Let a 1-D filter be h=[2,-1,3]. A library routine performs cross-correlation. Which filter should be
supplied to the routine to reproduce mathematical convolution with h, ignoring boundary effects?
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[2,-1,3]
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[-2,1,-3]
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[3,-1,2]
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[3,1,2]
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An image is smoothed successively with Gaussian kernels of standard deviations 2 and 3. Ignoring
discretization, the equivalent single Gaussian has standard deviation:
A hidden activation h is used by two downstream branches, and both branches affect the same
scalar loss L. During backpropagation, the gradient with respect to h is obtained by:
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Taking the larger of the two branch gradients
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Summing the gradient contributions from the two branches
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Multiplying the two branch gradients
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Averaging the two branch gradients regardless of the graph
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Suppose successive gradients keep pointing in a similar direction over several updates. Compared
with plain gradient descent using the same nominal learning rate, momentum tends to:
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Cancel updates in that direction
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Build velocity in that direction while smoothing short-term gradient
fluctuations
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Make the gradient exactly unbiased
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Force every parameter to use the same accumulated gradient
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A 3×3 convolution maps 16 input channels to 32 output channels. If the input spatial size changes
from 64×64 to 128×128 while the layer configuration is unchanged, the number of trainable
convolution weights:
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Doubles
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Quadruples
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Remains unchanged
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Is halved
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A depthwise-separable convolution first applies a spatial filter independently to each input channel
and then uses a 1×1 convolution across channels. Its main computational advantage over a dense
spatial convolution is that it:
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Eliminates channel mixing from the layer
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Factorizes spatial filtering and channel mixing into cheaper operations
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Uses a larger spatial kernel with the same parameter count
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Forces the number of output channels to equal the number of input channels
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When adapting a pretrained CNN to a related task with a relatively small labeled dataset, which
training choice is generally the more conservative starting point?
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Reinitialize the entire network and use a very large learning rate
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Retain pretrained features and update them cautiously, often with a smaller
learning rate than newly initialized layers
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Freeze the newly added prediction head and update only the old classifier
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Randomly permute pretrained channels before optimization
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An input feature map has spatial size 63×63. A 5×5 convolution is applied with stride 2 and
padding 1. Compute the output size along one spatial dimension.
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An image is smoothed successively by Gaussian kernels with σ1=1.2 and σ2=1.6. Ignoring
discretization, compute the equivalent single Gaussian standard deviation.
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A convolutional layer uses 3×3 kernels, 16 input channels and 32 output channels. The layer has
one bias per output channel. Compute the total number of trainable parameters.
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A depthwise-separable convolution receives 32 channels. It uses a 3×3 depthwise convolution
followed by a 1×1 pointwise convolution producing 64 output channels. Ignore biases. Compute
the total number of weights.
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