But the problem might be caused by the early assessment selecting relu and logistic as the best performers. Now that you know that the entire experiment works properly, you might retry tanh for the Lab case. tanh allows the NN to produce smooth transitions between negative and positive values within one node. Otherwise it needs increased complexity to achieve the same.

First of all I have to say you were right, gray patches were offset by one position because the author made a mistake in measuring GS0 twice and not recording the measure in patch GS23.

He has measured again the GS0-GS23 patches and made the union of measurements. I don't pretty much like the idea of mixing measurements taken in different times and possibly conditions, but OK.

I dropped the relu activation function and introduced tanh, thanks for the suggestion. It converges faster than sigmoid and performs better, so my best trade-off candidate this time is MLP_Lab_(50, 50)_tanh_identity:

MLP_XYZ_()_tanh_identity : ΔE_max = 33.6562 , ΔE_mean = 3.2097 , ΔE_median = 1.8020

MLP_Lab_()_tanh_identity : ΔE_max = 82.1350 , ΔE_mean = 28.3336 , ΔE_median = 21.5002

MLP_XYZ_()_logistic_identity : ΔE_max = 33.6562 , ΔE_mean = 3.2097 , ΔE_median = 1.8020

MLP_Lab_()_logistic_identity : ΔE_max = 82.1906 , ΔE_mean = 28.3471 , ΔE_median = 21.4991

MLP_XYZ_(3, 3)_tanh_identity : ΔE_max = 15.3840 , ΔE_mean = 2.4645 , ΔE_median = 1.8418

MLP_Lab_(3, 3)_tanh_identity : ΔE_max = 43.0895 , ΔE_mean = 11.6182 , ΔE_median = 9.2091

MLP_XYZ_(3, 3)_logistic_identity : ΔE_max = 18.1560 , ΔE_mean = 3.8059 , ΔE_median = 2.2673

MLP_Lab_(3, 3)_logistic_identity : ΔE_max = 77.2547 , ΔE_mean = 25.7759 , ΔE_median = 20.7278

**MLP_XYZ_(4, 4)_tanh_identity : ΔE_max = 11.2728 , ΔE_mean = 2.0082 , ΔE_median = 1.5386**MLP_Lab_(4, 4)_tanh_identity : ΔE_max = 37.5632 , ΔE_mean = 8.2402 , ΔE_median = 6.7438

MLP_XYZ_(4, 4)_logistic_identity : ΔE_max = 16.7437 , ΔE_mean = 2.3609 , ΔE_median = 1.6683

MLP_Lab_(4, 4)_logistic_identity : ΔE_max = 68.0552 , ΔE_mean = 17.6988 , ΔE_median = 12.4104

MLP_XYZ_(16, 16)_tanh_identity : ΔE_max = 13.7044 , ΔE_mean = 2.0632 , ΔE_median = 1.2234

MLP_Lab_(16, 16)_tanh_identity : ΔE_max = 3.9206 , ΔE_mean = 1.0084 , ΔE_median = 0.8693

MLP_XYZ_(16, 16)_logistic_identity : ΔE_max = 13.1919 , ΔE_mean = 1.9344 , ΔE_median = 1.2701

MLP_Lab_(16, 16)_logistic_identity : ΔE_max = 6.1042 , ΔE_mean = 1.3190 , ΔE_median = 1.0214

MLP_XYZ_(50, 50)_tanh_identity : ΔE_max = 14.7397 , ΔE_mean = 2.4049 , ΔE_median = 1.6943

**MLP_Lab_(50, 50)_tanh_identity : ΔE_max = 3.9451 , ΔE_mean = 0.6966 , ΔE_median = 0.5313**MLP_XYZ_(50, 50)_logistic_identity : ΔE_max = 26.3273 , ΔE_mean = 3.5872 , ΔE_median = 2.1889

MLP_Lab_(50, 50)_logistic_identity : ΔE_max = 4.0815 , ΔE_mean = 0.7272 , ΔE_median = 0.5018

MLP_XYZ_(100, 100)_tanh_identity : ΔE_max = 9.9610 , ΔE_mean = 1.5248 , ΔE_median = 1.0915

MLP_Lab_(100, 100)_tanh_identity : ΔE_max = 3.3160 , ΔE_mean = 0.5003 , ΔE_median = 0.3757

MLP_XYZ_(100, 100)_logistic_identity : ΔE_max = 29.8789 , ΔE_mean = 3.7231 , ΔE_median = 2.1818

MLP_Lab_(100, 100)_logistic_identity : ΔE_max = 3.7744 , ΔE_mean = 0.6649 , ΔE_median = 0.4671

MLP_XYZ_(200, 200)_tanh_identity : ΔE_max = 8.4625 , ΔE_mean = 1.4752 , ΔE_median = 0.9700

MLP_Lab_(200, 200)_tanh_identity : ΔE_max = 3.3737 , ΔE_mean = 0.4059 , ΔE_median = 0.2591

MLP_XYZ_(200, 200)_logistic_identity : ΔE_max = 16.8308 , ΔE_mean = 1.8797 , ΔE_median = 1.1590

MLP_Lab_(200, 200)_logistic_identity : ΔE_max = 4.2315 , ΔE_mean = 0.6553 , ΔE_median = 0.4166

Mean delta E is lower than 1, with max delta E below 4!

Quick and soft convergence:

Nice correlation (again lightness in dark and very bright patches gets the least accurate fit):

Good Delta E distribution gathered below 1:

Left half=prediction vs Right half=exact value (target):

Pretty impressive, right? the NN complexity is 2800 coeffs + 103 bias = 2903 numbers (if we consider 32-bit floating point numbers, that means

**11,3KB** are needed to store the profile's definition)

I also predicted one of the simplest models: MLP_XYZ_(4, 4)_tanh_identity : ΔE_max = 11.2728 , ΔE_mean = 2.0082 , ΔE_median = 1.5386

Not bad for a NN defined by 51 numbers:

Now I need to check how the NN behave for unseen colours, i.e., interpolating colours that are not in the chart. I expect the interpolations to be soft; any ringing behaviour would be bad news. I can also validate it on real images. I think tanh could help in providing soft transitions?

Regards