Backpropagation
Backpropagation is a systematic computational procedure for applying the chain rule to calculate gradients automatically. It operates by traversing a computational graph in a backwards direction—from the output loss back to the input parameters—multiplying matrices of partial derivatives at each step to determine how parameters affect the final output.
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Foundations of Large Language Models Course
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Forward Propagation
Update Weight Iteratively Until Convergence
Deep Learning Weight Initialization
What is the "cache" used for in our implementation of forward propagation and backward propagation?
Consider the following 1 hidden layer neural network:
Which of the following are true regarding activation outputs and vectors? (Check all that apply.)
Backpropagation
Objective Function
Backpropagation
Unfolding Operation
Detaching Computation
Optimization of Automatic Differentiation Libraries
Backpropagation
Forward Graph Traversal
Backward Graph Traversal
Automatic Differentiation with Dynamic Control Flow
Computational Graph of Forward Propagation
Derivation of the Gradient Descent Formula
Mini-Batch Gradient Descent
Epoch in Gradient Descent
Gradient Descent with Momentum
For logistic regression, the gradient is given by ∂∂θjJ(θ)=1m∑mi=1(hθ(x(i))−y(i))x(i)j. Which of these is a correct gradient descent update for logistic regression with a learning rate of α?
Suppose you have the following training set, and fit a logistic regression classifier .
Backpropagation
Batch vs Stochastic vs Mini-Batch Gradient Descent
Logistic Regression Gradient Descent Derivation
Learn After
Backpropagation Through Time (BPTT)
Back-Propagating through Discrete Stochastic Operations
Neural Network Learning Rate
Back-Propagation through Random Operations
Backward Propagation Formulation
True/False: During forward propagation, in the forward function for a layer ll you need to know what is the activation function in a layer (Sigmoid, tanh, ReLU, etc.). During back propagation, the corresponding backward function also needs to know what is the activation function for layer ll, since the gradient depends on it.
Back Propagation Illustrated Example
A neural network is trained to distinguish between images of 'apples' and 'oranges'. During a training iteration, it is shown an image of an apple but predicts 'orange' with a high degree of certainty. This results in a significant error value. What is the primary computational goal of the backpropagation step that immediately follows this prediction?
Token-Level Loss Calculation in a Backward Pass
Consider a simple neural network with one input neuron, one hidden neuron, and one output neuron. The network has a weight
w1connecting the input to the hidden neuron, and a weightw2connecting the hidden neuron to the output neuron. After a forward pass, an error is calculated based on the network's final output. To updatew1using the backpropagation algorithm, you must calculate the partial derivative of the error with respect tow1. Which of the following components is essential for determining how much of the final error is attributable to the hidden neuron's activity?Allocating Gradient Memory
Chain Rule for Tensors
Storage of Intermediate Variables in Backpropagation