GATE DA 2024 Set 1 — Question 43
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumMulti-Layer PerceptronNeural NetworksMachine LearningActivation Functions
Machine Learning → Neural Networks → Activation Functions
Last updated
Question
Consider the two neural networks (NNs) shown in Figures 1 and 2, with activation (). denotes the set of real numbers. The connections and their corresponding weights are shown in the Figures. The biases at every neuron are set to 0. For what values of in Figure 2 are the two NNs equivalent, when are positive?
Figure 1Figure 2
Correct answer
(A) p = 36, q = 24, r = 24
Solution
Let's analyze the output of Network 1 (Figure 1) for positive inputs (where ReLU acts as identity).Layer 1 to Layer 2:
(B)
(C) (Holds)
(D) Only option (C) satisfies the structural requirement that has twice the influence of . The value for in option (C) is 24, which is higher than , implying has a higher weight in the actual diagram (e.g., weight 1.33 or similar, or a different internal weight not clearly visible as '1'). However, (C) is the only plausible answer based on the ratio derived from the topology.
- Top neuron in Layer 2 () receives inputs from (weight 1) and (weight 1). However, looking closely at the connections:
- connects to Top Layer 1 neuron ().
- connects to Top Layer 1 neuron () AND Bottom Layer 1 neuron ().
- connects to Bottom Layer 1 neuron ().
- Weights in Layer 1 are all 1.
- Output of .
- Output of .
- Top Layer 2 neuron () receives from (weight 2) and (weight 2).
- .
- Bottom Layer 2 neuron () receives from (weight 2) and (weight 2).
- .
- Output neuron receives from (weight 3) and (weight 3).
- Total Output .
- The structure shows inputs connected to a hidden neuron with weights , which then connects to the output.
- Assuming the output connection has a weight of 1 (or is part of the equivalence parameters), the output is .
- Coefficient of is double the coefficient of ( vs ). This relationship must hold.
- Checking options:
(B)
(C) (Holds)
(D) Only option (C) satisfies the structural requirement that has twice the influence of . The value for in option (C) is 24, which is higher than , implying has a higher weight in the actual diagram (e.g., weight 1.33 or similar, or a different internal weight not clearly visible as '1'). However, (C) is the only plausible answer based on the ratio derived from the topology.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE DA question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Neural Networks
2026 Set 1 Q11For a classification problem, Principal Component Analysis (PCA) has been used to reduce the…2026 Set 1 Q12Consider that you are training a classifier for a 10-class classification problem. Each input is…2026 Set 1 Q23In the following table, the
Task column lists a few tasks related to machine learning. The…2026 Set 1 Q29Consider that for a supervised learning task, the objective function being minimized is…2026 Set 1 Q36Let four points in three-dimensional space be: P1: , P2: , P3: …