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Grade 11 AI & Computer Science Practice Questions — Set 6

20 questions from the Grade 11 bank, each with its answer and a full explanation. Set 6 of 11 · 221 questions in this grade.

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Question 101 · GRU Parameters · hard

Analyze GRU (Gated Recurrent Unit): hidden_size=65, input_size=79. Calculate total parameters, compare with LSTM (4 gates), and evaluate the gate structure — which of the following is correct?

  1. Parameters = 5135, counting only the input-to-hidden weights for a single gate; this ignores the hidden-to-hidden weights, biases, and the other two gates, so it undercounts the true total.
  2. Parameters = 3×(65×(65+79)+65) = 28275 (3 gates: reset, update, candidate); LSTM has 4×params because it has 4 gates; GRU is more parameter-efficient
  3. Parameters = 4×(65×(65+79)+65) = 37700, treating GRU as if it had four gates like LSTM; GRU actually has only three gates, so this overcounts by one full gate's worth of parameters.
  4. GRU has more parameters than LSTM for the same hidden and input sizes, since its reset and update gates each require larger weight matrices than any single LSTM gate.

Answer: B. Parameters = 3×(65×(65+79)+65) = 28275 (3 gates: reset, update, candidate); LSTM has 4×params because it has 4 gates; GRU is more parameter-efficient

ExplanationGRU has 3 gates (reset r, update z, candidate h'), each with parameters h×(h+x)+h. Total: 3×(65×(65+79)+65) = 3×(65×144+65) = 3×9425 = 28275. LSTM has 4 gates (input, forget, output, candidate), requiring 4×(65×144+65) = 37700 parameters — one full gate more than GRU. GRU is therefore more parameter-efficient and computationally faster while often matching LSTM performance on the same task. Both architectures address vanishing gradients through gating mechanisms; GRUs are preferred when computational resources are limited, while LSTMs are sometimes preferred for very long-range dependencies.

Question 102 · Conv2D Parameters · hard

For a Conv2D layer with in_channels=2, out_channels=9, and kernel_size=5×5, what is the total number of learnable parameters using the formula O×(I×K²+1)?

  1. Parameters = 50, counting only the weights for a single output filter (2×5×5) and ignoring the other 8 filters and all bias terms
  2. Parameters = 450, counting the weights across all 9 filters (9×2×5×5) but leaving out the 9 bias terms
  3. Parameters = 9, treating the parameter count as equal to the number of output channels while ignoring the weights and bias terms entirely
  4. Parameters = 459, because each of 9 output filters has I×K²=50 weights plus 1 bias: 9×(2×5×5+1) = 459

Answer: D. Parameters = 459, because each of 9 output filters has I×K²=50 weights plus 1 bias: 9×(2×5×5+1) = 459

ExplanationConv2D learnable parameters include weights and biases. Each of the 9 output filters has a kernel of size 2×5×5 (50 weights) plus 1 bias term, so the total is 9×(2×5×5+1) = 9×51 = 459 parameters. For example, a Conv2D(3, 64, 3) layer in a ResNet has 64×(3×3×3+1) = 1,792 parameters. Understanding parameter counts is essential for model complexity analysis and memory optimization.

Question 103 · Conv2D Parameters · hard

Analyze this Conv2D layer: in_channels=2, out_channels=10, kernel_size=5×5. Using the formula O×(I×K²+1), what is the total number of learnable parameters?

  1. Parameters = 500, without bias, since 10×(2×5×5) = 500 omits the bias term
  2. Parameters = 510, because each of 10 output filters has I×K²=50 weights plus 1 bias: 10×(2×5×5+1) = 510
  3. Parameters = 10, counting only the output channels and ignoring the kernel weights entirely
  4. Parameters = 50, treating that as the total per filter instead of multiplying by the 10 output filters

Answer: B. Parameters = 510, because each of 10 output filters has I×K²=50 weights plus 1 bias: 10×(2×5×5+1) = 510

ExplanationConv2D learnable parameters include both weights and biases. Each of the 10 output filters has a kernel of size 2×5×5, giving 50 weights, plus 1 bias term, for 51 parameters per filter. Total: 10×(2×5×5+1) = 10×51 = 510 parameters.

Question 104 · Conv2D Parameters · hard

A Conv2D layer has in_channels=3, out_channels=9, and kernel_size=5×5. Using the formula O×(I×K²+1), what is the total number of learnable parameters?

  1. Parameters = 9, equal only to the number of output channels, since this ignores every kernel weight and bias
  2. Parameters = 675, computed as 9×(3×5×5), which omits the bias term for each filter
  3. Parameters = 684, because each of 9 output filters has I×K²=75 weights plus 1 bias: 9×(3×5×5+1) = 684
  4. Parameters = 75, equal only to one output filter's weights (3×5×5), without multiplying by the 9 output filters or adding bias

Answer: C. Parameters = 684, because each of 9 output filters has I×K²=75 weights plus 1 bias: 9×(3×5×5+1) = 684

ExplanationConv2D learnable parameters include both weights and biases. Each of the 9 output filters has a kernel spanning all 3 input channels at 5×5, giving I×K² = 3×5×5 = 75 weights, plus 1 bias term per filter. Total parameters = O×(I×K²+1) = 9×(75+1) = 9×76 = 684.

Question 105 · Conv2D Parameters · hard

A Conv2D layer has in_channels=1, out_channels=12, and kernel_size=3×3. Using the formula O×(I×K²+1), how many total learnable parameters does this layer have?

  1. Parameters = 12, counting only the 12 bias terms and leaving out the weights entirely
  2. Parameters = 108, computed as 12×(1×3×3) by leaving the bias term out of each filter
  3. Parameters = 120, because each of 12 output filters has I×K²=9 weights plus 1 bias: 12×(1×3×3+1) = 120
  4. Parameters = 9, treating the 3×3 kernel size itself as the parameter count for the whole layer

Answer: C. Parameters = 120, because each of 12 output filters has I×K²=9 weights plus 1 bias: 12×(1×3×3+1) = 120

ExplanationConv2D learnable parameters include both weights and biases. Each of the 12 output filters has a kernel of size 1×3×3 (since in_channels=1), giving I×K²=1×3×3=9 weights, plus 1 bias term per filter, for 10 parameters per filter. Total: 12×(1×3×3+1) = 12×10 = 120 parameters. For comparison, a Conv2D(3, 64, 3) layer with 3 input channels would have 64×(3×3×3+1) = 1,792 parameters, showing how the parameter count scales with both input channels and output filters.

Question 106 · Conv2D Parameters · hard

A Conv2D layer has in_channels=3, out_channels=15, and kernel_size=5×5. What is the total number of learnable parameters in this layer?

  1. Parameters = 75, because this option gives the weight count for a single output filter (3×5×5) but never multiplies by the 15 output filters or adds any bias terms
  2. Parameters = 1125, because this option correctly computes 15×(3×5×5) for the weights but omits the bias term that each of the 15 output filters also requires
  3. Parameters = 15, because this option counts only one bias value per output filter and ignores the convolution weights entirely
  4. Parameters = 1140, because each of 15 output filters has I×K²=75 weights plus 1 bias: 15×(3×5×5+1) = 1140

Answer: D. Parameters = 1140, because each of 15 output filters has I×K²=75 weights plus 1 bias: 15×(3×5×5+1) = 1140

ExplanationConv2D learnable parameters include both weights and biases. Each of the 15 output filters has a kernel of size 3×5×5, giving 75 weights, plus 1 bias term, for 76 parameters per filter. Total parameters: 15×(3×5×5+1) = 15×76 = 1140. For comparison, a Conv2D(3, 64, 3) layer, as used in ResNet, has 64×(3×3×3+1) = 1,792 parameters. Understanding parameter counts like this is essential for analyzing model complexity and memory usage.

Question 107 · Conv2D Parameters · hard

A Conv2D layer processes feature maps with in_channels = 8, out_channels = 16, and a square kernel_size = 3×3, with bias enabled for every output filter. What is the total number of learnable parameters in this layer?

  1. Each of the 16 filters spans only the kernel footprint without depth, giving 16×3×3 = 144 total weights and no biases
  2. The layer contains 1,168 parameters, since each of the 16 filters holds 8×3×3 = 72 weights across the full input depth plus 1 bias, totaling 16×73
  3. Treating the kernel width as the only per-filter factor yields 16×(8×3+1) = 400 parameters
  4. Omitting the bias term, the 16 filters together require 16×8×3×3 = 1,152 weights

Answer: B. The layer contains 1,168 parameters, since each of the 16 filters holds 8×3×3 = 72 weights across the full input depth plus 1 bias, totaling 16×73

ExplanationA Conv2D filter's weight tensor spans the entire input depth, not just its spatial footprint, so its shape is (in_channels, kernel_height, kernel_width) = (8, 3, 3), giving 8×3×3 = 72 weights per filter. With bias enabled, each filter contributes one additional bias parameter, for 73 parameters per filter. Multiplying by the 16 output filters gives 16×73 = 1,168 total learnable parameters, matching the general formula out_channels×(in_channels×kernel_height×kernel_width+1). The claim that only 144 weights are needed drops the in_channels factor entirely, undercounting because it ignores that each filter must carry one weight per input channel at every kernel position. The claim of 400 mistakenly treats the kernel as contributing only its width rather than height×width, and also miscounts how depth interacts with the kernel. The claim of 1,152 weights correctly computes 16×8×3×3 but omits the 16 bias terms that are added, one per output filter, once bias is enabled.

Question 108 · Conv2D Parameters · hard

A Conv2D layer has in_channels=4, out_channels=16, and kernel_size=3×3. Using the formula O×(I×K²+1), what is the total number of learnable parameters, including biases?

  1. Parameters = 36, since only the kernel weights per filter (4×3×3) are counted and biases are ignored
  2. Parameters = 576, since it multiplies I×K²×O but omits the +1 bias term for each output filter
  3. Parameters = 16, since it counts only the number of output channels and ignores the kernel size and input channels entirely
  4. Parameters = 592, because each of 16 output filters has I×K²=36 weights plus 1 bias: 16×(4×3×3+1) = 592

Answer: D. Parameters = 592, because each of 16 output filters has I×K²=36 weights plus 1 bias: 16×(4×3×3+1) = 592

ExplanationConv2D learnable parameters include both weights and biases. Each of the 16 output filters convolves over all 4 input channels with a 3×3 kernel, giving I×K² = 4×3×3 = 36 weights per filter, plus 1 bias term per filter. Total parameters = 16×(36+1) = 16×37 = 592. For comparison, a Conv2D(3, 64, 3) layer, as used in early ResNet layers, has 64×(3×3×3+1) = 1,792 parameters — the same formula applied with different channel and filter counts.

Question 109 · Conv2D Parameters · hard

A Conv2D layer has in_channels=3, out_channels=16, and kernel_size=5×5. Using the formula O×(I×K²+1), what is the total number of learnable parameters, including biases?

  1. 75, since this counts only the weights in a single output filter's kernel (3×5×5) without adding a bias term or multiplying by the 16 output filters
  2. 1200, since this multiplies 16×3×5×5 to get the total kernel weights but omits the 16 bias terms, one per output filter
  3. 16, since this counts only one bias per output filter and ignores all the weights contributed by the kernels
  4. 1216, because each of 16 output filters has I×K²=75 weights plus 1 bias: 16×(3×5×5+1) = 1216

Answer: D. 1216, because each of 16 output filters has I×K²=75 weights plus 1 bias: 16×(3×5×5+1) = 1216

ExplanationFirst, conv2D learnable parameters include weights and biases. Each of 16 output filters has a kernel of size 3×5×5 (75 weights) plus 1 bias term. Then, total: 16×(3×5×5+1) = 16×76 = 1216 parameters. For example, a Conv2D(3, 64, 3) layer in a ResNet has 64×(3×3×3+1) = 1,792 parameters. Understanding parameter counts is essential for model complexity analysis and memory optimization.

Question 110 · Conv2D Parameters · hard

A Conv2D layer takes an input with in_channels = 6 and produces out_channels = 32 using a 3×3 kernel, with a bias term enabled for every output filter. Using the standard formula for a convolutional layer's learnable parameters, what is the total parameter count for this layer?

  1. Leaving out the bias term entirely gives 1728 parameters, computed as 32 filters times 6×3×3=54 weights each.
  2. Treating the kernel as a 3-wide row instead of a 3×3 area gives 608 parameters, computed as 32×(6×3+1)=32×19.
  3. Multiplying 32 output filters by 55 weights each (54 weights plus 1 bias) gives 1760 total learnable parameters.
  4. Swapping the input and output channel counts before applying the formula gives 1734 parameters, computed as 6×(32×3×3+1)=6×289.

Answer: C. Multiplying 32 output filters by 55 weights each (54 weights plus 1 bias) gives 1760 total learnable parameters.

ExplanationA Conv2D layer's learnable parameters equal out_channels × (in_channels × kernel_height × kernel_width + 1), where the +1 accounts for one bias per output filter. With in_channels=6, out_channels=32, and a 3×3 kernel, each filter contains 6×3×3=54 weights, and adding its shared bias gives 55 parameters per filter, so the layer totals 32×55=1760 learnable parameters. Dropping the bias term undercounts to 32×54=1728; treating the kernel as one-dimensional (using only its width of 3 instead of its full 3×3 area) undercounts far more severely to 32×19=608; and swapping which channel count multiplies the kernel versus which forms the outer product changes the whole structure, producing 6×289=1734 instead of grouping weights correctly per output filter. This exact computation is what deep learning frameworks report in a model summary, and it directly drives a convolutional layer's memory footprint and training cost.

Question 111 · Conv2D Parameters · hard

A Conv2D layer in a CNN is configured with in_channels = 8, out_channels = 16, and a kernel size of 5×5, with a learnable bias term included for each output filter. Using the standard formula for learnable parameters in a convolutional layer, what is the total number of learnable parameters in this layer?

  1. This layer contains 3,216 learnable parameters, since each of the 16 output filters convolves across all 8 input channels with a 5×5 kernel (8×5×5 = 200 weights) plus 1 bias term, giving 16×(200+1) = 3,216
  2. Only 3,200 parameters exist here, because bias terms are applied once per layer rather than once per output filter, so the 16 filters contribute only their 200 weights each with no per-filter bias added
  3. The layer has just 416 learnable parameters, because each output filter needs only one 5×5 kernel regardless of how many input channels feed into it, giving 16×(25+1) = 416
  4. This configuration yields 656 parameters, computed by pairing each of the 16 output filters with 8×5 weights plus 1 bias, since only one spatial dimension of the kernel multiplies against the input channels

Answer: A. This layer contains 3,216 learnable parameters, since each of the 16 output filters convolves across all 8 input channels with a 5×5 kernel (8×5×5 = 200 weights) plus 1 bias term, giving 16×(200+1) = 3,216

ExplanationEvery output filter in a Conv2D layer must span the full depth of the input, so each filter's weight count is in_channels × kernel_height × kernel_width, not just kernel_height × kernel_width. Here that is 8×5×5 = 200 weights per filter. Adding the one learnable bias that belongs to each individual output filter (not one shared bias for the whole layer) gives 200+1 = 201 parameters per filter. With 16 output filters, the total is 16×201 = 3,216 learnable parameters. The 3,200 figure comes from correctly computing the weights but wrongly treating bias as a single layer-wide term instead of one per filter. The 416 figure comes from ignoring the input-channel depth entirely, as if each filter only scanned a single input channel. The 656 figure comes from using only one dimension of the kernel (8×5) instead of squaring it (8×5×5), understating each filter's true weight count.

Question 112 · GRU Parameters · hard

Analyze GRU (Gated Recurrent Unit): hidden_size=110, input_size=70. Calculate total parameters, compare with LSTM (4 gates), and evaluate the gate structure?

  1. GRU has more parameters than LSTM.
  2. Parameters = 7700, counting only the input-to-hidden weights while ignoring the hidden-to-hidden weights and biases.
  3. Parameters = 4×(110×(110+70)+110), using the LSTM 4-gate formula instead of the correct 3-gate GRU formula.
  4. Parameters = 3×(110×(110+70)+110) = 59730 (3 gates: reset, update, candidate); LSTM has 4×params because it has 4 gates; GRU is more parameter-efficient.

Answer: D. Parameters = 3×(110×(110+70)+110) = 59730 (3 gates: reset, update, candidate); LSTM has 4×params because it has 4 gates; GRU is more parameter-efficient.

ExplanationGRU has 3 gates (reset r, update z, candidate h'), each with parameters h×(h+x)+h. Total: 3×(110×(110+70)+110) = 59730. LSTM has 4 gates (input, forget, output, candidate), requiring 4×params. GRU is more parameter-efficient and computationally faster while often matching LSTM performance. Both RNNs address vanishing gradients through gating mechanisms. GRUs are preferred when computational resources are limited; LSTMs are preferred for complex long-range dependencies.

Question 113 · Conv2D Parameters · hard

A Conv2D layer has in_channels=3, out_channels=12, and kernel_size=3×3. Using the formula O×(I×K²+1), what is the total number of learnable parameters (including biases)?

  1. 324, which is 12×27 and omits the required bias term for each of the 12 filters
  2. 336, because each of 12 output filters has I×K²=27 weights plus 1 bias: 12×(3×3×3+1) = 336
  3. 12, treating the parameter count as one bias per output channel while ignoring the kernel weights entirely
  4. 27, mistaking the weight count of a single filter for the total parameter count of the whole layer

Answer: B. 336, because each of 12 output filters has I×K²=27 weights plus 1 bias: 12×(3×3×3+1) = 336

ExplanationConv2D learnable parameters include both weights and biases. Each of the 12 output filters convolves across all 3 input channels with a 3×3 kernel, giving I×K² = 3×3×3 = 27 weights per filter, plus 1 bias term per filter. Total parameters = O×(I×K²+1) = 12×(27+1) = 12×28 = 336. The distractor that drops the bias term yields 324 (12×27), undercounting by 12 — one missing bias per filter. For comparison, a Conv2D(3, 64, 3) layer, as used in early ResNet stages, has 64×(3×3×3+1) = 1,792 parameters, showing how the same formula scales directly with the number of output channels.

Question 114 · Conv2D Parameters · hard

Analyze a Conv2D layer with in_channels=3, out_channels=14, and kernel_size=3×3. Using the formula Parameters = O×(I×K²+1), what is the total number of learnable parameters, and how does this affect the layer's memory usage?

  1. Parameters = 14, counting only one bias term per output filter and ignoring the weight tensors entirely
  2. Parameters = 378, computed as 14×27 by leaving the bias term out of each filter's parameter count
  3. Parameters = 392, because each of 14 output filters has I×K²=27 weights plus 1 bias: 14×(3×3×3+1) = 392
  4. Parameters = 27, treating the kernel weights of a single filter as the total for the whole layer

Answer: C. Parameters = 392, because each of 14 output filters has I×K²=27 weights plus 1 bias: 14×(3×3×3+1) = 392

ExplanationConv2D learnable parameters include both weights and biases. Each of the 14 output filters has a kernel spanning all 3 input channels, 3×3×3 = 27 weights, plus 1 bias term. Total: 14×(3×3×3+1) = 14×28 = 392 parameters. For example, a Conv2D(3, 64, 3) layer in a ResNet has 64×(3×3×3+1) = 1,792 parameters. Understanding parameter counts is essential for model complexity analysis and memory optimization.

Question 115 · Conv2D Parameters · hard

A Conv2D layer has in_channels=1, out_channels=14, and kernel_size=4×4. Using the formula O×(I×K²+1), what is the total number of learnable parameters in this layer?

  1. Parameters = 14, counting one bias term per output filter but omitting the I×K² kernel weights entirely
  2. Parameters = 224, without bias, using 14×(1×4×4) and leaving out the +1 bias term per filter
  3. Parameters = 238, because each of 14 output filters has I×K²=16 weights plus 1 bias: 14×(1×4×4+1) = 238
  4. Parameters = 16, treating I×K² alone as the per-filter weight count while ignoring the 14 output filters and the bias term

Answer: C. Parameters = 238, because each of 14 output filters has I×K²=16 weights plus 1 bias: 14×(1×4×4+1) = 238

ExplanationConv2D learnable parameters include weights and biases: each of the 14 output filters has a kernel of size 1×4×4 (16 weights) plus 1 bias term. Total: 14×(1×4×4+1) = 14×17 = 238 parameters. For comparison, a Conv2D(3, 64, 3) layer in a ResNet has 64×(3×3×3+1) = 1,792 parameters, using the same O×(I×K²+1) formula.

Question 116 · GRU Parameters · hard

Analyze GRU (Gated Recurrent Unit): hidden_size=151, input_size=40. Calculate total parameters, compare with LSTM (4 gates), and evaluate the gate structure?

  1. Parameters = 151×40 = 6040, only input-to-hidden, because GRU has a single gate that reads only the current input and ignores the previous hidden state entirely
  2. Parameters = 3×(151×(151+40)+151) = 86976 (3 gates: reset, update, candidate); LSTM has 4×params because it has 4 gates; GRU is more parameter-efficient
  3. Parameters = 4×(151×(151+40)+151) = 115968, since GRU uses 4 gates like LSTM: reset, update, candidate, and an extra output gate
  4. GRU has more parameters than LSTM because each of its 3 gates uses two separate weight matrices, one for input and one for hidden, counted as 4 independent gate-equivalents

Answer: B. Parameters = 3×(151×(151+40)+151) = 86976 (3 gates: reset, update, candidate); LSTM has 4×params because it has 4 gates; GRU is more parameter-efficient

ExplanationGRU has 3 gates (reset r, update z, candidate h'), each with parameters h×(h+x)+h. Total: 3×(151×(151+40)+151) = 86976. LSTM has 4 gates (input, forget, output, candidate), requiring 4×params for the same hidden and input sizes. GRU is therefore more parameter-efficient and computationally faster while often matching LSTM performance. GRUs are preferred when computational resources are limited; LSTMs are preferred for complex long-range dependencies.

Question 117 · Conv2D Parameters · hard

A Conv2D layer has in_channels=2, out_channels=10, and kernel_size=5×5. Using the parameter formula O×(I×K²+1), what is the total number of learnable parameters in this layer?

  1. 500, calculated as 10 output filters times 50 weights each, without including any bias terms
  2. 50, representing the weights contributed by a single output filter before biases are added
  3. 510, because each of 10 output filters has I×K²=50 weights plus 1 bias term, giving 10×(2×5×5+1)=510
  4. 60, computed as 10 output filters times 5+1 kernel dimension terms, ignoring the input channel count

Answer: C. 510, because each of 10 output filters has I×K²=50 weights plus 1 bias term, giving 10×(2×5×5+1)=510

ExplanationConv2D learnable parameters include both weights and biases. Each of the 10 output filters convolves over all 2 input channels with a 5×5 kernel, contributing I×K² = 2×5×5 = 50 weights, plus 1 bias term per filter, for 51 parameters per filter. Total parameters = O×(I×K²+1) = 10×(2×5×5+1) = 10×51 = 510. For comparison, a Conv2D(3, 64, 3) layer in a ResNet has 64×(3×3×3+1) = 1,792 parameters, showing how channel depth and kernel size compound quickly.

Question 118 · Conv2D Parameters · hard

A Conv2D layer has in_channels=4, out_channels=9, and kernel_size=4×4. Using the formula parameters = O×(I×K²+1), what is the total number of learnable parameters?

  1. Parameters = 9, counting only the output channels and ignoring the kernel size and input channels.
  2. Parameters = 576, from 9×(4×4×4) weights, but this omits the bias term for each output filter.
  3. Parameters = 585, because each of 9 output filters has I×K²=64 weights plus 1 bias: 9×(4×4×4+1) = 585.
  4. Parameters = 64, the weight count for one output filter, not multiplied by all 9 output filters.

Answer: C. Parameters = 585, because each of 9 output filters has I×K²=64 weights plus 1 bias: 9×(4×4×4+1) = 585.

ExplanationEach of the 9 output filters slides across all 4 input channels using a 4×4 kernel, giving 4×4×4 = 64 weight parameters per filter. Across all 9 filters that is 9×64 = 576 weights. Conv2D layers also learn one bias term per output filter, adding 9 more parameters, so the total is 576 + 9 = 585, matching 9×(4×4×4+1) = 9×65 = 585. The 576 count is a common near-miss: it correctly computes the weight total but forgets to add the 9 bias terms, one per output filter, which is exactly the gap between 576 and the correct 585.

Question 119 · GRU Parameters · hard

A GRU (Gated Recurrent Unit) has hidden_size=97 and input_size=88. What is its total parameter count, and how does this compare with an LSTM, which has 4 gates instead of GRU's 3?

  1. Parameters = 97 × 88 = 8536, counting only the input-to-hidden weights of a single gate while ignoring the hidden-to-hidden weights and biases
  2. Parameters = 3×(97×(97+88)+97) = 54126 (3 gates: reset, update, candidate); LSTM has 4×params because it has 4 gates; GRU is more parameter-efficient
  3. Parameters = 4×(97×(97+88)+97) = 72168, incorrectly treating GRU as having 4 gates the way LSTM does instead of its actual 3
  4. GRU has more parameters than LSTM for equal hidden_size and input_size, since each of its 3 gates carries a full hidden-to-hidden matrix that outweighs LSTM's extra gate

Answer: B. Parameters = 3×(97×(97+88)+97) = 54126 (3 gates: reset, update, candidate); LSTM has 4×params because it has 4 gates; GRU is more parameter-efficient

ExplanationGRU has 3 gates (reset r, update z, candidate h'), each with parameters h×(h+x)+h. Total: 3×(97×(97+88)+97) = 54126. LSTM has 4 gates (input, forget, output, candidate), requiring 4×params instead. GRU is more parameter-efficient and computationally faster while often matching LSTM performance. Both RNNs address vanishing gradients through gating mechanisms. GRUs are preferred when computational resources are limited; LSTMs are preferred for complex long-range dependencies.

Question 120 · Conv2D Parameters · hard

A Conv2D layer has in_channels=1, out_channels=14, and kernel_size=3×3. Using the formula Parameters = O×(I×K²+1), what is the total number of learnable parameters in this layer?

  1. Parameters = 14, counting only the output channels and ignoring the kernel weights entirely
  2. Parameters = 126, computed as 14×9 without including any bias terms
  3. Parameters = 140, because each of 14 output filters has I×K²=9 weights plus 1 bias: 14×(1×3×3+1) = 140
  4. Parameters = 9, treating the kernel size alone as the total parameter count for the whole layer

Answer: C. Parameters = 140, because each of 14 output filters has I×K²=9 weights plus 1 bias: 14×(1×3×3+1) = 140

ExplanationConv2D learnable parameters include both weights and biases. Each of the 14 output filters has a kernel of size 1×3×3, which is 9 weights, plus 1 bias term, giving 10 parameters per filter. Total: 14×(1×3×3+1) = 14×10 = 140 parameters. For comparison, a Conv2D(3, 64, 3) layer has 64×(3×3×3+1) = 1,792 parameters, showing the same formula scales with both channel count and kernel size. Omitting the +1 bias term per filter is the most common source of error in this calculation.
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