In the below network, find the values for (h1, h2, y1) when the activation function is ReLU for the point (1,1).

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The question asks: In the below network, find the values for (h1, h2, y1) when the activation function is ReLU for the point (1,1). First, restate what we know from the network diagram: there are input nodes X1 and X2 with values given as the point (1, 1). Each input connects to hidden neurons h1 and h2 with certain weights, and then the hidden neurons connect to the output y1 with their own weights. The activation function used at the hidden layer is ReLU, so after computing the weighted sums for h1 and h2, we apply ReLU to obtain their final values. The output y1 is computed from h1 and h2 (and possibly a bias) with its own weights, and we may or may not apply an activation at the output depending on the diagram (the prompt specifies ReLU for the hidden layer, so we assume y1 uses a linear combination of h1 and h2 and perhaps a bias). Important note about the provided data: the answer options are not visible in the prompt you shared. Without the explicit numerical options, we can only describe how to compute the values step by step and explain how each potential option would be evaluated, rather than selecting among them. Step-by-step approach to determine (h1, h2, y1) for (X1, X2) = (1, 1): 1) Compute the pre-activation value for h1: z_h1 = w_{X1->h1} * X1 + w_{X2->h1} * X2 + (any bias to h1). - Plug in X1 = 1 and X2 = 1, and use the weights shown on the diagram for connections into h1. If there is a bias term b_h1, include it as + b_h1. 2) Apply ReLU to obtain h1: h1 = ReLU(z_h1) = max(0, z_h1). 3) Compute the pre-activation value for h2: z_h2 = w_{X1->h2} * X1 + w_{X2->h2} * X2 + (any bias to h2). - Use the weights drawn into h2 from the inputs X1 and X2 (and any bias to h2). 4) Apply ReLU to obtain h2: h2 = ReLU(z_h2) = max(0, z_h2). 5) Compute the output pre-activation y1: z_y1 = w_{h1->y1} * h1 + w_{h2->y1} * h2 + (any bias to y1). 6) Determine y1: depending on whether there is an activation on the output, y1 = z_y1 (if linear output) or y1 = ReLU(z_y1) (if the output also uses an activation). The prompt states ReLU is used for the point (1,1); typically this refers to the hidden layer, so y1 may be linear unless specified otherwise. How to evaluate a candidate option for (h1, h2, y1): - For any proposed triple (a, b, c): - Check h1: verify that a = ReLU(z_h1) with z_h1 computed from X1 = 1, X2 = 1 and the exact weights into h1 (and any bias). If z_h1 <= 0, then a must be 0; otherwise a must equal z_h1. - Check h2: similarly, verify b = ReLU(z_h2) using the weights into h2 and inputs (and bias). If the resulting z_h2 <= 0, then b should be 0; otherwise b equals z_h2. - Check y1: compute z_y1 from h1 = a and h2 = b with the weights into y1 (and bias). If there is a post-activation on the output, apply it to z_y1 to compare with c; otherwise compare c directly to z_y1. Because the answer options are not provided in your prompt, I cannot select among them or verify which triple matches the network’s computation. If you can share the exact answer choices (the list of (h1, h2, y1) tuples), I can walk through each option with concrete numeric checks and identify which one aligns with the ReLU-based computations for the given inputs (1, 1). If you can attach the missing options, I’ll complete the analysis to pinpoint the correct triple and explain why each other option fails in turn.

COMP90049_2025_SM2 Lecture 15 Multilayer Perceptron Practice Quiz

In the below network, find the values for (h1, h2, y1) when the activation function is ReLU for the point (1,1).

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