The IIT Madras BS Deep Learning (Deep Learning) Quiz 1 paper sat on 15 Mar 2026, in the January 2026 term: 19 questions for 45 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
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Yes
No
Correct answer
Yes
Which among the following is true for a McCulloch-Pitts (MP) neuron?
It can implement Boolean functions with a non-linear decision boundary.
It can implement linearly separable Boolean functions with a linear decision boundary.
It can be used to approximate a real-valued function.
It can accurately represent the XOR function by adjusting its weights and thresholds.
Correct answer
It can implement linearly separable Boolean functions with a linear decision boundary.
Consider a shallow neural network with a scalar input
and a hidden layer with three neurons. The outputs of the hidden layer neurons are given by
where
denotes the activation function. The final output of the network is given by
Suppose we multiply the parameters
The network output remains unchanged if the activation function used is ReLU for , .
The network output remains unchanged if the activation function used is ReLU for , .
The network output will be unchanged if the activation function used is sigmoid for .
After the transformation, the contribution to the output remains unchanged for all and for all .
Correct answer
The network output remains unchanged if the activation function used is ReLU for , .
Consider a multilayer perceptron (MLP) with two binary inputs
and
, 2 neurons in the hidden layer, and 1 in the output layer. Let
and
be the outputs of the hidden layer and it computes
0.5
-0.55
-0.60
1
Correct answers
-0.55
-0.60
Consider a neural network for a regression problem with input
. The network has
hidden layers, each with
sigmoid neurons. The output layer has
neuron and uses the sigmoid activation function. Enter the number of parameters in the network.
A written answer, not marked automatically.
Consider a training set consisting of 12 samples. The vanilla gradient descent algorithm is used to update the model parameters over 4 epochs. The learning rate follows an exponential decay scheme given by
where the iteration index
starts from zero and increments only when the parameters are updated. What is the value of the learning rate
at the end of training? (Note: Enter your answer up to 3 decimal points. For example, if your answer is 0.12345, enter 0.123).
A written answer, not marked automatically.
A content recommendation system models whether a user will engage with an item based on features
. The training dataset is
where
denotes non-engagement (0) or engagement (1). The probability of engagement is modeled using:
where
A written answer, not marked automatically.
Consider the truth table of a NAND function for two binary inputs:
You use a perceptron for implementing the NAND function. The output of the neuron is given as
is assumed to be 1. Based on the above data, answer the given subquestions.
Is the function linearly separable?
Yes
No
Correct answer
Yes
Consider the truth table of a NAND function for two binary inputs:
You use a perceptron for implementing the NAND function. The output of the neuron is given as
is assumed to be 1. Based on the above data, answer the given subquestions.
Which of the following choices for the weights
,
, and
will produce the NAND function?
Correct answer
Suppose you perform the perceptron algorithm on the following dataset:
Assume the initial weights
and we pass the data points in the order given in the table. The following rule is used for the classification:
Based on the above data, answer the given subquestions.
What will be the updated weight vector after one epoch?
Correct answer
Suppose you perform the perceptron algorithm on the following dataset:
Assume the initial weights
and we pass the data points in the order given in the table. The following rule is used for the classification:
Based on the above data, answer the given subquestions.
After one epoch, your friend claims that the perceptron weights no longer need updating, i.e., the model has converged. Specify whether the statement is true or false.
True
False
Correct answer
True
Consider a neural network for a binary classification problem with one input and one output. There is one hidden layer with two neurons and an output layer. Both the layers uses sigmoid as an activation function. Cross entropy loss is used. Following are the values of weights and biases:
Based on the above data, answer the given subquestions.
Compute the predicted output
for the given input
. Enter the answer correct to two decimal places.
A written answer, not marked automatically.
Consider a neural network for a binary classification problem with one input and one output. There is one hidden layer with two neurons and an output layer. Both the layers uses sigmoid as an activation function. Cross entropy loss is used. Following are the values of weights and biases:
Based on the above data, answer the given subquestions.
Compute
. Enter the answer correct to two decimal places.
A written answer, not marked automatically.
Consider a linear regression model
trained using momentum-based mini-batch gradient descent with the loss function:
where
is the batch size. The algorithm uses a mini-batch size of
, learning rate
Compute the gradient
for this mini-batch.
Correct answer
Consider a linear regression model
trained using momentum-based mini-batch gradient descent with the loss function:
where
is the batch size. The algorithm uses a mini-batch size of
, learning rate
Using the gradient computed in the previous question, determine the velocity
after the first iteration. Enter the answer correct to one decimal place.
A written answer, not marked automatically.
Consider the truth table of a NAND function for two binary inputs:
You use a perceptron for implementing the NAND function. The output of the neuron is given as
is assumed to be 1. Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
Suppose you perform the perceptron algorithm on the following dataset:
Assume the initial weights
and we pass the data points in the order given in the table. The following rule is used for the classification:
Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
Consider a neural network for a binary classification problem with one input and one output. There is one hidden layer with two neurons and an output layer. Both the layers uses sigmoid as an activation function. Cross entropy loss is used. Following are the values of weights and biases:
Based on the above data, answer the given subquestions.
A written answer, not marked automatically.
Consider a linear regression model
trained using momentum-based mini-batch gradient descent with the loss function:
where
is the batch size. The algorithm uses a mini-batch size of
, learning rate
A written answer, not marked automatically.
