二分类场景下Binary Cross Entropy与Categorical Cross Entropy对比

Great question! This is a common point of confusion when transitioning between binary and multi-class classification tasks, so let’s break down why you almost never see the two-output softmax + categorical cross-entropy approach used for binary problems—even though it’s technically valid.

• Redundancy leads to unnecessary computation
  Binary classification is a yes/no, mutually exclusive task. If a model predicts an 80% chance of class A, that inherently means a 20% chance of class B. Using two output neurons forces the model to learn redundant weights and compute extra activations for no practical gain. It’s like carrying two identical phone chargers when you only need one: it doesn’t break anything, but it wastes space and energy, especially as your model scales up.

• Simpler, more stable workflow
  Mathematically, a two-output softmax in binary classification is equivalent to a single sigmoid (since softmax for two values simplifies to σ(z) and 1-σ(z)). But the single-output approach cuts out the extra softmax normalization step, making code shorter and reducing minor numerical stability risks. For example, in frameworks like TensorFlow/Keras, you can feed raw integer labels directly to binary cross-entropy, whereas categorical cross-entropy requires you to one-hot encode your labels—adding an extra preprocessing step that’s easy to forget or mess up.

• Community convention and readability
  Machine learning code is as much about communication as it is about math. The single-output sigmoid setup is the de facto standard for binary classification. When other developers see this structure, they immediately recognize the task type without extra mental work. Using two outputs would raise unnecessary questions (“Wait, is this secretly a multi-class task?”) and go against shared practices that make collaboration and code maintenance easier.

• No practical performance benefit
  While the two approaches are theoretically equivalent in terms of loss value (when labels are properly formatted), there’s no performance gain to be had from using two outputs. The single-output method is just as accurate, faster to train, and easier to debug. There’s simply no incentive to deviate from the simpler, more widely accepted approach.

Content of the question comes from stack exchange, question author MRm