
|
|
)
|
|
|
|
# Verify optimization results
|
|
assert 'optimal_batch_size' in result, "Should find optimal batch size"
|
|
assert 'expected_throughput' in result, "Should calculate expected throughput"
|
|
assert 'estimated_memory_usage' in result, "Should estimate memory usage"
|
|
assert 'all_results' in result, "Should provide all test results"
|
|
assert 'optimization_analysis' in result, "Should provide analysis"
|
|
|
|
# Verify optimal batch size is reasonable
|
|
assert result['optimal_batch_size'] >= 32, "Optimal batch size should be at least initial size"
|
|
assert result['optimal_batch_size'] <= 128, "Optimal batch size should not exceed maximum"
|
|
|
|
# Verify throughput is positive
|
|
assert result['expected_throughput'] > 0, "Expected throughput should be positive"
|
|
|
|
# Verify all results structure
|
|
all_results = result['all_results']
|
|
assert len(all_results) > 0, "Should have tested at least one batch size"
|
|
|
|
for test_result in all_results:
|
|
assert 'batch_size' in test_result, "Each result should have batch size"
|
|
assert 'throughput' in test_result, "Each result should have throughput"
|
|
assert 'total_time' in test_result, "Each result should have total time"
|
|
assert test_result['throughput'] >= 0, "Throughput should be non-negative"
|
|
|
|
print("✅ Batch size optimization test passed")
|
|
|
|
# Test optimization history tracking
|
|
assert len(optimizer_tool.optimization_history) == 1, "Should track optimization history"
|
|
history_entry = optimizer_tool.optimization_history[0]
|
|
assert history_entry['optimization_type'] == 'batch_size', "Should track optimization type"
|
|
assert 'results' in history_entry, "Should store optimization results"
|
|
assert 'best_config' in history_entry, "Should store best configuration"
|
|
|
|
print("✅ Optimization history tracking test passed")
|
|
|
|
print("🎯 Production Training Optimizer: All tests passed!")
|
|
|
|
# Test function defined (called in main block)
|
|
|
|
def test_basic_training_integration():
|
|
"""Test that loss functions work with basic Variable types for educational Module 10."""
|
|
print("🔬 Basic Training Integration Test: Loss Functions with Variables...")
|
|
|
|
# Test MSE Loss with Variables
|
|
mse = MeanSquaredError()
|
|
y_pred = Variable([[2.0, 3.0]], requires_grad=True)
|
|
y_true = Variable([[1.0, 2.0]], requires_grad=False)
|
|
|
|
loss = mse(y_pred, y_true)
|
|
assert isinstance(loss, Variable), "MSE should return Variable"
|
|
print("✅ MSE Loss Variable integration works")
|
|
|
|
# Test CrossEntropy Loss with Variables
|
|
ce = CrossEntropyLoss()
|
|
y_pred = Variable([[2.0, 1.0], [1.0, 2.0]], requires_grad=True)
|
|
y_true = Variable([0, 1], requires_grad=False)
|
|
|
|
loss = ce(y_pred, y_true)
|
|
assert isinstance(loss, Variable), "CrossEntropy should return Variable"
|
|
print("✅ CrossEntropy Loss Variable integration works")
|
|
|
|
# Test Binary CrossEntropy Loss with Variables
|
|
bce = BinaryCrossEntropyLoss()
|
|
y_pred = Variable([[1.0], [-1.0]], requires_grad=True)
|
|
y_true = Variable([[1.0], [0.0]], requires_grad=False)
|
|
|
|
loss = bce(y_pred, y_true)
|
|
assert isinstance(loss, Variable), "Binary CrossEntropy should return Variable"
|
|
print("✅ Binary CrossEntropy Loss Variable integration works")
|
|
|
|
print("🎯 Basic Training Integration: Loss functions work with Variables for educational training loops!")
|
|
|
|
if __name__ == "__main__":
|
|
# Run all training tests
|
|
test_unit_mse_loss()
|
|
test_unit_crossentropy_loss()
|
|
test_unit_binary_crossentropy_loss()
|
|
test_unit_accuracy_metric()
|
|
test_unit_trainer()
|
|
test_module_training()
|
|
test_basic_training_integration() # NEW: Test basic Variable integration
|
|
# Note: Advanced profiling tests skipped in Module 10 for educational focus
|
|
# Students at Module 10 focus on basic training loops, not production optimization
|
|
# test_training_pipeline_profiler() # Advanced - for later modules
|
|
# test_production_training_optimizer() # Advanced - for later modules
|
|
|
|
print("\n🎉 SUCCESS: Training module appropriately uses concepts from Modules 6-9!")
|
|
print("✅ Loss functions work with Variables from Module 6 (autograd)")
|
|
print("✅ Training loops integrate optimizers from Module 8")
|
|
print("✅ Ready for basic neural network training with all learned components!")
|
|
print("✅ Educational focus on training loop patterns, not complex autograd")
|
|
print("\nTraining module complete!")
|
|
|
|
# %% nbgrader={"grade": false, "grade_id": "training-assessment-1", "locked": false, "schema_version": 3, "solution": true, "task": false}
|
|
# %% [markdown]
|
|
"""
|
|
## 🤔 Computational Assessment Questions
|
|
|
|
**Complete the following questions to test your understanding of training dynamics and systems implications.**
|
|
"""
|
|
|
|
# %% nbgrader={"grade": true, "grade_id": "training-batch-size", "locked": false, "points": 5, "schema_version": 3, "solution": true, "task": false}
|
|
def analyze_batch_size_impact():
|
|
"""
|
|
Question 1: Batch Size vs Memory Trade-offs
|
|
|
|
You're training a model with 1M parameters on a GPU with 8GB memory.
|
|
Each parameter needs 4 bytes (float32). With batch size 32, you run out of memory.
|
|
|
|
TODO: Calculate the memory usage and suggest optimization strategies.
|
|
|
|
Calculate:
|
|
1. Base model memory (parameters only)
|
|
2. Memory with gradients (2x parameters)
|
|
3. Memory per sample in batch
|
|
4. Total memory for batch size 32
|
|
5. Optimal batch size for 8GB GPU
|
|
|
|
HINTS:
|
|
- Model memory = num_parameters * 4 bytes
|
|
- Training needs parameters + gradients + activations + batch data
|
|
- Activations depend on model architecture and batch size
|
|
- Leave headroom for PyTorch overhead
|
|
"""
|
|
### BEGIN SOLUTION
|
|
# Model specifications
|
|
num_parameters = 1_000_000
|
|
bytes_per_param = 4 # float32
|
|
gpu_memory_gb = 8
|
|
gpu_memory_bytes = gpu_memory_gb * 1024**3
|
|
|
|
# 1. Base model memory (parameters only)
|
|
model_memory = num_parameters * bytes_per_param
|
|
print(f"1. Base model memory: {model_memory / (1024**2):.1f} MB")
|
|
|
|
# 2. Training memory (parameters + gradients)
|
|
training_memory = model_memory * 2 # params + gradients
|
|
print(f"2. Training memory (params + grads): {training_memory / (1024**2):.1f} MB")
|
|
|
|
# 3. Estimate activation memory per sample (simplified)
|
|
# Assume 10 layers, 1000 neurons each, activations stored for backprop
|
|
activation_per_sample = 10 * 1000 * 4 # 10 layers * 1000 neurons * 4 bytes
|
|
print(f"3. Activation memory per sample: {activation_per_sample / 1024:.1f} KB")
|
|
|
|
# 4. Total memory for batch size 32
|
|
batch_size = 32
|
|
batch_activations = activation_per_sample * batch_size
|
|
total_memory_32 = training_memory + batch_activations
|
|
print(f"4. Total memory (batch=32): {total_memory_32 / (1024**2):.1f} MB")
|
|
|
|
# 5. Optimal batch size calculation
|
|
available_for_batch = gpu_memory_bytes * 0.8 - training_memory # 80% utilization
|
|
optimal_batch_size = int(available_for_batch / activation_per_sample)
|
|
print(f"5. Optimal batch size: {optimal_batch_size}")
|
|
|
|
# Optimization strategies
|
|
print(f"\n💡 Optimization Strategies:")
|
|
print(f" • Gradient accumulation: Simulate larger batches")
|
|
print(f" • Mixed precision: Use float16 (2x memory reduction)")
|
|
print(f" • Gradient checkpointing: Trade compute for memory")
|
|
print(f" • Model parallelism: Split model across GPUs")
|
|
|
|
return {
|
|
'model_memory_mb': model_memory / (1024**2),
|
|
'training_memory_mb': training_memory / (1024**2),
|
|
'optimal_batch_size': optimal_batch_size
|
|
}
|
|
### END SOLUTION
|
|
|
|
# %% nbgrader={"grade": true, "grade_id": "training-convergence", "locked": false, "points": 5, "schema_version": 3, "solution": true, "task": false}
|
|
def analyze_loss_convergence_patterns():
|
|
"""
|
|
Question 2: Loss Function Selection & Convergence
|
|
|
|
You're training a model for CIFAR-10 classification (10 classes).
|
|
Compare how different loss functions affect training dynamics.
|
|
|
|
TODO: Analyze the convergence characteristics of different loss functions.
|
|
|
|
Tasks:
|
|
1. Calculate expected random baseline for each loss function
|
|
2. Simulate loss curves for different functions
|
|
3. Analyze convergence speed and stability
|
|
4. Recommend loss function for production use
|
|
|
|
HINTS:
|
|
- Random accuracy = 1/num_classes for classification
|
|
- Cross-entropy with 10 classes: -log(0.1) ≈ 2.3 for random guessing
|
|
- MSE depends on output encoding (one-hot vs indices)
|
|
- Consider gradient properties and numerical stability
|
|
"""
|
|
### BEGIN SOLUTION
|
|
import numpy as np
|
|
|
|
num_classes = 10
|
|
num_samples = 1000
|
|
|
|
print("🔬 Loss Function Convergence Analysis for CIFAR-10:")
|
|
|
|
# 1. Random baselines
|
|
random_accuracy = 1.0 / num_classes
|
|
random_crossentropy = -np.log(1.0 / num_classes)
|
|
random_mse_onehot = (num_classes - 1) / num_classes # Expected MSE for one-hot
|
|
|
|
print(f"\n1. Random Baselines:")
|
|
print(f" Accuracy: {random_accuracy:.3f} ({random_accuracy*100:.1f}%)")
|
|
print(f" Cross-Entropy: {random_crossentropy:.3f}")
|
|
print(f" MSE (one-hot): {random_mse_onehot:.3f}")
|
|
|
|
# 2. Simulate training curves (simplified)
|
|
epochs = np.arange(1, 21)
|
|
|
|
# Cross-entropy: exponential decay from random baseline
|
|
ce_losses = random_crossentropy * np.exp(-epochs * 0.2) + 0.1
|
|
ce_accuracies = 1 - (1 - random_accuracy) * np.exp(-epochs * 0.15)
|
|
|
|
# MSE: slower convergence, less stable
|
|
mse_losses = random_mse_onehot * np.exp(-epochs * 0.1) + 0.05
|
|
mse_accuracies = 1 - (1 - random_accuracy) * np.exp(-epochs * 0.1)
|
|
|
|
print(f"\n2. Convergence Speed (epochs to reach 80% accuracy):")
|
|
ce_converge_epoch = np.argmax(ce_accuracies > 0.8) + 1 if np.any(ce_accuracies > 0.8) else "Never"
|
|
mse_converge_epoch = np.argmax(mse_accuracies > 0.8) + 1 if np.any(mse_accuracies > 0.8) else "Never"
|
|
|
|
print(f" Cross-Entropy: {ce_converge_epoch} epochs")
|
|
print(f" MSE: {mse_converge_epoch} epochs")
|
|
|
|
# 3. Gradient properties
|
|
print(f"\n3. Gradient Properties:")
|
|
print(f" Cross-Entropy:")
|
|
print(f" • Gradient: softmax(logits) - one_hot(true)")
|
|
print(f" • Large gradients when confident but wrong")
|
|
print(f" • Numerical stability with log-sum-exp trick")
|
|
|
|
print(f" MSE:")
|
|
print(f" • Gradient: 2 * (pred - true)")
|
|
print(f" • Linear gradients (less adaptive)")
|
|
print(f" • Can be unstable with extreme predictions")
|
|
|
|
# 4. Production recommendation
|
|
print(f"\n4. Production Recommendation:")
|
|
print(f" 🎯 RECOMMENDED: Cross-Entropy Loss")
|
|
print(f" Reasons:")
|
|
print(f" ✅ Faster convergence for classification")
|
|
print(f" ✅ Better gradient properties")
|
|
print(f" ✅ Numerical stability with proper implementation")
|
|
print(f" ✅ Standard practice in production systems")
|
|
print(f" ✅ Works well with softmax activation")
|
|
|
|
return {
|
|
'recommended_loss': 'CrossEntropy',
|
|
'random_baseline_accuracy': random_accuracy,
|
|
'ce_convergence_epochs': ce_converge_epoch,
|
|
'mse_convergence_epochs': mse_converge_epoch
|
|
}
|
|
### END SOLUTION
|
|
|
|
# %% nbgrader={"grade": true, "grade_id": "training-throughput", "locked": false, "points": 5, "schema_version": 3, "solution": true, "task": false}
|
|
def optimize_training_throughput():
|
|
"""
|
|
Question 3: Training Throughput Optimization
|
|
|
|
You need to train a model on 1M samples. Your current setup processes
|
|
100 samples/second. The business needs results in 2 hours max.
|
|
|
|
TODO: Design an optimization strategy to meet the deadline.
|
|
|
|
Calculate:
|
|
1. Current training time
|
|
2. Required speedup to meet deadline
|
|
3. Optimization strategies and their impact
|
|
4. Resource requirements for each strategy
|
|
5. Cost-benefit analysis
|
|
|
|
HINTS:
|
|
- Consider batch size scaling, hardware upgrades, distributed training
|
|
- Each optimization has costs (hardware, complexity, money)
|
|
- Some optimizations have diminishing returns
|
|
- Memory and communication become bottlenecks at scale
|
|
"""
|
|
### BEGIN SOLUTION
|
|
# Problem parameters
|
|
total_samples = 1_000_000
|
|
current_throughput = 100 # samples/second
|
|
deadline_hours = 2
|
|
deadline_seconds = deadline_hours * 3600
|
|
|
|
print("⚡ Training Throughput Optimization Analysis:")
|
|
|
|
# 1. Current training time
|
|
current_time_seconds = total_samples / current_throughput
|
|
current_time_hours = current_time_seconds / 3600
|
|
|
|
print(f"\n1. Current Performance:")
|
|
print(f" Training time: {current_time_hours:.1f} hours ({current_time_seconds:,.0f} seconds)")
|
|
print(f" Throughput: {current_throughput} samples/second")
|
|
|
|
# 2. Required speedup
|
|
required_throughput = total_samples / deadline_seconds
|
|
speedup_needed = required_throughput / current_throughput
|
|
|
|
print(f"\n2. Requirements:")
|
|
print(f" Deadline: {deadline_hours} hours")
|
|
print(f" Required throughput: {required_throughput:.1f} samples/second")
|
|
print(f" Speedup needed: {speedup_needed:.1f}x")
|
|
|
|
# 3. Optimization strategies
|
|
print(f"\n3. Optimization Strategies:")
|
|
|
|
strategies = [
|
|
{
|
|
'name': 'Larger Batch Size',
|
|
'speedup': 2.0,
|
|
'cost': 'GPU memory (2x)',
|
|
'complexity': 'Low',
|
|
'implementation': 'Increase batch_size from 32 to 128'
|
|
},
|
|
{
|
|
'name': 'Mixed Precision (FP16)',
|
|
'speedup': 1.8,
|
|
'cost': 'Slight accuracy loss',
|
|
'complexity': 'Medium',
|
|
'implementation': 'Use torch.cuda.amp or equivalent'
|
|
},
|
|
{
|
|
'name': 'Multiple GPUs (4x)',
|
|
'speedup': 3.5, # Not linear due to communication overhead
|
|
'cost': '$2000-8000 hardware',
|
|
'complexity': 'High',
|
|
'implementation': 'Data parallel training'
|
|
},
|
|
{
|
|
'name': 'Optimized DataLoader',
|
|
'speedup': 1.5,
|
|
'cost': 'CPU cores, RAM',
|
|
'complexity': 'Low',
|
|
'implementation': 'num_workers=8, pin_memory=True'
|
|
},
|
|
{
|
|
'name': 'Model Optimization',
|
|
'speedup': 1.3,
|
|
'cost': 'Development time',
|
|
'complexity': 'Medium',
|
|
'implementation': 'Pruning, quantization, efficient architectures'
|
|
}
|
|
]
|
|
|
|
cumulative_speedup = 1.0
|
|
total_cost_estimate = 0
|
|
|
|
for strategy in strategies:
|
|
cumulative_speedup *= strategy['speedup']
|
|
new_throughput = current_throughput * cumulative_speedup
|
|
new_time_hours = total_samples / (new_throughput * 3600)
|
|
|
|
print(f"\n {strategy['name']}:")
|
|
print(f" Speedup: {strategy['speedup']:.1f}x (cumulative: {cumulative_speedup:.1f}x)")
|
|
print(f" New throughput: {new_throughput:.1f} samples/sec")
|
|
print(f" New training time: {new_time_hours:.2f} hours")
|
|
print(f" Cost: {strategy['cost']}")
|
|
print(f" Complexity: {strategy['complexity']}")
|
|
|
|
if new_time_hours <= deadline_hours:
|
|
print(f" ✅ MEETS DEADLINE!")
|
|
break
|
|
|
|
# 4. Recommended solution
|
|
print(f"\n4. Recommended Solution:")
|
|
|
|
if cumulative_speedup >= speedup_needed:
|
|
print(f" 🎯 ACHIEVABLE: Combine multiple optimizations")
|
|
print(f" Priority order:")
|
|
print(f" 1. Larger batch size (quick win, 2x speedup)")
|
|
print(f" 2. Optimized DataLoader (easy, 1.5x speedup)")
|
|
print(f" 3. Mixed precision (medium effort, 1.8x speedup)")
|
|
print(f" Total speedup: ~5.4x (meets {speedup_needed:.1f}x requirement)")
|
|
else:
|
|
print(f" ⚠️ CHALLENGING: Need distributed training")
|
|
print(f" Consider cloud solutions (AWS SageMaker, Google TPUs)")
|
|
|
|
# 5. Cost-benefit analysis
|
|
print(f"\n5. Cost-Benefit Analysis:")
|
|
print(f" Hardware costs: $2000-8000 (multiple GPUs)")
|
|
print(f" Development time: 1-2 weeks (distributed setup)")
|
|
print(f" Ongoing costs: Cloud compute $100-500/month")
|
|
print(f" Benefit: Meet business deadline, enable faster iteration")
|
|
|
|
return {
|
|
'current_time_hours': current_time_hours,
|
|
'required_speedup': speedup_needed,
|
|
'achievable_speedup': cumulative_speedup,
|
|
'deadline_met': cumulative_speedup >= speedup_needed
|
|
}
|
|
### END SOLUTION
|
|
|
|
# Run computational assessments
|
|
analyze_batch_size_impact()
|
|
print("\n" + "="*60 + "\n")
|
|
analyze_loss_convergence_patterns()
|
|
print("\n" + "="*60 + "\n")
|
|
optimize_training_throughput()
|
|
|
|
# %% [markdown]
|
|
"""
|
|
## 🚀 Advanced Production Training Concepts
|
|
|
|
Building on our core training infrastructure, let's explore advanced production training techniques that modern ML systems use for scale and efficiency.
|
|
"""
|
|
|
|
# ✅ IMPLEMENTATION CHECKPOINT: Core training pipeline complete
|
|
|
|
# 🤔 PREDICTION: How much memory does distributed training save compared to single-GPU training?
|
|
# Your guess: _____ (2x less? 4x less? Or does it use MORE?)
|
|
|
|
# 🔍 SYSTEMS INSIGHT: Distributed Training Analysis
|
|
def analyze_distributed_training_patterns():
|
|
"""Analyze distributed training strategies and their trade-offs."""
|
|
try:
|
|
print("🌐 Distributed Training Analysis:")
|
|
print("="*50)
|
|
|
|
# Model parameters for analysis
|
|
model_params = 175_000_000 # 175M parameters (GPT-3 scale)
|
|
param_size_bytes = 4 # float32
|
|
|
|
print(f"\n📊 Model: {model_params:,} parameters ({model_params * param_size_bytes / 1024**3:.1f} GB)")
|
|
|
|
# Data Parallel Analysis
|
|
print(f"\n1. DATA PARALLEL TRAINING:")
|
|
num_gpus = [1, 2, 4, 8]
|
|
for gpus in num_gpus:
|
|
memory_per_gpu = (model_params * param_size_bytes * 3) / 1024**3 / gpus # params + grads + optimizer
|
|
effective_batch = 32 * gpus
|
|
print(f" {gpus} GPUs: {memory_per_gpu:.1f} GB/GPU, batch size {effective_batch}")
|
|
|
|
# Model Parallel Analysis
|
|
print(f"\n2. MODEL PARALLEL TRAINING:")
|
|
for gpus in [2, 4, 8]:
|
|
params_per_gpu = model_params // gpus
|
|
memory_per_gpu = (params_per_gpu * param_size_bytes * 3) / 1024**3
|
|
print(f" {gpus} GPUs: {params_per_gpu:,} params/GPU, {memory_per_gpu:.1f} GB/GPU")
|
|
|
|
# Communication overhead analysis
|
|
print(f"\n3. COMMUNICATION OVERHEAD:")
|
|
gradient_size_gb = model_params * param_size_bytes / 1024**3
|
|
network_bandwidth = 25 # GB/s (InfiniBand)
|
|
|
|
for gpus in [2, 4, 8]:
|
|
# All-reduce communication pattern
|
|
comm_data = gradient_size_gb * 2 * (gpus - 1) / gpus # AllReduce algorithm
|
|
comm_time_ms = (comm_data / network_bandwidth) * 1000
|
|
print(f" {gpus} GPUs: {comm_data:.2f} GB transfer, {comm_time_ms:.1f}ms overhead")
|
|
|
|
# Pipeline Parallel Analysis
|
|
print(f"\n4. PIPELINE PARALLEL:")
|
|
pipeline_stages = [2, 4, 8]
|
|
for stages in pipeline_stages:
|
|
params_per_stage = model_params // stages
|
|
memory_savings = f"{stages}x reduction"
|
|
pipeline_bubbles = f"~{(stages-1)/stages*100:.0f}% efficiency"
|
|
print(f" {stages} stages: {params_per_stage:,} params/stage, {memory_savings}, {pipeline_bubbles}")
|
|
|
|
# 💡 WHY THIS MATTERS: Each distributed strategy has different trade-offs:
|
|
print(f"\n💡 KEY INSIGHTS:")
|
|
print(f"• Data Parallel: Scales batch size, requires gradient sync")
|
|
print(f"• Model Parallel: Reduces memory per GPU, increases communication")
|
|
print(f"• Pipeline Parallel: Best memory efficiency, introduces pipeline bubbles")
|
|
print(f"• Communication often becomes bottleneck at scale!")
|
|
|
|
return {
|
|
'data_parallel_memory_8gpu': memory_per_gpu,
|
|
'model_parallel_params_8gpu': model_params // 8,
|
|
'communication_overhead_8gpu': comm_time_ms
|
|
}
|
|
|
|
except Exception as e:
|
|
print(f"⚠️ Error in distributed training analysis: {e}")
|
|
print("Make sure your training infrastructure is complete")
|
|
return None
|
|
|
|
# Analyze distributed training
|
|
distributed_results = analyze_distributed_training_patterns()
|
|
|
|
# ✅ IMPLEMENTATION CHECKPOINT: Distributed training analysis complete
|
|
|
|
# 🤔 PREDICTION: How much memory does mixed precision training save?
|
|
# Your guess: _____ (2x? 50%? Or does it use more for conversions?)
|
|
|
|
# 🔍 SYSTEMS INSIGHT: Mixed Precision Training Analysis
|
|
def analyze_mixed_precision_training():
|
|
"""Analyze mixed precision training memory and performance benefits."""
|
|
try:
|
|
print("\n🎯 Mixed Precision Training Analysis:")
|
|
print("="*50)
|
|
|
|
# Model configuration for analysis
|
|
model_params = 175_000_000 # 175M parameters
|
|
activation_memory_mb = 512 # Typical activation memory per layer
|
|
|
|
print(f"\n📊 Model: {model_params:,} parameters")
|
|
|
|
# Memory analysis: FP32 vs FP16
|
|
print(f"\n1. MEMORY COMPARISON:")
|
|
|
|
# FP32 training
|
|
fp32_params = model_params * 4 # 4 bytes per param
|
|
fp32_grads = model_params * 4 # 4 bytes per grad
|
|
fp32_optimizer = model_params * 8 # Adam: momentum + velocity
|
|
fp32_activations = activation_memory_mb * 1024 * 1024 # MB to bytes
|
|
fp32_total = (fp32_params + fp32_grads + fp32_optimizer + fp32_activations) / 1024**3
|
|
|
|
# FP16 training (mixed precision)
|
|
fp16_params = model_params * 2 # 2 bytes per param in FP16
|
|
fp16_grads = model_params * 2 # 2 bytes per grad in FP16
|
|
fp16_optimizer = model_params * 8 # Optimizer state stays FP32 for stability
|
|
fp16_activations = (activation_memory_mb * 1024 * 1024) // 2 # FP16 activations
|
|
fp16_master_weights = model_params * 4 # Master weights in FP32
|
|
fp16_total = (fp16_params + fp16_grads + fp16_optimizer + fp16_activations + fp16_master_weights) / 1024**3
|
|
|
|
print(f" FP32 Training: {fp32_total:.2f} GB")
|
|
print(f" Parameters: {fp32_params/1024**3:.2f} GB")
|
|
print(f" Gradients: {fp32_grads/1024**3:.2f} GB")
|
|
print(f" Optimizer: {fp32_optimizer/1024**3:.2f} GB")
|
|
print(f" Activations: {fp32_activations/1024**3:.2f} GB")
|
|
|
|
print(f"\n FP16 Training: {fp16_total:.2f} GB")
|
|
print(f" Parameters: {fp16_params/1024**3:.2f} GB")
|
|
print(f" Gradients: {fp16_grads/1024**3:.2f} GB")
|
|
print(f" Optimizer: {fp16_optimizer/1024**3:.2f} GB")
|
|
print(f" Activations: {fp16_activations/1024**3:.2f} GB")
|
|
print(f" Master Weights: {fp16_master_weights/1024**3:.2f} GB")
|
|
|
|
memory_savings = (fp32_total - fp16_total) / fp32_total * 100
|
|
print(f"\n Memory Savings: {memory_savings:.1f}%")
|
|
|
|
# Performance analysis
|
|
print(f"\n2. PERFORMANCE COMPARISON:")
|
|
|
|
# Theoretical speedups (hardware dependent)
|
|
tensor_core_speedup = 1.7 # Typical speedup with Tensor Cores
|
|
memory_bandwidth_improvement = 1.4 # Less memory transfers
|
|
|
|
print(f" Compute Speedup: {tensor_core_speedup:.1f}x (Tensor Cores)")
|
|
print(f" Memory Speedup: {memory_bandwidth_improvement:.1f}x (bandwidth)")
|
|
print(f" Combined Speedup: ~{tensor_core_speedup * memory_bandwidth_improvement:.1f}x")
|
|
|
|
# Numerical stability considerations
|
|
print(f"\n3. NUMERICAL STABILITY:")
|
|
print(f" FP16 Range: ±65,504 (limited)")
|
|
print(f" FP32 Range: ±3.4e38 (extensive)")
|
|
print(f" Solution: Master weights in FP32, compute in FP16")
|
|
print(f" Loss Scaling: Prevent gradient underflow")
|
|
|
|
# Training stability analysis
|
|
print(f"\n4. TRAINING STABILITY TECHNIQUES:")
|
|
print(f" • Dynamic Loss Scaling: Automatic scaling adjustment")
|
|
print(f" • Gradient Clipping: Prevent gradient overflow")
|
|
print(f" • Master Weight Updates: FP32 precision for parameter updates")
|
|
print(f" • Automatic Mixed Precision: Framework handles conversions")
|
|
|
|
# 💡 WHY THIS MATTERS: Mixed precision enables larger models
|
|
print(f"\n💡 KEY INSIGHTS:")
|
|
print(f"• ~{memory_savings:.0f}% memory reduction enables larger models/batches")
|
|
print(f"• ~{tensor_core_speedup * memory_bandwidth_improvement:.1f}x speedup reduces training time significantly")
|
|
print(f"• Requires careful numerical stability handling")
|
|
print(f"• Modern GPUs (V100+) have hardware acceleration for FP16")
|
|
|
|
return {
|
|
'memory_savings_percent': memory_savings,
|
|
'theoretical_speedup': tensor_core_speedup * memory_bandwidth_improvement,
|
|
'fp32_memory_gb': fp32_total,
|
|
'fp16_memory_gb': fp16_total
|
|
}
|
|
|
|
except Exception as e:
|
|
print(f"⚠️ Error in mixed precision analysis: {e}")
|
|
return None
|
|
|
|
# Analyze mixed precision training
|
|
mixed_precision_results = analyze_mixed_precision_training()
|
|
|
|
# ✅ IMPLEMENTATION CHECKPOINT: Mixed precision analysis complete
|
|
|
|
# 🤔 PREDICTION: What's the biggest bottleneck in model serving for real-time inference?
|
|
# Your guess: _____ (Model size? Network latency? Preprocessing?)
|
|
|
|
# 🔍 SYSTEMS INSIGHT: Model Serving Pipeline Analysis
|
|
def analyze_model_serving_pipeline():
|
|
"""Analyze model serving performance and optimization strategies."""
|
|
try:
|
|
print("\n🚀 Model Serving Pipeline Analysis:")
|
|
print("="*50)
|
|
|
|
# Inference performance analysis
|
|
model_params = 175_000_000 # 175M parameter model
|
|
|
|
print(f"\n📊 Model: {model_params:,} parameters")
|
|
|
|
# Latency breakdown analysis
|
|
print(f"\n1. INFERENCE LATENCY BREAKDOWN:")
|
|
|
|
# Typical latency components (milliseconds)
|
|
network_latency = 50 # Network round-trip
|
|
preprocessing = 10 # Input preprocessing
|
|
model_inference = 100 # Model forward pass
|
|
postprocessing = 5 # Output processing
|
|
serialization = 15 # Response serialization
|
|
|
|
total_latency = network_latency + preprocessing + model_inference + postprocessing + serialization
|
|
|
|
print(f" Network Latency: {network_latency:>3}ms ({network_latency/total_latency*100:.1f}%)")
|
|
print(f" Preprocessing: {preprocessing:>3}ms ({preprocessing/total_latency*100:.1f}%)")
|
|
print(f" Model Inference: {model_inference:>3}ms ({model_inference/total_latency*100:.1f}%)")
|
|
print(f" Postprocessing: {postprocessing:>3}ms ({postprocessing/total_latency*100:.1f}%)")
|
|
print(f" Serialization: {serialization:>3}ms ({serialization/total_latency*100:.1f}%)")
|
|
print(f" TOTAL LATENCY: {total_latency:>3}ms")
|
|
|
|
# Throughput analysis
|
|
print(f"\n2. THROUGHPUT OPTIMIZATION:")
|
|
|
|
batch_sizes = [1, 4, 16, 64]
|
|
for batch_size in batch_sizes:
|
|
# Model inference scales sublinearly with batch size
|
|
batch_inference_time = model_inference * (1 + 0.1 * (batch_size - 1))
|
|
per_sample_latency = batch_inference_time / batch_size
|
|
throughput = 1000 / per_sample_latency # samples/second
|
|
|
|
print(f" Batch size {batch_size:>2}: {per_sample_latency:>5.1f}ms/sample, {throughput:>6.1f} samples/sec")
|
|
|
|
# Memory optimization strategies
|
|
print(f"\n3. MEMORY OPTIMIZATION:")
|
|
|
|
# Model size optimizations
|
|
fp32_size = model_params * 4 / 1024**3 # GB
|
|
fp16_size = model_params * 2 / 1024**3 # GB
|
|
int8_size = model_params * 1 / 1024**3 # GB
|
|
|
|
print(f" FP32 Model: {fp32_size:.2f} GB")
|
|
print(f" FP16 Model: {fp16_size:.2f} GB ({fp16_size/fp32_size*100:.0f}% size)")
|
|
print(f" INT8 Model: {int8_size:.2f} GB ({int8_size/fp32_size*100:.0f}% size)")
|
|
|
|
# Caching strategies
|
|
print(f"\n4. CACHING STRATEGIES:")
|
|
print(f" • Model Caching: Keep model in GPU memory")
|
|
print(f" • KV-Cache: Store attention key-value pairs")
|
|
print(f" • Result Caching: Cache frequent query results")
|
|
print(f" • Preprocessing Cache: Cache tokenized inputs")
|
|
|
|
# Deployment patterns
|
|
print(f"\n5. DEPLOYMENT PATTERNS:")
|
|
print(f" • Single Model: Simple, low latency")
|
|
print(f" • Model Ensemble: Better accuracy, higher latency")
|
|
print(f" • A/B Testing: Compare model versions")
|
|
print(f" • Canary Deployment: Gradual rollout")
|
|
|
|
# Scaling analysis
|
|
print(f"\n6. SCALING STRATEGIES:")
|
|
replicas = [1, 2, 4, 8]
|
|
for replica_count in replicas:
|
|
requests_per_sec = 1000 / total_latency * replica_count
|
|
cost_multiplier = replica_count
|
|
print(f" {replica_count} replicas: {requests_per_sec:>6.1f} req/sec, {cost_multiplier}x cost")
|
|
|
|
# 💡 WHY THIS MATTERS: Serving is often more challenging than training
|
|
print(f"\n💡 KEY INSIGHTS:")
|
|
print(f"• Model inference is only {model_inference/total_latency*100:.0f}% of total latency")
|
|
print(f"• Batching improves throughput but increases latency")
|
|
print(f"• Quantization reduces memory by {int8_size/fp32_size*100:.0f}% (FP32→INT8)")
|
|
print(f"• Network and preprocessing often dominate latency")
|
|
print(f"• Horizontal scaling provides linear throughput improvement")
|
|
|
|
return {
|
|
'total_latency_ms': total_latency,
|
|
'model_inference_percent': model_inference/total_latency*100,
|
|
'quantization_memory_savings': (1 - int8_size/fp32_size)*100,
|
|
'max_throughput_single_replica': 1000/total_latency
|
|
}
|
|
|
|
except Exception as e:
|
|
print(f"⚠️ Error in model serving analysis: {e}")
|
|
return None
|
|
|
|
# Analyze model serving pipeline
|
|
serving_results = analyze_model_serving_pipeline()
|
|
|
|
print("\n" + "="*60 + "\n")
|
|
|
|
# %% [markdown]
|
|
"""
|
|
## 🤔 ML Systems Thinking: Reflection Questions
|
|
|
|
*After completing the computational assessments above, reflect on these broader systems questions:*
|
|
|
|
### 🏗️ Training Infrastructure Design
|
|
1. **Distributed Coordination**: When training on multiple GPUs, how do gradient synchronization and communication overhead affect the optimizations you calculated above?
|
|
|
|
2. **Fault Tolerance**: If your optimized training job crashes after 90 minutes (near the deadline), what checkpointing and recovery strategies would minimize lost progress?
|
|
|
|
3. **Resource Elasticity**: How would you design a training system that can automatically scale resources up/down based on deadline pressure and cost constraints?
|
|
|
|
### 📊 Production Training Operations
|
|
4. **Monitoring Integration**: Beyond the metrics you implemented, what operational metrics (GPU utilization, memory usage, network I/O) would you monitor to detect the bottlenecks you analyzed?
|
|
|
|
5. **Cost Optimization**: Given the cost-benefit analysis you performed, how would you build a system that automatically selects the most cost-effective optimization strategy?
|
|
|
|
6. **Pipeline Integration**: How would your throughput optimizations interact with data preprocessing, model validation, and deployment pipelines?
|
|
|
|
### ⚖️ Scale and Efficiency
|
|
7. **Memory Hierarchy**: How do the memory calculations you performed change when considering L1/L2 cache, GPU memory, and system RAM as a hierarchy?
|
|
|
|
8. **Convergence vs Throughput**: When is it better to train a smaller model faster rather than a larger model slower? How would you make this decision systematically?
|
|
|
|
9. **Multi-Tenancy**: How would you share GPU resources across multiple training jobs while maintaining the performance guarantees you calculated?
|
|
|
|
*These questions connect your quantitative analysis to the qualitative challenges of production ML systems.*
|
|
"""
|
|
|
|
# %% [markdown]
|
|
"""
|
|
## 🎯 MODULE SUMMARY: Training Pipelines
|
|
|
|
Congratulations! You've successfully implemented complete training pipelines:
|
|
|
|
### What You've Accomplished
|
|
✅ **Training Loops**: End-to-end training with loss computation and optimization
|
|
✅ **Loss Functions**: Implementation and integration of loss calculations
|
|
✅ **Metrics Tracking**: Monitoring accuracy and loss during training
|
|
✅ **Integration**: Seamless compatibility with neural networks and optimizers
|
|
✅ **Real Applications**: Training real models on real data
|
|
✅ **Pipeline Profiling**: Production-grade performance analysis and optimization
|
|
✅ **Systems Thinking**: Understanding training infrastructure at scale
|
|
|
|
### Key Concepts You've Learned
|
|
- **Training loops**: How to iterate over data, compute loss, and update parameters
|
|
- **Loss functions**: Quantifying model performance
|
|
- **Metrics tracking**: Monitoring progress and diagnosing issues
|
|
- **Integration patterns**: How training works with all components
|
|
- **Performance optimization**: Efficient training for large models
|
|
- **Pipeline profiling**: Identifying bottlenecks in training infrastructure
|
|
- **Production optimization**: Balancing throughput, memory, and resource utilization
|
|
|
|
### Professional Skills Developed
|
|
- **Training orchestration**: Building robust training systems
|
|
- **Loss engineering**: Implementing and tuning loss functions
|
|
- **Metrics analysis**: Understanding and improving model performance
|
|
- **Integration testing**: Ensuring all components work together
|
|
- **Performance profiling**: Optimizing training pipelines for production
|
|
- **Systems design**: Understanding distributed training challenges
|
|
|
|
### Ready for Advanced Applications
|
|
Your training pipeline implementations now enable:
|
|
- **Basic model training**: End-to-end training using concepts from Modules 6-9
|
|
- **Component integration**: Combining tensors, layers, optimizers, and data loaders
|
|
- **Educational experimentation**: Testing different loss functions and metrics
|
|
- **Foundation building**: Understanding training loop patterns for future modules
|
|
- **Conceptual understanding**: How all ML system components work together
|
|
- **Next module preparation**: Ready for more advanced training techniques
|
|
|
|
### Connection to Real ML Systems
|
|
Your implementations mirror production systems:
|
|
- **PyTorch**: `torch.nn.Module`, `torch.optim`, and training loops
|
|
- **TensorFlow**: `tf.keras.Model`, `tf.keras.optimizers`, and fit methods
|
|
- **Industry Standard**: Every major ML framework uses these exact patterns
|
|
- **Production Tools**: Similar to Ray Train, Horovod, and distributed training frameworks
|
|
|
|
### Next Steps
|
|
1. **Export your code**: `tito export 10_training`
|
|
2. **Test your implementation**: `tito test 10_training`
|
|
3. **Build evaluation pipelines**: Add benchmarking and validation
|
|
4. **Move to Module 12**: Add model compression and optimization!
|
|
|
|
**Ready for compression?** Your training pipelines are now ready for real-world deployment!
|
|
""" |