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Questions and Answers
Which of the following update strategies adjusts weights after processing every single training instance?
Which of the following update strategies adjusts weights after processing every single training instance?
- Online (correct)
- Mini batch
- Full batch
- Batch Gradient Descent
Early stopping, as a method to prevent overfitting, involves halting the training process when validation loss decreases while training loss continues to decrease.
Early stopping, as a method to prevent overfitting, involves halting the training process when validation loss decreases while training loss continues to decrease.
False (B)
What is the primary difference in how L1 (Lasso) and L2 (Ridge) regularization affect model weights in the context of preventing overfitting?
What is the primary difference in how L1 (Lasso) and L2 (Ridge) regularization affect model weights in the context of preventing overfitting?
L1 regularization shrinks some weights to zero, effectively performing feature selection, while L2 regularization reduces the magnitude of all weights without forcing any to zero.
The weight decay technique known as ______ regularization is characterized by its use of absolute values of weights and its ability to shrink weights to exactly zero, effectively performing feature selection.
The weight decay technique known as ______ regularization is characterized by its use of absolute values of weights and its ability to shrink weights to exactly zero, effectively performing feature selection.
Which method of regularization is computationally more expensive and time consuming?
Which method of regularization is computationally more expensive and time consuming?
A perceptron's decision boundary is best described as which of the following?
A perceptron's decision boundary is best described as which of the following?
A linear activation function is commonly used in the hidden layers of deep neural networks to introduce non-linearity.
A linear activation function is commonly used in the hidden layers of deep neural networks to introduce non-linearity.
Describe a scenario where using a ReLU activation function would be particularly advantageous compared to a sigmoid activation function.
Describe a scenario where using a ReLU activation function would be particularly advantageous compared to a sigmoid activation function.
The perceptron learning rule updates weights based on the difference between the ______ and the predicted output, scaled by the learning rate and corresponding input.
The perceptron learning rule updates weights based on the difference between the ______ and the predicted output, scaled by the learning rate and corresponding input.
Match each activation function with its primary characteristic:
Match each activation function with its primary characteristic:
What inherent limitation prevents a single-layer perceptron from effectively learning spatial dependencies within input data?
What inherent limitation prevents a single-layer perceptron from effectively learning spatial dependencies within input data?
Consider a perceptron attempting to classify images based on pixel values. Which limitation does it face when presented with different patterns containing the same count of 'on' pixels but in varied positions?
Consider a perceptron attempting to classify images based on pixel values. Which limitation does it face when presented with different patterns containing the same count of 'on' pixels but in varied positions?
A multi-layer perceptron (MLP) exclusively utilizes linear activation functions within its hidden layers to maintain computational efficiency.
A multi-layer perceptron (MLP) exclusively utilizes linear activation functions within its hidden layers to maintain computational efficiency.
In the perceptron learning rule, what is the role of the learning rate ($\eta$)?
In the perceptron learning rule, what is the role of the learning rate ($\eta$)?
Explain why a perceptron might get 'stuck' during training when dealing with data that is not perfectly linearly separable.
Explain why a perceptron might get 'stuck' during training when dealing with data that is not perfectly linearly separable.
In the context of multi-layer perceptrons, what is primarily adjusted during the backpropagation process to minimize the error between the predicted and actual outputs?
In the context of multi-layer perceptrons, what is primarily adjusted during the backpropagation process to minimize the error between the predicted and actual outputs?
According to the universal approximation theorem, a feedforward neural network with a single ______ layer can approximate any continuous function to arbitrary accuracy.
According to the universal approximation theorem, a feedforward neural network with a single ______ layer can approximate any continuous function to arbitrary accuracy.
Match the layer type in a Multi-Layer Perceptron (MLP) with its function:
Match the layer type in a Multi-Layer Perceptron (MLP) with its function:
In the context of Multi-Layer Perceptrons (MLPs), which component is responsible for applying a non-linear transformation to the weighted sum of outputs from the previous layer?
In the context of Multi-Layer Perceptrons (MLPs), which component is responsible for applying a non-linear transformation to the weighted sum of outputs from the previous layer?
What is the purpose of the 'feedforward' process in the operation of a multi-layer perceptron?
What is the purpose of the 'feedforward' process in the operation of a multi-layer perceptron?
In multi-layer perceptrons, what mathematical concept is used to update the weights during backpropagation, allowing the model to minimize prediction errors over time?
In multi-layer perceptrons, what mathematical concept is used to update the weights during backpropagation, allowing the model to minimize prediction errors over time?
Which of the following conditions is essential, according to the universal approximation theorem, for a neural network to theoretically approximate any continuous function?
Which of the following conditions is essential, according to the universal approximation theorem, for a neural network to theoretically approximate any continuous function?
The universal approximation theorem guarantees that a neural network can practically learn any function, regardless of architecture and training algorithm.
The universal approximation theorem guarantees that a neural network can practically learn any function, regardless of architecture and training algorithm.
In the context of neural network training, what role does the learning rate ($\eta$) play in the weight update process during gradient descent?
In the context of neural network training, what role does the learning rate ($\eta$) play in the weight update process during gradient descent?
In backpropagation, the error at the ______ layer is calculated first.
In backpropagation, the error at the ______ layer is calculated first.
What is the purpose of backpropagation in the context of training neural networks?
What is the purpose of backpropagation in the context of training neural networks?
In the equation $\delta_i = W_{i+1}^T \delta_{i+1} \odot \sigma'(z_i)$, what does the term $\sigma'(z_i)$ represent?
In the equation $\delta_i = W_{i+1}^T \delta_{i+1} \odot \sigma'(z_i)$, what does the term $\sigma'(z_i)$ represent?
Match each component with its corresponding description in the context of neural networks and backpropagation:
Match each component with its corresponding description in the context of neural networks and backpropagation:
Gradient descent is used to maximize the loss function by iteratively adjusting the weights of a neural network.
Gradient descent is used to maximize the loss function by iteratively adjusting the weights of a neural network.
Flashcards
Activation Function Purpose
Activation Function Purpose
Introduces non-linearity, enabling learning of complex functions.
Linear Activation Function
Linear Activation Function
Returns the input directly, without changes.
Step Activation Function
Step Activation Function
Outputs 1 if input exceeds a threshold, otherwise 0.
Sigmoid Activation Function
Sigmoid Activation Function
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ReLU Activation Function
ReLU Activation Function
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What is a Perceptron?
What is a Perceptron?
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Perceptron Structure
Perceptron Structure
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Perceptron Limitation
Perceptron Limitation
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Limitation of Single-Layer Perceptron
Limitation of Single-Layer Perceptron
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CNNs for Spatial Dependencies
CNNs for Spatial Dependencies
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Multi-Layer Perceptron (MLP)
Multi-Layer Perceptron (MLP)
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MLP Input Layer
MLP Input Layer
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MLP Hidden Layers
MLP Hidden Layers
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MLP Output Layer
MLP Output Layer
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MLP Feedforward Process
MLP Feedforward Process
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Universal Approximation Theorem
Universal Approximation Theorem
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Weight Update (Gradient Descent)
Weight Update (Gradient Descent)
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Learning Rate (η)
Learning Rate (η)
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Backpropagation
Backpropagation
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δm (Output Layer Error)
δm (Output Layer Error)
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δi (Hidden Layer Error)
δi (Hidden Layer Error)
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∇WiL
∇WiL
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A(i-1)^T
A(i-1)^T
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Online Weight Updates
Online Weight Updates
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Early Stopping
Early Stopping
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Weight Decay
Weight Decay
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L1 Regularization (Lasso)
L1 Regularization (Lasso)
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L2 Regularization (Ridge)
L2 Regularization (Ridge)
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Study Notes
- Multi-Layer Perceptron (MLP) introduces non-linearity to neurons, allowing them to learn and approximate complex functions.
Activation Functions
- Key types are Linear, Step, Sigmoid, and ReLU.
- Linear Activation: Returns the input without modification and rarely used.
- Step Activation: Outputs 1 if input is greater than a certain threshold, 0 otherwise.
- Sigmoid Activation: Maps input to a value between 0 and 1; useful for binary classification as output can be interpreted as probability.
- ReLU Activation: Returns input if positive, 0 otherwise, and it's computationally efficient.
Perceptrons
- A supervised learning algorithm classifies data points using a decision boundary (hyperplane).
- It takes multiple inputs, applies weights, sums them, applies an activation function, and outputs 0 or 1.
- It is limited by linearly-solvable problems.
Perceptron Structure
- Includes inputs (x1, x2, ..., xn), weights (w1, w2, ..., wn), and a bias (b).
- Formula: ∑(wi * xi) + b
Perceptron Functionality
- Weights are initialized randomly; inputs are passed through, output is computed, and compared to the correct label.
- If the prediction is incorrect, the weights are updated using the Perceptron Learning Rule.
- Update Equation: wi = wi + η(y - y^)xi, where y is the actual output, y^ is the predicted output, and η is the learning rate.
- This repeats until the perceptron correctly classifies all points.
Perceptron Limitations
- Only works for linearly separable data.
- Gets stuck if data cannot be perfectly separated.
- Perceptrons cannot distinguish between patterns with the same number of "on" pixels but in different positions.
- A perceptron works by computing ∑wi * xi + b. It only considers the sum of weighted inputs, and cannot learn spatial dependencies or treat patterns globally.
- Spatial dependencies requires pixels to appear in a specific order.
Solutions for Perceptron Limitations
- Multi-Layer Perceptron: use non-linear function and add Hidden layers.
- Convolutional Neural Networks(CNNs): apply convolutional filters to detect local spatial patterns.
Multi-Layer Perceptrons (MLP)
- MLPs are artificial neural networks with multiple layers of neurons, where each neuron is connected to every neuron in the previous and next layers.
MLP Structure
- Input Layer: Receives raw data (pixel values).
- Hidden Layers: Perform complex computations using weights, biases, and activation functions.
- Output Layer: Produces predictions based on learned features.
- Binary classification uses one neuron.
- Multi-class classification uses multiple neurons.
- Regression problems produce continuous values.
How MLPs Work
- Feedforward Process: Input values pass through layers, weights are applied, and each neuron applies its activation function and bias. The signal propagates until the output layer produces predictions.
- Backpropagation: Model compares its predictions with the actual output and calculates the error. This is propagated backward to update weights using gradient descent. This repeats until the model minimizes error.
Hidden Layers
- Each node applies a non-linear transformation to the weighted sum of outputs from nodes in previous layers.
- zi = ∑(wi * ai-1) or Ai = σ(zi)
- Activation Function: σi
- Activity Matrix: Ai
Universal Approximation Theorem
- A feedforward neural network with a single hidden layer can approximate any continuous function to arbitrary accuracy.
- The network must have enough hidden neurons; the activation function must not be too restricted.
- A neural network's ability to learn a function depends on the choice of architecture, hyperparameters, and training algorithms.
Weight Update (Gradient Descent)
- wi = wi - η∇wiL
- wi is the weight at layer i.
- ∇wiL is the gradient of the loss function with respect to wi
- η is the learning rate
- If the gradient is large, weights change more; if small, weights change less. Weights are updated opposite to the gradient because it minimizes the loss function.
Backpropagation (Adjusting Weights)
- δm = ∇AmL ⊙ σ'm(zm)
- δi = WTi+1 δi+1 ⊙ σ'(zi)
- ∇wiL = δi Ai-1T
- Error at the output layer is calculated first, then propagated backward, updating each layer's weights using the chain rule.
Backpropagation Equations Explained
- δm calculation:
- ∇AmL is the Gradient of the loss function with respect to activations Am (how much the loss changes when output changes).
- σ'm(zm) is the Derivative of the activation function at the output layer.
- Other Layers:
- δi is the error at hidden layer i.
- WTi+1 transposed weight from next layer.
- δi+1 Error propagated from the next layer.
- σ'(zi) is the derivative of the activation function at hidden layer i.
- Equation 3
- ∇wiL Gradient of the loss function with respect to weights at layer i.
- δi Error at layer i.
- Ai-1Transposed activations from previous layer (i-1).
Backpropagation and Updates
- Gradient descent minimizes the loss function by updating weights.
- Forward propagation computes predictions; backpropagation adjusts weights.
- Backpropagation uses the chain rule to distribute error signals layer by layer.
Frequency of Weight Updates
- Online: after each training example.
- Mini-batch: after a subset of training examples.
- Full batch: after all training examples.
Magnitude of Weight Updates
- Fixed global learning rate.
- Adaptive global learning rate.
- Adaptive local learning rate.
How to Prevent Overfitting
- Early Stopping: Stops training before overfitting by monitoring validation loss; training stops when validation loss increases while training loss decreases.
- Weight Decay: Reduces the complexity of the model by penalizing large weights.
- Adds a penalty to the loss function, discourages large weights.
Types of Weight Decay
- L1 Regularization (Lasso): Uses the absolute values of weights (L1-norm) to shrink weights to exactly zero, leading to feature selection.
- L2 Regularization (Ridge): Uses the squared values of weights (L2-norm) to reduce weight values without zeroing them. It prevents the model from relying too much on any single feature and can increase training time.
- Lasso encourages weights to exactly zero, Ridge shrinks all weights gradually.
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Description
Questions cover update strategies, early stopping, L1 (Lasso) and L2 (Ridge) regularization, weight decay, perceptron decision boundaries, and ReLU activation functions. It explores methods to prevent overfitting and improve model generalization.
