Unverified60% confidenceFactExact time
The mean squared error (MSE) cost function is defined as C(w,b) = 1/(2n) Σ ‖yᵢ − ŷᵢ‖², where each squared error term is always non-negative.
2
Sources
60%
Confidence
Long-term
Relevance
7/19/2026
First Seen
Sources
梯度下降与反向传播详解：神经网络学习机制从零拆解
Related Claims
UnverifiedUnder the assumption of a Gaussian output distribution, minimizing negative log-likelihood (NLL) and minimizing mean squared error (MSE) are mathematically completely equivalent.76% similarUnverifiedWhen using mean squared error (MSE) as the loss function, the negative gradient of the loss with respect to the predicted value is exactly equal to the residual y−prediction.71% similarUnverifiedWhen the quantile level τ=0.5, quantile loss degenerates to Mean Absolute Error (MAE).69% similarUnverifiedExpectiles are defined by asymmetrically weighting the squared loss: the solution to minimizing E[w_τ(Y−θ)²] is the τ-expectile, where the weight w_τ is τ when Y>θ and 1−τ otherwise.67% similarUnverifiedNear the loss minimum, the loss increase is approximately ΔL ≈ ½ · H · δ², where H is the curvature (second derivative) and δ is the quantization error range.66% similar
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