{"cells":[{"cell_type":"markdown","id":"6e352a75","metadata":{"id":"6e352a75"},"source":["# Lab 1: Your First MLP - Hyperparameter Ablation\n","\n","---\n","\n"]},{"cell_type":"markdown","id":"39b432b6","metadata":{"id":"39b432b6"},"source":["# **Part 1: Understanding Neural Networks**"]},{"cell_type":"markdown","id":"976f09cc","metadata":{"id":"976f09cc"},"source":["A neural network is a system designed to learn patterns in data by adjusting its internal parameters. It consists of layers of interconnected nodes (neurons) that transform data as it moves through the network, enabling it to model complex relationships.\n","\n","Key components, which we cover through this lab, include:\n","\n","- **Architecture:** The structure of the network, including the number of layers and neurons. These structural choices, often controlled by hyperparameters, define how the network processes and represents data.\n","- **Loss Function:** A mathematical expression that measures the error in the network’s predictions, guiding the training process to minimize this error.\n","- **Learning Process:** An iterative adjustment of the network’s parameters to improve its predictions. Hyperparameters play a key role in shaping how effectively this process works.\n","\n","Neural networks are highly versatile tools, capable of uncovering hierarchical patterns in data and solving a wide range of problems.\n"]},{"cell_type":"markdown","id":"e3822758","metadata":{"id":"e3822758"},"source":["## **1. Model Architecture Overview**"]},{"cell_type":"markdown","id":"f7a135bb","metadata":{"id":"f7a135bb"},"source":["The **architecture** of a neural network refers to its structural design—how layers and neurons are arranged and connected. This is a crucial factor in determining the model’s ability to represent data and solve specific problems. Key aspects of architecture include:\n","- **Layer Arrangement:** How layers are stacked (e.g., deep vs. shallow networks) and the relationships between them (e.g., feedforward vs. recurrent).  \n","- **Neuron Distribution:** The number of neurons per layer and how it varies across layers. This distribution influences how the model handles complexity and abstraction.  \n","- **Connections Between Layers:** The way neurons in one layer connect to neurons in another (e.g., fully connected, convolutional layers).\n","\n","\n","Different **architectural shapes** serve specific tasks and problem domains. For example:\n","- **Symmetric architectures** (e.g., hourglass-shaped):  \n","  - Typically have a narrowing middle (bottleneck) for efficient feature compression, followed by expansion to reconstruct or refine data.  \n","  - Common applications include image segmentation and pose estimation.\n","\n","- **Hierarchical architectures** (e.g., pyramid-shaped):  \n","  - Use progressively smaller layers, capturing multi-scale features.  \n","  - Well-suited for tasks like object detection or image classification, where details need to be processed at different scales.\n","\n","- **Uniform architectures** (e.g., cylinder-shaped):  \n","  - Maintain the same number of neurons across layers.  \n","  - Simpler design often used for sequential or time-dependent data, where the input-output relationship is less complex.\n","\n","\n","**Why Architecture Matters:**  \n","The choice of architecture affects a network’s capacity to model complexity and its computational efficiency. Understanding the relationship between architecture and performance is crucial for designing networks that solve specific tasks effectively.\n"]},{"cell_type":"markdown","id":"504b877e","metadata":{"id":"504b877e"},"source":["## **2. Measuring Error: Loss Functions in Neural Networks**\n"]},{"cell_type":"markdown","id":"02439234","metadata":{"id":"02439234"},"source":["Loss functions are critical for training neural networks, as they quantify the discrepancy between the model’s predictions and the true target values. By minimizing the loss, the network learns to improve its predictions over time. In this lab, we focus on classification tasks, using **Cross-Entropy Loss** as the primary metric. However, other loss functions, such as **Mean Squared Error**, are commonly used for different types of tasks.\n","\n","\n"]},{"cell_type":"markdown","source":["#### **What is a Loss Function?**\n","A loss function computes a scalar value that reflects the error between the predicted output $(\\hat{y})$ and the true target $(y)$. This scalar drives the optimization process, guiding adjustments to the network’s weights and biases.\n","\n"],"metadata":{"id":"5saBZLIdGVvn"},"id":"5saBZLIdGVvn"},{"cell_type":"markdown","source":["#### **Key Loss Functions**\n","\n","1. **Mean Squared Error (MSE):**  \n","   Commonly used for regression tasks, MSE calculates the average squared difference between predicted values and true values:\n","   $$\n","   \\text{MSE}(\\hat{\\mathbf{y}}, \\mathbf{y}) = \\frac{1}{k} \\sum_{i=1}^k (\\hat{y}_i - y_i)^2\n","   $$\n","   - **$\\hat{y}_i$:** Predicted value for the $i$-th output.  \n","   - **$y_i$:** True value for the $i$-th output.  \n","   - **$k$:** Number of outputs.  \n","   MSE penalizes larger errors more heavily, making it ideal for continuous-value predictions, such as predicting temperatures or stock prices.\n","\n","2. **Cross-Entropy Loss (CE):**  \n","   Used for classification tasks, Cross-Entropy Loss measures the dissimilarity between the predicted probability distribution $(\\hat{y})$ and the true distribution $(y)$ over $k$ classes:\n","   $$\n","   \\text{CE}(\\hat{\\mathbf{y}}, \\mathbf{y}) = - \\sum_{i=1}^k y_i \\log(\\hat{y}_i)\n","   $$\n","   - **$\\hat{y}_i$:** Predicted probability for the $i$-th class.  \n","   - **$y_i$:** Binary indicator (1 for the correct class, 0 otherwise).  \n","   Cross-entropy encourages the model to assign higher probabilities to the correct class while penalizing incorrect predictions.\n","\n","3. **Label Smoothing (Optional):**  \n","   For classification, **label smoothing** modifies the target distribution slightly to avoid overconfidence:\n","   $$\n","   y_i' = (1 - \\epsilon) y_i + \\frac{\\epsilon}{k}\n","   $$\n","   - **$\\epsilon$:** A small smoothing parameter.  \n","   This technique can improve generalization by preventing the model from being overly certain.\n","\n"],"metadata":{"id":"8O9GIJKCGZh0"},"id":"8O9GIJKCGZh0"},{"cell_type":"markdown","source":["Understanding loss functions is critical because they provide the feedback necessary to evaluate model performance. For this lab’s classification task, we will use **Cross-Entropy Loss**, but it’s important to recognize the broader utility of loss functions like **MSE** for other applications.\n"],"metadata":{"id":"qcTtiHutGc0h"},"id":"qcTtiHutGc0h"},{"cell_type":"markdown","id":"15c30a66","metadata":{"id":"15c30a66"},"source":["# **Part 2: Hyperparameters & Backprop**"]},{"cell_type":"markdown","id":"7bdc9fe5","metadata":{"id":"7bdc9fe5"},"source":["## **1. Hyperparameters Overview**"]},{"cell_type":"markdown","id":"2528f6c2","metadata":{"id":"2528f6c2"},"source":["\n","Hyperparameters are tunable settings that control training. Some of the below hyperparameters are typically fixed as part of the model's design, but can be experimented with during model tuning or ablation studies. They include:\n","- **Learning Rate:** Controls the size of weight updates during training.\n","- **Batch Size:** Number of samples used to compute gradients.\n","- **Regularization:** Reduces overfitting (e.g., dropout, L2 regularization).\n","- **Activation Functions:** Introduce non-linearity (e.g., ReLU, sigmoid).\n","- **Number of Epochs:** Determines how many passes the model makes through the training data.\n","- **Optimizer:** Determines how the model updates its weights during training (e.g., SGD, Adam).\n","- **Architecture - Number of Hidden Layers and Neurons per Hidden Layer:** Shapes the model architecture by defining its depth and width, controlling the model's ability to learn patterns and generalize.\n","\n"]},{"cell_type":"markdown","id":"63072590","metadata":{"id":"63072590"},"source":["### **Learning Rate: The Speed of Learning**"]},{"cell_type":"markdown","id":"fc2040c2","metadata":{"id":"fc2040c2"},"source":["\n","The learning rate $(\\eta)$ determines how large the steps are during training as the model updates its weights to minimize error.\n","It directly impacts how quickly the model converges to a solution. Think of it as the speed of a car: too slow, and you’ll take forever\n","to reach your destination; too fast, and you might miss the turn entirely.\n"]},{"cell_type":"markdown","id":"e800007f","metadata":{"id":"e800007f"},"source":["#### **Mathematical Context**\n","\n","The learning rate is a scaling factor in the weight update rule during gradient descent:\n","\n","$$\n","w^{t+1} = w^t - \\eta \\frac{\\partial L}{\\partial w}\n","$$\n","\n","Where:\n","- $w^t$: Weights at step $t$.  \n","- $\\eta$: Learning rate.  \n","- $\\frac{\\partial L}{\\partial w}$: Gradient of the loss function $L$ with respect to the weights.\n","\n","The learning rate affects how large the updates to the weights are:\n","- **Low learning rate:** Small, precise steps toward minimizing the loss.  \n","- **High learning rate:** Large steps that may overshoot the optimal value, leading to instability.\n"]},{"cell_type":"markdown","id":"891a1ee4","metadata":{"id":"891a1ee4"},"source":["#### **Range of Values and Trade-offs**\n","\n","| Learning Rate     | Effect                             | Pros                   | Cons                             |\n","|-------------------|------------------------------------|------------------------|----------------------------------|\n","| **Low (e.g., 0.001)** | Slow, stable convergence          | Reduces instability    | Requires more epochs            |\n","| **Optimal (e.g., 0.01)** | Fast and efficient learning      | Balances speed & stability | Requires careful tuning         |\n","| **High (e.g., 0.1)** | Fast, unstable updates            | Accelerates early progress | Risks divergence or oscillation |\n"]},{"cell_type":"markdown","source":["#### **Visualizing Its Effect**\n","\n","\n","When training with different learning rates:\n","- **Low Learning Rate:** Loss decreases steadily but requires many epochs to converge.  \n","- **Optimal Learning Rate:** Loss decreases quickly and stabilizes efficiently.  \n","- **High Learning Rate:** Loss may oscillate or even diverge.\n"],"metadata":{"id":"tz3baLSMde3-"},"id":"tz3baLSMde3-"},{"cell_type":"markdown","source":["![learningRate.png](data:image/png;base64,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)"],"metadata":{"id":"FeTRxMP0dgvy"},"id":"FeTRxMP0dgvy"},{"cell_type":"markdown","source":["### **Batch Size: The Size of Each Learning Step**  \n","\n"],"metadata":{"id":"gUBTl-F0vnJX"},"id":"gUBTl-F0vnJX"},{"cell_type":"markdown","source":["The batch size determines how many training samples the model processes before updating its weights. It’s a crucial hyperparameter that influences the trade-off between training speed and generalization. Think of batch size as the number of ingredients you prepare at a time when cooking: working with small batches gives you more control, but large batches are faster."],"metadata":{"id":"Hs0mbEely3F4"},"id":"Hs0mbEely3F4"},{"cell_type":"markdown","source":["\n","\n","#### **Mathematical Context**  \n","During training, the model computes the gradient of the loss function over a batch of data. For a batch size $m$, the gradient is:\n","\n","$$\n","\\frac{\\partial L}{\\partial w} = \\frac{1}{m} \\sum_{i=1}^{m} \\frac{\\partial L_i}{\\partial w}\n","$$\n","\n","Where:\n","- $m$: The batch size.  \n","- $L_i$: Loss for the $i$-th sample in the batch.\n","\n","A larger batch size results in smoother, more stable gradients, while a smaller batch size introduces more noise.\n","\n"],"metadata":{"id":"cKSpH9gixMPm"},"id":"cKSpH9gixMPm"},{"cell_type":"markdown","source":["#### **Range of Values and Trade-offs**\n","| Batch Size         | Effect                                     | Pros                     | Cons                              |\n","|--------------------|-------------------------------------------|--------------------------|-----------------------------------|\n","| **Small (e.g., 8)**   | Noisy gradients, better generalization    | Requires less memory      | Slower training                   |\n","| **Moderate (e.g., 32)**| Balanced trade-off between noise and stability | Good generalization      | Longer epochs than large batches  |\n","| **Large (e.g., 128)**  | Smooth gradients, faster convergence    | Efficient for large datasets | Risks overfitting or poor generalization |\n","\n","\n"],"metadata":{"id":"8bh-V0JSxP7m"},"id":"8bh-V0JSxP7m"},{"cell_type":"markdown","source":["#### **Visualizing Its Effect**  \n","Imagine plotting the loss curves for models trained with different batch sizes:\n","- **Small Batch Size:** Loss fluctuates but converges to a better generalization performance.  \n","- **Large Batch Size:** Loss decreases smoothly but may lead to overfitting if the dataset is small.  \n","\n"],"metadata":{"id":"8DocOzw8xSZp"},"id":"8DocOzw8xSZp"},{"cell_type":"markdown","source":["![batchSize.png](data:image/png;base64,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)"],"metadata":{"id":"4NmTiIAGewwZ"},"id":"4NmTiIAGewwZ"},{"cell_type":"markdown","source":["### **Regularization: Preventing Overfitting**  \n"],"metadata":{"id":"puwlCMXByupq"},"id":"puwlCMXByupq"},{"cell_type":"markdown","source":["Regularization helps a model generalize better to unseen data by discouraging overly complex solutions. Think of it as a penalty for “memorizing the training data” rather than learning useful patterns.\n"],"metadata":{"id":"rq7tYYjiy-Ex"},"id":"rq7tYYjiy-Ex"},{"cell_type":"markdown","source":["\n","#### **Mathematical Context**  \n","Regularization modifies the loss function to include a penalty term that discourages large weights. The two most common types are **L1** and **L2** regularization:\n","\n","1. **L1 Regularization (Lasso):**  \n","   Adds the absolute value of weights as a penalty:\n","\n","   $$\n","   L_{\\text{new}} = L_{\\text{original}} + \\lambda \\sum |w_i|\n","   $$\n","\n","   - Encourages sparsity by driving some weights to exactly zero.  \n","   - Useful for feature selection.\n","\n","2. **L2 Regularization (Ridge):**  \n","   Adds the square of weights as a penalty:\n","\n","   $$\n","   L_{\\text{new}} = L_{\\text{original}} + \\lambda \\sum w_i^2\n","   $$\n","\n","   - Shrinks weights toward zero, making the model more robust without eliminating features.\n","\n","Here:  \n","- $L_{\\text{original}}$: The original loss function.  \n","- $\\lambda$: The regularization strength (hyperparameter).  \n","- $w_i$: Individual weights of the model.\n"],"metadata":{"id":"sNPuuM77zEb2"},"id":"sNPuuM77zEb2"},{"cell_type":"markdown","source":["\n","#### **Range of Values and Trade-offs**\n","| Regularization Strength (\\(\\lambda\\)) | Effect                             | Pros                             | Cons                             |\n","|---------------------------------------|------------------------------------|----------------------------------|----------------------------------|\n","| **Low $(\\lambda = 0)$**             | No regularization applied          | Fits the training data perfectly | Risks overfitting                |\n","| **Moderate $(\\lambda = 0.01)$**     | Slight weight shrinkage            | Balances training and validation performance | Requires tuning                  |\n","| **High $(\\lambda = 0.1)$**          | Strong weight shrinkage            | Prevents overfitting             | Risks underfitting (oversimplifying the model) |\n"],"metadata":{"id":"-KjtMAC8zH7T"},"id":"-KjtMAC8zH7T"},{"cell_type":"markdown","source":["\n","#### **Visualizing Its Effect**\n","Imagine a simple regression problem with data points scattered around a trend line. Without regularization, the model might overfit, curving to pass through every point. With increasing regularization:\n","- **No Regularization $(\\lambda = 0)$**: The model fits all points, capturing noise.  \n","- **Moderate Regularization $(\\lambda = 0.01)$**: The model smooths out, fitting the general trend.  \n","- **High Regularization $(\\lambda = 0.1)$**: The model oversimplifies, failing to capture important features.\n","\n"],"metadata":{"id":"C8KCP8TkzKuP"},"id":"C8KCP8TkzKuP"},{"cell_type":"markdown","source":["![regularization.png](data:image/png;base64,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)"],"metadata":{"id":"YfHxw3VPedS8"},"id":"YfHxw3VPedS8"},{"cell_type":"markdown","source":["### **Activation Functions: Adding Non-Linearity to Learning**  \n"],"metadata":{"id":"_3L-VZtNz4ft"},"id":"_3L-VZtNz4ft"},{"cell_type":"markdown","source":["Activation functions are essential in neural networks because they introduce non-linearity. Without them, a neural network would essentially become a linear model, no matter how many layers it has. Activation functions enable the network to learn complex patterns and relationships in the data.\n","\n","Think of activation functions as \"decision gates\" that decide how much of the input signal passes through to the next layer.\n","\n"],"metadata":{"id":"F5zYR13Tz8qr"},"id":"F5zYR13Tz8qr"},{"cell_type":"markdown","source":["#### **Mathematical Context**  \n","Each neuron in a neural network computes a weighted sum of its inputs:\n","\n","$$\n","z = w \\cdot x + b\n","$$\n","\n","The activation function $f(z)$ then determines the output:\n","\n","$$\n","a = f(z)\n","$$\n","\n","Different activation functions have unique properties that affect how the network learns and processes information.\n","\n"],"metadata":{"id":"hV3dsoJz0CZp"},"id":"hV3dsoJz0CZp"},{"cell_type":"markdown","source":["#### **Common Activation Functions and Their Properties**\n","\n","| **Function**  | **Formula**                          | **Pros**                                | **Cons**                               |\n","|---------------|--------------------------------------|-----------------------------------------|----------------------------------------|\n","| **ReLU**      | $f(z) = \\max(0, z)$               | Efficient, avoids vanishing gradients   | Can lead to \"dead neurons\"             |\n","| **Sigmoid**   | $f(z) = \\frac{1}{1 + e^{-z}}$      | Smooth, interpretable output            | Vanishing gradients, slow convergence  |\n","| **Tanh**      | $f(z) = \\frac{e^z - e^{-z}}{e^z + e^{-z}}$ | Scales output between \\(-1\\) and \\(1\\)  | Still prone to vanishing gradients     |\n","| **Softmax**   | $f(z)_i = \\frac{e^{z_i}}{\\sum_j e^{z_j}}$ | Converts scores into probabilities      | Only used in the output layer          |\n","\n"],"metadata":{"id":"FCd-lKie0Gr5"},"id":"FCd-lKie0Gr5"},{"cell_type":"markdown","source":["#### **Why Activation Functions Matter**\n","1. **ReLU (Rectified Linear Unit):**  \n","   - Most commonly used activation function in hidden layers.  \n","   - Efficient to compute and avoids the vanishing gradient problem seen with sigmoid and tanh.  \n","   - **Challenge:** Can produce \"dead neurons\" when $z \\leq 0$, as the gradient becomes zero.\n","\n","2. **Sigmoid and Tanh:**  \n","   - Useful for tasks requiring bounded outputs (e.g., probabilities for sigmoid).  \n","   - **Challenge:** Gradients diminish as $z$ moves toward extreme values, slowing learning.\n","\n","3. **Softmax:**  \n","   - Converts raw scores into probabilities for multi-class classification problems.  \n","   - Typically used in the output layer for classification tasks.\n","\n"],"metadata":{"id":"eRM-Ch910Kfa"},"id":"eRM-Ch910Kfa"},{"cell_type":"markdown","source":["#### **Visualizing Activation Functions**  \n","Here are commonly used activation functions to highlight their differences. This plot demonstrates how each function transforms the input $z$ into the output $a$:\n","\n"],"metadata":{"id":"ubnCt3x-0O5_"},"id":"ubnCt3x-0O5_"},{"cell_type":"markdown","source":["![activation.png](data:image/png;base64,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)"],"metadata":{"id":"Yvsp02a0fh5A"},"id":"Yvsp02a0fh5A"},{"cell_type":"markdown","source":["### **Number of Epochs: How Long Should the Model Learn?**  \n"],"metadata":{"id":"lqIlP-9P0-kk"},"id":"lqIlP-9P0-kk"},{"cell_type":"markdown","source":["The number of epochs determines how many times the entire training dataset is passed through the model during training. It’s like practicing a skill—more practice can lead to mastery, but overdoing it might cause burnout or overfitting.\n"],"metadata":{"id":"3iYJBA471PfP"},"id":"3iYJBA471PfP"},{"cell_type":"markdown","source":["#### **What Happens During an Epoch?**  \n","During one epoch, the model:\n","1. Processes the entire training dataset, divided into batches.  \n","2. Updates its weights using gradient descent for each batch.\n","\n","The number of epochs determines how many times this process is repeated. A higher number of epochs allows the model to learn more, but it increases the risk of overfitting (performing well on the training data but poorly on unseen data).\n","\n","\n"],"metadata":{"id":"PF2LwXAq1SaQ"},"id":"PF2LwXAq1SaQ"},{"cell_type":"markdown","source":["#### **Range of Values and Trade-offs**\n","| **Epochs**       | **Effect**                            | **Pros**                          | **Cons**                          |\n","|-------------------|---------------------------------------|------------------------------------|-----------------------------------|\n","| **Low (e.g., 5)** | Limited learning; underfitting risk   | Faster training                   | May not capture data patterns     |\n","| **Optimal (e.g., 20-50)** | Balanced learning; generalizes well | Good trade-off between speed & accuracy | Requires careful tuning           |\n","| **High (e.g., 100+)** | Risk of overfitting                | Maximizes accuracy on training data | May lead to poor generalization   |\n","\n"],"metadata":{"id":"cnD1CECz1W5Q"},"id":"cnD1CECz1W5Q"},{"cell_type":"markdown","source":["#### **Visualizing Its Effect**  \n","Imagine you train a model for different numbers of epochs:\n","- **Too Few Epochs:** The model underfits, as it hasn’t learned enough patterns from the data. Validation loss decreases slightly or stays high.  \n","- **Optimal Number of Epochs:** Training loss decreases steadily, and validation loss stabilizes, indicating good generalization.  \n","- **Too Many Epochs:** Validation loss increases after a certain point, while training loss keeps decreasing, showing overfitting.\n","\n"],"metadata":{"id":"QPQH2rX-1ZhQ"},"id":"QPQH2rX-1ZhQ"},{"cell_type":"markdown","source":["![epochs.png](data:image/png;base64,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)"],"metadata":{"id":"gHV8T7KHfuFT"},"id":"gHV8T7KHfuFT"},{"cell_type":"markdown","source":["### **Optimizer: The Strategy for Learning**  \n"],"metadata":{"id":"Q-o0nLyg1eY_"},"id":"Q-o0nLyg1eY_"},{"cell_type":"markdown","source":["An optimizer determines how the model updates its weights during training to minimize the loss function. It defines the algorithm that drives gradient descent, making it one of the most crucial choices for training neural networks effectively.\n","\n","\n"],"metadata":{"id":"dJUO5ESO2GPB"},"id":"dJUO5ESO2GPB"},{"cell_type":"markdown","source":["#### **Mathematical Context**  \n","The optimizer updates weights based on the gradient of the loss function. The general weight update rule is:\n","\n","$$\n","w^{t+1} = w^t - \\eta \\cdot \\nabla L(w^t)\n","$$\n","\n","Where:\n","- $w^t$: Weights at step $t$.  \n","- $\\eta$: Learning rate.  \n","- $\\nabla L(w^t)$: Gradient of the loss function at $w^t$.\n","\n","Different optimizers modify this basic formula to improve performance. For example:\n","\n","1. **Stochastic Gradient Descent (SGD):**  \n","   $$\n","   w^{t+1} = w^t - \\eta \\cdot \\nabla L(w^t)\n","   $$\n","   - Simple and efficient but may converge slowly.\n","\n","2. **Adam (Adaptive Moment Estimation):**  \n","   $$\n","   m_t = \\beta_1 m_{t-1} + (1 - \\beta_1) \\nabla L(w^t)\n","   $$\n","   $$\n","   v_t = \\beta_2 v_{t-1} + (1 - \\beta_2) (\\nabla L(w^t))^2\n","   $$\n","   $$\n","   \\hat{m}_t = \\frac{m_t}{1 - \\beta_1^t}, \\quad \\hat{v}_t = \\frac{v_t}{1 - \\beta_2^t}\n","   $$\n","   $$\n","   w^{t+1} = w^t - \\eta \\cdot \\frac{\\hat{m}_t}{\\sqrt{\\hat{v}_t} + \\epsilon}\n","   $$\n","   - Combines momentum and adaptive learning rates for faster, more stable convergence.\n","\n"],"metadata":{"id":"dvJO2r3d2LwL"},"id":"dvJO2r3d2LwL"},{"cell_type":"markdown","source":["#### **Range of Choices and Trade-offs**\n","| Optimizer  | Behavior                                    | Pros                              | Cons                              |\n","|------------|--------------------------------------------|-----------------------------------|-----------------------------------|\n","| **SGD**    | Simple gradient-based updates              | Easy to implement, computationally efficient | May converge slowly, sensitive to learning rate. |\n","| **Momentum** | Adds momentum to SGD to smooth updates    | Reduces oscillations, accelerates convergence | Requires tuning of momentum parameter. |\n","| **Adam**   | Combines momentum and adaptive learning rates | Fast convergence, good default for many tasks | May generalize poorly if not tuned. |\n","| **RMSprop** | Scales learning rate based on gradient magnitude | Handles noisy updates well       | May not perform well on all tasks. |\n","\n"],"metadata":{"id":"QvLaVDdi2PZi"},"id":"QvLaVDdi2PZi"},{"cell_type":"markdown","source":["#### **Visualizing Its Effect**  \n","Imagine optimizing a loss function shaped like a bowl. Each optimizer takes a different path to reach the bottom:\n","- **SGD:** Takes steady, small steps, which may oscillate near the solution.  \n","- **Momentum:** Smooths oscillations by combining past gradients with the current one.  \n","- **Adam:** Adjusts step sizes adaptively, accelerating learning in some regions while slowing down in others.\n","\n"],"metadata":{"id":"P-1e4B862SFb"},"id":"P-1e4B862SFb"},{"cell_type":"markdown","source":["![optimizer.png](data:image/png;base64,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)"],"metadata":{"id":"h90bkriLgHWJ"},"id":"h90bkriLgHWJ"},{"cell_type":"markdown","source":["### **Architecture - Number of Hidden Layers and Neurons per Hidden Layer**\n","\n"],"metadata":{"id":"WD5cEnVK2WC2"},"id":"WD5cEnVK2WC2"},{"cell_type":"markdown","source":["The **number of hidden layers** determines the **depth** of a neural network, while the **number of neurons per hidden layer** defines its **width**. Together, they shape the architecture and control the model’s ability to learn patterns and generalize. These two hyperparameters must be balanced to align with the task requirements and the chosen architecture.\n","\n"],"metadata":{"id":"jHo3TcE35n-9"},"id":"jHo3TcE35n-9"},{"cell_type":"markdown","source":["#### **Why Do They Matter?**\n","1. **Depth:**  \n","   - More layers increase the model's ability to capture hierarchical features but can lead to overfitting or higher computational costs.  \n","   - Fewer layers result in simpler models that might underfit complex data.  \n","   - Depth is essential for defining architectural shapes like hourglass, pyramid, and cone.\n","\n","2. **Width:**  \n","   - More neurons per layer increase the model’s capacity to represent features.  \n","   - Fewer neurons result in a simpler model but may miss fine-grained patterns.  \n","   - Width affects architectural shapes like the tapering of a pyramid or the bottleneck of an hourglass.\n","\n","\n"],"metadata":{"id":"Iuq3EBsg5ssS"},"id":"Iuq3EBsg5ssS"},{"cell_type":"markdown","source":["#### **How They Relate to Shapes**\n","\n","| **Common Shapes**            | **Depth (Layers)** | **Example Width (Neurons per Layer)**          | **Common Use Cases**                                                                                     | **Examples**                                                                                     |\n","|-----------------------|--------------------|-----------------------------------------|----------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------|\n","| **Hourglass**         | 3-5+                | 128 → 64 → 32 → 64 → 128               | Symmetric tasks, encoder-decoder pipelines, feature refinement                                           | U-Net, VAEs, GAN discriminators, DensePose                                                     |\n","| **Pyramid**           | 4-8+                | 256 → 128 → 64 → 32                    | Hierarchical feature extraction, dimensionality reduction                                                | CNNs, ResNet (early layers), Vision Transformers (preprocessing)                               |\n","| **Inverted Pyramid**  | 4-8+                | 32 → 64 → 128 → 256                    | Expanding representations, synthesis, reconstruction tasks                                              | GAN generators, VAE decoders, PixelCNNs                                                       |\n","| **Cone**              | 4-8+                | 256 → 192 → 128 → 96 → 64              | Progressive generative refinement, smooth transitions                                                   | GAN generators, Progressive GANs                                                               |\n","| **Cylinder**          | 2-6+                | 128 → 128 → 128 → 128                  | Sequential or temporal patterns, simple-to-moderate complexity                                          | RNNs, LSTMs, GRUs, Transformer encoders                                                       |\n","\n"],"metadata":{"id":"MZAu4pQs5w_l"},"id":"MZAu4pQs5w_l"},{"cell_type":"markdown","id":"ea40cac7","metadata":{"id":"ea40cac7"},"source":["## **2. How Backpropagation Works**"]},{"cell_type":"markdown","source":["Backpropagation is the process that allows a neural network to learn by calculating and propagating gradients through the network. Each hyperparameter listed below influences different parts of this process, shaping the efficiency and outcome of training.\n","\n"],"metadata":{"id":"DJjz55rXCin5"},"id":"DJjz55rXCin5"},{"cell_type":"markdown","source":["#### **1. Forward Propagation**\n","- **What Happens:**  \n","  - The input data ($x \\in \\mathbb{R}^n$) is passed through the network layer by layer to produce a prediction ($\\hat{y}$).\n","  - Each layer computes:  \n","    $$\n","    z_i = W_i \\cdot a_{i-1} + b_i, \\quad a_i = f_i(z_i)\n","    $$  \n","    - $z_i$: Weighted sum of inputs at layer $i$.  \n","    - $a_i$: Output after applying the activation function $f_i(z_i)$.  \n","    \n","- **Hyperparameters Involved:**  \n","  - Activation Functions\n","  - Number of Hidden Layers and Neurons per Hidden Layer\n"],"metadata":{"id":"8Ntw30G4-ZME"},"id":"8Ntw30G4-ZME"},{"cell_type":"markdown","source":["#### **2. Loss Calculation**\n","- **What Happens:**  \n","  - The loss function quantifies the error between the predicted output ($\\hat{y}$) and the true target ($y$):  \n","    $$\n","    L = \\text{Loss}(y, \\hat{y})\n","    $$  \n","  - Examples:\n","    - **Cross-Entropy Loss** (classification tasks):  \n","      $$\n","      L = -\\sum_{i=1}^k y_i \\log(\\hat{y}_i)\n","      $$  \n","    - **Mean Squared Error (MSE)** (regression tasks):  \n","      $$\n","      L = \\frac{1}{N} \\sum_{i=1}^N (y_i - \\hat{y}_i)^2\n","      $$  \n","\n","- **Hyperparameters Involved:**  \n","  - Regularization\n"],"metadata":{"id":"uiKisi2f-dh8"},"id":"uiKisi2f-dh8"},{"cell_type":"markdown","source":["#### **3. Gradient Computation**\n","- **What Happens:**  \n","  - Gradients of the loss function are computed with respect to each parameter (weights $W_i$ and biases $b_i$) by applying the chain rule:\n","$$\n","\\frac{\\partial L}{\\partial z_i} = \\frac{\\partial L}{\\partial a_i} \\cdot f_i'(z_i)\n","$$\n","  - For hidden layers:\n","$$\n","\\frac{\\partial L}{\\partial z_i} = \\left(\\frac{\\partial L}{\\partial z_{i+1}} \\cdot W_{i+1}^\\top\\right) \\cdot f_i'(z_i)\n","$$  \n","\n","- **Hyperparameters Involved:**  \n","  - Batch Size\n"],"metadata":{"id":"kiqP4m8Q-g7b"},"id":"kiqP4m8Q-g7b"},{"cell_type":"markdown","source":["#### **4. Weight and Bias Updates**\n","- **What Happens:**  \n","  - Using the gradients, weights and biases are updated to reduce the loss:  \n","$$\n","W_i^{t+1} = W_i^t - \\eta \\cdot \\frac{\\partial L}{\\partial W_i}, \\quad b_i^{t+1} = b_i^t - \\eta \\cdot \\frac{\\partial L}{\\partial b_i}\n","$$  \n","    - $\\eta$: Learning rate that controls the size of the updates.\n","\n","- **Hyperparameters Involved:**  \n","  - Learning Rate\n","  - Optimizer"],"metadata":{"id":"SZ-S3rQ1_ehy"},"id":"SZ-S3rQ1_ehy"},{"cell_type":"markdown","source":["\n","#### **5. Iterative Process**\n","- **What Happens:**  \n","  - Steps 1–4 are repeated for each batch across all epochs.  \n","  - The network gradually converges as backpropagation iteratively adjusts parameters.\n","\n","- **Hyperparameters Involved:**  \n","  - Number of Epochs"],"metadata":{"id":"_Cv5EBsH_hIM"},"id":"_Cv5EBsH_hIM"},{"cell_type":"markdown","id":"d8a41c18","metadata":{"id":"d8a41c18"},"source":["## **3. For the Future: How and Why to Perform Ablations**"]},{"cell_type":"markdown","id":"0cd54059","metadata":{"id":"0cd54059"},"source":["Ablation studies are a methodical approach to evaluating the importance of different parts of a model. By systematically removing or altering elements, ablations reveal how each contributes to the model’s overall performance, helping identify essential components and opportunities for simplification.\n","\n","**Also, they are essential for your homework part 2s!**\n","\n","To perform an ablation:\n","1. **Choose an Element to Test:** Select a specific part of the model to modify or remove.  \n","2. **Make the Change and Evaluate:** Implement the change, retrain the model under the same conditions, and measure its performance.  \n","3. **Analyze the Results:** Compare the modified model’s performance to the original to determine the significance of the tested element.\n","\n","Ablation studies are essential because they provide insights into the inner workings of a model, ensuring designs are both effective and efficient."]},{"cell_type":"markdown","source":["# **Part 3: Practice with a Pipeline**"],"metadata":{"id":"oK4NqtbhCJxj"},"id":"oK4NqtbhCJxj"},{"cell_type":"markdown","source":["## Importing Essential Libraries"],"metadata":{"id":"dpurtjS01nuK"},"id":"dpurtjS01nuK"},{"cell_type":"code","source":["# Import Deep-Learning-Specific Libraries\n","import torch\n","import torchvision\n","import tensorflow\n","from torchsummary import summary\n","import numpy as np\n","from torch.utils.data import Dataset, DataLoader, random_split\n","import torchvision.transforms as transforms\n","from tensorflow.keras.datasets import mnist\n","import wandb\n","\n","# Import SciKit Learn for Additional Machine Learning Utilities\n","import sklearn\n","import sklearn.metrics\n","\n","# Import MatPlotLib and TQDM for Visualizing Our Input Data and Training Loop Progress.\n","import matplotlib.pyplot as plt\n","from tqdm.auto import tqdm"],"metadata":{"id":"loFAJeon1hc6"},"id":"loFAJeon1hc6","execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Ensuring the device\n","\n"],"metadata":{"id":"9ewOgQvL1ua3"},"id":"9ewOgQvL1ua3"},{"cell_type":"code","source":["# Ensure We Are Running on a GPU.\n","device = 'cuda' if torch.cuda.is_available() else 'cpu'\n","print(\"Device: \", device)\n","\n","# This check seems unimportant but if you didn't set up cuda before hand you'll have problems later. (This is done for you with colab and GCP but is a consideration for local)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"KqDw6Tey1vjJ","executionInfo":{"status":"ok","timestamp":1737228853660,"user_tz":300,"elapsed":226,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"6d07f2ea-fc04-47b1-cd33-b5cff0390bdb"},"id":"KqDw6Tey1vjJ","execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Device:  cpu\n"]}]},{"cell_type":"markdown","source":["## Data Loading and Preprocessing"],"metadata":{"id":"2TauVoXh1210"},"id":"2TauVoXh1210"},{"cell_type":"code","source":["(X_train, y_train), (X_test, y_test) = mnist.load_data()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"gWE1u04q12UH","executionInfo":{"status":"ok","timestamp":1737228888453,"user_tz":300,"elapsed":792,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"5065ab42-a943-4a2a-a6c4-27133c23f15a"},"id":"gWE1u04q12UH","execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n","\u001b[1m11490434/11490434\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 0us/step\n"]}]},{"cell_type":"code","source":["class MNISTDataset(Dataset):\n","    def __init__(self, data, labels, transform=None):\n","        self.data = data\n","        self.labels = labels\n","        self.transform = transform\n","\n","    def __len__(self):\n","        return len(self.data)\n","\n","    def __getitem__(self, idx):\n","\n","        image = self.data[idx]\n","        label = self.labels[idx]\n","\n","        if self.transform:\n","            image = self.transform(image)\n","\n","        return image, label"],"metadata":{"id":"vMdzTimW2ITl"},"id":"vMdzTimW2ITl","execution_count":null,"outputs":[]},{"cell_type":"code","source":["# Convert the data to PyTorch tensors\n","X_train = torch.tensor(X_train, dtype=torch.float32)\n","X_test = torch.tensor(X_test, dtype=torch.float32)\n","y_train = torch.tensor(y_train, dtype=torch.long)\n","y_test = torch.tensor(y_test, dtype=torch.long)\n","\n","# Define transforms including normalization\n","transform = transforms.Compose([\n","    transforms.Lambda(lambda x: x.unsqueeze(0)),  # Add a channel dimension (N, 1, H, W)\n","    transforms.Normalize((0.5,), (0.5,))          # Normalize to range [-1, 1] (mean=0.5, std=0.5)\n","])"],"metadata":{"id":"xzpB7Xi42K1J"},"id":"xzpB7Xi42K1J","execution_count":null,"outputs":[]},{"cell_type":"code","source":["# Create instances of the dataset class\n","train_dataset = MNISTDataset(X_train, y_train, transform=transform)\n","test_dataset = MNISTDataset(X_test, y_test, transform=transform)\n","\n","# Split the training dataset into train and validation sets\n","train_size = int(0.8 * len(train_dataset))  # 80% for training\n","val_size = len(train_dataset) - train_size  # Remaining 20% for validation\n","train_dataset, val_dataset = random_split(train_dataset, [train_size, val_size])\n","\n","# Create DataLoaders for batching\n","train_loader = DataLoader(train_dataset, batch_size=64, shuffle=True)\n","val_loader = DataLoader(val_dataset, batch_size=64, shuffle=False)\n","test_loader = DataLoader(test_dataset, batch_size=64, shuffle=False)"],"metadata":{"id":"I_AQ2vyo2NK-"},"id":"I_AQ2vyo2NK-","execution_count":null,"outputs":[]},{"cell_type":"code","source":["# Print dataset sizes\n","print(f\"Training set size: {len(train_dataset)}\")\n","print(f\"Validation set size: {len(val_dataset)}\")\n","print(f\"Test set size: {len(test_dataset)}\")"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"nZFAs0382Pbo","executionInfo":{"status":"ok","timestamp":1737229065486,"user_tz":300,"elapsed":246,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"8df1b523-1728-4377-a747-1fef0162fa12"},"id":"nZFAs0382Pbo","execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Training set size: 48000\n","Validation set size: 12000\n","Test set size: 10000\n"]}]},{"cell_type":"code","source":["# Test DataLoader\n","for images, labels in train_loader:\n","    print(f\"Batch images shape: {images.shape}\")\n","    print(f\"Batch labels shape: {labels.shape}\")\n","    break"],"metadata":{"id":"K9AU_GF42RtI"},"id":"K9AU_GF42RtI","execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Data Visualisation"],"metadata":{"id":"TOUsD6_c2WcE"},"id":"TOUsD6_c2WcE"},{"cell_type":"code","source":["# Get first training sample & label pair\n","for x, y in train_dataset:\n","  break"],"metadata":{"id":"FjciqPhE2UPN"},"id":"FjciqPhE2UPN","execution_count":null,"outputs":[]},{"cell_type":"code","source":["NUM_CHANNELS, HEIGHT, WIDTH = x.shape\n","print(\"Number of channels: \", NUM_CHANNELS)\n","print(\"Image height: \", HEIGHT)\n","print(\"Image width: \", WIDTH)"],"metadata":{"id":"9qzvVnyc2bBZ","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1737229140214,"user_tz":300,"elapsed":243,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"cdc86f40-5b47-4abf-c75a-69276670b424"},"id":"9qzvVnyc2bBZ","execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Number of channels:  1\n","Image height:  28\n","Image width:  28\n"]}]},{"cell_type":"code","source":["x.squeeze().shape"],"metadata":{"id":"Zf1hkO1N2dJI","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1737229146826,"user_tz":300,"elapsed":183,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"e1daee11-ffe3-46c5-c153-26526b668922"},"id":"Zf1hkO1N2dJI","execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["torch.Size([28, 28])"]},"metadata":{},"execution_count":10}]},{"cell_type":"code","source":["npimg = x.numpy()\n","plt.imshow(npimg.squeeze())\n","plt.title(f\"Digit {str(y)}\")\n","plt.show()"],"metadata":{"id":"jObYwqWy2fUs","colab":{"base_uri":"https://localhost:8080/","height":452},"executionInfo":{"status":"ok","timestamp":1737229149182,"user_tz":300,"elapsed":381,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"a6064a1d-bfa1-45aa-cd37-ebcd71786375"},"id":"jObYwqWy2fUs","execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]},{"cell_type":"markdown","source":["## Model Development"],"metadata":{"id":"KOhezaXL73ud"},"id":"KOhezaXL73ud"},{"cell_type":"markdown","source":["### How to develop a Single Layer Neural Network?"],"metadata":{"id":"ZvcjT1Wb75_E"},"id":"ZvcjT1Wb75_E"},{"cell_type":"code","source":["IN_SIZE = HEIGHT * WIDTH\n","HIDDEN_SIZE = 1024\n","OUT_SIZE = 10"],"metadata":{"id":"lWfBhUhw8urY"},"id":"lWfBhUhw8urY","execution_count":null,"outputs":[]},{"cell_type":"code","source":["model_1 = torch.nn.Sequential(\n","    torch.nn.Linear(IN_SIZE, HIDDEN_SIZE),\n","    torch.nn.ReLU(),\n","    torch.nn.Linear(HIDDEN_SIZE, OUT_SIZE)\n",")\n","model_1 = model_1.to(device)\n","summary(model_1, x.flatten().shape)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Vhh5IbzP72UT","executionInfo":{"status":"ok","timestamp":1737229641659,"user_tz":300,"elapsed":262,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"736f405a-d63f-4fd2-b077-90425201f707"},"id":"Vhh5IbzP72UT","execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["----------------------------------------------------------------\n","        Layer (type)               Output Shape         Param #\n","================================================================\n","            Linear-1                 [-1, 1024]         803,840\n","              ReLU-2                 [-1, 1024]               0\n","            Linear-3                   [-1, 10]          10,250\n","================================================================\n","Total params: 814,090\n","Trainable params: 814,090\n","Non-trainable params: 0\n","----------------------------------------------------------------\n","Input size (MB): 0.00\n","Forward/backward pass size (MB): 0.02\n","Params size (MB): 3.11\n","Estimated Total Size (MB): 3.12\n","----------------------------------------------------------------\n"]}]},{"cell_type":"markdown","source":["### Architecture 1: Cylinder Architecture"],"metadata":{"id":"XMQRfoUx7-S0"},"id":"XMQRfoUx7-S0"},{"cell_type":"code","source":["HIDDEN_SIZE = 512\n","\n","model_cylinder = torch.nn.Sequential(\n","    torch.nn.Linear(IN_SIZE, HIDDEN_SIZE),\n","    torch.nn.ReLU(),\n","    torch.nn.Linear(HIDDEN_SIZE, HIDDEN_SIZE),\n","    torch.nn.ReLU(),\n","    torch.nn.Linear(HIDDEN_SIZE, HIDDEN_SIZE),\n","    torch.nn.ReLU(),\n","    torch.nn.Linear(HIDDEN_SIZE, HIDDEN_SIZE),\n","    torch.nn.ReLU(),\n","    torch.nn.Linear(HIDDEN_SIZE, OUT_SIZE),\n","\n",")\n","model_cylinder = model_cylinder.to(device)\n","summary(model_cylinder, x.flatten().shape)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"pCZ2CmWR9m9D","executionInfo":{"status":"ok","timestamp":1737229959304,"user_tz":300,"elapsed":266,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"e5ba9091-f16a-4f6f-971e-c2c959c41778"},"id":"pCZ2CmWR9m9D","execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["----------------------------------------------------------------\n","        Layer (type)               Output Shape         Param #\n","================================================================\n","            Linear-1                  [-1, 512]         401,920\n","              ReLU-2                  [-1, 512]               0\n","            Linear-3                  [-1, 512]         262,656\n","              ReLU-4                  [-1, 512]               0\n","            Linear-5                  [-1, 512]         262,656\n","              ReLU-6                  [-1, 512]               0\n","            Linear-7                  [-1, 512]         262,656\n","              ReLU-8                  [-1, 512]               0\n","            Linear-9                   [-1, 10]           5,130\n","================================================================\n","Total params: 1,195,018\n","Trainable params: 1,195,018\n","Non-trainable params: 0\n","----------------------------------------------------------------\n","Input size (MB): 0.00\n","Forward/backward pass size (MB): 0.03\n","Params size (MB): 4.56\n","Estimated Total Size (MB): 4.59\n","----------------------------------------------------------------\n"]}]},{"cell_type":"code","source":[],"metadata":{"id":"vi2hXtOh8vZF"},"id":"vi2hXtOh8vZF","execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["### Architecture 2: Pyramid Architecture"],"metadata":{"id":"ShlbEuWa8BH5"},"id":"ShlbEuWa8BH5"},{"cell_type":"code","source":["model_pyramid = torch.nn.Sequential(\n","    torch.nn.Linear(IN_SIZE, 1024),\n","    torch.nn.ReLU(),\n","    torch.nn.Linear(1024, 512),\n","    torch.nn.ReLU(),\n","    torch.nn.Linear(512, 256),\n","    torch.nn.ReLU(),\n","    torch.nn.Linear(256, 128),\n","    torch.nn.ReLU(),\n","    torch.nn.Linear(128, OUT_SIZE),\n",")\n","model_pyramid = model_pyramid.to(device)\n","summary(model_pyramid, x.flatten().shape)"],"metadata":{"id":"F54ewveQ8v0V","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1737230131014,"user_tz":300,"elapsed":244,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"c926ffa5-bbb3-4c37-83e8-0f9430b3cfc7"},"id":"F54ewveQ8v0V","execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["----------------------------------------------------------------\n","        Layer (type)               Output Shape         Param #\n","================================================================\n","            Linear-1                 [-1, 1024]         803,840\n","              ReLU-2                 [-1, 1024]               0\n","            Linear-3                  [-1, 512]         524,800\n","              ReLU-4                  [-1, 512]               0\n","            Linear-5                  [-1, 256]         131,328\n","              ReLU-6                  [-1, 256]               0\n","            Linear-7                  [-1, 128]          32,896\n","              ReLU-8                  [-1, 128]               0\n","            Linear-9                   [-1, 10]           1,290\n","================================================================\n","Total params: 1,494,154\n","Trainable params: 1,494,154\n","Non-trainable params: 0\n","----------------------------------------------------------------\n","Input size (MB): 0.00\n","Forward/backward pass size (MB): 0.03\n","Params size (MB): 5.70\n","Estimated Total Size (MB): 5.73\n","----------------------------------------------------------------\n"]}]},{"cell_type":"markdown","source":["## Training and Evaluation Loop"],"metadata":{"id":"LZzfixXl8EOa"},"id":"LZzfixXl8EOa"},{"cell_type":"code","source":["def train_epoch(model, optimizer, criterion, data_loader):\n","    model.train()\n","    train_loss = 0\n","\n","    for i, (images, labels) in enumerate(tqdm(data_loader)):\n","      images = images.to(device)\n","      labels = labels.to(device)\n","\n","      output = model((images.flatten(start_dim=1)))\n","      loss = criterion(output, labels)\n","\n","      optimizer.zero_grad()\n","      loss.backward()\n","      optimizer.step()\n","\n","      train_loss += loss.item()\n","\n","    return train_loss / len(data_loader)"],"metadata":{"id":"wF-m0G0M8wZE"},"id":"wF-m0G0M8wZE","execution_count":null,"outputs":[]},{"cell_type":"code","source":["def eval(model, data_loader):\n","  model.eval()\n","\n","  true_labels = []\n","  pred_labels = []\n","\n","  for i, (images, labels) in enumerate(data_loader):\n","    images = images.to(device)\n","    labels = labels.to(device)\n","\n","    with torch.inference_mode():\n","      logits = model(images.flatten(start_dim=1))\n","\n","    preds = torch.argmax(logits, dim=1)\n","\n","    true_labels.extend(labels.cpu().numpy())\n","    pred_labels.extend(preds.cpu().numpy())\n","\n","  return sklearn.metrics.accuracy_score(true_labels, pred_labels)"],"metadata":{"id":"Ndqz3WNiAe7V"},"id":"Ndqz3WNiAe7V","execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["### Model Deployment and Training"],"metadata":{"id":"A28uvihf8Gk1"},"id":"A28uvihf8Gk1"},{"cell_type":"code","source":["optimizer = torch.optim.Adam(model_cylinder.parameters(), lr=0.001)\n","criterion = torch.nn.CrossEntropyLoss()\n","NUM_EPOCHS = 3\n","\n","for epoch in range(NUM_EPOCHS):\n","  train_loss = train_epoch(model_cylinder, optimizer, criterion, train_loader)\n","  val_acc = eval(model_cylinder, val_loader)\n","  print(f\"Epoch {epoch+1}/{NUM_EPOCHS}, Train Loss: {train_loss:.4f}, Val Acc: {val_acc:.4f}\")"],"metadata":{"id":"lx2llX2g8w7M","colab":{"base_uri":"https://localhost:8080/","height":165,"referenced_widgets":["2d906d95ef004d048f0ec4d8b62a08ec","fcbe4993fa3d44968d83f3e4f6f3313f","684f2f1edf444451887b1602be279fd1","82e260d5a5634b0f9fb5fccc88cfc5b2","f6d7f2ecd61745c68a6fd9c33daaa126","2f8b94a86b2a4fc1b42b15ca74180820","e2e3f5c2eed74faea7fc6acb517070b1","d83903ea8e7c4b8da361ee0975a4fc6e","ec441659a4cf4beaa64b4354afb239db","2173a3ec624d4da6a52f15940f99ffb3","c0fda4fffa2644dbb7da72662f754832","92de46b2d68a4738a33b07b8460d4749","865acc71720e40c18a2c310bff18b089","a7a3c2d2d3d44e45a771004130c61d9f","11d70cfd41b54b2aac4fb8755c9d1805","f44fdb986ca04a15beb1cd7ae54a68c0","7f51467adf8f4bf99e1d80416960911b","7a22a6a9d0d842848020313b655efdcb","7d162ed1c5334c029e225ee45a37010b","5151e97dc41d47e282df41218ea9c065","ab5b231f508a4f04ba4d01e959b7df52","ada091dc1eeb4116969954551d29c3c1","53d851927f6649d59115edbc39ebf86f","25bdd38162f1437a84cb7179d6ea7a5b","11f098eb4bf84a5f93e8f43c3f020832","6bf208bc284c4e0ba0636137f2c94fe4","2ccd9bd611114c518e021ff691cedd42","85c47fd35f574f1789f4f98bacdcaa09","41c5cce1b0e8459b9bfd2d6a5b149c72","61fd3fa1177c4174ae741d0634f26a2e","97b4c206d2374582b35728e266d8e982","90cdf0f8902c48fc838d4ae3b50bd896","4c70b48640164768b5eba2a83ef6a0b1"]},"executionInfo":{"status":"ok","timestamp":1737230921556,"user_tz":300,"elapsed":77262,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"8d8730cb-1a8b-4dd4-b80e-b641b4e707af"},"id":"lx2llX2g8w7M","execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["  0%|          | 0/750 [00:00<?, ?it/s]"],"application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"2d906d95ef004d048f0ec4d8b62a08ec"}},"metadata":{}},{"output_type":"stream","name":"stdout","text":["Epoch 1/3, Train Loss: 0.3122, Val Acc: 0.9390\n"]},{"output_type":"display_data","data":{"text/plain":["  0%|          | 0/750 [00:00<?, ?it/s]"],"application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"92de46b2d68a4738a33b07b8460d4749"}},"metadata":{}},{"output_type":"stream","name":"stdout","text":["Epoch 2/3, Train Loss: 0.1426, Val Acc: 0.9663\n"]},{"output_type":"display_data","data":{"text/plain":["  0%|          | 0/750 [00:00<?, ?it/s]"],"application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"53d851927f6649d59115edbc39ebf86f"}},"metadata":{}},{"output_type":"stream","name":"stdout","text":["Epoch 3/3, Train Loss: 0.1129, Val Acc: 0.9652\n"]}]},{"cell_type":"code","source":["optimizer = torch.optim.Adam(model_pyramid.parameters(), lr=0.001)\n","criterion = torch.nn.CrossEntropyLoss()\n","NUM_EPOCHS = 3\n","\n","for epoch in range(NUM_EPOCHS):\n","  train_loss = train_epoch(model_pyramid, optimizer, criterion, train_loader)\n","  val_acc = eval(model_pyramid, val_loader)\n","  print(f\"Epoch {epoch+1}/{NUM_EPOCHS}, Train Loss: {train_loss:.4f}, Val Acc: {val_acc:.4f}\")"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":165,"referenced_widgets":["139e5cefce0a4324bddbfcc9e5c44dbf","e3d8ebb5147a43daa1e3ac04ae3b2517","99076af758d34f88aba85aca8dd41444","69e9749fddea415994604df36c28cf6f","6d573351d3e0466e937cc799a5de6262","fc804b2170aa48659042d8fdf84b7600","5bc475ef0a7946829247a123951b2450","9b4d4cdf008b46daacf6300fd42c485f","0b769e41d5f044bd82586f6e1000cc1f","0af9887dd1a54b95875305cecf099a94","540450bc76064f10b39b06bde3ad7199","8d4182080354437aaf2a7eff9b84af24","e420809f5ab14cfc87241b0e6277f6e1","a5b443777e8a477aa35489aace5b2c12","a83119ecdf7348dbbb341060630cb749","93801f78fd7e41b58f3c28d09684ecbe","6acf67a5ff5b4cfcb8af6f67b9d887d8","a08115bd30b44925802b0609c28b6fbf","15e3f310c101457a8c264d685db86841","722fae7ce2c4446a95f265ea903669af","ebc5a38d1a6c41c99f6af7adef0ffaec","09ab15646f314da7901250051b20cbd1","ec0ace353c7548edb186d246566810ae","91216e43b1c74cd68958700582813d36","2d7f738e56914af4b7779273b72e8d77","11782f1808fb4ba891c9b2a19e3ee1a6","a7e3eb22738c4e5fbf11f9e3caec7262","908c89bf0210413ab80682bd58c71577","d370b0e1de1143c7b11755dd14df1274","8356cec44b8d4777b9ffcd85f16e6712","8f044dd876dd420eb7be6dfad7a02c45","e20cebbf348547b4bf1465643b9366a0","de4c36f6e4b9441299028f7de68cfcd2"]},"id":"7x-4jE4BCH4I","executionInfo":{"status":"ok","timestamp":1737231134405,"user_tz":300,"elapsed":86650,"user":{"displayName":"N Miya Sylvester","userId":"01424701477607648683"}},"outputId":"44e8147c-2613-4d75-e18b-19c5fbedbea8"},"id":"7x-4jE4BCH4I","execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["  0%|          | 0/750 [00:00<?, ?it/s]"],"application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"139e5cefce0a4324bddbfcc9e5c44dbf"}},"metadata":{}},{"output_type":"stream","name":"stdout","text":["Epoch 1/3, Train Loss: 0.2898, Val Acc: 0.9522\n"]},{"output_type":"display_data","data":{"text/plain":["  0%|          | 0/750 [00:00<?, ?it/s]"],"application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"8d4182080354437aaf2a7eff9b84af24"}},"metadata":{}},{"output_type":"stream","name":"stdout","text":["Epoch 2/3, Train Loss: 0.1243, Val Acc: 0.9587\n"]},{"output_type":"display_data","data":{"text/plain":["  0%|          | 0/750 [00:00<?, ?it/s]"],"application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"ec0ace353c7548edb186d246566810ae"}},"metadata":{}},{"output_type":"stream","name":"stdout","text":["Epoch 3/3, Train Loss: 0.0948, Val Acc: 0.9652\n"]}]},{"cell_type":"markdown","id":"2ab752fa","metadata":{"id":"2ab752fa"},"source":["# **Part 4: Hands-On Testing**"]},{"cell_type":"markdown","id":"3cf148e3","metadata":{"id":"3cf148e3"},"source":["## **1. [Simple, Sample Ablation Sheet](https://docs.google.com/spreadsheets/d/1xJkX_1utAIbdQ72jESSDZAKeHGApidalCKesgNzjz-0/edit?usp=sharing)**\n"]},{"cell_type":"markdown","id":"9ede7cd0","metadata":{"id":"9ede7cd0"},"source":["![image.png](data:image/png;base64,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)"]},{"cell_type":"markdown","id":"521b98e2","metadata":{"id":"521b98e2"},"source":["## **2. Group Activity**"]},{"cell_type":"markdown","id":"84c0fe7e","metadata":{"id":"84c0fe7e"},"source":["\n","1. Create a study group with your neighbor, just for today. (If you're on zoom, we will make break-out rooms.)\n","2. Assign each person specific parameters to test (e.g., learning rate, batch size).\n","  - You can use the sample ablation sheet we've linked above, just assign each group member to a set of ablations.\n","3. Each person records results in the ablation sheet.\n","4. Compare findings and discuss patterns observed.\n"]},{"cell_type":"markdown","id":"4dd08085","metadata":{"id":"4dd08085"},"source":["## **3. Reflect on the Results**"]},{"cell_type":"markdown","id":"6abf02a1","metadata":{"id":"6abf02a1"},"source":["\n","After everyone has done their ablations, discuss:\n","- What changes improved performance the most?\n","- Were there unexpected results?\n"]},{"cell_type":"markdown","source":["# **Bonus: Improving Neural Networks & General Reading**"],"metadata":{"id":"BHlw8XfoM5G-"},"id":"BHlw8XfoM5G-"},{"cell_type":"markdown","source":["### Optimizers\n"],"metadata":{"id":"4LMFzMv3DWER"},"id":"4LMFzMv3DWER"},{"cell_type":"markdown","source":["This section will discuss a few optimizers you may find useful going forward. Above we had used Adam, an extremely well explored optimizer which has many subsequent optimizers based on it. Among them for future homework you may find that the AdamW optimizer, or AdamP may be particularly interesting.\n","\n","\n","* AdamW's integrates weight decay, which makes it particularly suitable for complex models like CNNs, where it effectively helps in preventing overfitting, a common issue in such architectures. Weight decay works by gradually reducing the weights of the neurons in the network, encouraging simpler models and thus reducing overfitting.\n","\n","\n","* As for AdamP, it optimizes the model by adjusting the gradients in a way that is more sensitive to the structure of the data, potentially leading to more efficient and stable training.\n","\n","\n","* There is also the very classic approach of Stochastic Gradient Descent (SGD), which may prove to be a better optimizer in many cases, such as scenarios where simplicity and transparency in the optimization process are crucial. Unlike more complex optimizers, SGD relies on a straightforward update rule, which can be more interpretable and easier to debug. This makes it particularly effective in situations where the data is not excessively complex or when the model architecture is relatively simple. Moreover, SGD can sometimes escape local minima more effectively than algorithms like Adam, leading to better generalization in certain types of problems.\n","\n"],"metadata":{"id":"SqbFenFLDbj2"},"id":"SqbFenFLDbj2"},{"cell_type":"markdown","source":["Below will be a few simple code snippet examples of implementations of AdamW, AdamP, and SGD using PyTorch. Documentation will be provided, which I encourge you to read as well as the original papers. Going forward, think critically about why you would select a specific optimizer when creating a network as though the ones mentioned prior perform well generally, the small differences could help significantly in squeezing that last bit of performance out of a model."],"metadata":{"id":"3VtOE_qRDewN"},"id":"3VtOE_qRDewN"},{"cell_type":"code","source":["# Adam: The classic Adam Optimizer\n","optimizer   = torch.optim.Adam(___, ___) # https://pytorch.org/docs/stable/generated/torch.optim.Adam.html#torch.optim.Adam\n","\n","# AdamW: Notice when reading the pytorch documentation that AdamW allows a weight decay variable. This often improves performance by applying a form of regularization\n","optimizer   = torch.optim.AdamW(___, ___, ___) # https://pytorch.org/docs/stable/generated/torch.optim.Adam.html#torch.optim.AdamW\n","\n","\n","!pip3 install adamp\n","\n","from adamp import AdamP\n","\n","# AdamP: AdamP is a bit more fiddly as it is not natively included in torch and you must import it like above, or write it yourself\n","\n","optimizer   = AdamP(___, ___) # Link: https://pypi.org/project/adamp/\n","\n","\n","# SGD: The classic SGD optimizer\n","\n","optimizer   = torch.optim.SGD(___)  # Link: https://pytorch.org/docs/stable/generated/torch.optim.SGD.html\n","\n","\"\"\"\n","PAPERS:\n","\n","Adam:   https://arxiv.org/abs/1412.6980   \"Adam: A Method for Stochastic Optimization\"\n","AdamW:  https://arxiv.org/abs/1711.05101  \"AdamW: Decoupled Weight Decay Regularization\"\n","AdamP:  https://arxiv.org/abs/2006.08217  \"AdamP: Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights\"\n","\n","SGD is well explored enough that this paper is included to discuss momentum. Read if you are interested, this topic may appear later.\n","SGD:    https://www.cs.toronto.edu/%7Ehinton/absps/momentum.pdf\n","\"\"\""],"metadata":{"id":"wQS90AkjDE9D"},"id":"wQS90AkjDE9D","execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["### Dropout"],"metadata":{"id":"YKy6DjZTDlRS"},"id":"YKy6DjZTDlRS"},{"cell_type":"markdown","source":["Dropout is a regularization technique used to prevent overfitting in neural networks. It works by randomly deactivating a subset of neurons during training, forcing the network to learn more robust features that are not reliant on any specific set of neurons, thus enhancing the model's generalization ability. Dropout is an extremely useful tool that you can find yourself using very often and will be very helpful in future assignments. You may even find it useful to tune dropout between epochs sometimes.\n"],"metadata":{"id":"6Iom1gk0DoDU"},"id":"6Iom1gk0DoDU"},{"cell_type":"code","source":["\"\"\"\n","Please either create a network or fill in from earlier but with a dropout layer. Dropout is another tool that will show up\n","continually as you study deep learning. It is prolific and often takes other forms such as Drop Blocks and Drop Paths. The general concept for\n","what it does and the intuition is generally consistent however. Below implement the network using dropout. Documentation is provided below.\n","\n","Dropout:                https://pytorch.org/docs/stable/generated/torch.nn.Dropout.html#torch.nn.Dropout\n","\"\"\"\n","\n","# Define your network (Feel free to create your networks)\n","model_1 = torch.nn.Sequential(\n","\n","  torch.nn.____, # Declare your first linear layer. What should the input and output size be?\n","\n","  torch.nn.____, # Insert your dropout layer\n","\n","  torch.nn.____, # Declare your activation function\n","\n","\n","  # Add any additional layers here if you would like before the final layer\n","\n","\n","  torch.nn.____  # Declare your final linear layer that outputs the OUT_SIZE\n",")\n","\n","# Move the model to device. This step is required before training\n","model_1 = model_1.to(device)\n","\n","summary(model_1, x.flatten().shape)"],"metadata":{"id":"D4wCXdJODlza"},"id":"D4wCXdJODlza","execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["###Batch Normalization"],"metadata":{"id":"W4-YMtcQDs02"},"id":"W4-YMtcQDs02"},{"cell_type":"markdown","source":["Batch normalization (BatchNorm) is a technique used to improve the speed, performance, and stability of neural networks. It works by normalizing the inputs of each layer, ensuring that they have a mean of zero and a standard deviation of one, which helps to mitigate issues related to poor initialization and helps in faster convergence.\n","\n","BatchNorm though seeming to be quite a minor detail offers a significant impact on your network on more complex problems and can prove invaluable as an initial first step to improve your network. Below will be an example using code from before. Fill in with your neural network but this time, include batchnorm. This structure will be very helpful and repeat itself on future homeworks."],"metadata":{"id":"8PYPD5vKDvU0"},"id":"8PYPD5vKDvU0"},{"cell_type":"code","source":["\"\"\"\n","Please either create a network or fill in from earlier but with the correct values for batchnorm. Note that\n","batchnorm needs to take in the size of the current prior layer to work. Usually this is done either\n","before an activation or after and for each layer. Documentation is provided below.\n","\n","Batchnorm:              https://pytorch.org/docs/stable/generated/torch.nn.BatchNorm1d.html#torch.nn.BatchNorm1d\n","\n","\"\"\"\n","\n","# Define your network (Feel free to create your networks)\n","model_1 = torch.nn.Sequential(\n","\n","  torch.nn.____, # Declare your first linear layer. What should the input and output size be?\n","\n","  torch.nn.____, # Apply batch normalization\n","\n","  torch.nn.____, # Declare your activation function\n","\n","\n","  # Add any additional layers here if you would like before the final layer\n","\n","\n","  torch.nn.____  # Declare your final linear layer that outputs the OUT_SIZE\n",")\n","\n","# Move the model to device. This step is required before training\n","model_1 = model_1.to(device)\n","\n","summary(model_1, x.flatten(start_dim=0).to(device))"],"metadata":{"id":"jMMYNeZTDtTb"},"id":"jMMYNeZTDtTb","execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["### Schedulers"],"metadata":{"id":"ywrtihIADyE8"},"id":"ywrtihIADyE8"},{"cell_type":"markdown","source":["Schedulers are tools used in training neural networks to adjust the learning rate during training, which can lead to more effective and efficient optimization. There are many viable options in this regard, including writing your own, but you may find ReduceLROnPlateau or CosineAnnealingLR especially useful.\n","\n","* ReduceLROnPlateau works by monitoring a specified metric (like validation loss) and reducing the learning rate when this metric stops improving. Essentially, it implements a form of learning rate decay; if the model's performance plateaus, the learning rate decreases, which can help to escape local minima and continue learning.\n","\n","* CosineAnnealingLR works by adjusting the learning rate following a cosine curve. This means the learning rate starts high, decreases to a minimum, and then increases again. This approach can help in navigating the loss landscape more effectively by allowing the model to explore more during the periods of higher learning rates and refine its understanding of the data during the periods of lower learning rates."],"metadata":{"id":"PjUbSzKGD2Pr"},"id":"PjUbSzKGD2Pr"},{"cell_type":"code","source":["# All optimizers built into Torch: https://pytorch.org/docs/stable/optim.html\n","\n","# ReduceLRonPlateau\n","scheduler = torch.optim.lr_scheduler.ReduceLROnPlateau(optimizer, ___) # https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.ReduceLROnPlateau.html#torch.optim.lr_scheduler.ReduceLROnPlateau\n","\n","# CosineAnnealingLR\n","scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, ___) # https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.CosineAnnealingLR.html#torch.optim.lr_scheduler.CosineAnnealingLR\n","\n","\n","\"\"\"\n","PAPERS:\n","CosineAnnealingLR: https://arxiv.org/abs/1608.03983\n","\"\"\"\n"],"metadata":{"id":"EyCsU2uxDz9r"},"id":"EyCsU2uxDz9r","execution_count":null,"outputs":[]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3 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