损失函数

A prediction loss compares outputs with training targets according to a specified rule. Those targets can be labels or values constructed for the learning task; they should not automatically be called unquestionable truth. Implementations may produce per-example losses and then sum or average them for an optimization step. Choosing the rule matters. Mean squared error averages squared residuals, giving large residuals more influence than mean absolute error, which averages their absolute values. For residuals one and three, mean squared error is five, while mean absolute error is two. These are illustrative calculations rather than performance results from a dataset. Classification commonly uses cross-entropy. With a one-hot target and a predicted probability p for its class, the loss is minus log p. A lower probability for the target class gives a larger loss, so confident wrong predictions can incur high loss. The logarithm base determines the units: base-two loss is in bits, while a natural logarithm gives nats. For a target probability of one-quarter, minus log-base-two p is two bits. Gradient-based optimization needs usable derivative information, but differentiability requirements should not be generalized to every learning algorithm. Some losses have nondifferentiable points handled by an appropriate subgradient or surrogate. Accuracy is a discrete evaluation metric and is generally not directly useful as a gradient-training objective. A suitable training loss supplies an optimization signal; final task quality needs evaluation using the relevant metrics.