Question at position 46 Why can a single perceptron not learn the XOR function without additional layers?Why can a single perceptron not learn the XOR function without additional layers?Because XOR requires infinite training data to convergeBecause the XOR operation can be computed by biases aloneBecause a single perceptron cannot handle linear transformationsBecause XOR is not linearly separable and needs more complex representations

Question

BlackTom AI · Accepted Answer

Question examines why a single perceptron struggles with XOR without additional layers.
Option 1: 'Because XOR requires infinite training data to converge' This is not the core reason. XOR can be learned with finite data if the model capacity and structure are appropriate; the issue is not data quantity but representation capability.
Option 2: 'Because the XOR operation can be computed by biases alone' This statement mischaracterizes XOR. While biases influence decision boundaries, they do not enable a single perceptron to represent XOR, which requires a non-linear mapping that biases alone cannot achieve.
Option 3: 'Because a single perceptron cannot handle linear transformations' This is misleading. A single perceptron performs a linear threshold operation. The statement would be more accurate if it said it cannot represent non-linear decision boundaries, but as written it's focusing on linear transformations in a way that obscures the real limitation for XOR.
Option 4: 'Because XOR is not linearly separable and needs more complex representations' This correctly identifies the fundamental issue: XOR cannot be separated by a single straight line in input space, so a single perceptron, which creates only a linear decision boundary, cannot capture its pattern. To model XOR, we need either multiple layers (a small neural network) or a non-linear feature mapping that enables linear separability in a higher-dimensional space.

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