diff --git a/extra_tests/regression_fits/central_16.exportgrid b/extra_tests/regression_fits/central_16.exportgrid
index 68050334f8..503dbac86c 100644
--- a/extra_tests/regression_fits/central_16.exportgrid
+++ b/extra_tests/regression_fits/central_16.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
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+  -0.0002013336488744244, -0.00010433718853164464, 0.0004653719952329993, 0.0011868178844451904,
+  0.0023679069709032774, -0.0010139128426089883, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0006949883536435664, -0.0010792206740006804, 0.0002781025832518935,
+  -0.0001272016525035724, -4.542781243799254e-05, 0.0003553160058800131, 0.0007700162241235375,
+  0.0015817726962268353, -0.0006949884118512273, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004274652455933392, -0.0006301590474322438, 0.00012637417239602655,
+  -7.309525244636461e-05, -1.5502964743063785e-05, 0.0002453780616633594, 0.0004483770171646029,
+  0.000941615435294807, -0.0004274652455933392, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00021570049284491688, -0.0002962971630040556, 3.7409787182696164e-05,
+  -3.582327190088108e-05, -3.392364760657074e-06, 0.00014098382962401956, 0.0002151047228835523,
+  0.0004545498522929847, -0.00021570049284491688, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.70726876705885e-05, -8.231974061345682e-05, 1.1180580941072549e-06,
+  -1.202605380967725e-05, -2.50794158773715e-07, 5.150139986653812e-05, 6.472938548540697e-05,
+  0.0001318726281169802, -6.70726876705885e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 16
diff --git a/extra_tests/regression_fits/central_16.json b/extra_tests/regression_fits/central_16.json
index 8954787d8c..ea2c90be7e 100644
--- a/extra_tests/regression_fits/central_16.json
+++ b/extra_tests/regression_fits/central_16.json
@@ -51,44 +51,44 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 2.670100450515747,
-  "erf_vl": 2.59641432762146,
-  "chi2": 2.1027915477752686,
+  "erf_tr": 2.6700053215026855,
+  "erf_vl": 2.596088409423828,
+  "chi2": 2.1046974658966064,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.3208143986794203,
-    1.4723906730774663,
-    1.1834964225190123,
-    1.0011427029381073,
-    1.1961095151498038
+    1.3207831327275608,
+    1.4752541158950256,
+    1.1834874152294614,
+    1.0011426742289826,
+    1.1960979802612568
   ],
   "integrability": [
-    0.0009203124718646927,
-    0.0009203124718629718,
-    4.8332231357695044e-05,
-    0.4625758156180373,
-    0.0069634296232816695
+    0.0009203169902344266,
+    0.0009203169902324282,
+    4.8332353002611406e-05,
+    0.46257528662681513,
+    0.006963513907974672
   ],
   "timing": {
     "walltime": {
-      "Total": 18.60609221458435,
+      "Total": 18.85464835166931,
       "start": 0.0,
-      "replica_set": 0.3607151508331299,
-      "replica_fitted": 18.606019735336304,
-      "replica_set_to_replica_fitted": 18.245304584503174
+      "replica_set": 0.3591601848602295,
+      "replica_fitted": 18.854573249816895,
+      "replica_set_to_replica_fitted": 18.495413064956665
     },
     "cputime": {
-      "Total": 20.6525949,
+      "Total": 20.889074,
       "start": 0.0,
-      "replica_set": 0.6791323,
-      "replica_fitted": 20.6525204,
-      "replica_set_to_replica_fitted": 19.9733881
+      "replica_set": 0.6770135999999995,
+      "replica_fitted": 20.888997200000002,
+      "replica_set_to_replica_fitted": 20.211983600000003
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post168.dev0+5adb0639b",
-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/diagonal_45.exportgrid b/extra_tests/regression_fits/diagonal_45.exportgrid
index 0b7fd08fa1..eb4155994c 100644
--- a/extra_tests/regression_fits/diagonal_45.exportgrid
+++ b/extra_tests/regression_fits/diagonal_45.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.3064093589782715, 0.16341999173164368, 0.13691221177577972, 0.13695910573005676,
-  -16.513992309570312, 0.1371109038591385, 0.13706547021865845, 0.1631757915019989,
-  -2.3064093589782715, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2335848808288574, 0.16312070190906525, 0.13555094599723816, 0.13560424745082855,
-  -16.52280044555664, 0.13577209413051605, 0.13572050631046295, 0.16285274922847748,
-  -2.233584403991699, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.16306471824646, 0.1630817949771881, 0.13440623879432678, 0.13446685671806335,
-  -16.530073165893555, 0.13465246558189392, 0.13459394872188568, 0.16278783977031708,
-  -2.16306471824646, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.094778299331665, 0.16330263018608093, 0.13347546756267548, 0.1335444450378418,
-  -16.535701751708984, 0.13374976813793182, 0.13368333876132965, 0.16298015415668488,
-  -2.094778299331665, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.028651714324951, 0.16378164291381836, 0.13275517523288727, 0.1328335702419281,
-  -16.53957748413086, 0.13306067883968353, 0.13298533856868744, 0.16342788934707642,
-  -2.028651714324951, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9646183252334595, 0.16451890766620636, 0.13224320113658905, 0.13233231008052826,
-  -16.54157829284668, 0.1325836330652237, 0.13249816000461578, 0.16413086652755737,
-  -1.9646185636520386, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9026108980178833, 0.16551394760608673, 0.13193672895431519, 0.13203804194927216,
-  -16.541576385498047, 0.1323162168264389, 0.13221928477287292, 0.1650882512331009,
-  -1.9026108980178833, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8425647020339966, 0.16676665842533112, 0.13183341920375824, 0.13194860517978668,
-  -16.53943634033203, 0.13225649297237396, 0.13214662671089172, 0.1662997454404831,
-  -1.8425649404525757, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.784417748451233, 0.16827794909477234, 0.1319316178560257, 0.13206255435943604,
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-  -1.784417748451233, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7281088829040527, 0.17004872858524323, 0.1322294920682907, 0.13237838447093964,
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-  -1.7281088829040527, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6735799312591553, 0.17208008468151093, 0.13272546231746674, 0.13289470970630646,
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-  -1.6735799312591553, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6207737922668457, 0.17437414824962616, 0.13341864943504333, 0.1336110681295395,
-  -16.506389617919922, 0.13407446444034576, 0.1338931769132614, 0.17369869351387024,
-  -1.6207737922668457, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5696361064910889, 0.1769327074289322, 0.13430768251419067, 0.13452640175819397,
-  -16.49114227294922, 0.13503998517990112, 0.13483461737632751, 0.1761920154094696,
-  -1.5696364641189575, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5201129913330078, 0.1797587275505066, 0.13539229333400726, 0.1356409192085266,
-  -16.47271156311035, 0.13621023297309875, 0.13597770035266876, 0.17894653975963593,
-  -1.520113229751587, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4721533060073853, 0.18285447359085083, 0.13667121529579163, 0.13695378601551056,
-  -16.45088005065918, 0.13758501410484314, 0.13732177019119263, 0.18196390569210052,
-  -1.4721535444259644, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4257071018218994, 0.18622396886348724, 0.13814464211463928, 0.13846580684185028,
-  -16.425411224365234, 0.13916589319705963, 0.13886800408363342, 0.1852474957704544,
-  -1.4257068634033203, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.380725383758545, 0.18987026810646057, 0.13981181383132935, 0.14017681777477264,
-  -16.396068572998047, 0.1409534364938736, 0.14061640202999115, 0.1887996345758438,
-  -1.380725383758545, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3371615409851074, 0.19379805028438568, 0.14167308807373047, 0.1420879364013672,
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-- [0.0, 0.0, -1.294969916343689, 0.1980116367340088, 0.14372842013835907, 0.14419984817504883,
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-- [0.0, 0.0, -1.254106879234314, 0.20251573622226715, 0.1459776908159256, 0.14651338756084442,
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-- [0.0, 0.0, -1.214529275894165, 0.20731577277183533, 0.1484212726354599, 0.149029940366745,
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-- [0.0, 0.0, -1.1761959791183472, 0.21241797506809235, 0.15105995535850525, 0.15175148844718933,
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-- [0.0, 0.0, -1.1390669345855713, 0.2178276926279068, 0.15389327704906464, 0.1546788513660431,
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-- [0.0, 0.0, -1.1031030416488647, 0.22355212271213531, 0.15692229568958282, 0.1578146517276764,
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-  -1.1031032800674438, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0682672262191772, 0.22959782183170319, 0.16014687716960907, 0.16116037964820862,
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-  -1.0682672262191772, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0345221757888794, 0.23597198724746704, 0.16356711089611053, 0.16471807658672333,
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-  -1.034522294998169, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.001833200454712, 0.24268276989459991, 0.1671835482120514, 0.16849040985107422,
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-- [0.0, 0.0, -0.9701655507087708, 0.24973765015602112, 0.17099544405937195, 0.1724790781736374,
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-- [0.0, 0.0, -0.9394863843917847, 0.25714513659477234, 0.1750025749206543, 0.17668657004833221,
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-- [0.0, 0.0, -0.9097633957862854, 0.2649138569831848, 0.17920400202274323, 0.1811150759458542,
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-- [0.0, 0.0, -0.8809652328491211, 0.2730528712272644, 0.1835986077785492, 0.18576689064502716,
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-- [0.0, 0.0, -0.8530622124671936, 0.28157079219818115, 0.18818408250808716, 0.19064360857009888,
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-- [0.0, 0.0, -0.8260244131088257, 0.29047688841819763, 0.19295795261859894, 0.19574707746505737,
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-- [0.0, 0.0, -0.7998241186141968, 0.2997805178165436, 0.19791677594184875, 0.20107868313789368,
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-- [0.0, 0.0, -0.7744335532188416, 0.3094906806945801, 0.20305581390857697, 0.2066391408443451,
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-- [0.0, 0.0, -0.7498261332511902, 0.3196161985397339, 0.20836925506591797, 0.2124287486076355,
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-- [0.0, 0.0, -0.7259767055511475, 0.330165833234787, 0.2138499617576599, 0.21844694018363953,
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-- [0.0, 0.0, -0.7028602957725525, 0.3411475121974945, 0.21948887407779694, 0.22469212114810944,
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-- [0.0, 0.0, -0.6804531812667847, 0.3525686264038086, 0.22527512907981873, 0.2311616688966751,
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-  -0.6804531812667847, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6587321162223816, 0.3644353151321411, 0.23119540512561798, 0.23785120248794556,
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-- [0.0, 0.0, -0.6376755833625793, 0.376752644777298, 0.23723386228084564, 0.24475471675395966,
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-- [0.0, 0.0, -0.6172621846199036, 0.3895235061645508, 0.24337169528007507, 0.25186416506767273,
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-- [0.0, 0.0, -0.5974719524383545, 0.40274912118911743, 0.2495865374803543, 0.25916868448257446,
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+- [0.0, 0.0, -2.306413173675537, 0.16342006623744965, 0.1369123011827469, 0.13695918023586273,
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+  -0.018288379535079002, -0.0008565419702790678, 0.02082962915301323, 0.028925392776727676,
+  -0.011422806419432163, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.010446564294397831, -0.021331729367375374, 0.013421998359262943, -0.0036100083962082863,
+  -0.015268899500370026, -0.0007239296683110297, 0.01840796135365963, 0.026300307363271713,
+  -0.010446565225720406, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.009510123170912266, -0.019283650442957878, 0.011849727481603622, -0.003158372128382325,
+  -0.01261184923350811, -0.0005923781427554786, 0.01616840995848179, 0.023791221901774406,
+  -0.009510123170912266, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.008613583631813526, -0.017326146364212036, 0.010381162166595459, -0.0027411729097366333,
+  -0.010293715633451939, -0.0004642068815883249, 0.014105504378676414, 0.021399112418293953,
+  -0.0086135845631361, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.007757090497761965, -0.015462007373571396, 0.009016063064336777, -0.002358075464144349,
+  -0.008290430530905724, -0.0003415627288632095, 0.012213635258376598, 0.019124990329146385,
+  -0.007757090963423252, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00694080488756299, -0.013693788088858128, 0.007753963582217693, -0.002008614595979452,
+  -0.006577520631253719, -0.0002264244540128857, 0.010487011633813381, 0.016969837248325348,
+  -0.0069408053532242775, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006164954975247383, -0.012023855932056904, 0.0065942308865487576,
+  -0.001692193211056292, -0.005130337551236153, -0.00012059953587595373, 0.008919722400605679,
+  0.01493471022695303, -0.006164954975247383, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005429813172668219, -0.010454385541379452, 0.0055359951220452785,
+  -0.001408068579621613, -0.003924178890883923, -2.5706211090437137e-05, 0.007505699060857296,
+  0.013020713813602924, -0.005429813172668219, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004735718481242657, -0.008987355045974255, 0.004578148480504751, -0.001155346049927175,
+  -0.002934474730864167, 5.682831033482216e-05, 0.006238692905753851, 0.011229000054299831,
+  -0.004735718015581369, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0040831053629517555, -0.007624621037393808, 0.003719333093613386,
+  -0.0009329841705039144, -0.0021369813475757837, 0.0001257939584320411, 0.005112324375659227,
+  0.009560856968164444, -0.0040831053629517555, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0034725007135421038, -0.006367863155901432, 0.002957888413220644,
+  -0.0007397733861580491, -0.0015079365111887455, 0.0001802093320293352, 0.0041200220584869385,
+  0.008017652668058872, -0.0034725007135421038, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002904566703364253, -0.00521866837516427, 0.0022918502800166607, -0.0005743202054873109,
+  -0.0010242621647194028, 0.00021934453980065882, 0.0032550415489822626, 0.006600930821150541,
+  -0.0029045662377029657, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0023801280185580254, -0.004178531933575869, 0.0017188872443512082,
+  -0.0004350491217337549, -0.0006637463229708374, 0.0002427615545457229, 0.0025104533415287733,
+  0.005312430672347546, -0.0023801277857273817, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0019002227345481515, -0.0032488913275301456, 0.0012362486450001597,
+  -0.00032017441117204726, -0.0004052376316394657, 0.0002503675641492009, 0.0018791299080476165,
+  0.004154140595346689, -0.0019002229673787951, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0014661779860034585, -0.002431196393445134, 0.000840697786770761,
+  -0.00022768633789382875, -0.00022885488579049706, 0.00024247773399110883, 0.0013537403428927064,
+  0.0031283998396247625, -0.0014661782188341022, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010797050781548023, -0.0017269576201215386, 0.0005283892387524247,
+  -0.0001553230977151543, -0.00011619386350503191, 0.00021992676192894578, 0.0009267285349778831,
+  0.002237989567220211, -0.0010797049617394805, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0007430955301970243, -0.0011378959752619267, 0.000294724217383191,
+  -0.00010055392340291291, -5.056632653577253e-05, 0.00018424223526380956, 0.0005903394194319844,
+  0.0014863647520542145, -0.0007430954137817025, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004595293721649796, -0.0006661316729150712, 0.00013407066580839455,
+  -6.055389530956745e-05, -1.7248556105187163e-05, 0.00013794844562653452, 0.0003366422897670418,
+  0.000877970946021378, -0.0004595293430611491, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00023374040029011667, -0.00031462471815757453, 3.9268084947252646e-05,
+  -3.2220308639807627e-05, -3.7726056234532734e-06, 8.517845708411187e-05, 0.00015769174206070602,
+  0.0004189488245174289, -0.00023374040029011667, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -7.377251313300803e-05, -8.832968887872994e-05, 4.6725082825105346e-07,
+  -1.237015203514602e-05, -2.787790833735926e-07, 3.3221844205399975e-05, 4.615619400283322e-05,
+  0.00011895131319761276, -7.377251313300803e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 45
diff --git a/extra_tests/regression_fits/diagonal_45.json b/extra_tests/regression_fits/diagonal_45.json
index 8b87ceb346..fd464acbda 100644
--- a/extra_tests/regression_fits/diagonal_45.json
+++ b/extra_tests/regression_fits/diagonal_45.json
@@ -51,44 +51,44 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 3.3770644664764404,
-  "erf_vl": 3.2323124408721924,
-  "chi2": 2.2297255992889404,
+  "erf_tr": 3.3770620822906494,
+  "erf_vl": 3.2323102951049805,
+  "chi2": 2.229722023010254,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.3182267178222185,
-    1.54441465374414,
-    1.1791073518936193,
-    1.0015316488813237,
-    1.2179106362142496
+    1.318226912266057,
+    1.5444128182135202,
+    1.179107474257061,
+    1.0015316669311096,
+    1.2179101304602167
   ],
   "integrability": [
-    0.000898864207557748,
-    0.0008988642075570263,
-    4.724649568210726e-05,
-    0.462615229189395,
-    0.007050589891148817
+    0.0008988641238855122,
+    0.0008988641238834028,
+    4.724650636855898e-05,
+    0.46261481940746196,
+    0.0070505824987761034
   ],
   "timing": {
     "walltime": {
-      "Total": 17.62032151222229,
+      "Total": 18.131428241729736,
       "start": 0.0,
-      "replica_set": 0.3764665126800537,
-      "replica_fitted": 17.620244026184082,
-      "replica_set_to_replica_fitted": 17.24377751350403
+      "replica_set": 0.3876476287841797,
+      "replica_fitted": 18.131293058395386,
+      "replica_set_to_replica_fitted": 17.743645429611206
     },
     "cputime": {
-      "Total": 19.6138915,
+      "Total": 20.1227844,
       "start": 0.0,
-      "replica_set": 0.6932296000000004,
-      "replica_fitted": 19.6138119,
-      "replica_set_to_replica_fitted": 18.9205823
+      "replica_set": 0.704001100000001,
+      "replica_fitted": 20.1226482,
+      "replica_set_to_replica_fitted": 19.4186471
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post168.dev0+5adb0639b",
-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/feature_scaling_81.exportgrid b/extra_tests/regression_fits/feature_scaling_81.exportgrid
index f5f051df3f..bacc8df354 100644
--- a/extra_tests/regression_fits/feature_scaling_81.exportgrid
+++ b/extra_tests/regression_fits/feature_scaling_81.exportgrid
@@ -1,592 +1,592 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, 0.997025728225708, 0.42247551679611206, 0.4242808520793915, 0.4242810606956482,
-  0.062173016369342804, 0.4242996275424957, 0.42430007457733154, 0.4228055775165558,
-  0.997025728225708, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.965130090713501, 0.41094186902046204, 0.41292402148246765, 0.41292428970336914,
-  0.06504670530557632, 0.41294431686401367, 0.41294482350349426, 0.4113112986087799,
+- [0.0, 0.0, 0.9970256090164185, 0.4224754869937897, 0.4242808222770691, 0.4242810308933258,
+  0.06217297911643982, 0.42429959774017334, 0.42430004477500916, 0.422805517911911,
+  0.9970256090164185, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.965130090713501, 0.4109417796134949, 0.4129239618778229, 0.41292423009872437,
+  0.06504666060209274, 0.4129442572593689, 0.4129447638988495, 0.41131123900413513,
   0.965130090713501, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.9341124892234802, 0.3997729420661926, 0.40194931626319885, 0.40194955468177795,
-  0.06804734468460083, 0.4019712507724762, 0.40197187662124634, 0.4001864492893219,
-  0.9341124892234802, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.9039586186408997, 0.3889506161212921, 0.3913402855396271, 0.39134055376052856,
-  0.07118047773838043, 0.39136388897895813, 0.3913646340370178, 0.38941332697868347,
-  0.9039587378501892, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.8746535778045654, 0.37845852971076965, 0.3810824751853943, 0.3810828626155853,
-  0.07445184141397476, 0.381107896566391, 0.3811087906360626, 0.37897631525993347,
-  0.8746535778045654, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.8461817502975464, 0.3682803213596344, 0.3711616098880768, 0.3711620569229126,
-  0.07786741107702255, 0.37118902802467346, 0.3711901009082794, 0.3688596487045288,
-  0.8461817502975464, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.8185247182846069, 0.35840049386024475, 0.361564576625824, 0.36156514286994934,
-  0.08143347501754761, 0.3615940809249878, 0.36159542202949524, 0.3590487539768219,
-  0.8185247182846069, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.7916674017906189, 0.34880509972572327, 0.35227978229522705, 0.3522804379463196,
-  0.08515653759241104, 0.35231152176856995, 0.35231316089630127, 0.34953033924102783,
-  0.7916674017906189, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.7655916213989258, 0.33948034048080444, 0.34329620003700256, 0.3432970345020294,
-  0.08904335647821426, 0.34333035349845886, 0.34333232045173645, 0.3402916491031647,
-  0.7655915021896362, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.7402787804603577, 0.33041226863861084, 0.3346029818058014, 0.3346039950847626,
-  0.09310108423233032, 0.33463960886001587, 0.3346420228481293, 0.33131977915763855,
+- [0.0, 0.0, 0.9341123104095459, 0.39977285265922546, 0.4019491970539093, 0.4019494354724884,
+  0.06804729998111725, 0.40197113156318665, 0.4019717574119568, 0.4001863896846771,
+  0.9341123104095459, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.9039585590362549, 0.3889504373073578, 0.39134013652801514, 0.39134037494659424,
+  0.07118043303489685, 0.3913637101650238, 0.3913644850254059, 0.38941317796707153,
+  0.9039586782455444, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.8746534585952759, 0.3784584701061249, 0.3810824751853943, 0.3810828626155853,
+  0.07445178180932999, 0.381107896566391, 0.3811087906360626, 0.3789762556552887,
+  0.8746534585952759, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.8461816310882568, 0.368280291557312, 0.3711615800857544, 0.3711620271205902,
+  0.07786735147237778, 0.3711889982223511, 0.37119007110595703, 0.3688596189022064,
+  0.8461816310882568, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.8185245990753174, 0.3584004044532776, 0.3615644872188568, 0.3615650534629822,
+  0.08143341541290283, 0.36159399151802063, 0.3615953028202057, 0.35904866456985474,
+  0.8185245990753174, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.7916672825813293, 0.3488050401210785, 0.3522797226905823, 0.3522803485393524,
+  0.08515647053718567, 0.35231146216392517, 0.3523131012916565, 0.34953027963638306,
+  0.7916672825813293, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.765591561794281, 0.3394802510738373, 0.3432961106300354, 0.34329694509506226,
+  0.08904329687356949, 0.3433302640914917, 0.3433322310447693, 0.3402915596961975,
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+- [0.0, 0.0, 0.7402787804603577, 0.33041220903396606, 0.3346029222011566, 0.3346039354801178,
+  0.09310101717710495, 0.3346395492553711, 0.3346419632434845, 0.3313197195529938,
   0.7402786016464233, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.715711772441864, 0.32158881425857544, 0.32619139552116394, 0.3261926770210266,
-  0.09733705222606659, 0.32623061537742615, 0.32623353600502014, 0.32260382175445557,
-  0.7157118916511536, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.6918726563453674, 0.3129972219467163, 0.31805235147476196, 0.31805387139320374,
-  0.10175896435976028, 0.3180944323539734, 0.3180980086326599, 0.3141324818134308,
-  0.6918726563453674, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.6687429547309875, 0.30462488532066345, 0.3101772367954254, 0.31017911434173584,
-  0.10637491196393967, 0.31022214889526367, 0.3102265000343323, 0.3058944046497345,
-  0.6687429547309875, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.6463060975074768, 0.29645925760269165, 0.302558034658432, 0.30256029963493347,
-  0.11119324713945389, 0.3026060163974762, 0.30261126160621643, 0.2978789508342743,
-  0.6463060975074768, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.6245436072349548, 0.2884894013404846, 0.2951884865760803, 0.29519122838974,
-  0.11622272431850433, 0.29523974657058716, 0.2952461540699005, 0.29007694125175476,
-  0.6245436072349548, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.6034389138221741, 0.2807026207447052, 0.2880614101886749, 0.2880648076534271,
-  0.12147244811058044, 0.288115918636322, 0.2881236970424652, 0.2824775278568268,
+- [0.0, 0.0, 0.7157116532325745, 0.3215887248516083, 0.32619139552116394, 0.3261926770210266,
+  0.09733698517084122, 0.32623061537742615, 0.32623353600502014, 0.3226037621498108,
+  0.715711772441864, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.6918725371360779, 0.3129971921443939, 0.3180523216724396, 0.31805384159088135,
+  0.10175888985395432, 0.318094402551651, 0.3180979788303375, 0.314132422208786, 0.6918725371360779,
+  0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.6687428951263428, 0.3046248257160187, 0.31017717719078064, 0.31017905473709106,
+  0.1063748374581337, 0.3102220892906189, 0.3102264404296875, 0.3058943450450897,
+  0.6687428951263428, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.646306037902832, 0.2964591979980469, 0.30255797505378723, 0.3025602400302887,
+  0.11119317263364792, 0.3026059567928314, 0.30261120200157166, 0.2978788912296295,
+  0.646306037902832, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.6245435476303101, 0.28848931193351746, 0.29518839716911316, 0.2951911687850952,
+  0.11622263491153717, 0.29523965716362, 0.29524606466293335, 0.2900768518447876,
+  0.6245435476303101, 0.0, 0.0, 0.0]
+- [0.0, 0.0, 0.6034389138221741, 0.2807025611400604, 0.28806132078170776, 0.28806477785110474,
+  0.12147235870361328, 0.28811588883399963, 0.28812363743782043, 0.282477468252182,
   0.6034389138221741, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.5829735398292542, 0.2730865776538849, 0.2811703085899353, 0.2811744809150696,
-  0.12695200741291046, 0.28122833371162415, 0.28123775124549866, 0.27507099509239197,
-  0.5829735398292542, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.5631319880485535, 0.2656301259994507, 0.2745105028152466, 0.2745155990123749,
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+- [0.0, 0.0, -0.007258783094584942, -0.18766848742961884, -0.17469240725040436, 0.49565598368644714,
+  -0.3999912738800049, 0.7614696621894836, -0.06569922715425491, -0.27595803141593933,
+  -0.007258785888552666, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.007189908996224403, -0.1780310571193695, -0.1665094643831253, 0.4700365364551544,
+  -0.3814540505409241, 0.7263824939727783, -0.06154956668615341, -0.2657800018787384,
+  -0.007189910393208265, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.007105415686964989, -0.1681308001279831, -0.15815307199954987, 0.44404539465904236,
+  -0.3625134825706482, 0.690747082233429, -0.05707819014787674, -0.2555252015590668,
+  -0.007105416618287563, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00700386380776763, -0.15800800919532776, -0.14964428544044495, 0.41775745153427124,
+  -0.3432183265686035, 0.6546259522438049, -0.052332554012537, -0.2451731413602829,
+  -0.007003867533057928, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006883678492158651, -0.14771094918251038, -0.14100773632526398, 0.3912612795829773,
+  -0.32362863421440125, 0.6180959343910217, -0.047368112951517105, -0.23470285534858704,
+  -0.0068836756981909275, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006743332836776972, -0.13729062676429749, -0.1322716325521469, 0.3646526336669922,
+  -0.303806334733963, 0.581243634223938, -0.04224451258778572, -0.22409461438655853,
+  -0.006743333768099546, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006581289693713188, -0.1268063634634018, -0.12346642464399338, 0.3380393087863922,
+  -0.28382423520088196, 0.5441651940345764, -0.037028755992650986, -0.21332529187202454,
+  -0.006581287365406752, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006396039389073849, -0.1163199245929718, -0.11462518572807312, 0.3115346133708954,
+  -0.26375699043273926, 0.5069648623466492, -0.031790975481271744, -0.20237354934215546,
+  -0.006396040320396423, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006186164449900389, -0.10589559376239777, -0.10578383505344391, 0.2852574586868286,
+  -0.2436857968568802, 0.46975448727607727, -0.02660585753619671, -0.19121845066547394,
+  -0.006186165381222963, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005950323771685362, -0.09560240060091019, -0.09697827696800232, 0.259331613779068,
+  -0.22369185090065002, 0.43264833092689514, -0.021551009267568588, -0.17983724176883698,
+  -0.005950325634330511, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005687213037163019, -0.08550941199064255, -0.08824649453163147, 0.2338821440935135,
+  -0.20385950803756714, 0.39576420187950134, -0.016705138608813286, -0.1682083159685135,
+  -0.005687211640179157, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005393573548644781, -0.07560788094997406, -0.07955380529165268, 0.20883814990520477,
+  -0.18412171304225922, 0.3589315414428711, -0.0121067576110363, -0.15621598064899445,
+  -0.005393571685999632, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005015058442950249, -0.06443560868501663, -0.06946643441915512, 0.18041154742240906,
+  -0.16146843135356903, 0.31630417704582214, -0.007098678033798933, -0.14174993336200714,
+  -0.005015059839934111, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.004528959281742573, -0.0522780604660511, -0.058145977556705475, 0.14914563298225403,
-  -0.1361141800880432, 0.26819685101509094, -0.0020812659058719873, -0.12454032152891159,
+  -0.13611407577991486, 0.26819685101509094, -0.0020812659058719873, -0.12454032152891159,
   -0.00452895974740386, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.0039394875057041645, -0.04016786441206932, -0.04645965248346329, 0.1174611896276474,
-  -0.10977187007665634, 0.21778720617294312, 0.0021689727436751127, -0.10530885308980942,
+  -0.10977178812026978, 0.21778720617294312, 0.0021689727436751127, -0.10530885308980942,
   -0.003939487040042877, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.0032570683397352695, -0.028924373909831047, -0.035096604377031326,
-  0.08727145940065384, -0.08384823054075241, 0.16767007112503052, 0.005067787598818541,
+  0.08727145940065384, -0.08384816348552704, 0.16767007112503052, 0.005067787598818541,
   -0.0847068727016449, -0.0032570683397352695, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0024984569754451513, -0.019102437421679497, -0.02454613521695137,
-  0.05990167334675789, -0.059383004903793335, 0.11978520452976227, 0.006280406843870878,
+- [0.0, 0.0, -0.0024984569754451513, -0.019102437421679497, -0.024546142667531967,
+  0.05990169197320938, -0.05938296020030975, 0.11978521943092346, 0.006280398927628994,
   -0.06333517283201218, -0.002498456509783864, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0016857030568644404, -0.010992088355123997, -0.01510770432651043,
-  0.03610819950699806, -0.03705302253365517, 0.07543980330228806, 0.005725583527237177,
+- [0.0, 0.0, -0.0016857030568644404, -0.010992088355123997, -0.015107709914445877,
+  0.03610820695757866, -0.03705299645662308, 0.07543981075286865, 0.005725577473640442,
   -0.0417548343539238, -0.0016857030568644404, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0008439917583018541, -0.0046595982275903225, -0.00692000100389123,
-  0.016169007867574692, -0.01721937209367752, 0.035397157073020935, 0.003535676747560501,
+- [0.0, 0.0, -0.0008439917583018541, -0.0046595982275903225, -0.006920007988810539,
+  0.016169017180800438, -0.017219359055161476, 0.03539716452360153, 0.0035356697626411915,
   -0.02048454061150551, -0.0008439916418865323, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -2.368475909392639e-16, -1.601309236320958e-07, 2.2830751333913213e-07,
-  -3.536858272923382e-08, 2.679534247818083e-07, -9.377481546835043e-08, -1.7863698076325818e-07,
+  -3.536858272923382e-08, 2.6795322582984227e-07, -9.377481546835043e-08, -1.7863698076325818e-07,
   2.396037928065198e-07, 2.368475909392639e-16, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 81
diff --git a/extra_tests/regression_fits/feature_scaling_81.json b/extra_tests/regression_fits/feature_scaling_81.json
index fa77d5a984..72f073386b 100644
--- a/extra_tests/regression_fits/feature_scaling_81.json
+++ b/extra_tests/regression_fits/feature_scaling_81.json
@@ -51,44 +51,44 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 2.490976572036743,
-  "erf_vl": 2.0566506385803223,
-  "chi2": 1.4108951091766357,
+  "erf_tr": 2.4909772872924805,
+  "erf_vl": 2.056650400161743,
+  "chi2": 1.410895824432373,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.9705579690885773,
-    1.512324164715868,
-    1.2608150353204404,
-    1.1147020004036432,
-    2.925581113420889
+    1.970557910248621,
+    1.5123234861956554,
+    1.260815035320441,
+    1.1147019998011942,
+    2.9255811134208907
   ],
   "integrability": [
-    0.0038688098720738584,
-    0.003868809872073914,
-    2.2851325695821822e-05,
-    0.05472333077341307,
-    0.006996778654865254
+    0.0038688098720747743,
+    0.003868809872073886,
+    2.2851325695849578e-05,
+    0.05472333077341318,
+    0.006996780051849116
   ],
   "timing": {
     "walltime": {
-      "Total": 17.96898365020752,
+      "Total": 18.211228370666504,
       "start": 0.0,
-      "replica_set": 0.3639094829559326,
-      "replica_fitted": 17.968825101852417,
-      "replica_set_to_replica_fitted": 17.604915618896484
+      "replica_set": 0.39786696434020996,
+      "replica_fitted": 18.211086988449097,
+      "replica_set_to_replica_fitted": 17.813220024108887
     },
     "cputime": {
-      "Total": 19.9091685,
+      "Total": 20.0817579,
       "start": 0.0,
-      "replica_set": 0.6803557000000007,
-      "replica_fitted": 19.9090083,
-      "replica_set_to_replica_fitted": 19.2286526
+      "replica_set": 0.7005326000000007,
+      "replica_fitted": 20.081615399999997,
+      "replica_set_to_replica_fitted": 19.381082799999998
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post168.dev0+5adb0639b",
-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/flavour_29.json b/extra_tests/regression_fits/flavour_29.json
index bc5cc8c99d..871aa030f7 100644
--- a/extra_tests/regression_fits/flavour_29.json
+++ b/extra_tests/regression_fits/flavour_29.json
@@ -71,24 +71,24 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 7.240033864974976,
+      "Total": 7.520705223083496,
       "start": 0.0,
-      "replica_set": 0.37552475929260254,
-      "replica_fitted": 7.239804267883301,
-      "replica_set_to_replica_fitted": 6.864279508590698
+      "replica_set": 0.3701026439666748,
+      "replica_fitted": 7.520532608032227,
+      "replica_set_to_replica_fitted": 7.150429964065552
     },
     "cputime": {
-      "Total": 7.8813866,
+      "Total": 8.128277999999998,
       "start": 0.0,
-      "replica_set": 0.6917157000000005,
-      "replica_fitted": 7.8811553000000005,
-      "replica_set_to_replica_fitted": 7.1894396
+      "replica_set": 0.6848363999999991,
+      "replica_fitted": 8.1281039,
+      "replica_set_to_replica_fitted": 7.443267500000001
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post168.dev0+5adb0639b",
-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/no_lagrange_27.exportgrid b/extra_tests/regression_fits/no_lagrange_27.exportgrid
index d2139b3220..44109e223d 100644
--- a/extra_tests/regression_fits/no_lagrange_27.exportgrid
+++ b/extra_tests/regression_fits/no_lagrange_27.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.2586045265197754, 0.031726639717817307, 0.004528982564806938, 0.004577429965138435,
-  -16.76598358154297, 0.004731909371912479, 0.004684989806264639, 0.03147998824715614,
-  -2.2586045265197754, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1874330043792725, 0.03509604185819626, 0.006809327285736799, 0.006864415947347879,
-  -16.777868270874023, 0.007035227958112955, 0.006981979124248028, 0.034825485199689865,
-  -2.1874330043792725, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1185076236724854, 0.03860752284526825, 0.009186828508973122, 0.009249480441212654,
-  -16.788347244262695, 0.009438387118279934, 0.009377952665090561, 0.03831074759364128,
-  -2.1185076236724854, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0517561435699463, 0.042263396084308624, 0.01166181918233633, 0.01173308864235878,
-  -16.797321319580078, 0.01194205041974783, 0.011873448267579079, 0.04193789139389992,
-  -2.0517561435699463, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9871093034744263, 0.046066656708717346, 0.01423530001193285, 0.014316314831376076,
-  -16.80467414855957, 0.014547505415976048, 0.014469700865447521, 0.04570965841412544,
-  -1.9871095418930054, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9245011806488037, 0.050019241869449615, 0.01690688356757164, 0.016999032348394394,
-  -16.81031036376953, 0.017254866659641266, 0.017166581004858017, 0.049627725034952164,
-  -1.9245014190673828, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8638664484024048, 0.05412517488002777, 0.019678397104144096, 0.019783146679401398,
-  -16.8140926361084, 0.020066309720277786, 0.019966209307312965, 0.05369583144783974,
-  -1.8638662099838257, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8051422834396362, 0.058387432247400284, 0.02255026251077652, 0.022669412195682526,
-  -16.815900802612305, 0.022982889786362648, 0.02286934293806553, 0.057916656136512756,
-  -1.8051422834396362, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7482682466506958, 0.06280998885631561, 0.025524016469717026, 0.025659438222646713,
-  -16.815587997436523, 0.026006551459431648, 0.02587786875665188, 0.06229378655552864,
-  -1.748268485069275, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6931854486465454, 0.06739666312932968, 0.02860063686966896, 0.028754644095897675,
-  -16.813011169433594, 0.0291390772908926, 0.028993185609579086, 0.06683070957660675,
-  -1.6931854486465454, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6398369073867798, 0.07215236127376556, 0.03178221732378006, 0.03195736184716225,
-  -16.808000564575195, 0.03238323703408241, 0.032217856496572495, 0.07153186947107315,
-  -1.6398369073867798, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5881669521331787, 0.07708141952753067, 0.03507009521126747, 0.03526921197772026,
-  -16.80039405822754, 0.03574110567569733, 0.03555373474955559, 0.07640119642019272,
-  -1.5881671905517578, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5381226539611816, 0.08218872547149658, 0.038465917110443115, 0.03869233652949333,
-  -16.790002822875977, 0.0392153300344944, 0.03900305926799774, 0.08144309371709824,
-  -1.5381226539611816, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4896515607833862, 0.08748000115156174, 0.04197200760245323, 0.04222945496439934,
-  -16.77663803100586, 0.04280923306941986, 0.04256879538297653, 0.0866626724600792,
-  -1.4896515607833862, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4427040815353394, 0.09296058863401413, 0.04559015482664108, 0.04588283598423004,
-  -16.76007652282715, 0.04652570188045502, 0.04625349119305611, 0.0920647531747818,
-  -1.4427038431167603, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3972309827804565, 0.09863675385713577, 0.04932274669408798, 0.049655523151159286,
-  -16.740108489990234, 0.050368525087833405, 0.050060369074344635, 0.09765490144491196,
-  -1.3972313404083252, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3531851768493652, 0.10451453179121017, 0.0531717985868454, 0.0535501204431057,
-  -16.71648406982422, 0.05434109643101692, 0.05399240180850029, 0.10343847423791885,
-  -1.3531851768493652, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3105212450027466, 0.11060114204883575, 0.05714021623134613, 0.05757030472159386,
-  -16.68894386291504, 0.05844801291823387, 0.05805355682969093, 0.10942188650369644,
-  -1.3105212450027466, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.269194483757019, 0.11690317094326019, 0.06122996658086777, 0.0617188923060894,
-  -16.65721321105957, 0.06269308179616928, 0.06224702298641205, 0.11561089009046555,
-  -1.269194483757019, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2291626930236816, 0.1234283372759819, 0.06544392555952072, 0.06599968671798706,
-  -16.621002197265625, 0.06708124279975891, 0.06657702475786209, 0.12201225757598877,
-  -1.2291626930236816, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1903833150863647, 0.1301843225955963, 0.06978451460599899, 0.07041622698307037,
-  -16.579978942871094, 0.07161732017993927, 0.0710475891828537, 0.12863264977931976,
-  -1.1903833150863647, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1528165340423584, 0.13717932999134064, 0.07425437867641449, 0.07497238367795944,
-  -16.533809661865234, 0.07630649209022522, 0.07566303759813309, 0.1354791224002838,
-  -1.1528165340423584, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1164228916168213, 0.14442194998264313, 0.07885612547397614, 0.07967217266559601,
-  -16.482135772705078, 0.0811544805765152, 0.08042804896831512, 0.14255903661251068,
-  -1.1164228916168213, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.081164836883545, 0.1519210785627365, 0.08359239995479584, 0.08451973646879196,
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-  -0.0076299915090203285, -0.0003363830328453332, 0.01234579086303711, 0.019586192443966866,
-  -0.007516765501350164, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0067239380441606045, -0.013576099649071693, 0.008320383727550507,
-  -0.0016203082632273436, -0.006057800725102425, -0.0002170808002119884, 0.010607472620904446,
-  0.01738579012453556, -0.006723937578499317, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.005970462691038847, -0.011914538219571114, 0.007096795830875635, -0.0013390131061896682,
-  -0.004728228785097599, -0.00010765573824755847, 0.009028777480125427, 0.015306835994124413,
-  -0.005970461759716272, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.005256631411612034, -0.010353267192840576, 0.005978165660053492, -0.001089565921574831,
-  -0.0036190582904964685, -9.763737580215093e-06, 0.007603679783642292, 0.013350595720112324,
-  -0.005256631411612034, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0045827943831682205, -0.008894342929124832, 0.004963410086929798,
-  -0.0008709261892363429, -0.0027081063017249107, 7.51448460505344e-05, 0.006325974129140377,
-  0.011518382467329502, -0.0045827943831682205, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.003949393052607775, -0.007539683952927589, 0.004051202908158302, -0.0006819010013714433,
-  -0.001973418053239584, 0.00014583639858756214, 0.005189317744225264, 0.009811634197831154,
-  -0.003949393052607775, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.003356955712661147, -0.006291032303124666, 0.0032399233896285295,
-  -0.0005211122334003448, -0.0013934109592810273, 0.0002013064658967778, 0.004187168087810278,
-  0.008231881074607372, -0.003356955712661147, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.002806141972541809, -0.005150010343641043, 0.0025276481173932552,
-  -0.0003869914507959038, -0.0009470650693401694, 0.00024081621086224914, 0.00331281335093081,
-  0.006780819036066532, -0.002806141972541809, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0022977665066719055, -0.004118136130273342, 0.001912095700390637,
-  -0.00027776870410889387, -0.0006140987970866263, 0.000263926136540249, 0.0025593528989702463,
-  0.0054603382013738155, -0.002297766041010618, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.00183284527156502, -0.0031968525145202875, 0.0013905802043154836,
-  -0.00019144026737194508, -0.000375153060304001, 0.00027054143720306456, 0.0019196727080270648,
-  0.0042725820094347, -0.0018328457372263074, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0014126749010756612, -0.0023875883780419827, 0.0009599461918696761,
-  -0.00012575523578561842, -0.00021199058392085135, 0.0002609961957205087, 0.0013864663196727633,
-  0.0032200515270233154, -0.0014126751339063048, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0010389175731688738, -0.0016918065957725048, 0.0006164539372548461,
-  -7.817617006367072e-05, -0.00010769426444312558, 0.0002361559309065342, 0.0009521948522888124,
-  0.0023056971840560436, -0.0010389175731688738, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0007137911161407828, -0.0011111331405118108, 0.0003556484298314899,
-  -4.5844495616620407e-05, -4.6894216211512685e-05, 0.00019760489522013813, 0.0006091265822760761,
-  0.0015331616159528494, -0.0007137912907637656, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0004403645289130509, -0.0006475350237451494, 0.00017210117948707193,
-  -2.5534518499625847e-05, -1.6004962162696756e-05, 0.00014796429604757577, 0.0003493709082249552,
-  0.000907116336748004, -0.00044036449980922043, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0002231881517218426, -0.00030370691092684865, 5.89668306929525e-05,
-  -1.3609058441943489e-05, -3.502539129840443e-06, 9.152988059213385e-05, 0.0001650552439969033,
-  0.0004339909937698394, -0.00022318816627375782, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -6.99609299772419e-05, -8.410295413341373e-05, 6.957601272006286e-06,
-  -6.071605639590416e-06, -2.5896255806401314e-07, 3.590836422517896e-05, 4.902734872302972e-05,
-  0.00012388979666866362, -6.99609299772419e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.017572401091456413, -0.03766382858157158, 0.028805943205952644, -0.006965868640691042,
+  -0.04129317030310631, -0.0015836694510653615, 0.03972311317920685, 0.04800661280751228,
+  -0.017572401091456413, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.016394438222050667, -0.03509944677352905, 0.026414964348077774, -0.006307180039584637,
+  -0.03617781028151512, -0.0014946588780730963, 0.036091260612010956, 0.04465806856751442,
+  -0.016394440084695816, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.015254548750817776, -0.032597143203020096, 0.024127887561917305, -0.0056824167259037495,
+  -0.031494542956352234, -0.0013896108139306307, 0.03267071768641472, 0.04141857847571373,
+  -0.015254546888172626, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.014152820222079754, -0.030161825940012932, 0.021945632994174957, -0.005092052277177572,
+  -0.02722945436835289, -0.0012718370417132974, 0.02945706993341446, 0.03828955441713333,
+  -0.014152818359434605, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.013089331798255444, -0.027798039838671684, 0.019868973642587662, -0.0045364052057266235,
+  -0.02336704172194004, -0.0011444975389167666, 0.026445679366588593, 0.035272348672151566,
+  -0.013089331798255444, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.012064170092344284, -0.02551003359258175, 0.017898524180054665, -0.004015688318759203,
+  -0.019890500232577324, -0.0010105848778039217, 0.023631755262613297, 0.03236822411417961,
+  -0.012064170092344284, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.011077417992055416, -0.023301774635910988, 0.016034748405218124, -0.0035299768205732107,
+  -0.016781751066446304, -0.0008729498367756605, 0.021010370925068855, 0.029578428715467453,
+  -0.011077417992055416, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.010129177942872047, -0.021176939830183983, 0.01427793875336647, -0.0030792260076850653,
+  -0.014021715149283409, -0.0007342726457864046, 0.018576407805085182, 0.026904167607426643,
+  -0.010129177942872047, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.009219557978212833, -0.019138919189572334, 0.01262823585420847, -0.0026632610242813826,
+  -0.011590355075895786, -0.0005970718339085579, 0.016324620693922043, 0.024346599355340004,
+  -0.009219557978212833, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.008348697796463966, -0.017190881073474884, 0.011085589416325092, -0.002281768713146448,
+  -0.009466909803450108, -0.0004637008532881737, 0.014249605126678944, 0.021906916052103043,
+  -0.008348697796463966, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.007516759913414717, -0.015335740521550179, 0.009649788960814476, -0.001934309839271009,
+  -0.007630010135471821, -0.0003363537252880633, 0.012345810420811176, 0.019586296752095222,
+  -0.007516759913414717, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006723932456225157, -0.013576147146522999, 0.008320406079292297, -0.0016202934784814715,
+  -0.006057816091924906, -0.00021705373364966363, 0.010607492178678513, 0.017385883256793022,
+  -0.006723933387547731, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005970459897071123, -0.01191458385437727, 0.007096811663359404, -0.0013390027452260256,
+  -0.004728242289274931, -0.00010763164755189791, 0.00902879610657692, 0.015306920744478703,
+  -0.005970458500087261, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005256627686321735, -0.010353305377066135, 0.005978181958198547, -0.0010895535815507174,
+  -0.0036190669052302837, -9.74191334535135e-06, 0.007603697013109922, 0.013350670225918293,
+  -0.0052566262893378735, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0045827897265553474, -0.008894374594092369, 0.00496342359110713, -0.0008709157700650394,
+  -0.002708112122491002, 7.516530604334548e-05, 0.00632599089294672, 0.011518445797264576,
+  -0.0045827897265553474, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003949389792978764, -0.00753971328958869, 0.004051214084029198, -0.0006818916881456971,
+  -0.0019734231755137444, 0.00014585194003302604, 0.005189329851418734, 0.009811689145863056,
+  -0.003949389792978764, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003356953151524067, -0.006291055586189032, 0.0032399340998381376,
+  -0.0005211042589507997, -0.0013934143353253603, 0.0002013208722928539, 0.0041871811263263226,
+  0.008231927640736103, -0.0033569526858627796, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0028061389457434416, -0.005150028970092535, 0.002527655567973852,
+  -0.00038698577554896474, -0.0009470674558542669, 0.0002408301952527836, 0.003312826156616211,
+  0.006780857685953379, -0.002806139411404729, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002297763479873538, -0.004118151962757111, 0.0019121022196486592,
+  -0.000277762912446633, -0.00061410031048581, 0.0002639367594383657, 0.002559361746534705,
+  0.005460371263325214, -0.002297763479873538, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0018328434089198709, -0.0031968627590686083, 0.0013905850937590003,
+  -0.00019143597455695271, -0.0003751539043150842, 0.0002705518272705376, 0.00191968260332942,
+  0.004272608086466789, -0.001832843292504549, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0014126733876764774, -0.002387598156929016, 0.0009599495097063482,
+  -0.0001257522526429966, -0.00021199110778979957, 0.00026100382092408836, 0.0013864737702533603,
+  0.0032200724817812443, -0.001412673620507121, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010389158269390464, -0.0016918126493692398, 0.000616456673014909,
+  -7.817376899765804e-05, -0.00010769451910164207, 0.0002361623919568956, 0.000952201196923852,
+  0.002305712318047881, -0.0010389159433543682, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0007137901266105473, -0.0011111374478787184, 0.0003556498559191823,
+  -4.58432623418048e-05, -4.6894328988855705e-05, 0.0001976095518330112, 0.0006091312388889492,
+  0.0015331722097471356, -0.0007137901266105473, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004403635975904763, -0.0006475372356362641, 0.00017210222722496837,
+  -2.5533528969390318e-05, -1.6004998542484827e-05, 0.00014796745381318033, 0.00034937405143864453,
+  0.0009071227395907044, -0.0004403636557981372, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00022318765695672482, -0.0003037077549379319, 5.896746370126493e-05,
+  -1.3608444533019792e-05, -3.502546405798057e-06, 9.153143764706329e-05, 0.00016505680105183274,
+  0.00043399399146437645, -0.00022318765695672482, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.99607262504287e-05, -8.410315058426932e-05, 6.957801360840676e-06,
+  -6.071408733987482e-06, -2.5896312649820175e-07, 3.5908953577745706e-05, 4.902794535155408e-05,
+  0.00012389077164698392, -6.996071897447109e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 27
diff --git a/extra_tests/regression_fits/no_lagrange_27.json b/extra_tests/regression_fits/no_lagrange_27.json
index aae13af206..ac8acfd4df 100644
--- a/extra_tests/regression_fits/no_lagrange_27.json
+++ b/extra_tests/regression_fits/no_lagrange_27.json
@@ -51,44 +51,44 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1098,
-  "erf_tr": 2.8000125885009766,
-  "erf_vl": 2.488626718521118,
-  "chi2": 2.0644302368164062,
+  "erf_tr": 2.8000152111053467,
+  "erf_vl": 2.48862624168396,
+  "chi2": 2.0644352436065674,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.3221023191915289,
-    1.4870345587210063,
-    1.1735323019190385,
-    1.0005950030908517,
-    1.221984399084671
+    1.3221020624883704,
+    1.4870359495902816,
+    1.1735315998209264,
+    1.0005949415170394,
+    1.2219866415152165
   ],
   "integrability": [
-    0.0009426986289356454,
-    0.0009426986289332584,
-    5.00080153632565e-05,
-    0.474627502262591,
-    0.007130859827155556
+    0.0009427009790689833,
+    0.0009427009790676788,
+    5.000833846158237e-05,
+    0.47462602704763324,
+    0.007130771817171588
   ],
   "timing": {
     "walltime": {
-      "Total": 21.26565957069397,
+      "Total": 22.511044025421143,
       "start": 0.0,
-      "replica_set": 0.365405797958374,
-      "replica_fitted": 21.265546083450317,
-      "replica_set_to_replica_fitted": 20.900140285491943
+      "replica_set": 0.35729169845581055,
+      "replica_fitted": 22.51093602180481,
+      "replica_set_to_replica_fitted": 22.153644323349
     },
     "cputime": {
-      "Total": 23.1746251,
+      "Total": 24.3750598,
       "start": 0.0,
-      "replica_set": 0.6833834000000003,
-      "replica_fitted": 23.1745104,
-      "replica_set_to_replica_fitted": 22.491127
+      "replica_set": 0.6750459000000006,
+      "replica_fitted": 24.3749498,
+      "replica_set_to_replica_fitted": 23.6999039
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post168.dev0+5adb0639b",
-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/no_msr_92.exportgrid b/extra_tests/regression_fits/no_msr_92.exportgrid
index 96642f50db..89cf717c78 100644
--- a/extra_tests/regression_fits/no_msr_92.exportgrid
+++ b/extra_tests/regression_fits/no_msr_92.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.436049222946167, 0.5029186010360718, 0.4756280779838562, 0.4756723940372467,
-  -0.5346566438674927, 0.4758351147174835, 0.47579219937324524, 0.5026591420173645,
-  -2.436049222946167, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.3587565422058105, 0.49267613887786865, 0.46429160237312317, 0.4643419682979584,
-  -0.5346137881278992, 0.4645218253135681, 0.46447324752807617, 0.4923914968967438,
+- [0.0, 0.0, -2.436048984527588, 0.5029179453849792, 0.47562751173973083, 0.47567182779312134,
+  -0.5346566438674927, 0.47583451867103577, 0.4757916033267975, 0.502658486366272,
+  -2.436048984527588, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.3587565422058105, 0.49267563223838806, 0.4642910957336426, 0.46434152126312256,
+  -0.5346137881278992, 0.4645213782787323, 0.4644727408885956, 0.4923909902572632,
   -2.3587565422058105, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2839322090148926, 0.4830087721347809, 0.45348507165908813, 0.4535422921180725,
-  -0.5345005989074707, 0.4537412226200104, 0.45368605852127075, 0.4826965928077698,
-  -2.2839317321777344, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2114970684051514, 0.47390520572662354, 0.4431951642036438, 0.4432602524757385,
-  -0.5343125462532043, 0.44348031282424927, 0.4434177279472351, 0.47356289625167847,
-  -2.211496591567993, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1413755416870117, 0.46535608172416687, 0.4334104359149933, 0.43348437547683716,
-  -0.5340442061424255, 0.43372780084609985, 0.4336569011211395, 0.4649806618690491,
-  -2.1413750648498535, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0734925270080566, 0.45735087990760803, 0.4241181015968323, 0.4242021441459656,
-  -0.5336904525756836, 0.42447158694267273, 0.42439112067222595, 0.4569392204284668,
+- [0.0, 0.0, -2.2839324474334717, 0.48300841450691223, 0.4534847140312195, 0.45354193449020386,
+  -0.5345005989074707, 0.4537408947944641, 0.4536857008934021, 0.4826962351799011,
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+  -0.00071636529173702, 0.004708305466920137, 0.039352431893348694, 0.04381523281335831,
   -0.015983734279870987, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.014807788655161858, -0.025861691683530807, 0.022075235843658447, -0.005682544782757759,
-  -0.0006256871274672449, 0.004430473782122135, 0.035695645958185196, 0.04057187959551811,
-  -0.014807790517807007, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.01367407850921154, -0.023846514523029327, 0.02000480890274048, -0.005049563478678465,
-  -0.0005421940586529672, 0.004170515108853579, 0.03225070983171463, 0.037438735365867615,
-  -0.01367407850921154, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.012582681141793728, -0.02189153991639614, 0.018040090799331665, -0.004455771762877703,
-  -0.00046585893142037094, 0.003925913944840431, 0.029013486579060555, 0.034417394548654556,
-  -0.012582683935761452, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.011533679440617561, -0.020000897347927094, 0.016181401908397675, -0.0039014704525470734,
-  -0.00039658884634263813, 0.003694316605105996, 0.02597968466579914, 0.03150942549109459,
-  -0.011533676646649837, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.010527150705456734, -0.01817842572927475, 0.014428910799324512, -0.003386780619621277,
-  -0.00033422926208004355, 0.003473520278930664, 0.023144811391830444, 0.028716368600726128,
-  -0.010527150705456734, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.009563207626342773, -0.016427693888545036, 0.012782620266079903, -0.0029117008671164513,
-  -0.0002785706310532987, 0.0032614900264889, 0.02050425484776497, 0.026039738208055496,
-  -0.009563205763697624, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.008641955442726612, -0.014752032235264778, 0.01124237384647131, -0.0024760409723967314,
-  -0.0002293534344062209, 0.0030563287436962128, 0.01805318146944046, 0.02348104491829872,
-  -0.008641954511404037, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.007763552479445934, -0.013154522515833378, 0.009807835333049297, -0.0020794745068997145,
-  -0.00018627381359692663, 0.0028563414234668016, 0.015786653384566307, 0.021041832864284515,
-  -0.007763552479445934, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.006928155664354563, -0.011637980118393898, 0.00847847294062376, -0.0017214871477335691,
-  -0.00014898771769367158, 0.002659987658262253, 0.013699499890208244, 0.01872359775006771,
-  -0.006928155664354563, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.006135988514870405, -0.010205043479800224, 0.0072535742074251175,
-  -0.0014014156768098474, -0.0001171187759609893, 0.0024659272748976946, 0.011786450631916523,
-  0.01652795448899269, -0.006135988049209118, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.005387314595282078, -0.00885811448097229, 0.006132219452410936, -0.0011184073518961668,
-  -9.026244515553117e-05, 0.0022730189375579357, 0.010042057372629642, 0.01445652823895216,
-  -0.005387315060943365, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.004682452417910099, -0.0075993905775249004, 0.005113252904266119,
-  -0.000871420546900481, -6.799188122386113e-05, 0.0020803366787731647, 0.008460699580609798,
-  0.012511027045547962, -0.004682452417910099, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.004021810367703438, -0.006430902052670717, 0.00419530039653182, -0.0006592247518710792,
-  -4.986461499356665e-05, 0.0018871984211727977, 0.007036624941974878, 0.010693293064832687,
-  -0.004021810367703438, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0034058766905218363, -0.0053544919937849045, 0.003376698587089777,
-  -0.00048037603846751153, -3.5427558032097295e-05, 0.0016931943828240037, 0.005763907451182604,
-  0.009005282074213028, -0.00340587692335248, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0028352648951113224, -0.004371849820017815, 0.0026555065996944904,
-  -0.00033320175134576857, -2.4223780201282352e-05, 0.0014982157154008746, 0.004636469762772322,
-  0.007449144497513771, -0.0028352648951113224, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.002310738433152437, -0.003484537126496434, 0.0020294554997235537,
-  -0.00021578193991445005, -1.5798503227415495e-05, 0.0013025127118453383, 0.0036480852868407965,
-  0.006027275696396828, -0.0023107388988137245, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0018332541221752763, -0.002693992340937257, 0.0014958946267142892,
-  -0.00012592315033543855, -9.705580851004925e-06, 0.001106772106140852, 0.0027923868037760258,
-  0.0047423760406672955, -0.0018332544714212418, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0014040329260751605, -0.0020015875343233347, 0.0010517493356019258,
-  -6.111864786362275e-05, -5.514273652806878e-06, 0.0009122195187956095, 0.002062898827716708,
-  0.003597593866288662, -0.0014040329260751605, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0010246438905596733, -0.0014086527517065406, 0.0006934127886779606,
-  -1.8502647435525432e-05, -2.816112100845203e-06, 0.0007207721937447786, 0.0014530462212860584,
-  0.002596649108454585, -0.0010246438905596733, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0006971847615204751, -0.0009165705414488912, 0.0004166446451563388,
-  5.217645593802445e-06, -1.232516297022812e-06, 0.0005353152519091964, 0.0009562805644236505,
-  0.0017441519303247333, -0.0006971846451051533, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0004245503805577755, -0.000526891031768173, 0.00021636120800394565,
-  1.3864385437045712e-05, -4.2274362499483686e-07, 0.0003601557691581547, 0.0005662397597916424,
-  0.0010460607009008527, -0.00042455040966160595, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0002110152563545853, -0.00024158031737897545, 8.629774674773216e-05,
-  1.1947815437451936e-05, -9.295886371774031e-08, 0.0002019732928602025, 0.00027722661616280675,
-  0.0005106807802803814, -0.0002110152563545853, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -6.37346674920991e-05, -6.366728484863415e-05, 1.8300721421837807e-05,
-  4.955136319040321e-06, -6.9050871687181825e-09, 7.228500180644915e-05, 8.57160339364782e-05,
-  0.000151331681990996, -6.37346674920991e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.014807787723839283, -0.025861704722046852, 0.022075239568948746, -0.005682538729161024,
+  -0.000625687011051923, 0.004430471919476986, 0.035695645958185196, 0.04057188704609871,
+  -0.014807788655161858, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.013674077577888966, -0.023846520110964775, 0.020004812628030777, -0.005049556493759155,
+  -0.0005421940586529672, 0.00417050626128912, 0.032250698655843735, 0.03743873909115791,
+  -0.013674077577888966, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.012582679279148579, -0.021891547366976738, 0.018040094524621964, -0.004455766174942255,
+  -0.00046585898962803185, 0.00392591068521142, 0.029013480991125107, 0.03441740199923515,
+  -0.012582681141793728, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.011533675715327263, -0.020000899210572243, 0.016181407496333122, -0.003901462769135833,
+  -0.0003965887881349772, 0.0036943128798156977, 0.025979677215218544, 0.03150942921638489,
+  -0.011533675715327263, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.010527149774134159, -0.018178429454565048, 0.014428914524614811, -0.003386775264516473,
+  -0.000334229291183874, 0.00347351492382586, 0.023144803941249847, 0.028716372326016426,
+  -0.010527149774134159, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.009563203901052475, -0.016427697613835335, 0.012782623060047626, -0.0029116959776729345,
+  -0.0002785706310532987, 0.0032614837400615215, 0.020504247397184372, 0.026039740070700645,
+  -0.009563203901052475, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.008641955442726612, -0.014752035960555077, 0.01124237384647131, -0.002476038644090295,
+  -0.00022935344895813614, 0.0030563275795429945, 0.01805317960679531, 0.02348104864358902,
+  -0.008641955442726612, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00776355154812336, -0.013154524378478527, 0.009807839058339596, -0.0020794698502868414,
+  -0.00018627376994118094, 0.0028563395608216524, 0.015786651521921158, 0.021041834726929665,
+  -0.007763552013784647, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006928154267370701, -0.01163798663765192, 0.008478476665914059, -0.0017214847030118108,
+  -0.0001489877322455868, 0.0026599850971251726, 0.013699496164917946, 0.018723607063293457,
+  -0.006928154733031988, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006135987583547831, -0.010205047205090523, 0.007253575604408979, -0.0014014129992574453,
+  -0.00011711879778886214, 0.002465923549607396, 0.01178644597530365, 0.01652795635163784,
+  -0.006135988514870405, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005387313663959503, -0.008858118206262589, 0.006132219452410936, -0.001118405838496983,
+  -9.02624597074464e-05, 0.002273016842082143, 0.010042055509984493, 0.01445652823895216,
+  -0.0053873141296207905, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004682451486587524, -0.007599393371492624, 0.005113252904266119, -0.0008714196737855673,
+  -6.799191032769158e-05, 0.002080336445942521, 0.008460698649287224, 0.012511028908193111,
+  -0.004682451486587524, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0040218099020421505, -0.006430904380977154, 0.004195300862193108,
+  -0.0006592236459255219, -4.986461499356665e-05, 0.0018871986540034413, 0.007036625407636166,
+  0.010693294927477837, -0.004021809436380863, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0034058766905218363, -0.005354492925107479, 0.0033766995184123516,
+  -0.00048037435044534504, -3.54275616700761e-05, 0.001693193567916751, 0.005763906054198742,
+  0.009005282074213028, -0.0034058764576911926, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0028352648951113224, -0.004371851682662964, 0.002655508229508996,
+  -0.00033319980138912797, -2.422377838229295e-05, 0.0014982132706791162, 0.004636466968804598,
+  0.007449144963175058, -0.0028352648951113224, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002310738433152437, -0.00348453875631094, 0.002029455965384841, -0.00021578144514933228,
+  -1.5798506865394302e-05, 0.0013025117805227637, 0.003648084355518222, 0.00602727709338069,
+  -0.002310738433152437, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0018332540057599545, -0.0026939930394291878, 0.0014958955580368638,
+  -0.00012592221901286393, -9.705579941510223e-06, 0.0011067718733102083, 0.002792386570945382,
+  0.00474237697198987, -0.001833254238590598, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0014040326932445168, -0.002001587999984622, 0.0010517496848478913,
+  -6.111822585808113e-05, -5.514274107554229e-06, 0.0009122192277573049, 0.002062898362055421,
+  0.0035975940991193056, -0.0014040324604138732, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010246436577290297, -0.0014086529845371842, 0.0006934131379239261,
+  -1.8502421880839393e-05, -2.816112100845203e-06, 0.000720771960914135, 0.0014530456392094493,
+  0.002596649108454585, -0.0010246435413137078, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0006971846451051533, -0.0009165707742795348, 0.0004166447906754911,
+  5.217917077970924e-06, -1.2325160696491366e-06, 0.0005353152519091964, 0.0009562804480083287,
+  0.001744152745231986, -0.0006971846451051533, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004245503223501146, -0.000526891031768173, 0.00021636142628267407,
+  1.3864630091120489e-05, -4.22743568151418e-07, 0.00036015562363900244, 0.0005662395269609988,
+  0.0010460608173161745, -0.0004245503223501146, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00021101518359500915, -0.00024158033193089068, 8.629779767943546e-05,
+  1.1947875464102253e-05, -9.295886371774031e-08, 0.0002019731909967959, 0.0002772264997474849,
+  0.0005106807802803814, -0.00021101518359500915, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.37346674920991e-05, -6.366728484863415e-05, 1.830075416364707e-05,
+  4.955160875397269e-06, -6.905087612807392e-09, 7.228499453049153e-05, 8.571602666052058e-05,
+  0.00015133171109482646, -6.373466021614149e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 92
diff --git a/extra_tests/regression_fits/no_msr_92.json b/extra_tests/regression_fits/no_msr_92.json
index fc1f4dffcf..c87ab8a66d 100644
--- a/extra_tests/regression_fits/no_msr_92.json
+++ b/extra_tests/regression_fits/no_msr_92.json
@@ -51,44 +51,44 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 6.576579570770264,
-  "erf_vl": 5.858458042144775,
-  "chi2": 3.3300070762634277,
+  "erf_tr": 6.576577663421631,
+  "erf_vl": 5.858455181121826,
+  "chi2": 3.330012321472168,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.3370215612846568,
-    0.9939697370835859,
-    1.1791487483710792,
-    1.0013385141386437,
-    1.1751094831216375
+    1.337021614754758,
+    0.9939697379044121,
+    1.1791486314894875,
+    1.0013385222517424,
+    1.1751097571490132
   ],
   "integrability": [
-    0.0009919884760162465,
-    0.000991988476016628,
-    4.665318033393595e-05,
+    0.000991988403256927,
+    0.000991988403257052,
+    4.665317624120979e-05,
     0.4762776866555213,
-    0.007486370101105047
+    0.007486370741389338
   ],
   "timing": {
     "walltime": {
-      "Total": 29.779701471328735,
+      "Total": 31.462430477142334,
       "start": 0.0,
-      "replica_set": 0.37215209007263184,
-      "replica_fitted": 29.779524326324463,
-      "replica_set_to_replica_fitted": 29.40737223625183
+      "replica_set": 0.3577704429626465,
+      "replica_fitted": 31.46228003501892,
+      "replica_set_to_replica_fitted": 31.104509592056274
     },
     "cputime": {
-      "Total": 31.8365965,
+      "Total": 33.54510500000001,
       "start": 0.0,
-      "replica_set": 0.6885683,
-      "replica_fitted": 31.8364179,
-      "replica_set_to_replica_fitted": 31.1478496
+      "replica_set": 0.6758694999999992,
+      "replica_fitted": 33.5449531,
+      "replica_set_to_replica_fitted": 32.869083599999996
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post168.dev0+5adb0639b",
-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/no_sumrules_18.exportgrid b/extra_tests/regression_fits/no_sumrules_18.exportgrid
index d4998dac9f..feb23099da 100644
--- a/extra_tests/regression_fits/no_sumrules_18.exportgrid
+++ b/extra_tests/regression_fits/no_sumrules_18.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.4447741508483887, 0.48206236958503723, 0.45488396286964417, 0.45492807030677795,
-  -0.536359429359436, 0.45496705174446106, 0.4549233019351959, 0.48199930787086487,
-  -2.4447741508483887, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.3672447204589844, 0.4723908603191376, 0.44413235783576965, 0.44418245553970337,
-  -0.5363330245018005, 0.44422563910484314, 0.4441758990287781, 0.47232168912887573,
-  -2.3672447204589844, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2921900749206543, 0.463274210691452, 0.4338918924331665, 0.4339488744735718,
-  -0.5362372398376465, 0.43399661779403687, 0.4339401423931122, 0.46319836378097534,
-  -2.2921900749206543, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.219531536102295, 0.45470181107521057, 0.424150288105011, 0.4242149293422699,
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+- [0.0, 0.0, -0.018394090235233307, -0.0014669123338535428, 0.0372183658182621, -0.001791887218132615,
+  -0.0009148367680609226, -0.00021145712526049465, 0.04003899171948433, 0.020664356648921967,
+  -0.018394090235233307, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.01713460311293602, -0.001384240691550076, 0.0341024175286293, -0.0015092183602973819,
+  -0.0008103917934931815, -8.484295540256426e-05, 0.03661656379699707, 0.019247738644480705,
+  -0.01713460311293602, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.015917476266622543, -0.0012908242642879486, 0.031135976314544678,
+  -0.0012402792926877737, -0.0007129594450816512, 4.0676663047634065e-05, 0.033369194716215134,
+  0.017881590873003006, -0.015917474403977394, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.014742772094905376, -0.0011892345501109958, 0.028318235650658607,
+  -0.000986485043540597, -0.000622656021732837, 0.00016301171854138374, 0.030294813215732574,
+  0.01656525954604149, -0.014742772094905376, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.01361055951565504, -0.0010818762239068747, 0.025648197159171104, -0.0007491065771318972,
+  -0.0005395213374868035, 0.0002802291128318757, 0.027391178533434868, 0.015298159793019295,
+  -0.01361055951565504, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.012520892545580864, -0.0009709763107821345, 0.023124700412154198,
+  -0.000529265555087477, -0.00046352503704838455, 0.00039054660010151565, 0.02465588040649891,
   0.014079791493713856, -0.012520892545580864, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.01147384475916624, -0.0008586063631810248, 0.020746421068906784, -0.00032793093123473227,
-  -0.0003945713397115469, 0.0004923317464999855, 0.022086333483457565, 0.01290971226990223,
-  -0.01147384475916624, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.010469482280313969, -0.0007466541137546301, 0.018511872738599777,
-  -0.00014591107901651412, -0.0003325043071527034, 0.0005841305828653276, 0.01967979036271572,
+- [0.0, 0.0, -0.011473842896521091, -0.0008586078183725476, 0.020746421068906784,
+  -0.0003279313095845282, -0.00039457142702303827, 0.0004923318629153073, 0.022086329758167267,
+  0.012909709475934505, -0.011473842896521091, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.010469482280313969, -0.0007466551032848656, 0.018511874601244926,
+  -0.00014591083163395524, -0.00033250427804887295, 0.0005841303500346839, 0.019679788500070572,
   0.011787579394876957, -0.010469482280313969, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.009507897309958935, -0.000636862067040056, 0.01641940325498581, 1.61264088092139e-05,
-  -0.0002771134895738214, 0.0006646249676123261, 0.01743335649371147, 0.010713131166994572,
+- [0.0, 0.0, -0.009507897309958935, -0.0006368624744936824, 0.01641940325498581, 1.6126299669849686e-05,
+  -0.0002771134313661605, 0.0006646253168582916, 0.01743335649371147, 0.010713131166994572,
   -0.009507897309958935, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.008589192293584347, -0.0005307927494868636, 0.014467176049947739,
-  0.00015768976300023496, -0.00022813845134805888, 0.0007326831691898406, 0.015343951992690563,
-  0.009686189703643322, -0.008589192293584347, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.007713504135608673, -0.0004298672138247639, 0.01265321671962738, 0.0002784412354230881,
-  -0.00018527508655097336, 0.0007873280555941164, 0.013408349826931953, 0.008706679567694664,
-  -0.0077135032042860985, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.006880980916321278, -0.00033533640089444816, 0.010975318029522896,
-  0.00037821594742126763, -0.0001481798681197688, 0.0008277639281004667, 0.011623109690845013,
-  0.007774599362164736, -0.006880980916321278, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.006091827992349863, -0.0002482970885466784, 0.009431135840713978,
-  0.0004570324090309441, -0.00011647688370430842, 0.0008533856016583741, 0.009984670206904411,
-  0.006890084128826857, -0.006091827992349863, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.005346294958144426, -0.00016968593990895897, 0.008018126711249352,
-  0.0005150960059836507, -8.976261597126722e-05, 0.0008637791033834219, 0.00848926417529583,
-  0.006053364835679531, -0.005346293561160564, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.004644683562219143, -0.00010028374526882544, 0.006733530666679144,
-  0.0005528087494894862, -6.761175609426573e-05, 0.0008587403572164476, 0.0071329413913190365,
-  0.005264792125672102, -0.0046446844935417175, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.003987387754023075, -4.0707061998546124e-05, 0.005574400071054697,
-  0.0005707963136956096, -4.958324643666856e-05, 0.0008382961386814713, 0.005911580752581358,
-  0.004524869844317436, -0.003987387754023075, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.003374875755980611, 8.593507118348498e-06, 0.004537553060799837, 0.0005699176108464599,
-  -3.522587940096855e-05, 0.0008027199655771255, 0.004820843227207661, 0.003834233619272709,
-  -0.003374875755980611, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0028077424503862858, 4.734058165922761e-05, 0.003619573311880231,
-  0.0005513000069186091, -2.4084714823402464e-05, 0.000752573658246547, 0.0038561937399208546,
-  0.003193708835169673, -0.002807741751894355, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0022867275401949883, 7.54374050302431e-05, 0.0028167918790131807,
-  0.0005163656896911561, -1.570707536302507e-05, 0.0006887359195388854, 0.0030128806829452515,
-  0.0026043171528726816, -0.0022867275401949883, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.008589194156229496, -0.0005307944375090301, 0.014467175118625164,
+  0.00015769105812069029, -0.00022813845134805888, 0.0007326834602281451, 0.015343951061367989,
+  0.009686188772320747, -0.008589194156229496, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.007713504135608673, -0.0004298663407098502, 0.012653215788304806,
+  0.0002784417010843754, -0.00018527507199905813, 0.0007873285794630647, 0.013408350758254528,
+  0.00870667863637209, -0.007713503669947386, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006880981381982565, -0.00033533747773617506, 0.010975317098200321,
+  0.0003782164421863854, -0.00014817988267168403, 0.0008277643355540931, 0.011623110622167587,
+  0.007774599827826023, -0.00688098045065999, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006091827526688576, -0.0002482963027432561, 0.009431138634681702,
+  0.0004570335440803319, -0.00011647686187643558, 0.0008533865329809487, 0.009984669275581837,
+  0.0068900855258107185, -0.006091827526688576, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005346294026821852, -0.0001696867257123813, 0.008018126711249352,
+  0.0005150957149453461, -8.976263052318245e-05, 0.0008637791033834219, 0.00848926417529583,
+  0.006053364835679531, -0.005346294026821852, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004644683562219143, -0.00010028399265138432, 0.006733530201017857,
+  0.0005528090987354517, -6.761173426639289e-05, 0.0008587405318394303, 0.007132940925657749,
+  0.005264793056994677, -0.0046446844935417175, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003987387288361788, -4.070678187417798e-05, 0.005574400071054697,
+  0.0005707963136956096, -4.958324643666856e-05, 0.0008382959640584886, 0.005911580752581358,
+  0.004524869844317436, -0.003987387288361788, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003374875523149967, 8.593724487582222e-06, 0.004537553060799837, 0.0005699180183000863,
+  -3.522588303894736e-05, 0.000802720314823091, 0.004820843227207661, 0.003834234084933996,
+  -0.003374875523149967, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002807742217555642, 4.734005779027939e-05, 0.0036195728462189436,
+  0.0005512997158803046, -2.4084714823402464e-05, 0.0007525734254159033, 0.0038561932742595673,
+  0.003193708835169673, -0.002807741519063711, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0022867275401949883, 7.543749961769208e-05, 0.0028167918790131807,
+  0.0005163657478988171, -1.570707536302507e-05, 0.0006887360941618681, 0.0030128811486065388,
+  0.0026043171528726816, -0.0022867273073643446, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.0018127619987353683, 9.29874659050256e-05, 0.0021252550650388002,
-  0.00046688542352057993, -9.648977538745385e-06, 0.0006124668871052563, 0.002285919850692153,
+  0.00046688542352057993, -9.648976629250683e-06, 0.0006124668871052563, 0.002285919850692153,
   0.0020673221442848444, -0.0018127619987353683, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0013870393158867955, 0.00010031546844402328, 0.0015407162718474865,
-  0.0004050442948937416, -5.481877906277077e-06, 0.0005254875286482275, 0.0016701002605259418,
-  0.0015842977445572615, -0.0013870393158867955, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.001011091866530478, 9.800394036574289e-05, 0.0010585769778117537,
-  0.00033353568869642913, -2.799450840029749e-06, 0.0004300965229049325, 0.0011599526042118669,
-  0.0011572003131732345, -0.001011091866530478, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0006869720527902246, 8.695988799445331e-05, 0.0006738803931511939,
-  0.0002557182451710105, -1.2251739462953992e-06, 0.0003293681365903467, 0.0007497863844037056,
-  0.0007885367376729846, -0.0006869720527902246, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0004175136855337769, 6.852877413621172e-05, 0.00038125846185721457,
-  0.0001758696453180164, -4.20208749574158e-07, 0.00022748230549041182, 0.00043371974606998265,
-  0.0004816175205633044, -0.0004175136855337769, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0002069003094220534, 4.474492743611336e-05, 0.00017493950144853443,
-  9.968577796826139e-05, -9.239793286042186e-08, 0.00013039051555097103, 0.00020585798483807594,
-  0.00024111005768645555, -0.0002069003094220534, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -6.212705193320289e-05, 1.901147152238991e-05, 4.897643157164566e-05,
-  3.549793109414168e-05, -6.863166479575966e-09, 4.7500550863333046e-05, 6.099927850300446e-05,
-  7.451765850419179e-05, -6.212704465724528e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0013870391994714737, 0.00010031545389210805, 0.0015407162718474865,
+  0.0004050442366860807, -5.481878361024428e-06, 0.0005254875286482275, 0.0016701002605259418,
+  0.0015842977445572615, -0.0013870391994714737, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010110917501151562, 9.800397674553096e-05, 0.001058576861396432,
+  0.00033353574690409005, -2.7994499305350473e-06, 0.00043009661021642387, 0.0011599527206271887,
+  0.0011572003131732345, -0.0010110917501151562, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0006869719945825636, 8.695988799445331e-05, 0.0006738805095665157,
+  0.00025571821606718004, -1.2251739462953992e-06, 0.00032936810748651624, 0.0007497863844037056,
+  0.0007885367376729846, -0.0006869719945825636, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004175136564299464, 6.852885417174548e-05, 0.0003812584327533841,
+  0.00017586970352567732, -4.202087779958674e-07, 0.00022748237824998796, 0.0004337197751738131,
+  0.0004816175496671349, -0.0004175136564299464, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00020690029487013817, 4.4744894694304094e-05, 0.00017493947234470397,
+  9.968574886443093e-05, -9.239793286042186e-08, 0.00013039048644714057, 0.00020585792663041502,
+  0.0002411100285826251, -0.00020690029487013817, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.212703738128766e-05, 1.9011475160368718e-05, 4.897643520962447e-05,
+  3.549793837009929e-05, -6.863166035486756e-09, 4.7500550863333046e-05, 6.0999274865025654e-05,
+  7.451765850419179e-05, -6.212703738128766e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 18
diff --git a/extra_tests/regression_fits/no_sumrules_18.json b/extra_tests/regression_fits/no_sumrules_18.json
index 0c041c1598..df7888cb29 100644
--- a/extra_tests/regression_fits/no_sumrules_18.json
+++ b/extra_tests/regression_fits/no_sumrules_18.json
@@ -51,44 +51,44 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 5.303783893585205,
-  "erf_vl": 5.399436950683594,
-  "chi2": 3.260410785675049,
+  "erf_tr": 5.3037943840026855,
+  "erf_vl": 5.3994460105896,
+  "chi2": 3.260413646697998,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.3348380690548445,
-    0.9938354337481484,
-    1.0016686539415425,
-    0.990576006962812,
-    1.0071507365751575
+    1.334838194261321,
+    0.9938354337963408,
+    1.0016686481364248,
+    0.9905760062890283,
+    1.0071507465033542
   ],
   "integrability": [
-    0.00022732430079470262,
-    0.00022732430079495936,
-    1.0915414520598632e-05,
-    0.4772165492177008,
-    0.001817994052543806
+    0.00022732430443259122,
+    0.00022732430443293816,
+    1.0915415287984787e-05,
+    0.4772165119647979,
+    0.0018179939506805104
   ],
   "timing": {
     "walltime": {
-      "Total": 25.12443494796753,
+      "Total": 26.5335693359375,
       "start": 0.0,
-      "replica_set": 0.3976583480834961,
-      "replica_fitted": 25.12428593635559,
-      "replica_set_to_replica_fitted": 24.726627588272095
+      "replica_set": 0.3634805679321289,
+      "replica_fitted": 26.533432006835938,
+      "replica_set_to_replica_fitted": 26.16995143890381
     },
     "cputime": {
-      "Total": 27.074280200000004,
+      "Total": 28.4186657,
       "start": 0.0,
-      "replica_set": 0.7145655,
-      "replica_fitted": 27.074129300000003,
-      "replica_set_to_replica_fitted": 26.359563800000004
+      "replica_set": 0.6786007000000005,
+      "replica_fitted": 28.4185265,
+      "replica_set_to_replica_fitted": 27.7399258
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post168.dev0+5adb0639b",
-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/no_vsr_54.exportgrid b/extra_tests/regression_fits/no_vsr_54.exportgrid
index 65c81c99d0..b71ccbb37a 100644
--- a/extra_tests/regression_fits/no_vsr_54.exportgrid
+++ b/extra_tests/regression_fits/no_vsr_54.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.3827311992645264, 0.17211571335792542, 0.14561806619167328, 0.14566439390182495,
-  -16.24201011657715, 0.14570114016532898, 0.14565514028072357, 0.17205661535263062,
-  -2.3827311992645264, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.307499647140503, 0.17171138525009155, 0.14416088163852692, 0.1442134529352188,
-  -16.250553131103516, 0.14425407350063324, 0.14420188963413239, 0.17164653539657593,
-  -2.3074991703033447, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2346489429473877, 0.17157544195652008, 0.14292940497398376, 0.1429891735315323,
-  -16.257577896118164, 0.14303408563137054, 0.1429748386144638, 0.17150425910949707,
-  -2.2346489429473877, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1641042232513428, 0.17170625925064087, 0.14192040264606476, 0.14198827743530273,
-  -16.26297950744629, 0.142038032412529, 0.14197072386741638, 0.1716282218694687,
-  -2.164104700088501, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.095792293548584, 0.17210251092910767, 0.14113061130046844, 0.14120769500732422,
-  -16.266658782958984, 0.1412626951932907, 0.14118629693984985, 0.17201681435108185,
-  -2.095792531967163, 0.0, 0.0, 0.0]
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+- [0.0, 0.0, -7.334386464208364e-05, -5.5192426771100145e-06, 2.377108648943249e-05,
+  1.0776415365398861e-05, -2.519729207506316e-07, 1.4744923646503594e-05, 2.7760992452385835e-05,
+  4.09428212151397e-05, -7.334385009016842e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 54
diff --git a/extra_tests/regression_fits/no_vsr_54.json b/extra_tests/regression_fits/no_vsr_54.json
index beafc32837..7541524c30 100644
--- a/extra_tests/regression_fits/no_vsr_54.json
+++ b/extra_tests/regression_fits/no_vsr_54.json
@@ -51,44 +51,44 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 3.6618897914886475,
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   "version": {
     "tensorflow": "2.15.0, mkl=??",
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-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/normal_fit_72.exportgrid b/extra_tests/regression_fits/normal_fit_72.exportgrid
index a027de87fb..2932bc2ec4 100644
--- a/extra_tests/regression_fits/normal_fit_72.exportgrid
+++ b/extra_tests/regression_fits/normal_fit_72.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
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+  -0.005872880574315786, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005165372975170612, -0.008569507859647274, 0.0059692468494176865,
+  -0.0013857267331331968, -0.002337299520149827, 0.0004515867040026933, 0.008043548092246056,
+  0.011860144324600697, -0.005165372975170612, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004498424008488655, -0.007346407510340214, 0.004957635421305895, -0.0011044371640309691,
+  -0.001749701565131545, 0.00046611169818788767, 0.006707595661282539, 0.01023237407207489,
+  -0.004498424008488655, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003872379893437028, -0.006213533692061901, 0.004049193579703569, -0.0008610023651272058,
+  -0.0012755331117659807, 0.0004726607585325837, 0.005515445489436388, 0.008716976270079613,
+  -0.0038723794277757406, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0032876692712306976, -0.005172074772417545, 0.0032419476192444563,
+  -0.0006536798900924623, -0.000900991668459028, 0.00047011722926981747, 0.004460963420569897,
+  0.007315000984817743, -0.0032876692712306976, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0027448502369225025, -0.004223080351948738, 0.0025336272083222866,
+  -0.0004805249336641282, -0.0006126118823885918, 0.00045763031812384725, 0.003537838812917471,
+  0.006027661729604006, -0.002744849771261215, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0022446303628385067, -0.0033674845471978188, 0.0019216308137401938,
+  -0.000339367485139519, -0.0003973772400058806, 0.00043463570182211697, 0.002739544725045562,
+  0.004856371786445379, -0.0022446310613304377, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0017879169899970293, -0.002606116933748126, 0.0014029686572030187,
+  -0.00022778724087402225, -0.00024284416576847434, 0.00040091649862006307, 0.002059327671304345,
+  0.003802782855927944, -0.0017879169899970293, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.001375883468426764, -0.0019397555151954293, 0.0009742138208821416,
+  -0.00014308940444607288, -0.00013727320765610784, 0.00035668289638124406, 0.001490216702222824,
+  0.0028688944876194, -0.001375883468426764, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010100580984726548, -0.001369151403196156, 0.0006313967169262469,
+  -8.225525380112231e-05, -6.976014992687851e-05, 0.0003026777121704072, 0.0010249806800857186,
+  0.0020571306813508272, -0.0010100580984726548, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0006925066118128598, -0.0008951330091804266, 0.00036988654755987227,
+  -4.1896815673680976e-05, -3.0386136131710373e-05, 0.00024036849208641797, 0.0006561630871146917,
+  0.0013705696910619736, -0.000692506495397538, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004261105495970696, -0.0005187256610952318, 0.00018416937382426113,
+  -1.8177463061874732e-05, -1.0374041266913991e-05, 0.00017227062198799103, 0.0003761099651455879,
+  0.0008132564253173769, -0.0004261104913894087, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0002151751541532576, -0.0002414338378002867, 6.746427970938385e-05,
+  -6.7076402956445236e-06, -2.270961203976185e-06, 0.0001025893579935655, 0.0001771329843904823,
+  0.00039088522316887975, -0.00021517512504942715, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.701839447487146e-05, -6.598907202715054e-05, 1.0872927305172198e-05,
+  -2.417644964225474e-06, -1.679551075994823e-07, 3.886634294758551e-05, 5.219167360337451e-05,
+  0.00011260561586823314, -6.701839447487146e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 72
diff --git a/extra_tests/regression_fits/normal_fit_72.json b/extra_tests/regression_fits/normal_fit_72.json
index f02f237d23..9d12a53fe0 100644
--- a/extra_tests/regression_fits/normal_fit_72.json
+++ b/extra_tests/regression_fits/normal_fit_72.json
@@ -49,46 +49,46 @@
       "trainable": false
     }
   ],
-  "stop_epoch": 1667,
-  "best_epoch": 365,
-  "erf_tr": 3.862401008605957,
-  "erf_vl": 4.220080375671387,
-  "chi2": 2.4093308448791504,
+  "stop_epoch": 1688,
+  "best_epoch": 386,
+  "erf_tr": 3.8196349143981934,
+  "erf_vl": 4.181242942810059,
+  "chi2": 2.3859992027282715,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.3077516647379444,
-    1.2693092406788389,
-    1.1686582018448737,
-    1.0014198240309733,
-    1.1888768971089245
+    1.3172170310450748,
+    1.2737718180572153,
+    1.1682106289760015,
+    0.9969939105106653,
+    1.178227991809247
   ],
   "integrability": [
-    0.0009303889601154358,
-    0.0009303889601145476,
-    4.6177159219396025e-05,
-    0.4885604307055469,
-    0.0067930201184924766
+    0.000922872146476017,
+    0.0009228721464754619,
+    6.687239761005159e-05,
+    0.528376147150993,
+    0.006918032886459646
   ],
   "timing": {
     "walltime": {
-      "Total": 24.668087005615234,
+      "Total": 25.596290588378906,
       "start": 0.0,
-      "replica_set": 0.37459492683410645,
-      "replica_fitted": 24.667866468429565,
-      "replica_set_to_replica_fitted": 24.29327154159546
+      "replica_set": 0.4257495403289795,
+      "replica_fitted": 25.596144676208496,
+      "replica_set_to_replica_fitted": 25.170395135879517
     },
     "cputime": {
-      "Total": 27.1846608,
+      "Total": 28.3766029,
       "start": 0.0,
-      "replica_set": 0.688195799999999,
-      "replica_fitted": 27.1844376,
-      "replica_set_to_replica_fitted": 26.4962418
+      "replica_set": 0.7320899000000001,
+      "replica_fitted": 28.376455399999998,
+      "replica_set_to_replica_fitted": 27.6443655
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post168.dev0+5adb0639b",
-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/trainable_prepro_61.exportgrid b/extra_tests/regression_fits/trainable_prepro_61.exportgrid
index e4b65faa81..781ff81c0d 100644
--- a/extra_tests/regression_fits/trainable_prepro_61.exportgrid
+++ b/extra_tests/regression_fits/trainable_prepro_61.exportgrid
@@ -1,590 +1,590 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
-- [0.0, 0.0, -2.007188320159912, 0.6650366187095642, 0.6647647619247437, 0.6647701859474182,
-  -15.805452346801758, 0.6731979846954346, 0.6732022762298584, 0.6733971834182739,
-  -2.007188320159912, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9466973543167114, 0.6447261571884155, 0.6444252133369446, 0.6444316506385803,
-  -15.637469291687012, 0.6531933546066284, 0.6531983613967896, 0.653412401676178,
-  -1.9466973543167114, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.007188558578491, 0.6650367975234985, 0.664764940738678, 0.6647703051567078,
+  -15.805450439453125, 0.6731981039047241, 0.673202395439148, 0.6733973026275635,
+  -2.007188558578491, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.9466972351074219, 0.644726037979126, 0.644425094127655, 0.644431471824646,
+  -15.637470245361328, 0.6531932353973389, 0.6531982421875, 0.6534122228622437, -1.9466972351074219,
+  0.0, 0.0, 0.0]
 - [0.0, 0.0, -1.8882776498794556, 0.625101625919342, 0.6247684359550476, 0.6247758269309998,
   -15.469232559204102, 0.6338849663734436, 0.6338908076286316, 0.6341255307197571,
   -1.8882776498794556, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -1.8318673372268677, 0.6061420440673828, 0.6057731509208679, 0.6057818531990051,
   -15.30066204071045, 0.6152523756027222, 0.6152591705322266, 0.6155166625976562,
   -1.8318675756454468, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7774062156677246, 0.5878275632858276, 0.5874189734458923, 0.5874292850494385,
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-  -1.7774064540863037, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.7774064540863037, 0.5878276228904724, 0.5874190926551819, 0.5874293446540833,
+  -15.131654739379883, 0.5972758531570435, 0.5972838997840881, 0.5975663065910339,
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 - [0.0, 0.0, -1.724837064743042, 0.5701389908790588, 0.5696865916252136, 0.5696985721588135,
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   -1.724836826324463, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6741019487380981, 0.553057074546814, 0.5525559782981873, 0.5525700449943542,
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-- [0.0, 0.0, -1.6251477003097534, 0.536564290523529, 0.5360091924667358, 0.5360256433486938,
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+- [0.0, 0.0, -1.6741020679473877, 0.5530571341514587, 0.552556037902832, 0.552570104598999,
+  -14.79195499420166, 0.5632152557373047, 0.5632261037826538, 0.5635656118392944,
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+- [0.0, 0.0, -1.6251479387283325, 0.536564290523529, 0.5360091924667358, 0.5360256433486938,
+  -14.621048927307129, 0.5470947027206421, 0.5471073389053345, 0.5474795699119568,
+  -1.6251481771469116, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -1.5779227018356323, 0.5206431150436401, 0.5200280547142029, 0.5200473666191101,
-  -14.44929027557373, 0.5315576791763306, 0.5315723419189453, 0.5319803357124329,
+  -14.449288368225098, 0.5315576791763306, 0.5315723419189453, 0.5319803357124329,
   -1.5779227018356323, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -1.5323753356933594, 0.5052765011787415, 0.5045949220657349, 0.5046175718307495,
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   -1.5323753356933594, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4884580373764038, 0.4904487729072571, 0.48969343304634094, 0.4897199273109436,
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+- [0.0, 0.0, -1.488458275794983, 0.49044889211654663, 0.4896935522556305, 0.48972004652023315,
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 - [0.0, 0.0, -1.4461228847503662, 0.47614410519599915, 0.47530680894851685, 0.4753379225730896,
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-- [0.0, 0.0, -1.405325174331665, 0.46234768629074097, 0.46141940355300903, 0.4614558815956116,
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-- [0.0, 0.0, -1.29172945022583, 0.4238678812980652, 0.4226016104221344, 0.42266038060188293,
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-- [0.0, 0.0, -1.2566618919372559, 0.4119672179222107, 0.4105622470378876, 0.4106311798095703,
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-- [0.0, 0.0, -1.2229286432266235, 0.4005087912082672, 0.39894965291023254, 0.399030476808548,
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-- [0.0, 0.0, -1.1904942989349365, 0.3894813656806946, 0.3877507448196411, 0.3878454864025116,
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   -1.1904942989349365, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1593239307403564, 0.3788738548755646, 0.37695252895355225, 0.3770635724067688,
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-- [0.0, 0.0, -1.1293838024139404, 0.3686758875846863, 0.3665422797203064, 0.36667242646217346,
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-- [0.0, 0.0, -1.1006417274475098, 0.358877569437027, 0.35650765895843506, 0.3566601872444153,
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   -0.024718202650547028, 0.0, 0.0, 0.0]
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-  -0.02306290902197361, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.021467771381139755, -0.060050807893276215, 0.04646987468004227, 0.03755426034331322,
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-- [0.0, 0.0, -0.019932277500629425, -0.056831907480955124, 0.043438125401735306, 0.035534825176000595,
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+- [0.0, 0.0, -0.021467769518494606, -0.060050807893276215, 0.04646987468004227, 0.03755425661802292,
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+- [0.0, 0.0, -0.019932277500629425, -0.05683190003037453, 0.04343812167644501, 0.035534825176000595,
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   -0.019932281225919724, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.01845591887831688, -0.05361296609044075, 0.0404873862862587, 0.03351966291666031,
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-- [0.0, 0.0, -0.017038192600011826, -0.05040309578180313, 0.03762011602520943, 0.031513433903455734,
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+- [0.0, 0.0, -0.017038192600011826, -0.05040309205651283, 0.03762011229991913, 0.031513430178165436,
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   -0.01567860320210457, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.014376689679920673, -0.044046249240636826, 0.032145097851753235, 0.02754661999642849,
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-- [0.0, 0.0, -0.013131970539689064, -0.04091686010360718, 0.029541676864027977, 0.02559558115899563,
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+- [0.0, 0.0, -0.013131970539689064, -0.04091685637831688, 0.02954167313873768, 0.02559557743370533,
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   -0.013131972402334213, 0.0, 0.0, 0.0]
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   -0.011944017373025417, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.010812407359480858, -0.034799519926309586, 0.024613207206130028, 0.02178253047168255,
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+- [0.0, 0.0, -0.010812407359480858, -0.034799523651599884, 0.024613207206130028, 0.02178253047168255,
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   -0.010812405496835709, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.00973674189299345, -0.03182877227663994, 0.02229207009077072, 0.01993042416870594,
-  -0.020882153883576393, -0.0054532908834517, -0.002346266759559512, 0.019609292969107628,
-  -0.00973674189299345, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.008716662414371967, -0.02892809361219406, 0.02006891369819641, 0.018121354281902313,
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-  -0.008716664277017117, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.00775183504447341, -0.026106029748916626, 0.017945600673556328, 0.016360444948077202,
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-  -0.00775183504447341, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.006841971538960934, -0.023371243849396706, 0.01592409797012806, 0.014652988873422146,
-  -0.012848636135458946, -0.004151066765189171, -0.0024993258994072676, 0.01464438159018755,
-  -0.006841971538960934, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0059868404641747475, -0.020732462406158447, 0.014006378129124641,
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+- [0.0, 0.0, -0.009736740961670876, -0.03182877227663994, 0.02229207381606102, 0.01993042603135109,
+  -0.020882153883576393, -0.0054532908834517, -0.0023462676908820868, 0.019609292969107628,
+  -0.009736740961670876, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.008716661483049393, -0.02892809361219406, 0.02006891369819641, 0.018121352419257164,
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+- [0.0, 0.0, -0.007751832716166973, -0.026106027886271477, 0.01794559881091118, 0.016360441222786903,
+  -0.015295428223907948, -0.004575176630169153, -0.002506696153432131, 0.016251515597105026,
+  -0.007751832716166973, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006841970607638359, -0.023371241986751556, 0.01592409610748291, 0.014652988873422146,
+  -0.012848636135458946, -0.004151065833866596, -0.0024993254337459803, 0.014644378796219826,
+  -0.006841970607638359, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0059868404641747475, -0.020732462406158447, 0.014006377197802067,
+  0.01300437655299902, -0.010635212995111942, -0.0037378263659775257, -0.002441328950226307,
   0.013089039362967014, -0.005986839532852173, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.005186258815228939, -0.01819854974746704, 0.012194515205919743, 0.011420145630836487,
-  -0.008654522709548473, -0.003336170222610235, -0.002338581020012498, 0.011588730849325657,
+- [0.0, 0.0, -0.005186258815228939, -0.018198547884821892, 0.012194514274597168, 0.011420144699513912,
+  -0.008654520846903324, -0.0033361692912876606, -0.0023385800886899233, 0.011588728986680508,
   -0.0051862578839063644, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.004440127871930599, -0.015778575092554092, 0.01049072202295065, 0.009906021878123283,
-  -0.006904028356075287, -0.0029468650463968515, -0.0021969997324049473, 0.010146995075047016,
-  -0.004440127871930599, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0037484243512153625, -0.013481860980391502, 0.008897374384105206,
-  0.008467930369079113, -0.005379221402108669, -0.0025707699824124575, -0.002022574655711651,
-  0.00876769982278347, -0.0037484243512153625, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0031112446449697018, -0.011318106204271317, 0.0074171083979308605,
-  0.007112082559615374, -0.004073587246239185, -0.0022088875994086266, -0.0018213912844657898,
-  0.007455189246684313, -0.0031112446449697018, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004440126474946737, -0.015778575092554092, 0.01049072202295065, 0.009906020946800709,
+  -0.006904028356075287, -0.002946865512058139, -0.002197000663727522, 0.010146994143724442,
+  -0.004440126474946737, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0037484238855540752, -0.013481860049068928, 0.008897373452782631,
+  0.008467930369079113, -0.005379220936447382, -0.002570768352597952, -0.002022573258727789,
+  0.008767697960138321, -0.0037484238855540752, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003111243946477771, -0.011318105272948742, 0.007417107932269573, 0.007112081628292799,
+  -0.004073586780577898, -0.002208887366577983, -0.0018213908188045025, 0.007455188315361738,
+  -0.003111243946477771, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.0025288208853453398, -0.009297503158450127, 0.0060528917238116264,
   0.005845014471560717, -0.0029785633087158203, -0.0018624247750267386, -0.0015996773727238178,
   0.006214385852217674, -0.0025288208853453398, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.002001565182581544, -0.007430894300341606, 0.004808136261999607, 0.004673698917031288,
-  -0.0020834479946643114, -0.0015328620793297887, -0.0013638491509482265, 0.005050963722169399,
-  -0.002001565182581544, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0015301386592909694, -0.005730059929192066, 0.003686889773234725,
-  0.0036057105753570795, -0.0013753327075392008, -0.0012220817152410746, -0.0011206098133698106,
-  0.003971633967012167, -0.0015301386592909694, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0011155320098623633, -0.004208045080304146, 0.0026940442621707916,
-  0.0026494080666452646, -0.0008389418944716454, -0.0009325185674242675, -0.0008770746062509716,
-  0.002984505845233798, -0.0011155320098623633, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.000759243150241673, -0.0028798324055969715, 0.0018357854569330812,
-  0.0018143568886443973, -0.0004564860137179494, -0.0006674373871646821, -0.0006410078494809568,
-  0.002099770586937666, -0.0007592432666569948, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0004635540535673499, -0.001763383042998612, 0.0011202656896784902,
-  0.0011119645787402987, -0.0002073735377052799, -0.00043138256296515465, -0.00042122870218008757,
-  0.0013308264315128326, -0.000463553995359689, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.00023213210806716233, -0.0008818600326776505, 0.0005590427899733186,
-  0.0005568687338382006, -6.779085379093885e-05, -0.00023111059272196144, -0.00022847899526823312,
+- [0.0, 0.0, -0.0020015647169202566, -0.007430892903357744, 0.0048081353306770325,
+  0.0046736979857087135, -0.0020834477618336678, -0.0015328616136685014, -0.0013638486852869391,
+  0.005050962325185537, -0.0020015647169202566, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0015301386592909694, -0.005730059463530779, 0.003686889773234725,
+  0.0036057105753570795, -0.001375332591123879, -0.001222081365995109, -0.001120609580539167,
+  0.00397163350135088, -0.0015301386592909694, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0011155317770317197, -0.0042080446146428585, 0.002694044029340148,
+  0.002649407833814621, -0.0008389418944716454, -0.0009325185092166066, -0.0008770745480433106,
+  0.0029845056124031544, -0.0011155317770317197, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0007592430920340121, -0.002879832172766328, 0.0018357853405177593,
+  0.0018143567722290754, -0.0004564860137179494, -0.0006674372707493603, -0.000641007733065635,
+  0.0020997701212763786, -0.0007592432084493339, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004635540535673499, -0.0017633828101679683, 0.0011202655732631683,
+  0.001111964462324977, -0.00020737350860144943, -0.0004313824465498328, -0.0004212285275571048,
+  0.001330826198682189, -0.000463553995359689, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00023213210806716233, -0.0008818600908853114, 0.0005590427899733186,
+  0.0005568687338382006, -6.779083923902363e-05, -0.0002311105781700462, -0.00022847899526823312,
   0.0006966661894693971, -0.00023213210806716233, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -7.16399954399094e-05, -0.0002694059512577951, 0.00017080880934372544,
-  0.00017058996309060603, -9.925642189045902e-06, -7.79822439653799e-05, -7.772142998874187e-05,
-  0.00022814117255620658, -7.16399954399094e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -7.16399954399094e-05, -0.00026940598036162555, 0.00017080882389564067,
+  0.00017058996309060603, -9.925640370056499e-06, -7.798225124133751e-05, -7.772142998874187e-05,
+  0.0002281411871081218, -7.16399954399094e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 q20: 2.7224999999999997
 replica: 61
diff --git a/extra_tests/regression_fits/trainable_prepro_61.json b/extra_tests/regression_fits/trainable_prepro_61.json
index 16192808ac..db5b3f5ba8 100644
--- a/extra_tests/regression_fits/trainable_prepro_61.json
+++ b/extra_tests/regression_fits/trainable_prepro_61.json
@@ -51,44 +51,44 @@
   ],
   "stop_epoch": 1100,
   "best_epoch": 1099,
-  "erf_tr": 83.88550567626953,
-  "erf_vl": 88.8935546875,
-  "chi2": 59.15237808227539,
+  "erf_tr": 83.88552856445312,
+  "erf_vl": 88.89352416992188,
+  "chi2": 59.15236282348633,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.0440971744004135,
-    1.528025761219303,
-    1.003308423800452,
-    0.9979762394415533,
-    1.419281059365766
+    1.0440971720839172,
+    1.5280262072729438,
+    1.0033084215844166,
+    0.9979762330411598,
+    1.4192811360785857
   ],
   "integrability": [
-    0.1109853852540276,
-    0.11098538525402574,
-    0.0002027637756321643,
-    0.008434453862718683,
-    0.0018140712927553482
+    0.11098538525402664,
+    0.11098538525402585,
+    0.0002027638274733623,
+    0.00843445386271846,
+    0.0018140712927551261
   ],
   "timing": {
     "walltime": {
-      "Total": 19.53623390197754,
+      "Total": 19.603114128112793,
       "start": 0.0,
-      "replica_set": 0.4048268795013428,
-      "replica_fitted": 19.536094903945923,
-      "replica_set_to_replica_fitted": 19.13126802444458
+      "replica_set": 0.3588278293609619,
+      "replica_fitted": 19.60303783416748,
+      "replica_set_to_replica_fitted": 19.24421000480652
     },
     "cputime": {
-      "Total": 21.8017812,
+      "Total": 21.8009634,
       "start": 0.0,
-      "replica_set": 0.7218703000000009,
-      "replica_fitted": 21.8016403,
-      "replica_set_to_replica_fitted": 21.079769999999996
+      "replica_set": 0.6759696999999996,
+      "replica_fitted": 21.800885700000002,
+      "replica_set_to_replica_fitted": 21.124916
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post168.dev0+5adb0639b",
-    "validphys": "4.0.8.post168.dev0+5adb0639b"
+    "nnpdf": "4.0.8.post297.dev0+234efa01e",
+    "validphys": "4.0.8.post297.dev0+234efa01e"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/weights.h5 b/extra_tests/regression_fits/weights.h5
index e14a37baeb..8947719636 100644
Binary files a/extra_tests/regression_fits/weights.h5 and b/extra_tests/regression_fits/weights.h5 differ
diff --git a/extra_tests/regression_fits/weights_feature.h5 b/extra_tests/regression_fits/weights_feature.h5
index d1fe2daaf8..3d0085e058 100644
Binary files a/extra_tests/regression_fits/weights_feature.h5 and b/extra_tests/regression_fits/weights_feature.h5 differ
diff --git a/extra_tests/regression_fits/weights_flavour.h5 b/extra_tests/regression_fits/weights_flavour.h5
index 1380587eb9..76dd352f7d 100644
Binary files a/extra_tests/regression_fits/weights_flavour.h5 and b/extra_tests/regression_fits/weights_flavour.h5 differ
diff --git a/n3fit/runcards/examples/developing_weights.h5 b/n3fit/runcards/examples/developing_weights.h5
index 385ea55a75..9dfa9372d1 100644
Binary files a/n3fit/runcards/examples/developing_weights.h5 and b/n3fit/runcards/examples/developing_weights.h5 differ
diff --git a/n3fit/src/n3fit/backends/__init__.py b/n3fit/src/n3fit/backends/__init__.py
index 3c48317a86..3676dd25d7 100644
--- a/n3fit/src/n3fit/backends/__init__.py
+++ b/n3fit/src/n3fit/backends/__init__.py
@@ -11,7 +11,6 @@
     Input,
     Lambda,
     base_layer_selector,
-    concatenate,
     regularizer_selector,
 )
 from n3fit.backends.keras_backend.internal_state import (
diff --git a/n3fit/src/n3fit/backends/keras_backend/MetaModel.py b/n3fit/src/n3fit/backends/keras_backend/MetaModel.py
index 50c89cf74a..2533d8456f 100644
--- a/n3fit/src/n3fit/backends/keras_backend/MetaModel.py
+++ b/n3fit/src/n3fit/backends/keras_backend/MetaModel.py
@@ -440,7 +440,7 @@ def get_layer_replica_weights(layer, i_replica: int):
     Get the weights for the given single replica ``i_replica``,
     from a ``layer`` that contains the weights of all the replicas.
 
-    Note that the layer could be  a complete NN with many separated sub_layers
+    Note that the layer could be a complete NN with many separated sub_layers
     each of which containing weights for all replicas together.
     This functions separates the per-replica weights and returns the list of weight as if the
     input ``layer`` were made of _only_ replica ``i_replica``.
diff --git a/n3fit/src/n3fit/backends/keras_backend/base_layers.py b/n3fit/src/n3fit/backends/keras_backend/base_layers.py
index 14215e9cf6..6f5044ea0c 100644
--- a/n3fit/src/n3fit/backends/keras_backend/base_layers.py
+++ b/n3fit/src/n3fit/backends/keras_backend/base_layers.py
@@ -17,34 +17,40 @@
     The names of the layer and the activation function are the ones to be used in the n3fit runcard.
 """
 
-from tensorflow.keras.layers import Lambda, LSTM, Dropout, Concatenate
-from tensorflow.keras.layers import concatenate, Input # pylint: disable=unused-import
+from tensorflow import expand_dims, math, nn
 from tensorflow.keras.layers import Dense as KerasDense
-from tensorflow import expand_dims
+from tensorflow.keras.layers import Dropout, Lambda
+from tensorflow.keras.layers import Input  # pylint: disable=unused-import
+from tensorflow.keras.layers import LSTM, Concatenate
 from tensorflow.keras.regularizers import l1_l2
-from tensorflow import nn, math
 
 from n3fit.backends import MetaLayer
+from n3fit.backends.keras_backend.multi_dense import MultiDense
+
 
 # Custom activation functions
 def square_activation(x):
-    """ Squares the input """
-    return x*x
+    """Squares the input"""
+    return x * x
+
 
 def modified_tanh(x):
-    """ A non-saturating version of the tanh function """
-    return math.abs(x)*nn.tanh(x)
+    """A non-saturating version of the tanh function"""
+    return math.abs(x) * nn.tanh(x)
+
 
 def leaky_relu(x):
-    """ Computes the Leaky ReLU activation function """
+    """Computes the Leaky ReLU activation function"""
     return nn.leaky_relu(x, alpha=0.2)
 
+
 custom_activations = {
-    "square" : square_activation,
+    "square": square_activation,
     "leaky_relu": leaky_relu,
     "modified_tanh": modified_tanh,
 }
 
+
 def LSTM_modified(**kwargs):
     """
     LSTM asks for a sample X timestep X features kind of thing so we need to reshape the input
@@ -61,9 +67,11 @@ def ReshapedLSTM(input_tensor):
 
     return ReshapedLSTM
 
+
 class Dense(KerasDense, MetaLayer):
     pass
 
+
 def dense_per_flavour(basis_size=8, kernel_initializer="glorot_normal", **dense_kwargs):
     """
     Generates a list of layers which can take as an input either one single layer
@@ -85,7 +93,7 @@ def dense_per_flavour(basis_size=8, kernel_initializer="glorot_normal", **dense_
 
     # Need to generate a list of dense layers
     dense_basis = [
-        base_layer_selector("dense", kernel_initializer=initializer, **dense_kwargs)
+        base_layer_selector("single_dense", kernel_initializer=initializer, **dense_kwargs)
         for initializer in kernel_initializer
     ]
 
@@ -116,13 +124,26 @@ def apply_dense(xinput):
 
 layers = {
     "dense": (
+        MultiDense,
+        {
+            "input_shape": (1,),
+            "replica_seeds": None,
+            "kernel_initializer": "glorot_normal",
+            "units": 5,
+            "activation": "sigmoid",
+            "kernel_regularizer": None,
+            "is_first_layer": False,
+        },
+    ),
+    # This one is only used inside dense_per_flavour
+    "single_dense": (
         Dense,
         {
             "input_shape": (1,),
             "kernel_initializer": "glorot_normal",
             "units": 5,
             "activation": "sigmoid",
-            "kernel_regularizer": None
+            "kernel_regularizer": None,
         },
     ),
     "dense_per_flavour": (
@@ -143,31 +164,28 @@ def apply_dense(xinput):
     "concatenate": (Concatenate, {}),
 }
 
-regularizers = {
-    'l1_l2': (l1_l2, {'l1': 0., 'l2': 0.})
-    }
+regularizers = {'l1_l2': (l1_l2, {'l1': 0.0, 'l2': 0.0})}
+
 
 def base_layer_selector(layer_name, **kwargs):
     """
-        Given a layer name, looks for it in the `layers` dictionary and returns an instance.
+    Given a layer name, looks for it in the `layers` dictionary and returns an instance.
 
-        The layer dictionary defines a number of defaults
-        but they can be overwritten/enhanced through kwargs
+    The layer dictionary defines a number of defaults
+    but they can be overwritten/enhanced through kwargs
 
-        Parameters
-        ----------
-            `layer_name
-                str with the name of the layer
-            `**kwargs`
-                extra optional arguments to pass to the layer (beyond their defaults)
+    Parameters
+    ----------
+        `layer_name
+            str with the name of the layer
+        `**kwargs`
+            extra optional arguments to pass to the layer (beyond their defaults)
     """
     try:
         layer_tuple = layers[layer_name]
     except KeyError as e:
         raise NotImplementedError(
-            "Layer not implemented in keras_backend/base_layers.py: {0}".format(
-                layer_name
-            )
+            "Layer not implemented in keras_backend/base_layers.py: {0}".format(layer_name)
         ) from e
 
     layer_class = layer_tuple[0]
@@ -182,6 +200,7 @@ def base_layer_selector(layer_name, **kwargs):
 
     return layer_class(**layer_args)
 
+
 def regularizer_selector(reg_name, **kwargs):
     """Given a regularizer name looks in the `regularizer` dictionary and
     return an instance.
@@ -204,7 +223,8 @@ def regularizer_selector(reg_name, **kwargs):
         reg_tuple = regularizers[reg_name]
     except KeyError:
         raise NotImplementedError(
-            "Regularizer not implemented in keras_backend/base_layers.py: {0}".format(reg_name))
+            "Regularizer not implemented in keras_backend/base_layers.py: {0}".format(reg_name)
+        )
 
     reg_class = reg_tuple[0]
     reg_args = reg_tuple[1]
diff --git a/n3fit/src/n3fit/backends/keras_backend/multi_dense.py b/n3fit/src/n3fit/backends/keras_backend/multi_dense.py
new file mode 100644
index 0000000000..b8caa9a3fd
--- /dev/null
+++ b/n3fit/src/n3fit/backends/keras_backend/multi_dense.py
@@ -0,0 +1,169 @@
+from typing import List
+
+import tensorflow as tf
+from tensorflow.keras.initializers import Initializer
+from tensorflow.keras.layers import Dense
+
+
+class MultiDense(Dense):
+    """
+    Dense layer for multiple replicas at the same time.
+
+    For the first layer in the network, (for which ``is_first_layer`` should be set to True),
+    the input shape is (batch_size, gridsize, features), still without a replica axis.
+    In this case this layer acts as a stack of single dense layers,
+    with their own kernel and bias, acting on the same input.
+
+    For subsequent layers, the input already contains multiple replicas, and the shape is
+    (batch_size, replicas, gridsize, features).
+    In this case, the input for each replica is multiplied by its own slice of the kernel.
+
+    Weights are initialized using a `replica_seeds` list of seeds, and are identical to the
+    weights of a list of single dense layers with the same `replica_seeds`.
+
+    Parameters
+    ----------
+    replica_seeds: List[int]
+        List of seeds per replica for the kernel initializer.
+    kernel_initializer: Initializer
+        Initializer class for the kernel.
+    is_first_layer: bool (default: False)
+        Whether this is the first MultiDense layer in the network, and so the input shape
+        does not contain a replica axis.
+    """
+
+    def __init__(
+        self,
+        replica_seeds: List[int],
+        kernel_initializer: Initializer,
+        is_first_layer: bool = False,
+        **kwargs,
+    ):
+        super().__init__(**kwargs)
+        self.replicas = len(replica_seeds)
+        self.replica_seeds = replica_seeds
+        self.kernel_initializer = MultiInitializer(
+            single_initializer=kernel_initializer, replica_seeds=replica_seeds
+        )
+        self.bias_initializer = MultiInitializer(
+            single_initializer=self.bias_initializer, replica_seeds=replica_seeds
+        )
+        self.is_first_layer = is_first_layer
+
+        # Definition of the convolution between the input of the layer and the kernel parameters
+        # it is defined during the build stage.
+        self.matmul = None
+
+    def build(self, input_shape):
+        input_dim = input_shape[-1]
+        self.kernel = self.add_weight(
+            name="kernel",
+            shape=(self.replicas, input_dim, self.units),
+            initializer=self.kernel_initializer,
+            regularizer=self.kernel_regularizer,
+            constraint=self.kernel_constraint,
+        )
+        if self.use_bias:
+            self.bias = self.add_weight(
+                name="bias",
+                shape=(self.replicas, 1, self.units),
+                initializer=self.bias_initializer,
+                regularizer=self.bias_regularizer,
+                constraint=self.bias_constraint,
+            )
+        else:
+            self.bias = None
+        self.input_spec.axes = {-1: input_dim}
+        self.built = True
+
+        # Using tensordot here for numerical stability with 4.0 fits
+        # TODO: benchmark against the replica-agnostic einsum below and make that default
+        # see https://github.com/NNPDF/nnpdf/pull/1905#discussion_r1489344081
+        if self.replicas == 1:
+            matmul = lambda inputs: tf.tensordot(inputs, self.kernel[0], [[-1], [0]])
+            if self.is_first_layer:
+                # Manually add replica dimension
+                self.matmul = lambda x: tf.expand_dims(matmul(x), axis=1)
+            else:
+                self.matmul = matmul
+        else:
+            einrule = "bnf,rfg->brng" if self.is_first_layer else "brnf,rfg->brng"
+            self.matmul = lambda inputs: tf.einsum(einrule, inputs, self.kernel)
+
+    def call(self, inputs):
+        """
+        Compute output of shape (batch_size, replicas, gridsize, units).
+
+        For the first layer, this is equivalent to
+        applying each replica separately and concatenating along the last axis.
+        If the input already contains multiple replica outputs, it is equivalent
+        to applying each replica to its corresponding input.
+        """
+        if inputs.dtype.base_dtype != self._compute_dtype_object.base_dtype:
+            inputs = tf.cast(inputs, dtype=self._compute_dtype_object)
+
+        outputs = self.matmul(inputs)
+
+        # Reshape the output back to the original ndim of the input.
+        if not tf.executing_eagerly():
+            output_shape = self.compute_output_shape(inputs.shape.as_list())
+            outputs.set_shape(output_shape)
+
+        if self.use_bias:
+            outputs = outputs + self.bias
+
+        if self.activation is not None:
+            outputs = self.activation(outputs)
+
+        return outputs
+
+    def compute_output_shape(self, input_shape):
+        if not self.is_first_layer:
+            # Remove the replica axis from the input shape.
+            input_shape = input_shape[:1] + input_shape[2:]
+
+        output_shape = super().compute_output_shape(input_shape)
+
+        # Add back the replica axis to the output shape.
+        output_shape = output_shape[:1] + [self.replicas] + output_shape[1:]
+
+        return output_shape
+
+    def get_config(self):
+        config = super().get_config()
+        config.update({"is_first_layer": self.is_first_layer, "replica_seeds": self.replica_seeds})
+        return config
+
+
+class MultiInitializer(Initializer):
+    """
+    Multi replica initializer that exactly replicates a stack of single replica initializers.
+
+    Weights are stacked on the first axis, and per replica seeds are added to a base seed of the
+    given single replica initializer.
+
+    Parameters
+    ----------
+        single_initializer: Initializer
+            Initializer class for the kernel.
+        replica_seeds: List[int]
+            List of seeds per replica for the kernel initializer.
+    """
+
+    def __init__(self, single_initializer: Initializer, replica_seeds: List[int]):
+        self.initializer_class = type(single_initializer)
+        self.initializer_config = single_initializer.get_config()
+        self.base_seed = single_initializer.seed if hasattr(single_initializer, "seed") else None
+        self.replica_seeds = replica_seeds
+
+    def __call__(self, shape, dtype=None, **kwargs):
+        shape = shape[1:]  # Remove the replica axis from the shape.
+        per_replica_weights = []
+        for replica_seed in self.replica_seeds:
+            if self.base_seed is not None:
+                self.initializer_config["seed"] = self.base_seed + replica_seed
+            single_initializer = self.initializer_class.from_config(self.initializer_config)
+
+            per_replica_weights.append(single_initializer(shape, dtype, **kwargs))
+
+        return tf.stack(per_replica_weights, axis=0)
diff --git a/n3fit/src/n3fit/checks.py b/n3fit/src/n3fit/checks.py
index 885785a268..36ae24d52c 100644
--- a/n3fit/src/n3fit/checks.py
+++ b/n3fit/src/n3fit/checks.py
@@ -427,10 +427,9 @@ def check_fiatlux_pdfs_id(replicas, fiatlux):
                 f"Cannot generate a photon replica with id larger than the number of replicas of the PDFs set {luxset.name}:\nreplica id={max_id}, replicas of {luxset.name} = {pdfs_ids}"
             )
 
+
 @make_argcheck
 def check_multireplica_qed(replicas, fiatlux):
     if fiatlux is not None:
         if len(replicas) > 1:
-            raise CheckError(
-                "At the moment, running a multireplica QED fits is not allowed."
-            )
+            raise CheckError("At the moment, running a multireplica QED fits is not allowed.")
diff --git a/n3fit/src/n3fit/model_gen.py b/n3fit/src/n3fit/model_gen.py
index fc180f392f..5c338135a1 100644
--- a/n3fit/src/n3fit/model_gen.py
+++ b/n3fit/src/n3fit/model_gen.py
@@ -719,7 +719,6 @@ def generate_nn(
     nodes_list = list(nodes)  # so we can modify it
     x_input = Input(shape=(None, nodes_in), batch_size=1, name='xgrids_processed')
 
-    custom_args = {}
     if layer_type == "dense_per_flavour":
         # set the arguments that will define the layer
         # but careful, the last layer must be nodes = 1
@@ -728,39 +727,51 @@ def generate_nn(
         # come from the runcard
         nodes_list[-1] = 1
         basis_size = last_layer_nodes
-        custom_args['basis_size'] = basis_size
 
-        def initializer_generator(seed, i_layer):
-            seed += i_layer * basis_size
-            initializers = [
-                MetaLayer.select_initializer(initializer_name, seed=seed + b)
-                for b in range(basis_size)
-            ]
-            return initializers
-
-    else:  # "dense"
+        def layer_generator(i_layer, nodes_out, activation):
+            """Generate the ``i_layer``-th dense_per_flavour layer for all replicas."""
+            layers = []
+            for replica_seed in replica_seeds:
+                seed = replica_seed + i_layer * basis_size
+                initializers = [
+                    MetaLayer.select_initializer(initializer_name, seed=seed + b)
+                    for b in range(basis_size)
+                ]
+                layer = base_layer_selector(
+                    layer_type,
+                    kernel_initializer=initializers,
+                    units=nodes_out,
+                    activation=activation,
+                    input_shape=(nodes_in,),
+                    basis_size=basis_size,
+                )
+                layers.append(layer)
+
+            return layers
+
+    elif layer_type == "dense":
         reg = regularizer_selector(regularizer, **regularizer_args)
-        custom_args['regularizer'] = reg
-
-        def initializer_generator(seed, i_layer):
-            seed += i_layer
-            return MetaLayer.select_initializer(initializer_name, seed=seed)
 
-    # First create all the layers...
-    # list_of_pdf_layers[d][r] is the layer at depth d for replica r
-    list_of_pdf_layers = []
-    for i_layer, (nodes_out, activation) in enumerate(zip(nodes_list, activations)):
-        layers = [
-            base_layer_selector(
+        def layer_generator(i_layer, nodes_out, activation):
+            """Generate the ``i_layer``-th MetaLayer.MultiDense layer for all replicas."""
+            return base_layer_selector(
                 layer_type,
-                kernel_initializer=initializer_generator(replica_seed, i_layer),
+                replica_seeds=replica_seeds,
+                kernel_initializer=MetaLayer.select_initializer(initializer_name, seed=i_layer),
                 units=nodes_out,
                 activation=activation,
-                input_shape=(nodes_in,),
-                **custom_args,
+                is_first_layer=(i_layer == 0),
+                regularizer=reg,
             )
-            for replica_seed in replica_seeds
-        ]
+
+    else:
+        raise ValueError(f"{layer_type=} not recognized during model generation")
+
+    # First create all the layers
+    # list_of_pdf_layers[d][r] is the layer at depth d for replica r
+    list_of_pdf_layers = []
+    for i_layer, (nodes_out, activation) in enumerate(zip(nodes_list, activations)):
+        layers = layer_generator(i_layer, nodes_out, activation)
         list_of_pdf_layers.append(layers)
         nodes_in = int(nodes_out)
 
@@ -775,6 +786,14 @@ def initializer_generator(seed, i_layer):
         list_of_pdf_layers[-1] = [lambda x: concat(layer(x)) for layer in list_of_pdf_layers[-1]]
 
     # Apply all layers to the input to create the models
+    if layer_type == "dense":
+        pdfs = x_input
+        for layer in list_of_pdf_layers:
+            pdfs = layer(pdfs)
+        model = MetaModel({'NN_input': x_input}, pdfs, name=NN_LAYER_ALL_REPLICAS)
+
+        return model
+
     pdfs = [layer(x_input) for layer in list_of_pdf_layers[0]]
 
     for layers in list_of_pdf_layers[1:]:
diff --git a/n3fit/src/n3fit/tests/regressions/weights_1.h5 b/n3fit/src/n3fit/tests/regressions/weights_1.h5
index f9f822c188..0f8cd42ccf 100644
Binary files a/n3fit/src/n3fit/tests/regressions/weights_1.h5 and b/n3fit/src/n3fit/tests/regressions/weights_1.h5 differ
diff --git a/n3fit/src/n3fit/tests/regressions/weights_3.h5 b/n3fit/src/n3fit/tests/regressions/weights_3.h5
index 4ba36e4efe..44a9bfff3f 100644
Binary files a/n3fit/src/n3fit/tests/regressions/weights_3.h5 and b/n3fit/src/n3fit/tests/regressions/weights_3.h5 differ
diff --git a/n3fit/src/n3fit/tests/test_modelgen.py b/n3fit/src/n3fit/tests/test_modelgen.py
index ffdaa254b6..c87523f838 100644
--- a/n3fit/src/n3fit/tests/test_modelgen.py
+++ b/n3fit/src/n3fit/tests/test_modelgen.py
@@ -26,16 +26,17 @@
 
 
 def test_generate_dense_network():
-    nn = generate_nn("dense", **COMMON_ARGS).get_layer(f"{NN_PREFIX}_0")
+    nn = generate_nn("dense", **COMMON_ARGS)
 
     # The number of layers should be input layer + len(OUT_SIZES)
     assert len(nn.layers) == len(OUT_SIZES) + 1
     # Check that the number of parameters is as expected
-    # We expect 4 weights where the two first ones are
-    # (INSIZE, OUT_SIZE[0]) (OUT_SIZE[0],)
-    # and the second one
-    # (OUT_SIZE[0], OUT_SIZE[1]) (OUT_SIZE[1],)
-    expected_sizes = [(INSIZE, OUT_SIZES[0]), (OUT_SIZES[0],), OUT_SIZES, (OUT_SIZES[1],)]
+    expected_sizes = [
+        (1, INSIZE, OUT_SIZES[0]),
+        (1, 1, OUT_SIZES[0]),
+        (1, *OUT_SIZES),
+        (1, 1, OUT_SIZES[1]),
+    ]
     for weight, esize in zip(nn.weights, expected_sizes):
         assert weight.shape == esize
 
diff --git a/n3fit/src/n3fit/tests/test_multidense.py b/n3fit/src/n3fit/tests/test_multidense.py
new file mode 100644
index 0000000000..6c7df89e3a
--- /dev/null
+++ b/n3fit/src/n3fit/tests/test_multidense.py
@@ -0,0 +1,67 @@
+import numpy as np
+import tensorflow as tf
+from tensorflow.keras import Sequential
+from tensorflow.keras.initializers import GlorotUniform
+from tensorflow.keras.layers import Dense
+
+from n3fit.backends.keras_backend.multi_dense import MultiDense
+
+
+def test_multidense():
+    replicas = 2
+    multi_dense_model = Sequential(
+        [
+            MultiDense(
+                units=8,
+                replica_seeds=[42, 43],
+                is_first_layer=True,
+                kernel_initializer=GlorotUniform(seed=0),
+            ),
+            MultiDense(units=4, replica_seeds=[52, 53], kernel_initializer=GlorotUniform(seed=100)),
+        ]
+    )
+    single_models = [
+        Sequential(
+            [
+                Dense(units=8, kernel_initializer=GlorotUniform(seed=42 + r)),
+                Dense(units=4, kernel_initializer=GlorotUniform(seed=52 + r + 100)),
+            ]
+        )
+        for r in range(replicas)
+    ]
+
+    gridsize, features = 100, 3
+    multi_dense_model.build(input_shape=(None, gridsize, features))
+    for single_model in single_models:
+        single_model.build(input_shape=(None, gridsize, features))
+
+    test_input = tf.random.uniform(shape=(1, gridsize, features))
+    multi_dense_output = multi_dense_model(test_input)
+    single_dense_output = tf.stack(
+        [single_model(test_input) for single_model in single_models], axis=1
+    )
+
+    np.testing.assert_allclose(multi_dense_output, single_dense_output, atol=1e-6, rtol=1e-4)
+
+
+def test_initializers():
+    input_shape = (None, 3, 1)
+    dense_layers = []
+    for r in range(2):
+        dense_layer = Dense(units=2, kernel_initializer=GlorotUniform(seed=42 + r))
+        dense_layer.build(input_shape=input_shape)
+        dense_layers.append(dense_layer)
+    stacked_weights = tf.stack([dense_layer.weights[0] for dense_layer in dense_layers], axis=0)
+
+    multi_dense_layer = MultiDense(
+        units=2,
+        replica_seeds=[0, 1],
+        is_first_layer=True,
+        kernel_initializer=GlorotUniform(seed=42),
+    )
+    multi_dense_layer.build(input_shape=input_shape)
+
+    multi_dense_weights = multi_dense_layer.weights[0].numpy()
+    stacked_weights = stacked_weights.numpy()
+
+    np.testing.assert_allclose(multi_dense_weights, stacked_weights)