The main problem in your test is that your X has the same scale as your noise level (0-1), as a result, adding a noise changes your data distribution significantly.

This is your data distribution before and after adding noise.

It is like the noise is 50-200% more than your initial data. That's why you get a better result with CV than the "ground truth weights". Because the new fitted model by CV is tuned for an X with a new distribution.

However, if you increase your X values scale, for example 100*np.random.rand(ntrials,nneurons), the your data have same distribution before and after adding noise.

Now if you run your code, you will get what you expected.

The main problem in your test is that your X has the same scale as your noise level (0-1), as a result, adding a noise changes your data distribution significantly.

This is your data distribution before and after adding noise.

It is like the noise is 50-200% more than your initial data. That's why you get a better result with CV than the "ground truth weights". Because the new fitted model by CV is tuned for an X with a new distribution.

However, if you increase your X values scale, for example, 100*np.random.rand(ntrials,nneurons), your data have the same distribution before and after adding noise.

Now if you run your code, you will get what you expected.

The main problem in your test is that your X has the same scale as your noise level (0-1), as a result, adding a noise changes your data distribution significantly.

This is your data distribution before and after adding noise.

It is like the noise is 50-200% more than your initial data. That's why you get a better result with CV than the "ground truth weights". Because the new fitted model by CV is tuned for an X with a new distribution.

However, if you increase your X values, for example 100*np.random.rand(ntrials,nneurons), the your data have same distribution before and after adding noise.

Now if you run your code, you will get what you expected.

The main problem in your test is that your X has the same scale as your noise level (0-1), as a result, adding a noise changes your data distribution significantly.

This is your data distribution before and after adding noise.

It is like the noise is 50-200% more than your initial data. That's why you get a better result with CV than the "ground truth weights". Because the new fitted model by CV is tuned for an X with a new distribution.

However, if you increase your X values scale, for example 100*np.random.rand(ntrials,nneurons), the your data have same distribution before and after adding noise.

Now if you run your code, you will get what you expected.