Question at position 65 Why is argmax considered unsuitable for backpropagation in classification tasks?Why is argmax considered unsuitable for backpropagation in classification tasks?Its derivative is effectively zero, preventing gradient-based parameter updatesIt introduces negative probabilities for less likely classesIts probabilities often exceed 1, making the network unstable

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BlackTom AI · Accepted Answer

The question asks why argmax is considered unsuitable for backpropagation in classification tasks. We will evaluate each option in turn.
Option 1: Its derivative is effectively zero, preventing gradient-based parameter updates. This is the correct intuition. The argmax operation is a non-differentiable, piecewise-constant function: small changes in input do not change the argmax until a threshold is crossed, and at the decision boundary the derivative does not provide meaningful gradient information. In practice, this means that using argmax directly in the loss or as part of the computation graph yields near-zero or undefined gradients, which prevents effective parameter updates via gradient descent.
Option 2: It introduces negative probabilities for less likely classes. Argmax does not assign any probabilities at all; it selects a single class as the maximum. It does not produce negative probabilities, because probabilities are not produced by argmax itself. Therefore, this claim is inaccurate—argmax is a discrete decision, not a probabilistic output.
Option 3: Its probabilities often exceed 1, making the network unstable. This statement is incorrect because argmax does not output probabilities at all. It returns an index corresponding to the largest value among inputs; there is no probability value produced by argmax that could exceed 1. The notion of probabilities exceeding 1 does not apply to the argmax operation.
In summary, the central issue with argmax for backpropagation is its non-differentiability and, more importantly, the absence of useful gradients, which blocks gradient-based optimization. The other options mischaracterize what argmax outputs or how it behaves, since it neither produces probabilities nor values outside the [0,1] range, and it does not inherently introduce negative probabilities.

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