When fitting a lasso, is normalization performed even if fit_intercept=False?

I'm trying to understand what's the stopping criterion on the (sub)gradient norm, in order to scale gradient_tol correctly.

If I understood correctly, for a quadratic datatif/family="gaussian", and vanishing coefs, the grad argument of _norm_min_subgrad should be X.T @ y / len(y)

When I debug, I see this being true only when I have previously centered and normalized X. otherwise, even if in my GeneralizedLinearRegressor I have set fit_intercept=False, I see:

• a P1 array which is not constant
• in update_quadratics(), gradient_rows is equal to y / len(y) as expected, however grad = gradient_rows @ data.X does not yield a grad equal to X.T @ y / len(y).
  It seems this is due to X being a
  Mat: <class 'tabmat.dense_matrix.DenseMatrix'> of shape (10, 5). Shift: [0. 0. 0. 0. 0.] Mult: [1.03404146 1.22010398 0.81522932 1.0686763 1.27198591] so scaling happens.

Why is this the case eventhough clf.scale_predictors, and clf._center_predictors are False ?

To reproduce, print gradient_rows and grad in update_quadratics, and run:

from glum import GeneralizedLinearRegressor
import numpy as np

np.random.seed(0)
X = np.random.randn(10, 5)
y = np.random.randn(10)
X -= X.mean(axis=0)
alpha = 0.001


clf = GeneralizedLinearRegressor(
    alpha=alpha, gradient_tol=1000, fit_intercept=False, family="gaussian",
    l1_ratio=1, verbose=10).fit(X, y)

print("grad rows should be", y / len(y))  # it is
print("grad should be", X.T @ y / len(y))   # it is not!

If you center and scale X before, then the problem disappears

Start with GeneralizedLinearRegressor.fit and the update_quadratics() path mentioned in the report, then inspect _norm_min_subgrad and tabmat's DenseMatrix shift and multiplier values. Run the provided reproduction and compare the transformed X with the expected X.T @ y / len(y). Done means establishing whether scaling is intended when fit_intercept=False and documenting or correcting the behavior with a regression test.