Recipe: LIME Basics¶

What you'll build: LIME explaining a purely linear network. Weighted least squares on noise-free linear data recovers the true weights almost exactly.

CMake target: lime_basics_recipe (examples/recipes/lime_basics.cpp).

Run it: ./build/lime_basics_recipe (Windows: build\Release\lime_basics_recipe.exe).

Code¶

LinearModule linear(3, 2, &backend);
linear.set_weight({1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f});
linear.set_bias({100.0f, 100.0f});  // deliberately large/irrelevant

ExplainerContext ctx({&linear});
auto predict = [&ctx](const Tensor& x) { return ctx.forward_pass(x); };

Tensor input(Shape({1, 3}), &backend, {1.0f, 1.0f, 1.0f});

LIME lime;
Attribution attr = lime.explain(predict, input, /*target_index=*/1, /*num_samples=*/300,
                                 /*sigma=*/1.0f, /*l2_lambda=*/0.0f, /*seed=*/42, &backend);

Full source: examples/recipes/lime_basics.cpp.

Expected output¶

LIME recipe -- output 1 of a linear network, true weight column [2, 4, 6]

feature    LIME coeff  true weight
x0             2.0000          2.0
x1             4.0000          4.0
x2             6.0000          6.0
...

What's happening¶

LIME::explain() draws 300 Gaussian perturbations of the input (standard deviation sigma=1.0). It weights each one with an exponential locality kernel of the same width. Then it fits a local linear surrogate model g(z) = f(x) + w^T(z - x).

The network is already exactly linear, so w matches the true weight column to four decimal places. The large bias doesn't matter: the surrogate only sees output differences, so any constant term cancels.