Interpret neural network results.

A pricing actuary trains a feedforward network on policy-level pure premium and gets a validation RMSE of 412 against a GLM benchmark of 438. Before recommending the network, you have to explain what it learned, why it generalizes, and which inputs drove the lift. That is interpretation, not training.

Architecture in one sentence. Input $x\in {\mathbb{R}}^p$ is multiplied by weight matrix $W_1$, shifted by bias $b_1$, passed through activation $g_1$, and the result becomes the input to the next layer. The output layer's activation has to match the response.

$$\hat{y}=g_L\left(W_L{g}_{L-1}\right(\cdots g_1(W_{1}x+b_1)\cdots )+b_L)$$

KEY: If the output activation is sigmoid and the network reports $\hat{y}=0.83$, that is the predicted probability the observation belongs to class 1, not a regression score. Round only when a class label is needed.

You read two curves: training loss vs. epoch and validation loss vs. epoch. Three patterns:

• Both falling and close together ⇒ undertrained or well-fit. Train longer or stop early.
• Training falls, validation flat or rising ⇒ overfitting. Add dropout, L2, early stopping, or shrink the network.

Common mistakes

• Reading hidden-layer weights as feature effects. Hidden weights have no marginal interpretation; sign and magnitude depend on the next layer's transform. The right tool is permutation importance or a PDP, not the first weight matrix.
• Stopping at minimum training loss. Training loss keeps falling as the network memorizes noise. Early stopping uses minimum validation loss; otherwise overfitting is guaranteed.
• Treating sigmoid output as a probability without calibration. A raw sigmoid is rank-correct but often miscalibrated. If you need true probabilities (e.g., reserve discounting), apply Platt scaling or isotonic regression to the validation set first.

Bottom line

• A neural network stacks affine transforms inside nonlinear activations: $\hat{y}=g_L(W_L{g}_{L-1}(\cdots g_1(W_{1}x+b_1)\cdots )+b_L)$. Interpret the output layer, not hidden weights.
• Output activation sets task type: linear = regression, sigmoid = binary probability, softmax = multiclass probability summing to 1, ReLU = nonnegative regression (e.g., claim count).
• Hidden weights have no marginal meaning; use permutation importance, partial dependence plots (PDPs), and individual conditional expectation (ICE) curves instead.
• Permutation importance ranks variables by the validation loss jump after shuffling one column; PDPs show average marginal effect, ICE curves expose interactions PDPs average away.

Exam shortcut

If the question asks "predicted probability" and the output activation is sigmoid, compute $1/(1+e^{-z})$ directly; ignore everything in the hidden layers. If the question asks for variable importance and gives a table of permuted-vs-baseline losses, rank by the difference, not the ratio; the largest gap is the most important variable.

The full lesson (about 2,252 words, 15 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• C9

Browse all free MAS-II lessons or jump into free MAS-II practice questions.