[BUG] `Lars` produces incorrect coefficients, intercept, predictions, and score on a simple exact linear dataset

[apiqwe]

Describe the bug

cuml.linear_model.Lars produces an incorrect fitted model for a simple one-feature dataset that follows the exact linear relationship y = X.

For:

X = np.array([[1], [2], [3]])
y = np.array([1, 2, 3])

the equivalent sklearn.linear_model.Lars model correctly recovers a coefficient of 1.0, an intercept numerically equal to zero, exact predictions [1.0, 2.0, 3.0], and an R² score of 1.0.

cuML instead returns:

coef: [0.14285713]
intercept: 2.0
pred: [2.142857  2.2857141 2.4285715]
score: 0.14285727909631873

The discrepancy affects the fitted parameters as well as downstream predict() and score() results.

Steps/Code to reproduce bug

cuML reproducer:

import numpy as np
from cuml.linear_model import Lars

X = np.array([[1], [2], [3]])
y = np.array([1, 2, 3])

m = Lars().fit(X, y)

print("coef:", m.coef_)
print("intercept:", m.intercept_)
print("pred:", m.predict(X))
print("score:", m.score(X, y))

Output:

coef: [0.14285713]
intercept: 2.0
pred: [2.142857  2.2857141 2.4285715]
score: 0.14285727909631873

For comparison, the equivalent scikit-learn code:

import numpy as np
from sklearn.linear_model import Lars

X = np.array([[1], [2], [3]])
y = np.array([1, 2, 3])

m = Lars().fit(X, y)

print("coef:", m.coef_)
print("intercept:", m.intercept_)
print("pred:", m.predict(X))
print("score:", m.score(X, y))

Output:

coef: [1.]
intercept: 4.440892098500626e-16
pred: [1. 2. 3.]
score: 1.0

Expected behavior

For this dataset, the target follows the exact linear relationship:

y = 1 * X + 0

Therefore, Lars().fit(X, y) should recover a coefficient approximately equal to 1.0 and an intercept approximately equal to 0.0.

Predictions on the training samples should be approximately:

[1.0, 2.0, 3.0]

and the coefficient of determination should be:

R² = 1.0

The cuML implementation should produce a fitted model consistent with this exact solution and with the equivalent scikit-learn estimator.

Environment details (please complete the following information):

• Environment location: Docker
• Linux Distro/Architecture: Ubuntu 24.04 / x86_64
• GPU Model/Driver: NVIDIA GeForce RTX 4090 / 595.71.05
• CUDA: 13.2
• Method of cuDF & cuML install: conda

conda list:

# packages in environment at /opt/conda/envs/rapids-26.08:
#
# Name              Version       Build                                      Channel
python              3.14.6        h242f9ac_102_cp314                         conda-forge
numpy               2.4.6         py314h2b28147_0                            conda-forge
scipy               1.16.3        py314hf07bd8e_2                            conda-forge
scikit-learn        1.9.0         np2py314hf09ca88_0                         conda-forge
rapids              26.08.00      cuda13_260806_c2656556                     rapidsai
cuml                26.08.00      cuda13_cp311_abi3_260805_265b9da6          rapidsai
libcuml             26.08.00      cuda13_260805_265b9da6                     rapidsai
cudf                26.08.00      cuda13_cp311_abi3_260805_ff5b362d          rapidsai
libraft             26.08.00      cuda13_260805_ebf92684                     rapidsai
libraft-headers     26.08.00      cuda13_260805_ebf92684                     rapidsai
pylibraft           26.08.00      cuda13_cp311_abi3_260805_ebf92684          rapidsai
cuvs                26.08.01      cuda13_cp311_abi3_260806_25b1be43          rapidsai
libcuvs             26.08.01      cuda13_260806_25b1be43                     rapidsai
cupy                14.1.1        py314hdea9c46_0                            conda-forge
cupy-core           14.1.1        py314hcd3b49b_0                            conda-forge
numba               0.64.0        py314h8169c2f_0                            conda-forge
numba-cuda          0.30.4        py314h42812f9_0                            conda-forge
rmm                 26.08.00      cuda13_cp311_abi3_260805_42d059f1          rapidsai
librmm              26.08.00      cuda13_260805_42d059f1                     rapidsai
cuda-version        13.3           hcbadf70_3                                 conda-forge
cuda-bindings       13.3.1        py314h42812f9_1                            conda-forge
cuda-cudart         13.3.29       hecca717_0                                 conda-forge
cuda-nvrtc          13.3.33       hecca717_0                                 conda-forge
libcublas           13.6.0.2      h676940d_0                                 conda-forge
libcusolver         12.2.6.9      h676940d_0                                 conda-forge
libcusparse         12.8.2.51     hecca717_0                                 conda-forge
libcurand           10.4.3.29     h676940d_0                                 conda-forge

Additional context

This reproducer is intentionally minimal. It contains only one feature and three samples, and the target is exactly equal to the feature value:

X = [[1],
     [2],
     [3]]

y = [1, 2, 3]

There is no noise, no multicollinearity, and no ambiguity in the expected linear solution.

The scikit-learn implementation recovers:

coef = [1.]
intercept ≈ 0

which exactly explains the data.

By contrast, cuML returns:

coef = [0.14285713]
intercept = 2.0

which corresponds to predictions shifted toward the target mean and leaves most of the variance unexplained.

Because the error is already visible in coef_ and intercept_, the incorrect predict() and score() results appear to be consequences of an incorrect fitted Lars solution rather than isolated issues in those methods.