The optimization of deep neural networks almost always relies on reducing the value of a loss function. For classification tasks, the loss function we used was cross entropy. Could we have instead just have used accuracy as the loss function? Why or why not? Hint: Think about what the loss function would look like

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Question

The optimization of deep neural networks almost always relies on reducing the value of a loss function. For classification tasks, the loss function we used was cross entropy. Could we have instead just have used accuracy as the loss function? Why or why not? Hint: Think about what the loss function would look like

Answer using up to 3 sentences max.

BlackTom AI · Accepted Answer

The question asks whether we could have used accuracy as the loss function for training deep neural networks on classification tasks, instead of cross-entropy, and to provide reasoning for the answer.
First, accuracy measures the proportion of correct predictions and is a discrete, non-differentiable metric that only changes when a prediction crosses the decision threshold (e.g., from incorrect to correct). This means it provides essentially no gradient information to guide optimization, so gradient-based methods cannot use it to adjust network weights.
Second, cross-entropy, by contrast, is smooth and differentiable with respect to the network’s outputs, yielding meaningful gradients at every training example that indicate how to adjust predictions to become more probable for the correct class. This enables effective optimization via backpropagation, whereas accuracy cannot drive learning in a fine-grained way.
Third, using accuracy as a loss would also create optimization dynamics that are non-smooth and often plateaus, making it difficult for the model to learn from intermediate states or handle mini-batch updates consistently. In short, accuracy is a useful evaluation metric but not a suitable objective for training neural networks; cross-entropy provides the necessary differentiable signal for gradient-based optimization.

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