diff --git a/extra_tests/regression_fits/central_16.exportgrid b/extra_tests/regression_fits/central_16.exportgrid
index 503dbac86cfee4f0c535d52bc9bb41f56c37a896..f7a1c4867c02388e8732658afb6bf72505ef6227 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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+- [0.0, 0.0, -0.0010139032965525985, -0.001640691072680056, 0.0005001270910724998,
+  -0.00020125420996919274, -0.00010387294605607167, 0.0004656038072425872, 0.001187065034173429,
+  0.00236827926710248, -0.0010139032965525985, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0006949784583412111, -0.0010792419780045748, 0.0002781673101708293,
+  -0.00012714476906694472, -4.522580638877116e-05, 0.00035548117011785507, 0.0007701903814449906,
+  0.0015820282278582454, -0.0006949784583412111, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00042745628161355853, -0.0006301675457507372, 0.000126415237900801,
+  -7.305805047508329e-05, -1.543406324344687e-05, 0.00024548458168283105, 0.0004484878445509821,
+  0.0009417735855095088, -0.0004274562234058976, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00021569371165242046, -0.00029629794880747795, 3.743174238479696e-05,
+  -3.5802790080197155e-05, -3.3772944334486965e-06, 0.00014104122237768024, 0.00021516370179597288,
+  0.0004546306445263326, -0.00021569371165242046, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.706928252242506e-05, -8.231806714320555e-05, 1.1257181995460996e-06,
+  -1.2018663255730644e-05, -2.496806814633601e-07, 5.152112862560898e-05, 6.474938709288836e-05,
+  0.00013189841411076486, -6.706927524646744e-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 ea2c90be7e3ab77d7d15c54b16f15829edb489b5..c5e586f79ea43442d84f0a247dcb57bd5e03ce97 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": 2.6700053215026855,
-  "erf_vl": 2.596088409423828,
-  "chi2": 2.1046974658966064,
+  "erf_tr": 2.670098304748535,
+  "erf_vl": 2.5964081287384033,
+  "chi2": 2.1027894020080566,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.3207831327275608,
-    1.4752541158950256,
-    1.1834874152294614,
-    1.0011426742289826,
-    1.1960979802612568
+    1.320814433685272,
+    1.4723886173965648,
+    1.1834960676986725,
+    1.0011427382272051,
+    1.196111193543841
   ],
   "integrability": [
-    0.0009203169902344266,
-    0.0009203169902324282,
-    4.8332353002611406e-05,
-    0.46257528662681513,
-    0.006963513907974672
+    0.0009203124209320734,
+    0.0009203124209312685,
+    4.8332128016359555e-05,
+    0.4625752046704281,
+    0.006963436899239506
   ],
   "timing": {
     "walltime": {
-      "Total": 18.85464835166931,
+      "Total": 20.482789754867554,
       "start": 0.0,
-      "replica_set": 0.3591601848602295,
-      "replica_fitted": 18.854573249816895,
-      "replica_set_to_replica_fitted": 18.495413064956665
+      "replica_set": 0.38495421409606934,
+      "replica_fitted": 20.482685327529907,
+      "replica_set_to_replica_fitted": 20.097731113433838
     },
     "cputime": {
-      "Total": 20.889074,
+      "Total": 22.8096241,
       "start": 0.0,
-      "replica_set": 0.6770135999999995,
-      "replica_fitted": 20.888997200000002,
-      "replica_set_to_replica_fitted": 20.211983600000003
+      "replica_set": 0.6998853,
+      "replica_fitted": 22.809518,
+      "replica_set_to_replica_fitted": 22.1096327
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ 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 eb4155994c88e7d29169b0a564d27a36ffffbef3..74c4ca69424091836cedd9cd722abbbf188e1a75 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, -2.306413173675537, 0.16342006623744965, 0.1369123011827469, 0.13695918023586273,
-  -16.513973236083984, 0.13711097836494446, 0.1370655596256256, 0.16317586600780487,
-  -2.306413173675537, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.233588218688965, 0.16312028467655182, 0.13555052876472473, 0.13560384511947632,
-  -16.522781372070312, 0.13577169179916382, 0.13572008907794952, 0.16285233199596405,
-  -2.2335877418518066, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1630680561065674, 0.16308163106441498, 0.13440610468387604, 0.1344667226076126,
-  -16.530052185058594, 0.13465234637260437, 0.13459381461143494, 0.16278767585754395,
-  -2.1630680561065674, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.094780921936035, 0.1633024513721466, 0.13347531855106354, 0.13354429602622986,
-  -16.535680770874023, 0.13374963402748108, 0.1336831897497177, 0.16297999024391174,
-  -2.094780921936035, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0286550521850586, 0.16378167271614075, 0.13275523483753204, 0.13283362984657288,
-  -16.53955841064453, 0.1330607533454895, 0.1329854130744934, 0.1634279191493988,
-  -2.0286550521850586, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9646214246749878, 0.16451886296272278, 0.13224317133426666, 0.13233228027820587,
-  -16.54155921936035, 0.1325835883617401, 0.1324981302022934, 0.1641308218240738,
-  -1.9646217823028564, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.902613878250122, 0.16551391780376434, 0.13193675875663757, 0.13203807175159454,
-  -16.54155731201172, 0.1323162466287613, 0.1322193145751953, 0.1650882214307785,
-  -1.902613878250122, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8425673246383667, 0.16676653921604156, 0.13183334469795227, 0.1319485306739807,
-  -16.539417266845703, 0.132256418466568, 0.13214653730392456, 0.16629961133003235,
-  -1.8425675630569458, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.784420371055603, 0.16827784478664398, 0.13193151354789734, 0.13206246495246887,
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-  -1.784420371055603, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7281112670898438, 0.17004846036434174, 0.1322292536497116, 0.13237814605236053,
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-  -1.7281112670898438, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6735825538635254, 0.17207995057106018, 0.13272537291049957, 0.1328946053981781,
-  -16.51863670349121, 0.1333128660917282, 0.1331528276205063, 0.1714639961719513,
-  -1.6735825538635254, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.620776653289795, 0.1743740290403366, 0.13341856002807617, 0.13361097872257233,
-  -16.506370544433594, 0.1340743750333786, 0.13389307260513306, 0.1736985743045807,
-  -1.620776653289795, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5696386098861694, 0.17693264782428741, 0.13430769741535187, 0.13452641665935516,
-  -16.491125106811523, 0.13504000008106232, 0.1348346322774887, 0.17619197070598602,
-  -1.5696388483047485, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5201154947280884, 0.1797586977481842, 0.13539232313632965, 0.1356409341096878,
-  -16.472694396972656, 0.13621024787425995, 0.13597771525382996, 0.17894650995731354,
-  -1.5201157331466675, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4721556901931763, 0.18285460770130157, 0.13667136430740356, 0.1369539350271225,
-  -16.45085906982422, 0.13758517801761627, 0.13732193410396576, 0.18196402490139008,
-  -1.4721559286117554, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4257094860076904, 0.18622396886348724, 0.13814470171928406, 0.13846586644649506,
-  -16.425395965576172, 0.1391659528017044, 0.1388680636882782, 0.1852474957704544,
-  -1.4257092475891113, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3807276487350464, 0.18987040221691132, 0.13981199264526367, 0.14017699658870697,
-  -16.396047592163086, 0.14095360040664673, 0.14061658084392548, 0.18879978358745575,
-  -1.3807276487350464, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3371635675430298, 0.19379813969135284, 0.1416732519865036, 0.14208810031414032,
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-  -1.3371638059616089, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2949720621109009, 0.1980116367340088, 0.14372847974300385, 0.1441999077796936,
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-- [0.0, 0.0, -1.2541087865829468, 0.20251575112342834, 0.14597776532173157, 0.1465134620666504,
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-  -1.2541087865829468, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2145310640335083, 0.20731577277183533, 0.14842133224010468, 0.14902999997138977,
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-- [0.0, 0.0, -1.1761982440948486, 0.21241798996925354, 0.15106002986431122, 0.1517515480518341,
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-  -1.1761982440948486, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.139068841934204, 0.21782775223255157, 0.15389341115951538, 0.15467901527881622,
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-  -1.139068841934204, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.103104829788208, 0.22355204820632935, 0.15692228078842163, 0.1578146368265152,
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-  -1.103105068206787, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0682686567306519, 0.22959774732589722, 0.1601468175649643, 0.16116033494472504,
-  -15.985340118408203, 0.16295865178108215, 0.16206739842891693, 0.22736354172229767,
-  -1.0682686567306519, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.034523844718933, 0.23597198724746704, 0.1635671705007553, 0.1647181361913681,
-  -15.906577110290527, 0.16671793162822723, 0.165713831782341, 0.2335226684808731,
-  -1.0345240831375122, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.001834750175476, 0.24268263578414917, 0.1671835035085678, 0.16849036514759064,
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-  -1.0018346309661865, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9701670408248901, 0.2497376650571823, 0.17099551856517792, 0.17247915267944336,
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-- [0.0, 0.0, -0.9394879937171936, 0.25714513659477234, 0.17500263452529907, 0.17668667435646057,
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-  -0.9394879937171936, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.90976482629776, 0.2649139165878296, 0.17920413613319397, 0.18111521005630493,
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-- [0.0, 0.0, -0.8809667229652405, 0.27305278182029724, 0.1835986077785492, 0.18576692044734955,
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-- [0.0, 0.0, -0.8530634641647339, 0.28157079219818115, 0.1881842017173767, 0.19064372777938843,
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-- [0.0, 0.0, -0.826025664806366, 0.29047688841819763, 0.19295808672904968, 0.19574719667434692,
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-- [0.0, 0.0, -0.7998253703117371, 0.29978057742118835, 0.19791695475578308, 0.201078861951828,
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-- [0.0, 0.0, -0.7744348645210266, 0.30949079990386963, 0.20305605232715607, 0.2066393792629242,
-  -14.788352012634277, 0.211903378367424, 0.20908038318157196, 0.3038780391216278,
-  -0.7744348645210266, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7498273849487305, 0.31961631774902344, 0.2083694487810135, 0.21242891252040863,
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-  -0.74982750415802, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7259777784347534, 0.3301658630371094, 0.21385003626346588, 0.2184470146894455,
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-  -0.7259776592254639, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.7028614282608032, 0.3411475419998169, 0.21948905289173126, 0.22469229996204376,
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-  -0.7028614282608032, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6804541945457458, 0.35256877541542053, 0.22527535259723663, 0.23116189241409302,
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-  -0.6804541945457458, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6587333083152771, 0.36443546414375305, 0.23119564354419708, 0.23785144090652466,
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-- [0.0, 0.0, -0.6376766562461853, 0.37675273418426514, 0.23723410069942474, 0.24475494027137756,
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-  -0.6376766562461853, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.6172631978988647, 0.38952362537384033, 0.2433719038963318, 0.25186434388160706,
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-  -0.6172631978988647, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5974729657173157, 0.40274932980537415, 0.24958674609661102, 0.2591688632965088,
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-  -0.5974729657173157, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5782867670059204, 0.4164275825023651, 0.2558523714542389, 0.2666545808315277,
-  -12.543069839477539, 0.28077462315559387, 0.27381226420402527, 0.4034808874130249,
-  -0.5782867670059204, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5596864819526672, 0.4305534362792969, 0.2621384263038635, 0.27430441975593567,
-  -12.193120002746582, 0.2900708317756653, 0.28249093890190125, 0.41634121537208557,
-  -0.5596863627433777, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5416556000709534, 0.4451172649860382, 0.26840940117836, 0.2820965051651001,
-  -11.81893539428711, 0.2997012734413147, 0.2914881408214569, 0.4295157194137573,
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-- [0.0, 0.0, -0.5241780877113342, 0.46010416746139526, 0.27462488412857056, 0.2900046408176422,
-  -11.419413566589355, 0.30966106057167053, 0.3008105456829071, 0.44297829270362854,
-  -0.5241780877113342, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.5072401762008667, 0.4754934012889862, 0.2807384729385376, 0.2979968190193176,
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+- [0.0, 0.0, -0.011422792449593544, -0.023467453196644783, 0.015098084695637226, -0.004096267279237509,
+  -0.01828838884830475, -0.0008565728203393519, 0.02082960680127144, 0.028925472870469093,
+  -0.011422794312238693, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.010446553118526936, -0.021331816911697388, 0.01342203002423048, -0.0036099969875067472,
+  -0.01526891253888607, -0.0007239545811899006, 0.018407944589853287, 0.02630038373172283,
+  -0.010446553118526936, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00951011199504137, -0.019283724948763847, 0.01184975728392601, -0.003158364910632372,
+  -0.01261185947805643, -0.0005924039869569242, 0.016168396919965744, 0.02379128523170948,
+  -0.00951011385768652, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.008613575249910355, -0.01732621155679226, 0.010381186380982399, -0.002741164295002818,
+  -0.010293722152709961, -0.0004642237618099898, 0.014105495065450668, 0.021399175748229027,
+  -0.008613577112555504, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.007757081184536219, -0.01546207070350647, 0.009016080759465694, -0.0023580684792250395,
+  -0.008290437050163746, -0.00034157882328145206, 0.012213625945150852, 0.019125046208500862,
+  -0.007757082115858793, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006940797902643681, -0.01369384117424488, 0.007753979880362749, -0.002008607378229499,
+  -0.006577525287866592, -0.00022643711417913437, 0.01048700325191021, 0.016969889402389526,
+  -0.006940798833966255, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006164947059005499, -0.01202390156686306, 0.006594246719032526, -0.0016921852948144078,
+  -0.0051303403452038765, -0.00012061450252076611, 0.008919713087379932, 0.014934752136468887,
+  -0.006164947524666786, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005429806187748909, -0.01045442745089531, 0.005536009091883898, -0.0014080626424401999,
+  -0.003924181684851646, -2.571785262261983e-05, 0.007505691144615412, 0.013020751066505909,
+  -0.005429805256426334, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004735712427645922, -0.00898739229887724, 0.004578159656375647, -0.001155342091806233,
+  -0.0029344765935093164, 5.681974289473146e-05, 0.006238687317818403, 0.011229036375880241,
+  -0.004735713358968496, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004083100240677595, -0.007624650839716196, 0.0037193403113633394,
+  -0.0009329815511591733, -0.0021369829773902893, 0.00012578765745274723, 0.005112320650368929,
+  0.009560885839164257, -0.004083100240677595, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0034724967554211617, -0.006367887835949659, 0.0029578953981399536,
+  -0.0007397696608677506, -0.001507937558926642, 0.00018020269635599107, 0.004120017401874065,
+  0.008017675951123238, -0.0034724962897598743, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002904562745243311, -0.005218689329922199, 0.002291855402290821, -0.000574317469727248,
+  -0.0010242630960419774, 0.00021933876269031316, 0.003255037125200033, 0.006600949447602034,
+  -0.002904562745243311, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0023801245260983706, -0.004178548697382212, 0.001718891435302794,
+  -0.00043504752102307975, -0.0006637468468397856, 0.00024275736359413713, 0.0025104505475610495,
+  0.005312446970492601, -0.002380124991759658, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0019002200569957495, -0.0032489041332155466, 0.001236251788213849,
+  -0.0003201733634341508, -0.00040523792267777026, 0.00025036538136191666, 0.00187912886030972,
+  0.004154152702540159, -0.0019002199405804276, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.001466176239773631, -0.0024312061723321676, 0.0008406996494159102,
+  -0.000227685333811678, -0.00022885504586156458, 0.00024247635155916214, 0.0013537395279854536,
+  0.0031284098513424397, -0.001466176239773631, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010797035647556186, -0.0017269651871174574, 0.0005283903446979821,
+  -0.00015532266115769744, -0.00011619392171269283, 0.0002199259033659473, 0.0009267281857319176,
+  0.002237997017800808, -0.0010797035647556186, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0007430942496284842, -0.0011378999333828688, 0.000294725236017257,
+  -0.00010055329039460048, -5.056637019151822e-05, 0.00018424182781018317, 0.0005903392448090017,
+  0.0014863689430058002, -0.000743094424251467, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00045952864456921816, -0.0006661344086751342, 0.00013407092774286866,
+  -6.05537679803092e-05, -1.7248572476091795e-05, 0.000137948285555467, 0.00033664226066321135,
+  0.000877973681781441, -0.00045952864456921816, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0002337401092518121, -0.0003146260278299451, 3.926815406884998e-05,
+  -3.222027589799836e-05, -3.7726092614320805e-06, 8.517834794474766e-05, 0.00015769166930112988,
+  0.00041894998867064714, -0.00023374013835564256, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -7.37723967176862e-05, -8.833003812469542e-05, 4.6725278934900416e-07,
+  -1.2370160220598336e-05, -2.787792823255586e-07, 3.3221844205399975e-05, 4.615620491676964e-05,
+  0.00011895166971953586, -7.377240399364382e-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 fd464acbda07ec8140be4dc4411456908eecfea1..4fd13215e71293f2e4662aab0f258bab39a4ff81 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": 3.3770620822906494,
+  "erf_tr": 3.3770642280578613,
   "erf_vl": 3.2323102951049805,
-  "chi2": 2.229722023010254,
+  "chi2": 2.2297263145446777,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.318226912266057,
-    1.5444128182135202,
-    1.179107474257061,
-    1.0015316669311096,
-    1.2179101304602167
+    1.3182265509206665,
+    1.5444147441704428,
+    1.1791074624024902,
+    1.0015316549599111,
+    1.2179114648035199
   ],
   "integrability": [
-    0.0008988641238855122,
-    0.0008988641238834028,
-    4.724650636855898e-05,
-    0.46261481940746196,
-    0.0070505824987761034
+    0.0008988639456246617,
+    0.0008988639456223302,
+    4.7246536836742514e-05,
+    0.4626150503754609,
+    0.007050594722385117
   ],
   "timing": {
     "walltime": {
-      "Total": 18.131428241729736,
+      "Total": 19.21068048477173,
       "start": 0.0,
-      "replica_set": 0.3876476287841797,
-      "replica_fitted": 18.131293058395386,
-      "replica_set_to_replica_fitted": 17.743645429611206
+      "replica_set": 0.3876974582672119,
+      "replica_fitted": 19.2105815410614,
+      "replica_set_to_replica_fitted": 18.82288408279419
     },
     "cputime": {
-      "Total": 20.1227844,
+      "Total": 21.2651539,
       "start": 0.0,
-      "replica_set": 0.704001100000001,
-      "replica_fitted": 20.1226482,
-      "replica_set_to_replica_fitted": 19.4186471
+      "replica_set": 0.7038960999999997,
+      "replica_fitted": 21.265053100000003,
+      "replica_set_to_replica_fitted": 20.561157
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/feature_scaling_81.json b/extra_tests/regression_fits/feature_scaling_81.json
index 72f073386b70c6a94766431dc1d42490ace8c7d6..620be972b5d9781f07c5251248018cba215826ff 100644
--- a/extra_tests/regression_fits/feature_scaling_81.json
+++ b/extra_tests/regression_fits/feature_scaling_81.json
@@ -71,24 +71,24 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 18.211228370666504,
+      "Total": 19.78455400466919,
       "start": 0.0,
-      "replica_set": 0.39786696434020996,
-      "replica_fitted": 18.211086988449097,
-      "replica_set_to_replica_fitted": 17.813220024108887
+      "replica_set": 0.3843960762023926,
+      "replica_fitted": 19.78445529937744,
+      "replica_set_to_replica_fitted": 19.40005922317505
     },
     "cputime": {
-      "Total": 20.0817579,
+      "Total": 21.797165300000003,
       "start": 0.0,
-      "replica_set": 0.7005326000000007,
-      "replica_fitted": 20.081615399999997,
-      "replica_set_to_replica_fitted": 19.381082799999998
+      "replica_set": 0.7009340999999996,
+      "replica_fitted": 21.797065099999998,
+      "replica_set_to_replica_fitted": 21.096131
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ No newline at end of file
diff --git a/extra_tests/regression_fits/flavour_29.exportgrid b/extra_tests/regression_fits/flavour_29.exportgrid
index 192fb76349f5a0a2c441b138cb2d1d9cc670587f..73362ea913bc94c4b1ff73a4f92a3bb0f3681662 100644
--- a/extra_tests/regression_fits/flavour_29.exportgrid
+++ b/extra_tests/regression_fits/flavour_29.exportgrid
@@ -87,9 +87,9 @@ pdfgrid:
 - [0.0, 0.0, -0.14895430207252502, 0.24588581919670105, 0.3680756986141205, 0.10286284238100052,
   -1.6412948369979858, 0.16512326896190643, 0.4689398407936096, 0.244236558675766,
   -0.14895425736904144, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.15229447185993195, 0.24562674760818481, 0.37209370732307434, 0.10177303850650787,
-  -1.5791362524032593, 0.16366641223430634, 0.4733952283859253, 0.24422100186347961,
-  -0.15229450166225433, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.15229448676109314, 0.24562668800354004, 0.37209367752075195, 0.10177300125360489,
+  -1.5791362524032593, 0.16366635262966156, 0.4733951985836029, 0.24422094225883484,
+  -0.15229453146457672, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.15574216842651367, 0.24535757303237915, 0.37624379992485046, 0.10064376890659332,
   -1.515177845954895, 0.1621570885181427, 0.47799140214920044, 0.24419888854026794,
   -0.15574213862419128, 0.0, 0.0, 0.0]
@@ -153,11 +153,11 @@ pdfgrid:
 - [0.0, 0.0, -0.25425276160240173, 0.2364824414253235, 0.4980448782444, 0.07307767868041992,
   0.21004416048526764, 0.12294769287109375, 0.6101816296577454, 0.2408454716205597,
   -0.2542527914047241, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.2609139382839203, 0.23570077121257782, 0.5066717863082886, 0.07188008725643158,
-  0.3206326365470886, 0.1208682730793953, 0.6193326711654663, 0.24034471809864044,
+- [0.0, 0.0, -0.2609139382839203, 0.23570077121257782, 0.5066717863082886, 0.07188010215759277,
+  0.3206326365470886, 0.12086828798055649, 0.6193326711654663, 0.24034471809864044,
   -0.2609139680862427, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.2677140533924103, 0.234847292304039, 0.5155699253082275, 0.07077652961015701,
-  0.43332526087760925, 0.1188407614827156, 0.6287373900413513, 0.23976650834083557,
+- [0.0, 0.0, -0.2677140533924103, 0.234847292304039, 0.5155699253082275, 0.07077653706073761,
+  0.43332526087760925, 0.1188407689332962, 0.6287373900413513, 0.23976650834083557,
   -0.2677140533924103, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.27462679147720337, 0.2339085042476654, 0.524726927280426, 0.06978268921375275,
   0.5479415655136108, 0.11687824130058289, 0.6383780837059021, 0.23909516632556915,
@@ -177,8 +177,8 @@ pdfgrid:
 - [0.0, 0.0, -0.3092227876186371, 0.22725816071033478, 0.5732590556144714, 0.06697443127632141,
   1.1380325555801392, 0.10848188400268555, 0.6886995434761047, 0.23356397449970245,
   -0.3092227876186371, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.3156188428401947, 0.225355863571167, 0.5830909609794617, 0.06692209094762802,
-  1.255548119544983, 0.10715459287166595, 0.6986900568008423, 0.23181523382663727,
+- [0.0, 0.0, -0.3156188428401947, 0.2253558486700058, 0.5830909609794617, 0.06692209094762802,
+  1.255548119544983, 0.10715459287166595, 0.6986900568008423, 0.23181524872779846,
   -0.3156188428401947, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.32159385085105896, 0.22319084405899048, 0.5927444100379944, 0.06704737991094589,
   1.370976209640503, 0.10595400631427765, 0.7084061503410339, 0.22976996004581451,
@@ -192,8 +192,8 @@ pdfgrid:
 - [0.0, 0.0, -0.33569902181625366, 0.21482810378074646, 0.6193123459815979, 0.06837309151887894,
   1.6935606002807617, 0.10304156690835953, 0.7344648241996765, 0.22152163088321686,
   -0.3356989622116089, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.33871889114379883, 0.21134883165359497, 0.6269066333770752, 0.06905965507030487,
-  1.789278507232666, 0.10225197672843933, 0.741624116897583, 0.21798917651176453,
+- [0.0, 0.0, -0.33871889114379883, 0.21134881675243378, 0.62690669298172, 0.06905965507030487,
+  1.789278507232666, 0.10225197672843933, 0.7416241765022278, 0.21798916161060333,
   -0.33871889114379883, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.34073489904403687, 0.20751141011714935, 0.6336542963981628, 0.06981994956731796,
   1.8772753477096558, 0.10151956230401993, 0.7477944493293762, 0.2140510380268097,
@@ -315,11 +315,11 @@ pdfgrid:
 - [0.0, 0.0, -0.08735264092683792, 0.033624690026044846, 0.3773176074028015, 0.04446864128112793,
   0.9675965309143066, 0.04508081451058388, 0.42720267176628113, 0.030822429805994034,
   -0.08735264092683792, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0824020653963089, 0.03150033950805664, 0.36699178814888, 0.04302497208118439,
-  0.9228903651237488, 0.04344648867845535, 0.4153457283973694, 0.028661807999014854,
+- [0.0, 0.0, -0.0824020653963089, 0.031500332057476044, 0.36699178814888, 0.043024979531764984,
+  0.9228903651237488, 0.04344649612903595, 0.4153457283973694, 0.02866179868578911,
   -0.08240208029747009, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.07766158133745193, 0.029486387968063354, 0.3567582666873932, 0.04159330949187279,
-  0.8793783783912659, 0.04183930158615112, 0.40360790491104126, 0.02662038616836071,
+- [0.0, 0.0, -0.07766158133745193, 0.029486380517482758, 0.3567582666873932, 0.041593313217163086,
+  0.8793783783912659, 0.04183930531144142, 0.40360790491104126, 0.026620378717780113,
   -0.07766158133745193, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.07312697917222977, 0.027578741312026978, 0.34662488102912903, 0.040175627917051315,
   0.8370882868766785, 0.04026041179895401, 0.3919968903064728, 0.024693578481674194,
@@ -363,9 +363,9 @@ pdfgrid:
 - [0.0, 0.0, -0.030635468661785126, 0.010702569968998432, 0.22663074731826782, 0.023699302226305008,
   0.40207329392433167, 0.022679267451167107, 0.2552758455276489, 0.008126295171678066,
   -0.030635468661785126, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.02844409830868244, 0.009889432229101658, 0.21844594180583954, 0.022617358714342117,
-  0.3771832585334778, 0.021568574011325836, 0.24599450826644897, 0.007366144564002752,
-  -0.02844409830868244, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.02844409830868244, 0.009889423847198486, 0.21844594180583954, 0.022617347538471222,
+  0.3771832585334778, 0.02156856842339039, 0.24599450826644897, 0.007366136647760868,
+  -0.02844410203397274, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -0.02637934312224388, 0.00912958849221468, 0.21042375266551971, 0.021564824506640434,
   0.3534272015094757, 0.02049296349287033, 0.23690243065357208, 0.006661758758127689,
   -0.02637934312224388, 0.0, 0.0, 0.0]
@@ -522,9 +522,9 @@ pdfgrid:
 - [0.0, 0.0, -2.928620233433321e-05, 4.5309374399948865e-05, 0.006419737357646227,
   0.00022756221005693078, 0.0007320509757846594, 0.0001349138474324718, 0.007175615523010492,
   -5.0080634537152946e-05, -2.9286195058375597e-05, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2459134925156832e-05, 3.9259328332263976e-05, 0.005591817665845156,
-  0.00019066590175498277, 0.0005718927131965756, 0.000109249354864005, 0.006249779369682074,
-  -4.378720041131601e-05, -2.2459140382125042e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.2459134925156832e-05, 3.9259066397789866e-05, 0.005591817665845156,
+  0.00019066604727413505, 0.0005718927131965756, 0.00010924947127932683, 0.006249779369682074,
+  -4.378743324195966e-05, -2.2459140382125042e-05, 0.0, 0.0, 0.0]
 - [0.0, 0.0, -1.7001650121528655e-05, 3.3831860491773114e-05, 0.0048376163467764854,
   0.0001584526035003364, 0.0004413191054482013, 8.740081830183044e-05, 0.005406470969319344,
   -3.7972240534145385e-05, -1.7001650121528655e-05, 0.0, 0.0, 0.0]
diff --git a/extra_tests/regression_fits/flavour_29.json b/extra_tests/regression_fits/flavour_29.json
index 871aa030f779fd344b9974817cd927afe7ad5cbf..d222928a79f4544b8ea1dc455826cdfe0ff87f09 100644
--- a/extra_tests/regression_fits/flavour_29.json
+++ b/extra_tests/regression_fits/flavour_29.json
@@ -56,11 +56,11 @@
   "chi2": 3.895918846130371,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.1046911082279192,
+    1.1046911095057348,
     1.2122842009645642,
-    0.99064649188045,
+    0.9906464918872098,
     0.990491641076893,
-    0.9907081134354656
+    0.9907081134568303
   ],
   "integrability": [
     0.4676428288221359,
@@ -71,24 +71,24 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 7.520705223083496,
+      "Total": 8.190976619720459,
       "start": 0.0,
-      "replica_set": 0.3701026439666748,
-      "replica_fitted": 7.520532608032227,
-      "replica_set_to_replica_fitted": 7.150429964065552
+      "replica_set": 0.39362668991088867,
+      "replica_fitted": 8.190709829330444,
+      "replica_set_to_replica_fitted": 7.797083139419556
     },
     "cputime": {
-      "Total": 8.128277999999998,
+      "Total": 8.850825799999999,
       "start": 0.0,
-      "replica_set": 0.6848363999999991,
-      "replica_fitted": 8.1281039,
-      "replica_set_to_replica_fitted": 7.443267500000001
+      "replica_set": 0.7093926999999995,
+      "replica_fitted": 8.8505578,
+      "replica_set_to_replica_fitted": 8.141165100000002
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ 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 44109e223dd942759b15c9cf13e5aaf33dca38d1..5459329ed833588614ca1de6d80c6d6dff69579f 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, -2.2586069107055664, 0.03173479065299034, 0.004537232685834169, 0.004585680551826954,
-  -16.76595687866211, 0.004740157630294561, 0.004693238064646721, 0.03148813918232918,
-  -2.2586069107055664, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1874356269836426, 0.03510401397943497, 0.006817394867539406, 0.006872483529150486,
-  -16.777841567993164, 0.0070432936772704124, 0.006990044843405485, 0.034833453595638275,
-  -2.1874356269836426, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1185097694396973, 0.0386151522397995, 0.00919452216476202, 0.009257174097001553,
-  -16.788318634033203, 0.009446079842746258, 0.00938564445823431, 0.03831837698817253,
-  -2.1185097694396973, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.051758289337158, 0.042271122336387634, 0.011669640429317951, 0.0117409098893404,
-  -16.797290802001953, 0.011949869804084301, 0.011881266720592976, 0.04194561764597893,
-  -2.051758289337158, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9871115684509277, 0.046073608100414276, 0.01424234639853239, 0.014323360286653042,
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-  -1.9871118068695068, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.924503207206726, 0.05002637580037117, 0.016914116218686104, 0.017006264999508858,
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-- [0.0, 0.0, -1.8638683557510376, 0.05413173511624336, 0.019685059785842896, 0.019789809361100197,
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-  -1.8638681173324585, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.80514395236969, 0.05839383974671364, 0.022556789219379425, 0.02267593890428543,
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-- [0.0, 0.0, -1.6931872367858887, 0.06740277260541916, 0.028606904670596123, 0.0287608802318573,
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-- [0.0, 0.0, -1.639838695526123, 0.07215816527605057, 0.031788166612386703, 0.03196331113576889,
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   -1.639838695526123, 0.0, 0.0, 0.0]
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-- [0.0, 0.0, -1.538124442100525, 0.08219420164823532, 0.038471538573503494, 0.03869795799255371,
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-- [0.0, 0.0, -1.4896533489227295, 0.08748524636030197, 0.0419774129986763, 0.04223485663533211,
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-- [0.0, 0.0, -1.4427058696746826, 0.0929657444357872, 0.04559546709060669, 0.04588814824819565,
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-- [0.0, 0.0, -1.3972324132919312, 0.09864147007465363, 0.04932761564850807, 0.049660392105579376,
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+  -0.007516763173043728, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006723935715854168, -0.013576141558587551, 0.008320409804582596, -0.0016202916158363223,
+  -0.006057804450392723, -0.00021705882681999356, 0.010607491247355938, 0.017385877668857574,
+  -0.006723935715854168, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005970459897071123, -0.011914572678506374, 0.007096816785633564, -0.001338999718427658,
+  -0.004728231579065323, -0.0001076333865057677, 0.009028797969222069, 0.01530691422522068,
+  -0.005970459897071123, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005256629083305597, -0.010353297926485538, 0.005978186149150133, -0.0010895503219217062,
+  -0.003619059920310974, -9.746539035404567e-06, 0.007603692822158337, 0.01335066370666027,
+  -0.005256630014628172, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004582791589200497, -0.00889437086880207, 0.004963425919413567, -0.0008709144894964993,
+  -0.0027081072330474854, 7.516307232435793e-05, 0.00632599089294672, 0.011518443003296852,
+  -0.004582791589200497, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003949390258640051, -0.0075397067703306675, 0.004051216412335634,
+  -0.0006818902911618352, -0.0019734192173928022, 0.00014585057215299457, 0.005189330317080021,
+  0.009811685420572758, -0.003949389792978764, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003356954315677285, -0.006291051395237446, 0.003239935729652643, -0.0005211022798903286,
+  -0.0013934114249423146, 0.00020131962082814425, 0.004187180660665035, 0.00823192484676838,
+  -0.0033569536171853542, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002806139877066016, -0.005150026176124811, 0.002527657663449645, -0.0003869845240842551,
+  -0.0009470655932091177, 0.00024082866730168462, 0.0033128252252936363, 0.006780855357646942,
+  -0.002806140575557947, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0022977644111961126, -0.004118149168789387, 0.0019121031509712338,
+  -0.00027776273782365024, -0.0006140992045402527, 0.00026393606094643474, 0.0025593626778572798,
+  0.0054603684693574905, -0.0022977644111961126, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0018328441074118018, -0.00319686159491539, 0.0013905864907428622,
+  -0.0001914350432343781, -0.00037515314761549234, 0.0002705501392483711, 0.00191968132276088,
+  0.004272606689482927, -0.0018328441074118018, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0014126739697530866, -0.0023875958286225796, 0.0009599507320672274,
+  -0.00012575133587233722, -0.00021199068578425795, 0.00026100283139385283, 0.0013864731881767511,
+  0.003220070619136095, -0.0014126742025837302, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010389164090156555, -0.0016918114852160215, 0.0006164572550915182,
+  -7.817315781721845e-05, -0.00010769431537482888, 0.00023616159160155803, 0.0009522004402242601,
+  0.002305711153894663, -0.0010389162926003337, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0007137901848182082, -0.001111136400140822, 0.000355650408891961,
+  -4.584273119689897e-05, -4.689424531534314e-05, 0.00019760921713896096, 0.0006091310060583055,
+  0.0015331710455939174, -0.000713790359441191, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004403638595249504, -0.0006475365371443331, 0.00017210266378242522,
+  -2.5533141524647363e-05, -1.6004965800675564e-05, 0.0001479669735999778, 0.00034937364398501813,
+  0.0009071220410987735, -0.0004403638595249504, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00022318775882013142, -0.0003037076094187796, 5.896755828871392e-05,
+  -1.360836085950723e-05, -3.5025398119614692e-06, 9.153129940386862e-05, 0.0001650566846365109,
+  0.0004339938168413937, -0.0002231877442682162, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.996076990617439e-05, -8.410307782469317e-05, 6.957830464671133e-06,
+  -6.071380539651727e-06, -2.5896267175085086e-07, 3.59088990080636e-05, 4.902789441985078e-05,
+  0.00012389066978357732, -6.996076263021678e-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 ac8acfd4df7353610e404104e7444203a4f5b10e..05764ec3b6915e847757169c4db8566d0e0a4fe8 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": 2.8000152111053467,
-  "erf_vl": 2.48862624168396,
-  "chi2": 2.0644352436065674,
+  "erf_tr": 2.800015926361084,
+  "erf_vl": 2.4886276721954346,
+  "chi2": 2.0644304752349854,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.3221020624883704,
-    1.4870359495902816,
-    1.1735315998209264,
-    1.0005949415170394,
-    1.2219866415152165
+    1.322102073510827,
+    1.4870355053260238,
+    1.173531467693787,
+    1.0005949565556946,
+    1.2219864889799885
   ],
   "integrability": [
-    0.0009427009790689833,
-    0.0009427009790676788,
-    5.000833846158237e-05,
-    0.47462602704763324,
-    0.007130771817171588
+    0.0009427017867010556,
+    0.0009427017866987519,
+    5.0008315951366455e-05,
+    0.4746261388063424,
+    0.007130760874131559
   ],
   "timing": {
     "walltime": {
-      "Total": 22.511044025421143,
+      "Total": 24.390008687973022,
       "start": 0.0,
-      "replica_set": 0.35729169845581055,
-      "replica_fitted": 22.51093602180481,
-      "replica_set_to_replica_fitted": 22.153644323349
+      "replica_set": 0.37442827224731445,
+      "replica_fitted": 24.389841318130493,
+      "replica_set_to_replica_fitted": 24.01541304588318
     },
     "cputime": {
-      "Total": 24.3750598,
+      "Total": 26.249403,
       "start": 0.0,
-      "replica_set": 0.6750459000000006,
-      "replica_fitted": 24.3749498,
-      "replica_set_to_replica_fitted": 23.6999039
+      "replica_set": 0.6909512000000007,
+      "replica_fitted": 26.2492338,
+      "replica_set_to_replica_fitted": 25.5582826
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ 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 89cf717c7876b04366c1b78c644a808550cb49c2..f0306e57aa132115e4b8e750be3ad5e8b9e20be7 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, -2.436048984527588, 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, -2.2839324474334717, 0.48300841450691223, 0.4534847140312195, 0.45354193449020386,
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+- [0.0, 0.0, -2.436049461364746, 0.5029183626174927, 0.4756278991699219, 0.4756722152233124,
+  -0.5346566438674927, 0.4758349061012268, 0.4757919907569885, 0.5026589035987854,
+  -2.436049461364746, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.3587567806243896, 0.49267593026161194, 0.46429142355918884, 0.46434175968170166,
+  -0.5346137881278992, 0.4645216166973114, 0.46447306871414185, 0.49239128828048706,
+  -2.3587567806243896, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.2839324474334717, 0.48300865292549133, 0.4534849524497986, 0.45354217290878296,
+  -0.5345005989074707, 0.4537411034107208, 0.4536859095096588, 0.4826964735984802,
   -2.2839319705963135, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2114975452423096, 0.47390493750572205, 0.4431948661804199, 0.44325998425483704,
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-  -2.2114970684051514, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.141375780105591, 0.4653558135032654, 0.433410108089447, 0.4334840774536133,
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-- [0.0, 0.0, -2.0734925270080566, 0.4573505222797394, 0.42411768436431885, 0.42420175671577454,
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   -2.0734925270080566, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.007777690887451, 0.44988030195236206, 0.41530656814575195, 0.4154021143913269,
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-  -2.007777690887451, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9441611766815186, 0.4429369270801544, 0.4069660007953644, 0.40707457065582275,
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   -1.9441611766815186, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8825767040252686, 0.43651238083839417, 0.3990854322910309, 0.3992089033126831,
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-- [0.0, 0.0, -1.8229581117630005, 0.43059974908828735, 0.39165517687797546, 0.3917955756187439,
-  -0.531302809715271, 0.3922003209590912, 0.392067551612854, 0.4300050437450409, -1.8229581117630005,
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-- [0.0, 0.0, -1.7652437686920166, 0.42519256472587585, 0.38466599583625793, 0.3848254978656769,
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-- [0.0, 0.0, -1.5031625032424927, 0.40555092692375183, 0.35603493452072144, 0.35633715987205505,
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-- [0.0, 0.0, -1.4556572437286377, 0.403072714805603, 0.35151776671409607, 0.3518610894680023,
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-- [0.0, 0.0, -1.4096680879592896, 0.40107059478759766, 0.34738689661026, 0.3477769196033478,
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-- [0.0, 0.0, -1.3651463985443115, 0.3995431065559387, 0.34363624453544617, 0.34407928586006165,
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+  -0.000333200121531263, -2.422377838229295e-05, 0.0014982144348323345, 0.0046364679001271725,
+  0.007449145894497633, -0.0028352646622806787, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0023107382003217936, -0.003484538523480296, 0.0020294557325541973,
+  -0.00021578175073955208, -1.5798506865394302e-05, 0.0013025120133534074, 0.003648084821179509,
+  0.006027276162058115, -0.002310738433152437, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0018332538893446326, -0.0026939930394291878, 0.001495894743129611,
+  -0.00012592299026437104, -9.705582669994328e-06, 0.001106772106140852, 0.0027923868037760258,
+  0.00474237697198987, -0.0018332538893446326, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0014040326932445168, -0.0020015884656459093, 0.0010517494520172477,
+  -6.111852417234331e-05, -5.51427456230158e-06, 0.0009122190531343222, 0.0020628981292247772,
+  0.003597594564780593, -0.0014040326932445168, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010246435413137078, -0.0014086529845371842, 0.0006934128468856215,
+  -1.8502623788663186e-05, -2.816112100845203e-06, 0.0007207721355371177, 0.0014530461048707366,
   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, -0.0006971845286898315, -0.0009165707742795348, 0.00041664481977932155,
+  5.217855232331203e-06, -1.2325161833359743e-06, 0.0005353152519091964, 0.0009562805062159896,
+  0.001744152745231986, -0.0006971845286898315, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004245503223501146, -0.0005268911481834948, 0.00021636132441926748,
+  1.3864486390957609e-05, -4.2274362499483686e-07, 0.00036015553632751107, 0.0005662395269609988,
+  0.0010460607009008527, -0.0004245503223501146, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00021101518359500915, -0.0002415803464828059, 8.629779040347785e-05,
+  1.1947884559049271e-05, -9.295886371774031e-08, 0.00020197330741211772, 0.0002772265870589763,
+  0.0005106808384880424, -0.00021101518359500915, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.373464566422626e-05, -6.3667306676507e-05, 1.8300721421837807e-05,
+  4.955135409545619e-06, -6.905088945075022e-09, 7.228501635836437e-05, 8.57160339364782e-05,
+  0.00015133175475057214, -6.373464566422626e-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 c87ab8a66d499df780975f67b42e3f4c552d8cf2..2c90ee4bf53234a004033b7a619ef6bdb81e2475 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": 6.576577663421631,
-  "erf_vl": 5.858455181121826,
-  "chi2": 3.330012321472168,
+  "erf_tr": 6.576578617095947,
+  "erf_vl": 5.858458518981934,
+  "chi2": 3.3300085067749023,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.337021614754758,
-    0.9939697379044121,
-    1.1791486314894875,
-    1.0013385222517424,
-    1.1751097571490132
+    1.3370216884066382,
+    0.9939697374308255,
+    1.1791486738858517,
+    1.0013385257857281,
+    1.1751098009017222
   ],
   "integrability": [
-    0.000991988403256927,
-    0.000991988403257052,
-    4.665317624120979e-05,
-    0.4762776866555213,
-    0.007486370741389338
+    0.0009919884178089394,
+    0.0009919884178089672,
+    4.6653176695957144e-05,
+    0.4762776866555214,
+    0.0074863710906354144
   ],
   "timing": {
     "walltime": {
-      "Total": 31.462430477142334,
+      "Total": 33.80535387992859,
       "start": 0.0,
-      "replica_set": 0.3577704429626465,
-      "replica_fitted": 31.46228003501892,
-      "replica_set_to_replica_fitted": 31.104509592056274
+      "replica_set": 0.3920779228210449,
+      "replica_fitted": 33.8051962852478,
+      "replica_set_to_replica_fitted": 33.41311836242676
     },
     "cputime": {
-      "Total": 33.54510500000001,
+      "Total": 36.0601982,
       "start": 0.0,
-      "replica_set": 0.6758694999999992,
-      "replica_fitted": 33.5449531,
-      "replica_set_to_replica_fitted": 32.869083599999996
+      "replica_set": 0.7084465000000009,
+      "replica_fitted": 36.0600387,
+      "replica_set_to_replica_fitted": 35.3515922
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ 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 feb23099dadaa86acde871990a6449977b60d376..0f7c0b80800084d5e4b2415c0553bc5a4a983a5f 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, -2.4447743892669678, 0.48206278681755066, 0.4548843801021576, 0.4549284875392914,
-  -0.536359429359436, 0.4549674689769745, 0.45492371916770935, 0.4819997251033783,
-  -2.4447743892669678, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.3672444820404053, 0.47239094972610474, 0.44413238763809204, 0.44418248534202576,
-  -0.5363330841064453, 0.4442256689071655, 0.44417592883110046, 0.4723217785358429,
-  -2.3672444820404053, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.292189836502075, 0.4632740914821625, 0.43389183282852173, 0.433948814868927,
-  -0.536237359046936, 0.4339965581893921, 0.4339400827884674, 0.4631982445716858,
-  -2.292189836502075, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.219531774520874, 0.4547020196914673, 0.4241504669189453, 0.424215167760849,
-  -0.5360674858093262, 0.4242679178714752, 0.42420387268066406, 0.45461875200271606,
-  -2.219531297683716, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1491925716400146, 0.44666483998298645, 0.4148966372013092, 0.41497012972831726,
-  -0.5358185172080994, 0.41502857208251953, 0.41495582461357117, 0.44657355546951294,
+- [0.0, 0.0, -2.4447741508483887, 0.4820624589920044, 0.45488405227661133, 0.4549281895160675,
+  -0.5363594889640808, 0.4549671411514282, 0.4549234211444855, 0.48199939727783203,
+  -2.4447741508483887, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.3672447204589844, 0.4723908007144928, 0.44413232803344727, 0.444182425737381,
+  -0.5363330841064453, 0.44422560930252075, 0.4441758692264557, 0.47232162952423096,
+  -2.3672447204589844, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.2921900749206543, 0.4632740318775177, 0.43389177322387695, 0.43394866585731506,
+  -0.5362372994422913, 0.43399640917778015, 0.43394002318382263, 0.463198184967041,
+  -2.2921900749206543, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.219531536102295, 0.45470163226127625, 0.4241500794887543, 0.42421478033065796,
+  -0.5360674858093262, 0.42426756024360657, 0.424203485250473, 0.454618364572525,
+  -2.2195310592651367, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.1491925716400146, 0.4466646611690521, 0.4148964583873749, 0.41496992111206055,
+  -0.5358185172080994, 0.4150283634662628, 0.41495564579963684, 0.4465733468532562,
   -2.1491920948028564, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.081099271774292, 0.43915292620658875, 0.4061186909675598, 0.406202107667923,
-  -0.5354853272438049, 0.4062667489051819, 0.40618422627449036, 0.4390527904033661,
+- [0.0, 0.0, -2.081099271774292, 0.4391527473926544, 0.4061184525489807, 0.40620186924934387,
+  -0.5354853868484497, 0.40626654028892517, 0.40618401765823364, 0.43905261158943176,
   -2.081099033355713, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.015179395675659, 0.43215829133987427, 0.3978063464164734, 0.39790108799934387,
-  -0.5350622534751892, 0.3979726731777191, 0.3978789746761322, 0.43204841017723083,
+- [0.0, 0.0, -2.015179395675659, 0.4321581721305847, 0.3978062868118286, 0.3979009687900543,
+  -0.5350622534751892, 0.39797255396842957, 0.3978789150714874, 0.43204832077026367,
   -2.0151796340942383, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9513647556304932, 0.42567235231399536, 0.3899489939212799, 0.3900565505027771,
-  -0.5345432758331299, 0.3901357054710388, 0.3900294303894043, 0.42555174231529236,
+- [0.0, 0.0, -1.9513647556304932, 0.42567211389541626, 0.3899487555027008, 0.390056312084198,
+  -0.5345432758331299, 0.3901354670524597, 0.3900291621685028, 0.42555150389671326,
   -1.951364517211914, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8895868062973022, 0.41968756914138794, 0.38253676891326904, 0.38265886902809143,
-  -0.5339220762252808, 0.38274648785591125, 0.38262590765953064, 0.4195552468299866,
+- [0.0, 0.0, -1.8895868062973022, 0.4196873903274536, 0.3825365900993347, 0.3826586902141571,
+  -0.5339220762252808, 0.38274630904197693, 0.3826257288455963, 0.41955509781837463,
   -1.8895868062973022, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8297812938690186, 0.41419750452041626, 0.3755607306957245, 0.37569934129714966,
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+- [0.0, 0.0, -1.8297812938690186, 0.4141974449157715, 0.3755606710910797, 0.3756992518901825,
+  -0.5331918001174927, 0.37579646706581116, 0.37565964460372925, 0.41405242681503296,
   -1.8297812938690186, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7718851566314697, 0.40919622778892517, 0.36901241540908813, 0.36916977167129517,
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-  -1.7718851566314697, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7158371210098267, 0.4046774208545685, 0.3628828823566437, 0.36306145787239075,
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-- [0.0, 0.0, -1.6615782976150513, 0.40063637495040894, 0.35716453194618225, 0.35736721754074097,
-  -0.5302715301513672, 0.3574994206428528, 0.3572997748851776, 0.40044495463371277,
-  -1.6615782976150513, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6090515851974487, 0.39706841111183167, 0.35184982419013977, 0.3520798087120056,
-  -0.5290276408195496, 0.35222622752189636, 0.3519999086856842, 0.3968583941459656,
-  -1.6090515851974487, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5582014322280884, 0.39396971464157104, 0.3469318151473999, 0.34719276428222656,
-  -0.5276327729225159, 0.3473551571369171, 0.3470986485481262, 0.3937394320964813,
-  -1.5582014322280884, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5089744329452515, 0.3913365602493286, 0.34240344166755676, 0.34269949793815613,
-  -0.5260778069496155, 0.3428795635700226, 0.3425888419151306, 0.3910839855670929,
-  -1.5089744329452515, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4613181352615356, 0.38916635513305664, 0.3382587432861328, 0.338594526052475,
-  -0.5243513584136963, 0.3387943506240845, 0.3384650647640228, 0.3888894021511078,
-  -1.4613181352615356, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4151825904846191, 0.38745662569999695, 0.3344917595386505, 0.3348725438117981,
-  -0.5224425792694092, 0.33509424328804016, 0.3347212076187134, 0.38715294003486633,
+- [0.0, 0.0, -1.7718852758407593, 0.40919607877731323, 0.3690122961997986, 0.3691696524620056,
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+- [0.0, 0.0, -1.7158372402191162, 0.40467745065689087, 0.36288291215896606, 0.36306148767471313,
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+  -1.715837001800537, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.6615784168243408, 0.4006364047527313, 0.35716456174850464, 0.35736724734306335,
+  -0.530271589756012, 0.35749945044517517, 0.3572998046875, 0.40044498443603516, -1.6615784168243408,
+  0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.6090518236160278, 0.3970683515071869, 0.3518497347831726, 0.35207974910736084,
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+  -1.6090518236160278, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.5582013130187988, 0.39396971464157104, 0.3469318151473999, 0.34719276428222656,
+  -0.5276327133178711, 0.3473551571369171, 0.3470986485481262, 0.3937394320964813,
+  -1.5582013130187988, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.5089741945266724, 0.39133647084236145, 0.3424033522605896, 0.34269940853118896,
+  -0.5260777473449707, 0.34287944436073303, 0.34258875250816345, 0.39108386635780334,
+  -1.5089741945266724, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.4613178968429565, 0.3891662359237671, 0.33825862407684326, 0.3385944366455078,
+  -0.5243514776229858, 0.3387942612171173, 0.3384649157524109, 0.38888928294181824,
+  -1.4613178968429565, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.4151825904846191, 0.387456476688385, 0.3344915807247162, 0.3348723351955414,
+  -0.5224426984786987, 0.33509403467178345, 0.33472102880477905, 0.387152761220932,
   -1.4151825904846191, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3705190420150757, 0.3862054944038391, 0.3310965895652771, 0.33152833580970764,
-  -0.5203388333320618, 0.33177438378334045, 0.3313520550727844, 0.38587239384651184,
-  -1.3705192804336548, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3272806406021118, 0.38541141152381897, 0.3280678689479828, 0.3285572826862335,
-  -0.5180276036262512, 0.32883045077323914, 0.32835227251052856, 0.3850461542606354,
-  -1.3272806406021118, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2854208946228027, 0.38507378101348877, 0.32540076971054077, 0.3259553611278534,
-  -0.515494704246521, 0.32625874876976013, 0.32571762800216675, 0.38467323780059814,
-  -1.2854208946228027, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2448961734771729, 0.38519200682640076, 0.32309016585350037, 0.3237186074256897,
-  -0.5127255320549011, 0.32405558228492737, 0.3234434127807617, 0.3847528100013733,
-  -1.2448961734771729, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2056634426116943, 0.3857663869857788, 0.32113173604011536, 0.32184359431266785,
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+- [0.0, 0.0, -0.0028077424503862858, 4.734039248432964e-05, 0.0036195728462189436,
+  0.0005512995994649827, -2.4084714823402464e-05, 0.000752573658246547, 0.0038561932742595673,
+  0.0031937090680003166, -0.002807741751894355, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0022867273073643446, 7.543752872152254e-05, 0.0028167921118438244,
+  0.000516365806106478, -1.570707536302507e-05, 0.0006887360359542072, 0.003012880915775895,
   0.0026043171528726816, -0.0022867273073643446, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0018127619987353683, 9.29874659050256e-05, 0.0021252550650388002,
-  0.00046688542352057993, -9.648976629250683e-06, 0.0006124668871052563, 0.002285919850692153,
-  0.0020673221442848444, -0.0018127619987353683, 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, -0.001812762231566012, 9.298733493778855e-05, 0.0021252550650388002,
+  0.0004668851906899363, -9.648977538745385e-06, 0.0006124664796516299, 0.002285919850692153,
+  0.0020673214457929134, -0.001812762231566012, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0013870391994714737, 0.00010031535930465907, 0.0015407161554321647,
+  0.0004050442366860807, -5.481877906277077e-06, 0.0005254874122329056, 0.00167010014411062,
+  0.0015842976281419396, -0.0013870391994714737, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.001011091866530478, 9.80038385023363e-05, 0.00105857674498111, 0.00033353560138493776,
+  -2.799450840029749e-06, 0.00043009649380110204, 0.0011599526042118669, 0.0011572001967579126,
+  -0.0010110919829457998, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0006869718199595809, 8.696002623764798e-05, 0.0006738804513588548,
+  0.00025571833248250186, -1.2251737189217238e-06, 0.00032936831121332943, 0.0007497864426113665,
+  0.0007885368540883064, -0.0006869719945825636, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00041751362732611597, 6.852889055153355e-05, 0.000381258490961045,
+  0.00017586973262950778, -4.2020872115244856e-07, 0.00022748242190573364, 0.000433719833381474,
+  0.00048161757877096534, -0.00041751362732611597, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00020690028031822294, 4.474492743611336e-05, 0.00017493950144853443,
+  9.968579252017662e-05, -9.23979257549945e-08, 0.00013039053010288626, 0.00020585798483807594,
+  0.00024111005768645555, -0.0002069003094220534, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.212705193320289e-05, 1.9011475160368718e-05, 4.897643520962447e-05,
+  3.549793837009929e-05, -6.863166479575966e-09, 4.7500550863333046e-05, 6.0999274865025654e-05,
+  7.451765850419179e-05, -6.212704465724528e-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 df7888cb298528b6da7cd6dca2dcdf83e88bfa40..8e5f95e4ae134829db52c6c74e7f9242b6217ca0 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": 5.3037943840026855,
-  "erf_vl": 5.3994460105896,
-  "chi2": 3.260413646697998,
+  "erf_tr": 5.303784370422363,
+  "erf_vl": 5.399442672729492,
+  "chi2": 3.2604198455810547,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.334838194261321,
-    0.9938354337963408,
-    1.0016686481364248,
-    0.9905760062890283,
-    1.0071507465033542
+    1.3348380879587267,
+    0.9938354367951591,
+    1.0016686524387772,
+    0.9905760067696133,
+    1.0071507400671937
   ],
   "integrability": [
-    0.00022732430443259122,
-    0.00022732430443293816,
-    1.0915415287984787e-05,
-    0.4772165119647979,
-    0.0018179939506805104
+    0.000227324335355987,
+    0.00022732433535575802,
+    1.0915415316406496e-05,
+    0.477216564118862,
+    0.001817993746953725
   ],
   "timing": {
     "walltime": {
-      "Total": 26.5335693359375,
+      "Total": 29.39768624305725,
       "start": 0.0,
-      "replica_set": 0.3634805679321289,
-      "replica_fitted": 26.533432006835938,
-      "replica_set_to_replica_fitted": 26.16995143890381
+      "replica_set": 0.4022369384765625,
+      "replica_fitted": 29.397472381591797,
+      "replica_set_to_replica_fitted": 28.995235443115234
     },
     "cputime": {
-      "Total": 28.4186657,
+      "Total": 31.500726199999995,
       "start": 0.0,
-      "replica_set": 0.6786007000000005,
-      "replica_fitted": 28.4185265,
-      "replica_set_to_replica_fitted": 27.7399258
+      "replica_set": 0.7186190999999997,
+      "replica_fitted": 31.500510499999997,
+      "replica_set_to_replica_fitted": 30.7818914
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ 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 b71ccbb37a429d46b3c938cee67688f8c1646075..acd72ec4e51694983eb846744912863c6ba3a604 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, -2.3827309608459473, 0.17211303114891052, 0.14561547338962555, 0.14566178619861603,
-  -16.24198341369629, 0.14569853246212006, 0.14565253257751465, 0.17205394804477692,
-  -2.3827309608459473, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.3074989318847656, 0.17170847952365875, 0.1441579908132553, 0.1442105770111084,
-  -16.250526428222656, 0.14425119757652283, 0.14419899880886078, 0.17164362967014313,
-  -2.3074984550476074, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2346484661102295, 0.1715724766254425, 0.14292648434638977, 0.1429862529039383,
-  -16.257551193237305, 0.14303116500377655, 0.1429719179868698, 0.1715013086795807,
-  -2.2346484661102295, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.1641037464141846, 0.17170359194278717, 0.14191779494285583, 0.1419856697320938,
-  -16.262956619262695, 0.14203542470932007, 0.14196811616420746, 0.171625554561615,
-  -2.1641042232513428, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0957915782928467, 0.1720997393131256, 0.1411278247833252, 0.14120490849018097,
-  -16.266630172729492, 0.14125990867614746, 0.1411835253238678, 0.1720140278339386,
-  -2.095791816711426, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.029642105102539, 0.1727607101202011, 0.1405544877052307, 0.14064207673072815,
-  -16.26845932006836, 0.1407029777765274, 0.14061622321605682, 0.17266668379306793,
-  -2.02964186668396, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9655840396881104, 0.17368559539318085, 0.1401948481798172, 0.14029431343078613,
-  -16.268310546875, 0.1403617113828659, 0.14026325941085815, 0.17358240485191345,
-  -1.9655842781066895, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.903552532196045, 0.17487427592277527, 0.14004649221897125, 0.1401594579219818,
-  -16.266056060791016, 0.14023414254188538, 0.14012236893177032, 0.174761101603508,
-  -1.903552770614624, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8434830904006958, 0.17632679641246796, 0.14010728895664215, 0.14023558795452118,
-  -16.261550903320312, 0.14031830430030823, 0.1401914656162262, 0.1762026697397232,
-  -1.8434830904006958, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7853120565414429, 0.17804379761219025, 0.14037546515464783, 0.14052115380764008,
-  -16.254636764526367, 0.14061275124549866, 0.14046883583068848, 0.1779075711965561,
-  -1.7853120565414429, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7289798259735107, 0.18002648651599884, 0.1408497840166092, 0.1410152167081833,
-  -16.24515724182129, 0.1411166489124298, 0.14095337688922882, 0.17987701296806335,
-  -1.7289801836013794, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6744275093078613, 0.18227620422840118, 0.1415289044380188, 0.14171668887138367,
-  -16.232933044433594, 0.14182919263839722, 0.1416439563035965, 0.18211226165294647,
-  -1.6744275093078613, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.621598482131958, 0.18479429185390472, 0.14241141080856323, 0.14262458682060242,
-  -16.217777252197266, 0.14274923503398895, 0.14253917336463928, 0.1846143752336502,
-  -1.6215981245040894, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5704368352890015, 0.18758344650268555, 0.14349709451198578, 0.14373904466629028,
-  -16.199491500854492, 0.1438772976398468, 0.14363904297351837, 0.18738606572151184,
-  -1.5704368352890015, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5208903551101685, 0.19064536690711975, 0.14478467404842377, 0.145059272646904,
-  -16.177854537963867, 0.14521262049674988, 0.1449424773454666, 0.19042883813381195,
-  -1.5208903551101685, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4729069471359253, 0.19398394227027893, 0.14627480506896973, 0.14658640325069427,
-  -16.152652740478516, 0.14675650000572205, 0.14645031094551086, 0.1937464028596878,
-  -1.4729069471359253, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4264365434646606, 0.19760140776634216, 0.14796629548072815, 0.148319810628891,
-  -16.12363624572754, 0.14850863814353943, 0.1481616050004959, 0.19734087586402893,
-  -1.4264365434646606, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3814303874969482, 0.20150169730186462, 0.14985962212085724, 0.15026061236858368,
-  -16.090547561645508, 0.15047022700309753, 0.1500770002603531, 0.20121589303016663,
-  -1.381430745124817, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.337842345237732, 0.20568925142288208, 0.15195536613464355, 0.15241017937660217,
-  -16.0531005859375, 0.15264290571212769, 0.1521974354982376, 0.20537568628787994,
-  -1.3378421068191528, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2956260442733765, 0.21016763150691986, 0.15425315499305725, 0.15476888418197632,
-  -16.011009216308594, 0.1550273597240448, 0.1545228809118271, 0.2098236083984375,
-  -1.2956260442733765, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.2547379732131958, 0.21494218707084656, 0.15675421059131622, 0.1573389172554016,
-  -15.96394157409668, 0.15762610733509064, 0.15705493092536926, 0.2145647555589676,
-  -1.2547379732131958, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.215134859085083, 0.22001773118972778, 0.15945890545845032, 0.16012167930603027,
-  -15.911578178405762, 0.16044077277183533, 0.15979428589344025, 0.21960358321666718,
-  -1.2151345014572144, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.1767754554748535, 0.22539964318275452, 0.1623680293560028, 0.16311904788017273,
-  -15.853538513183594, 0.16347381472587585, 0.16274231672286987, 0.2249452769756317,
-  -1.1767754554748535, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.139620065689087, 0.23109367489814758, 0.1654823273420334, 0.1663331687450409,
-  -15.789449691772461, 0.16672763228416443, 0.16590026021003723, 0.23059509694576263,
-  -1.1396198272705078, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.103629231452942, 0.23710612952709198, 0.16880294680595398, 0.1697666347026825,
-  -15.718890190124512, 0.17020535469055176, 0.1692698895931244, 0.23655900359153748,
-  -1.103629231452942, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0687657594680786, 0.2434430718421936, 0.17233048379421234, 0.17342162132263184,
-  -15.641426086425781, 0.17390981316566467, 0.1728525608778, 0.24284270405769348,
-  -1.0687655210494995, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.0349925756454468, 0.25011152029037476, 0.17606613039970398, 0.17730116844177246,
-  -15.5565767288208, 0.17784447968006134, 0.17665012180805206, 0.24945256114006042,
-  -1.0349925756454468, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.002274751663208, 0.2571180462837219, 0.18001031875610352, 0.18140779435634613,
-  -15.463855743408203, 0.1820126175880432, 0.1806640326976776, 0.25639474391937256,
-  -1.002274751663208, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9705778956413269, 0.2644701302051544, 0.18416409194469452, 0.18574470281600952,
-  -15.362715721130371, 0.18641828000545502, 0.18489636480808258, 0.26367613673210144,
-  -0.9705778956413269, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9398683905601501, 0.2721748948097229, 0.18852777779102325, 0.19031482934951782,
-  -15.252589225769043, 0.19106508791446686, 0.1893484741449356, 0.2713032364845276,
-  -0.9398683905601501, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.9101145267486572, 0.2802397906780243, 0.19310146570205688, 0.19512097537517548,
-  -15.132872581481934, 0.19595696032047272, 0.1940220147371292, 0.27928268909454346,
-  -0.9101145267486572, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8812848925590515, 0.28867238759994507, 0.19788523018360138, 0.20016628503799438,
-  -15.002922058105469, 0.20109805464744568, 0.1989184021949768, 0.28762131929397583,
-  -0.8812848925590515, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.853349506855011, 0.29748019576072693, 0.20287854969501495, 0.20545369386672974,
-  -14.862046241760254, 0.20649252831935883, 0.2040390819311142, 0.29632568359375,
-  -0.853349506855011, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.826278805732727, 0.3066703677177429, 0.2080802321434021, 0.21098566055297852,
-  -14.709525108337402, 0.2121441811323166, 0.20938466489315033, 0.30540212988853455,
-  -0.826278805732727, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.8000448346138, 0.3162502944469452, 0.21348878741264343, 0.21676477789878845,
-  -14.544585227966309, 0.21805711090564728, 0.21495601534843445, 0.31485670804977417,
-  -0.8000449538230896, 0.0, 0.0, 0.0]
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+- [0.0, 0.0, -0.02657165564596653, -0.007117399945855141, 0.05371961370110512, -0.007085320074111223,
+  -0.08006542921066284, -0.006639036815613508, 0.056737761944532394, 0.02279762737452984,
+  -0.02657165564596653, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.025096528232097626, -0.00685518141835928, 0.04995095729827881, -0.006623605266213417,
+  -0.07230221480131149, -0.00631206389516592, 0.052583854645490646, 0.021407656371593475,
+  -0.025096524506807327, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.02366153709590435, -0.006572420708835125, 0.04633062332868576, -0.00616504717618227,
+  -0.06500953435897827, -0.00597247714176774, 0.04861066862940788, 0.020069748163223267,
+  -0.023661533370614052, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.022266780957579613, -0.0062727308832108974, 0.042858466506004333,
+  -0.005711935926228762, -0.058185018599033356, -0.005623413249850273, 0.04481673240661621,
+  0.018782494589686394, -0.02226678468286991, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.02091236785054207, -0.005959502421319485, 0.03953418508172035, -0.005266409832984209,
+  -0.05182409659028053, -0.005267856642603874, 0.041200410574674606, 0.017544563859701157,
+  -0.02091236785054207, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.019598353654146194, -0.005635929759591818, 0.036357298493385315, -0.004830448422580957,
+  -0.04591995105147362, -0.004908624105155468, 0.037759844213724136, 0.01635468378663063,
+  -0.019598353654146194, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.01832478679716587, -0.0053050341084599495, 0.03332716226577759, -0.00440592784434557,
+  -0.040463887155056, -0.0045484136790037155, 0.03449307382106781, 0.015211658552289009,
+  -0.01832478679716587, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.017091717571020126, -0.0049696327187120914, 0.03044300526380539, -0.0039945621974766254,
+  -0.03544530272483826, -0.004189762286841869, 0.031397923827171326, 0.014114368706941605,
+  -0.017091717571020126, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.015899164602160454, -0.004632356110960245, 0.027703851461410522, -0.0035979209933429956,
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+  -0.015899164602160454, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.014747164212167263, -0.004295667167752981, 0.02510862983763218, -0.003217458724975586,
+  -0.026669450104236603, -0.0034865408670157194, 0.02571296878159046, 0.01205285545438528,
+  -0.014747164212167263, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.013635734096169472, -0.003961862996220589, 0.022656062617897987, -0.0028544883243739605,
+  -0.02288287691771984, -0.0031463420018553734, 0.023118047043681145, 0.011086747981607914,
+  -0.013635734096169472, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.012564901262521744, -0.003633052110671997, 0.020344754680991173, -0.002510183723643422,
+  -0.019475365057587624, -0.0028164172545075417, 0.02068447321653366, 0.01016261801123619,
+  -0.012564901262521744, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.011534703895449638, -0.0033111951779574156, 0.018173130229115486,
+  -0.0021855852100998163, -0.016429029405117035, -0.0024986006319522858, 0.018409280106425285,
+  0.00927970465272665, -0.011534703895449638, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.010545185767114162, -0.002998076379299164, 0.016139473766088486, -0.0018815916264429688,
+  -0.01372496783733368, -0.0021945650223642588, 0.01628934219479561, 0.00843734573572874,
+  -0.010545185767114162, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.009596411138772964, -0.0026953325141221285, 0.014241903088986874,
+  -0.0015989708481356502, -0.011343417689204216, -0.0019058528123423457, 0.014321384020149708,
+  0.0076349517330527306, -0.009596413001418114, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.008688464760780334, -0.0024044483434408903, 0.012478362768888474,
+  -0.0013383495388552547, -0.009263895452022552, -0.0016338569112122059, 0.012501954101026058,
+  0.006872015073895454, -0.008688465692102909, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.007821468636393547, -0.002126748440787196, 0.010846656747162342, -0.0011002023238688707,
+  -0.007465343456715345, -0.0013798169093206525, 0.010827455669641495, 0.006148129235953093,
+  -0.007821469567716122, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006995563395321369, -0.0018634166335687041, 0.009344369173049927,
+  -0.0008848576690070331, -0.005926266312599182, -0.0011448203586041927, 0.009294084273278713,
+  0.005462956614792347, -0.006995563395321369, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.006210951134562492, -0.0016154833137989044, 0.00796893797814846, -0.0006924899062141776,
+  -0.004624939989298582, -0.0009297882788814604, 0.00789790041744709, 0.0048162746243178844,
+  -0.006210951134562492, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.005467887036502361, -0.0013838447630405426, 0.006717599928379059,
+  -0.0005231115501374006, -0.0035395286977291107, -0.0007354851113632321, 0.006634766235947609,
+  0.004207954742014408, -0.005467887036502361, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0047666882164776325, -0.0011692509287968278, 0.005587369203567505,
+  -0.0003765633737202734, -0.002648250199854374, -0.0005624928744509816, 0.005500337574630976,
+  0.0036379641387611628, -0.0047666882164776325, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.004107762593775988, -0.0009723110706545413, 0.004575072787702084,
+  -0.0002524988376535475, -0.0019295522943139076, -0.00041120362584479153, 0.004490090534090996,
+  0.003106401301920414, -0.004107763059437275, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.003491614945232868, -0.0007934949244372547, 0.0036772729363292456,
+  -0.00015037917182780802, -0.0013622656697407365, -0.00028180822846479714, 0.003599263960495591,
+  0.0026134736835956573, -0.003491614945232868, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002918885089457035, -0.0006331344484351575, 0.0028902897611260414,
+  -6.944399501662701e-05, -0.0009257813799194992, -0.00017427168495487422, 0.002822863170877099,
+  0.002159528434276581, -0.002918885089457035, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0023903714027255774, -0.0004914196324534714, 0.002210155362263322,
+  -8.692840310686734e-06, -0.0006002244190312922, -8.83101747604087e-05, 0.002155635505914688,
+  0.0017450633458793163, -0.0023903721012175083, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0019070891430601478, -0.00036839762469753623, 0.0016325738979503512,
+  3.314974674140103e-05, -0.0003666328848339617, -2.3351256459136494e-05, 0.0015920336591079831,
+  0.001370745594613254, -0.0019070891430601478, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0014703371562063694, -0.00026397017063573003, 0.0011528959730640054,
+  5.767705442849547e-05, -0.00020715135906357318, 2.1513440515263937e-05, 0.001126193325035274,
+  0.001037450972944498, -0.0014703371562063694, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010817993897944689, -0.00017788371769711375, 0.0007660301052965224,
+  6.686647975584492e-05, -0.00010522351658437401, 4.760629963129759e-05, 0.0007518648053519428,
+  0.0007462984649464488, -0.0010817993897944689, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0007437380845658481, -0.00010972093150485307, 0.00046638253843411803,
+  6.3172476075124e-05, -4.5813063479727134e-05, 5.677539229509421e-05, 0.0004623728746082634,
+  0.0004987384309060872, -0.0007437379681505263, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0004592995101120323, -5.8879399148281664e-05, 0.00024771204334683716,
+  4.967952554579824e-05, -1.5634177543688565e-05, 5.1588434871518984e-05, 0.000250518845859915,
+  0.0002966740867123008, -0.0004592995101120323, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0002331753057660535, -2.4530612790840678e-05, 0.0001029323466354981,
+  3.0378012525034137e-05, -3.4210108879051404e-06, 3.570221088011749e-05, 0.00010848270176211372,
+  0.00014272864791564643, -0.00023317527666222304, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -7.334586553042755e-05, -5.529012014449108e-06, 2.375976873736363e-05,
+  1.0765395018097479e-05, -2.5290665917054866e-07, 1.4732843737874646e-05, 2.7748608772526495e-05,
+  4.092912786290981e-05, -7.334588008234277e-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 7541524c3069f33ea79a4c59d24904bbfa37bfa1..522ce699c61d18ae0c146dd13d7cf6d88c77f5b8 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": 3.6618833541870117,
-  "erf_vl": 4.0898518562316895,
-  "chi2": 2.1583468914031982,
+  "erf_tr": 3.661821126937866,
+  "erf_vl": 4.091275691986084,
+  "chi2": 2.160372734069824,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.3149939495169196,
-    1.473723931769428,
-    1.000778573042579,
-    0.9905270866398914,
-    1.0083087542495537
+    1.3149667741301097,
+    1.4760812976596676,
+    1.0007785975159469,
+    0.990527008299963,
+    1.0083078478644185
   ],
   "integrability": [
-    0.00021743890010994527,
-    0.00021743890010883504,
-    1.0915954532286776e-05,
-    0.4652465507388106,
-    0.0017131859785863846
+    0.00021744489913735898,
+    0.00021744489913599896,
+    1.0915751402440499e-05,
+    0.46524765342473895,
+    0.0017132273933366804
   ],
   "timing": {
     "walltime": {
-      "Total": 18.737892866134644,
+      "Total": 20.7750883102417,
       "start": 0.0,
-      "replica_set": 0.36391282081604004,
-      "replica_fitted": 18.737794876098633,
-      "replica_set_to_replica_fitted": 18.373882055282593
+      "replica_set": 0.38233232498168945,
+      "replica_fitted": 20.774923086166382,
+      "replica_set_to_replica_fitted": 20.392590761184692
     },
     "cputime": {
-      "Total": 20.7538624,
+      "Total": 23.2345513,
       "start": 0.0,
-      "replica_set": 0.6703723999999998,
-      "replica_fitted": 20.753763,
-      "replica_set_to_replica_fitted": 20.0833906
+      "replica_set": 0.6974461999999999,
+      "replica_fitted": 23.2343851,
+      "replica_set_to_replica_fitted": 22.536938900000003
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ 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 2932bc2ec4381a5821843f3c039c4de8e15974f5..96a485716a1b80367388aefb39cedd3d1ddba17d 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]
 pdfgrid:
-- [0.0, 0.0, -2.4065639972686768, 0.2450128048658371, 0.21476727724075317, 0.21481451392173767,
-  -10.534016609191895, 0.2149643450975418, 0.21491913497447968, 0.24477365612983704,
-  -2.406564474105835, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.3303158283233643, 0.24177557229995728, 0.21032096445560455, 0.21037472784519196,
-  -10.541108131408691, 0.210540309548378, 0.21048903465270996, 0.2415132224559784,
-  -2.3303158283233643, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.2564823627471924, 0.2388850599527359, 0.20617173612117767, 0.2062329351902008,
-  -10.547290802001953, 0.2064160406589508, 0.20635782182216644, 0.2385973036289215,
-  -2.2564823627471924, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.184988260269165, 0.23633743822574615, 0.2023136168718338, 0.20238317549228668,
-  -10.552496910095215, 0.20258572697639465, 0.2025197297334671, 0.23602186143398285,
-  -2.1849887371063232, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.115757703781128, 0.23412948846817017, 0.1987411379814148, 0.1988202929496765,
-  -10.556656837463379, 0.19904430210590363, 0.19896946847438812, 0.23378337919712067,
-  -2.115757465362549, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -2.0487189292907715, 0.23225761950016022, 0.19544823467731476, 0.19553829729557037,
-  -10.559697151184082, 0.19578613340854645, 0.19570128619670868, 0.23187805712223053,
-  -2.0487186908721924, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.983801245689392, 0.23071986436843872, 0.19243046641349792, 0.19253288209438324,
-  -10.561540603637695, 0.1928071677684784, 0.1927109658718109, 0.23030366003513336,
-  -1.983801245689392, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.9209378957748413, 0.22951386868953705, 0.189682736992836, 0.18979927897453308,
-  -10.562102317810059, 0.19010286033153534, 0.18999382853507996, 0.22905750572681427,
-  -1.9209378957748413, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.860063076019287, 0.2286383956670761, 0.1872011125087738, 0.18733367323875427,
-  -10.561288833618164, 0.1876697540283203, 0.18754622340202332, 0.2281380593776703,
-  -1.860062837600708, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.8011125326156616, 0.2280920445919037, 0.18498121201992035, 0.18513205647468567,
-  -10.559006690979004, 0.18550418317317963, 0.18536421656608582, 0.22754353284835815,
-  -1.8011125326156616, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.7440258264541626, 0.2278742641210556, 0.18301938474178314, 0.18319101631641388,
-  -10.555150985717773, 0.18360306322574615, 0.1834445297718048, 0.2272729128599167,
-  -1.7440258264541626, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6887425184249878, 0.22798480093479156, 0.18131206929683685, 0.18150731921195984,
-  -10.54961109161377, 0.18196377158164978, 0.18178430199623108, 0.2273256480693817,
-  -1.6887425184249878, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.6352050304412842, 0.22842390835285187, 0.17985601723194122, 0.1800781637430191,
-  -10.542267799377441, 0.1805838644504547, 0.1803806573152542, 0.22770141065120697,
-  -1.6352050304412842, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5833574533462524, 0.22919277846813202, 0.17864881455898285, 0.1789015829563141,
-  -10.53299617767334, 0.1794619858264923, 0.17923198640346527, 0.22840088605880737,
-  -1.5833576917648315, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.5331461429595947, 0.23029246926307678, 0.1776876151561737, 0.17797517776489258,
-  -10.521656036376953, 0.17859627306461334, 0.17833611369132996, 0.22942455112934113,
-  -1.5331461429595947, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4845175743103027, 0.23172445595264435, 0.1769697368144989, 0.17729690670967102,
-  -10.508106231689453, 0.17798545956611633, 0.17769122123718262, 0.23077328503131866,
-  -1.4845175743103027, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.4374215602874756, 0.23349116742610931, 0.17649327218532562, 0.1768655627965927,
-  -10.492189407348633, 0.17762906849384308, 0.17729640007019043, 0.23244886100292206,
-  -1.4374213218688965, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -1.3918087482452393, 0.2355954945087433, 0.1762564778327942, 0.1766800433397293,
-  -10.47374153137207, 0.17752677202224731, 0.17715083062648773, 0.23445330560207367,
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+- [0.0, 0.0, -0.0052778879180550575, -0.008990956470370293, 0.006015332415699959,
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+- [0.0, 0.0, -0.004598336294293404, -0.007712222170084715, 0.004991475958377123, -0.0011117745889350772,
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+- [0.0, 0.0, -0.0033639161847531796, -0.005437097977846861, 0.003256432246416807,
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+- [0.0, 0.0, -0.001832868903875351, -0.0027474239468574524, 0.0014005053089931607,
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+- [0.0, 0.0, -0.0014116567326709628, -0.002047537826001644, 0.0009690625593066216,
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+  0.002908359281718731, -0.0014116567326709628, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0010373605182394385, -0.0014474663184955716, 0.0006248857825994492,
+  -9.356541704619303e-05, -7.132535392884165e-05, 0.000256813334999606, 0.0009840881684795022,
+  0.0020827800035476685, -0.0010373605182394385, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0007121165399439633, -0.0009481889428570867, 0.0003632246807683259,
+  -5.132606747793034e-05, -3.1064591894391924e-05, 0.0002090574853355065, 0.0006277010543271899,
+  0.0013854565331712365, -0.0007121165399439633, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00043890526285395026, -0.0005509257316589355, 0.00017840650980360806,
+  -2.529961238906253e-05, -1.0604557246551849e-05, 0.00015303630789276212, 0.00035826582461595535,
+  0.0008203523466363549, -0.0004389053210616112, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.00022217907826416194, -0.00025744838058017194, 6.34312818874605e-05,
+  -1.123877245845506e-05, -2.3211810002976563e-06, 9.282430255552754e-05, 0.0001678739645285532,
+  0.00039306041435338557, -0.0002221790491603315, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.951462273718789e-05, -7.091680163284764e-05, 9.051329470821656e-06,
+  -4.328504473960493e-06, -1.7165162091714592e-07, 3.573266803869046e-05, 4.914800956612453e-05,
+  0.00011257095320615917, -6.951462273718789e-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 9d12a53fe001f8681da151949c6b913ab35b7b25..5ba917395204010bd02392c12189f5b331ef4e81 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": 1688,
-  "best_epoch": 386,
-  "erf_tr": 3.8196349143981934,
-  "erf_vl": 4.181242942810059,
-  "chi2": 2.3859992027282715,
+  "stop_epoch": 1702,
+  "best_epoch": 400,
+  "erf_tr": 3.785813331604004,
+  "erf_vl": 4.147735118865967,
+  "chi2": 2.364035129547119,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.3172170310450748,
-    1.2737718180572153,
-    1.1682106289760015,
-    0.9969939105106653,
-    1.178227991809247
+    1.3241317467975082,
+    1.27799809169975,
+    1.1699576063062493,
+    0.9969979836415483,
+    1.1936096402729792
   ],
   "integrability": [
-    0.000922872146476017,
-    0.0009228721464754619,
-    6.687239761005159e-05,
-    0.528376147150993,
-    0.006918032886459646
+    0.000914250413189821,
+    0.0009142504131890439,
+    6.752895887940369e-05,
+    0.5550887137651436,
+    0.007037573843261868
   ],
   "timing": {
     "walltime": {
-      "Total": 25.596290588378906,
+      "Total": 27.138862133026123,
       "start": 0.0,
-      "replica_set": 0.4257495403289795,
-      "replica_fitted": 25.596144676208496,
-      "replica_set_to_replica_fitted": 25.170395135879517
+      "replica_set": 0.38606929779052734,
+      "replica_fitted": 27.13863968849182,
+      "replica_set_to_replica_fitted": 26.752570390701294
     },
     "cputime": {
-      "Total": 28.3766029,
+      "Total": 30.034188999999998,
       "start": 0.0,
-      "replica_set": 0.7320899000000001,
-      "replica_fitted": 28.376455399999998,
-      "replica_set_to_replica_fitted": 27.6443655
+      "replica_set": 0.7043999000000003,
+      "replica_fitted": 30.0339653,
+      "replica_set_to_replica_fitted": 29.3295654
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ 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 781ff81c0d60578c34a414411411376a2c1092d8..d6c2703dadd70edd5fc4a160db79108138b73a2b 100644
--- a/extra_tests/regression_fits/trainable_prepro_61.exportgrid
+++ b/extra_tests/regression_fits/trainable_prepro_61.exportgrid
@@ -1,79 +1,79 @@
 labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
 pdfgrid:
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-  0.00397163350135088, -0.0015301386592909694, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.002001565182581544, -0.0074308933690190315, 0.004808136261999607,
+  0.004673698917031288, -0.0020834477618336678, -0.0015328616136685014, -0.0013638486852869391,
+  0.005050962790846825, -0.002001565182581544, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.0015301386592909694, -0.005730059929192066, 0.0036868900060653687,
+  0.0036057105753570795, -0.0013753327075392008, -0.0012220815988257527, -0.0011206098133698106,
+  0.003971633967012167, -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, -0.0007592430920340121, -0.0028798324055969715, 0.0018357854569330812,
+  0.0018143568886443973, -0.0004564860137179494, -0.0006674373871646821, -0.0006410078494809568,
+  0.0020997703541070223, -0.0007592432084493339, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.000463553995359689, -0.0017633828101679683, 0.0011202655732631683,
+  0.001111964462324977, -0.00020737350860144943, -0.0004313824756536633, -0.0004212286148685962,
+  0.0013308260822668672, -0.0004635539080481976, 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, -0.00026940598036162555, 0.00017080882389564067,
-  0.00017058996309060603, -9.925640370056499e-06, -7.798225124133751e-05, -7.772142998874187e-05,
+  0.00017058996309060603, -9.925639460561797e-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
diff --git a/extra_tests/regression_fits/trainable_prepro_61.json b/extra_tests/regression_fits/trainable_prepro_61.json
index db5b3f5ba8ba0304c21e7cd6092cef7c9a922dd7..8442536b24b4c96a928b48bda1354d8cd71a1aa3 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": 83.88552856445312,
-  "erf_vl": 88.89352416992188,
-  "chi2": 59.15236282348633,
+  "erf_tr": 83.88551330566406,
+  "erf_vl": 88.89353942871094,
+  "chi2": 59.15235900878906,
   "pos_state": "POS_VETO",
   "arc_lengths": [
-    1.0440971720839172,
-    1.5280262072729438,
-    1.0033084215844166,
-    0.9979762330411598,
-    1.4192811360785857
+    1.0440971854791903,
+    1.5280261822454786,
+    1.0033084216442367,
+    0.9979762378240656,
+    1.4192810423200604
   ],
   "integrability": [
-    0.11098538525402664,
-    0.11098538525402585,
-    0.0002027638274733623,
-    0.00843445386271846,
-    0.0018140712927551261
+    0.11098538525402746,
+    0.11098538525402579,
+    0.00020276382838291251,
+    0.008434453979133893,
+    0.0018140712345475762
   ],
   "timing": {
     "walltime": {
-      "Total": 19.603114128112793,
+      "Total": 21.60775899887085,
       "start": 0.0,
-      "replica_set": 0.3588278293609619,
-      "replica_fitted": 19.60303783416748,
-      "replica_set_to_replica_fitted": 19.24421000480652
+      "replica_set": 0.3911454677581787,
+      "replica_fitted": 21.60759949684143,
+      "replica_set_to_replica_fitted": 21.216454029083252
     },
     "cputime": {
-      "Total": 21.8009634,
+      "Total": 23.8026402,
       "start": 0.0,
-      "replica_set": 0.6759696999999996,
-      "replica_fitted": 21.800885700000002,
-      "replica_set_to_replica_fitted": 21.124916
+      "replica_set": 0.7076198999999992,
+      "replica_fitted": 23.8024797,
+      "replica_set_to_replica_fitted": 23.094859800000002
     }
   },
   "version": {
     "tensorflow": "2.15.0, mkl=??",
     "numpy": "1.24.4",
-    "nnpdf": "4.0.8.post297.dev0+234efa01e",
-    "validphys": "4.0.8.post297.dev0+234efa01e"
+    "nnpdf": "4.0.8.post339.dev0+bc76939f2",
+    "validphys": "4.0.8.post339.dev0+bc76939f2"
   }
 }
\ No newline at end of file
diff --git a/n3fit/src/n3fit/backends/keras_backend/operations.py b/n3fit/src/n3fit/backends/keras_backend/operations.py
index 5d7638537f74bf85c6c751695e92db264258500a..fe62dfd24e5c5c6dc88fdc1c18d15213dbf76076 100644
--- a/n3fit/src/n3fit/backends/keras_backend/operations.py
+++ b/n3fit/src/n3fit/backends/keras_backend/operations.py
@@ -212,6 +212,12 @@ def flatten(x):
     return tf.reshape(x, (-1,))
 
 
+@tf.function
+def reshape(x, shape):
+    """reshape tensor x"""
+    return tf.reshape(x, shape)
+
+
 def boolean_mask(*args, **kwargs):
     """
     Applies a boolean mask to a tensor
diff --git a/n3fit/src/n3fit/checks.py b/n3fit/src/n3fit/checks.py
index 36ae24d52cc6c603b29d596eded289bc1bcdb46a..e1df9e28653f133f905964e827ec8a2de57d911b 100644
--- a/n3fit/src/n3fit/checks.py
+++ b/n3fit/src/n3fit/checks.py
@@ -380,11 +380,6 @@ def check_consistent_parallel(parameters, parallel_models, same_trvl_per_replica
     """
     if not parallel_models:
         return
-    if not same_trvl_per_replica:
-        raise CheckError(
-            "Replicas cannot be run in parallel with different training/validation "
-            " masks, please set `same_trvl_per_replica` to True in the runcard"
-        )
     if parameters.get("layer_type") != "dense":
         raise CheckError("Parallelization has only been tested with layer_type=='dense'")
 
diff --git a/n3fit/src/n3fit/layers/losses.py b/n3fit/src/n3fit/layers/losses.py
index 4315919907385cced18021a376601ad824ea05ad..1d330ef8f59fe64251d40e621ac87949b1d0ce48 100644
--- a/n3fit/src/n3fit/layers/losses.py
+++ b/n3fit/src/n3fit/layers/losses.py
@@ -8,6 +8,7 @@
 
 """
 import numpy as np
+
 from n3fit.backends import MetaLayer
 from n3fit.backends import operations as op
 
@@ -38,9 +39,6 @@ class LossInvcovmat(MetaLayer):
     """
 
     def __init__(self, invcovmat, y_true, mask=None, covmat=None, **kwargs):
-        # If we have a diagonal matrix, padd with 0s and hope it's not too heavy on memory
-        if len(invcovmat.shape) == 1:
-            invcovmat = np.diag(invcovmat)
         self._invcovmat = op.numpy_to_tensor(invcovmat)
         self._covmat = covmat
         self._y_true = op.numpy_to_tensor(y_true)
@@ -56,9 +54,7 @@ class LossInvcovmat(MetaLayer):
         """Transform the inverse covmat and the mask into
         weights of the layers"""
         init = MetaLayer.init_constant(self._invcovmat)
-        self.kernel = self.builder_helper(
-            "invcovmat", (self._ndata, self._ndata), init, trainable=False
-        )
+        self.kernel = self.builder_helper("invcovmat", self._invcovmat.shape, init, trainable=False)
         mask_shape = (1, 1, self._ndata)
         if self._mask is None:
             init_mask = MetaLayer.init_constant(np.ones(mask_shape))
@@ -79,17 +75,24 @@ class LossInvcovmat(MetaLayer):
         self.mask.assign(new_mask)
 
     def call(self, y_pred, **kwargs):
-        tmp_raw = self._y_true - y_pred
+        obs_diff_raw = self._y_true - y_pred
         # TODO: most of the time this is a y * I multiplication and can be skipped
         # benchmark how much time (if any) is lost in this in actual fits for the benefit of faster kfolds
-        tmp = op.op_multiply([tmp_raw, self.mask])
-        if tmp.shape[1] == 1:
-            # einsum is not well suited for CPU, so use tensordot if not multimodel
-            right_dot = op.tensor_product(self.kernel, tmp[0, 0, :], axes=1)
-            res = op.tensor_product(tmp[0, :, :], right_dot, axes=1)
+        obs_diff = op.op_multiply([obs_diff_raw, self.mask])
+
+        # The experimental loss doesn't depend on replicas, so it doesn't have a replica axis and
+        # must be treated separately
+        experimental_loss = len(self.kernel.shape) == 2
+        one_replica = obs_diff.shape[1] == 1
+
+        if one_replica:  # einsum is not well suited for CPU, so use tensordot if single replica
+            kernel = self.kernel if experimental_loss else self.kernel[0]
+            right_dot = op.tensor_product(kernel, obs_diff[0, 0, :], axes=1)
+            loss = op.tensor_product(obs_diff[0, :, :], right_dot, axes=1)
         else:
-            res = op.einsum("bri, ij, brj -> r", tmp, self.kernel, tmp)
-        return res
+            einstr = "bri, ij, brj -> r" if experimental_loss else "bri, rij, brj -> r"
+            loss = op.einsum(einstr, obs_diff, self.kernel, obs_diff)
+        return loss
 
 
 class LossLagrange(MetaLayer):
diff --git a/n3fit/src/n3fit/layers/mask.py b/n3fit/src/n3fit/layers/mask.py
index 877df3b502965af07ce01f816ccf20de7a3d7cd6..2b0bff6c00f27ff466b1f6d55f8f0b76a7367ad8 100644
--- a/n3fit/src/n3fit/layers/mask.py
+++ b/n3fit/src/n3fit/layers/mask.py
@@ -1,10 +1,12 @@
+from numpy import count_nonzero
+
 from n3fit.backends import MetaLayer
 from n3fit.backends import operations as op
 
 
 class Mask(MetaLayer):
     """
-    This layers applies a boolean mask to a rank-1 input tensor.
+    This layers applies a boolean mask to an input tensor.
     The mask admit a multiplier for all outputs which will be internally
     saved as a weight so it can be updated during trainig.
 
@@ -14,34 +16,50 @@ class Mask(MetaLayer):
 
     Parameters
     ----------
-        bool_mask: np.array
+        bool_mask: np.array of shape (n_replicas, n_features)
             numpy array with the boolean mask to be applied
         c: float
             constant multiplier for every output
-        axis: int
-            axis in which to apply the mask
     """
 
-    def __init__(self, bool_mask=None, c=None, axis=None, **kwargs):
+    def __init__(self, bool_mask=None, c=None, **kwargs):
         if bool_mask is None:
             self.mask = None
+            self.last_dim = -1
         else:
             self.mask = op.numpy_to_tensor(bool_mask, dtype=bool)
+            self.last_dim = count_nonzero(bool_mask[0, ...])
         self.c = c
-        self.axis = axis
+        self.masked_output_shape = None
         super().__init__(**kwargs)
 
     def build(self, input_shape):
         if self.c is not None:
             initializer = MetaLayer.init_constant(value=self.c)
-            self.kernel = self.builder_helper(
-                "mask", (1,), initializer, trainable=False
-            )
+            self.kernel = self.builder_helper("mask", (1,), initializer, trainable=False)
+        # Make sure reshape will succeed: set the last dimension to the unmasked data length and before-last to
+        # the number of replicas
+        if self.mask is not None:
+            self.masked_output_shape = [-1 if d is None else d for d in input_shape]
+            self.masked_output_shape[-1] = self.last_dim
+            self.masked_output_shape[-2] = self.mask.shape[-2]
         super(Mask, self).build(input_shape)
 
     def call(self, ret):
+        """
+        Apply the mask to the input tensor, and multiply by the constant if present.
+
+        Parameters
+        ----------
+            ret: Tensor of shape (batch_size, n_replicas, n_features)
+
+        Returns
+        -------
+            Tensor of shape (batch_size, n_replicas, n_features)
+        """
         if self.mask is not None:
-            ret = op.boolean_mask(ret, self.mask, axis=self.axis)
+            flat_res = op.boolean_mask(ret, self.mask, axis=1)
+            ret = op.reshape(flat_res, shape=self.masked_output_shape)
         if self.c is not None:
             ret = ret * self.kernel
         return ret
diff --git a/n3fit/src/n3fit/model_gen.py b/n3fit/src/n3fit/model_gen.py
index 5c338135a1e09bfcdfb1769aa66bdbd433e466b7..219bbdfc11ebd9b160c28b6c05404e907bdcc708 100644
--- a/n3fit/src/n3fit/model_gen.py
+++ b/n3fit/src/n3fit/model_gen.py
@@ -32,6 +32,7 @@ from n3fit.layers import (
     AddPhoton,
     FkRotation,
     FlavourToEvolution,
+    Mask,
     ObsRotation,
     Preprocessing,
     losses,
@@ -56,6 +57,7 @@ class ObservableWrapper:
 
     name: str
     observables: list
+    trvl_mask_layer: Mask
     dataset_xsizes: list
     invcovmat: np.array = None
     covmat: np.array = None
@@ -69,8 +71,22 @@ class ObservableWrapper:
         """Generates the corresponding loss function depending on the values the wrapper
         was initialized with"""
         if self.invcovmat is not None:
+            if self.rotation:
+                # If we have a matrix diagonal only, padd with 0s and hope it's not too heavy on memory
+                invcovmat_matrix = np.eye(self.invcovmat.shape[-1]) * self.invcovmat[..., np.newaxis]
+                if self.covmat is not None:
+                    covmat_matrix = np.eye(self.covmat.shape[-1]) * self.covmat[..., np.newaxis]
+                else:
+                    covmat_matrix = self.covmat
+            else:
+                covmat_matrix = self.covmat
+                invcovmat_matrix = self.invcovmat
             loss = losses.LossInvcovmat(
-                self.invcovmat, self.data, mask, covmat=self.covmat, name=self.name
+                invcovmat_matrix,
+                self.data,
+                mask,
+                covmat=covmat_matrix,
+                name=self.name
             )
         elif self.positivity:
             loss = losses.LossPositivity(name=self.name, c=self.multiplier)
@@ -95,10 +111,15 @@ class ObservableWrapper:
         else:
             output_layers = [obs(pdf) for obs in self.observables]
 
-        # Finally concatenate all observables (so that experiments are one single entitiy)
-        ret = op.concatenate(output_layers, axis=2)
+        # Finally concatenate all observables (so that experiments are one single entity)
+        ret = op.concatenate(output_layers, axis=-1)
+
         if self.rotation is not None:
             ret = self.rotation(ret)
+
+        if self.trvl_mask_layer is not None:
+            ret = self.trvl_mask_layer(ret)
+
         return ret
 
     def __call__(self, pdf_layer, mask=None):
@@ -108,7 +129,14 @@ class ObservableWrapper:
 
 
 def observable_generator(
-    spec_dict, positivity_initial=1.0, integrability=False
+    spec_dict,
+    mask_array=None,
+    training_data=None,
+    validation_data=None,
+    invcovmat_tr=None,
+    invcovmat_vl=None,
+    positivity_initial=1.0,
+    integrability=False,
 ):  # pylint: disable=too-many-locals
     """
     This function generates the observable models for each experiment.
@@ -157,9 +185,7 @@ def observable_generator(
     spec_name = spec_dict["name"]
     dataset_xsizes = []
     model_inputs = []
-    model_obs_tr = []
-    model_obs_vl = []
-    model_obs_ex = []
+    model_observables = []
     # The first step is to compute the observable for each of the datasets
     for dataset in spec_dict["datasets"]:
         # Get the generic information of the dataset
@@ -180,50 +206,14 @@ def observable_generator(
         # list of validphys.coredata.FKTableData objects
         #   these will then be used to check how many different pdf inputs are needed
         #   (and convolutions if given the case)
-
-        if spec_dict["positivity"]:
-            # Positivity (and integrability, which is a special kind of positivity...)
-            # enters only at the "training" part of the models
-            obs_layer_tr = Obs_Layer(
-                dataset.fktables_data,
-                dataset.training_fktables(),
-                operation_name,
-                name=f"dat_{dataset_name}",
-            )
-            obs_layer_ex = obs_layer_vl = None
-        elif spec_dict.get("data_transformation_tr") is not None:
-            # Data transformation needs access to the full array of output data
-            obs_layer_ex = Obs_Layer(
-                dataset.fktables_data,
-                dataset.fktables(),
-                operation_name,
-                name=f"exp_{dataset_name}",
-            )
-            obs_layer_tr = obs_layer_vl = obs_layer_ex
-        else:
-            obs_layer_tr = Obs_Layer(
-                dataset.fktables_data,
-                dataset.training_fktables(),
-                operation_name,
-                name=f"dat_{dataset_name}",
-            )
-            obs_layer_ex = Obs_Layer(
-                dataset.fktables_data,
-                dataset.fktables(),
-                operation_name,
-                name=f"exp_{dataset_name}",
-            )
-            obs_layer_vl = Obs_Layer(
-                dataset.fktables_data,
-                dataset.validation_fktables(),
-                operation_name,
-                name=f"val_{dataset_name}",
-            )
+        obs_layer = Obs_Layer(
+            dataset.fktables_data, dataset.fktables(), operation_name, name=f"dat_{dataset_name}"
+        )
 
         # If the observable layer found that all input grids are equal, the splitting will be None
         # otherwise the different xgrids need to be stored separately
         # Note: for pineappl grids, obs_layer_tr.splitting should always be None
-        if obs_layer_tr.splitting is None:
+        if obs_layer.splitting is None:
             xgrid = dataset.fktables_data[0].xgrid
             model_inputs.append(xgrid)
             dataset_xsizes.append(len(xgrid))
@@ -232,9 +222,7 @@ def observable_generator(
             model_inputs += xgrids
             dataset_xsizes.append(sum([len(i) for i in xgrids]))
 
-        model_obs_tr.append(obs_layer_tr)
-        model_obs_vl.append(obs_layer_vl)
-        model_obs_ex.append(obs_layer_ex)
+        model_observables.append(obs_layer)
 
     # Check whether all xgrids of all observables in this experiment are equal
     # if so, simplify the model input
@@ -245,11 +233,25 @@ def observable_generator(
     # Reshape all inputs arrays to be (1, nx)
     model_inputs = np.concatenate(model_inputs).reshape(1, -1)
 
-    full_nx = sum(dataset_xsizes)
+    # Make the mask layers...
+    if mask_array is not None:
+        tr_mask_layer = Mask(mask_array, name=f"trmask_{spec_name}")
+        vl_mask_layer = Mask(~mask_array, name=f"vlmask_{spec_name}")
+    else:
+        tr_mask_layer = None
+        vl_mask_layer = None
+
+    # Make rotations of the final data (if any)
+    if spec_dict.get("data_transformation") is not None:
+        obsrot = ObsRotation(spec_dict.get("data_transformation"))
+    else:
+        obsrot = None
+
     if spec_dict["positivity"]:
         out_positivity = ObservableWrapper(
             spec_name,
-            model_obs_tr,
+            model_observables,
+            tr_mask_layer,
             dataset_xsizes,
             multiplier=positivity_initial,
             positivity=not integrability,
@@ -259,38 +261,33 @@ def observable_generator(
         layer_info = {
             "inputs": model_inputs,
             "output_tr": out_positivity,
-            "experiment_xsize": full_nx,
+            "experiment_xsize": sum(dataset_xsizes),
         }
         # For positivity we end here
         return layer_info
 
-    # Generate the loss function and rotations of the final data (if any)
-    if spec_dict.get("data_transformation_tr") is not None:
-        obsrot_tr = ObsRotation(spec_dict.get("data_transformation_tr"))
-        obsrot_vl = ObsRotation(spec_dict.get("data_transformation_vl"))
-    else:
-        obsrot_tr = None
-        obsrot_vl = None
-
     out_tr = ObservableWrapper(
         spec_name,
-        model_obs_tr,
+        model_observables,
+        tr_mask_layer,
         dataset_xsizes,
-        invcovmat=spec_dict["invcovmat"],
-        data=spec_dict["expdata"],
-        rotation=obsrot_tr,
+        invcovmat=invcovmat_tr,
+        data=training_data,
+        rotation=obsrot,
     )
     out_vl = ObservableWrapper(
         f"{spec_name}_val",
-        model_obs_vl,
+        model_observables,
+        vl_mask_layer,
         dataset_xsizes,
-        invcovmat=spec_dict["invcovmat_vl"],
-        data=spec_dict["expdata_vl"],
-        rotation=obsrot_vl,
+        invcovmat=invcovmat_vl,
+        data=validation_data,
+        rotation=obsrot,
     )
     out_exp = ObservableWrapper(
         f"{spec_name}_exp",
-        model_obs_ex,
+        model_observables,
+        None,
         dataset_xsizes,
         invcovmat=spec_dict["invcovmat_true"],
         covmat=spec_dict["covmat"],
@@ -303,7 +300,7 @@ def observable_generator(
         "output": out_exp,
         "output_tr": out_tr,
         "output_vl": out_vl,
-        "experiment_xsize": full_nx,
+        "experiment_xsize": sum(dataset_xsizes),
     }
     return layer_info
 
diff --git a/n3fit/src/n3fit/model_trainer.py b/n3fit/src/n3fit/model_trainer.py
index acbcc8b3cd854a3532147e314eca483c9ebd0d9b..59acff377a17c47ce8e5963a44c93d897b3be7b3 100644
--- a/n3fit/src/n3fit/model_trainer.py
+++ b/n3fit/src/n3fit/model_trainer.py
@@ -15,9 +15,8 @@ import logging
 import numpy as np
 
 from n3fit import model_gen
-from n3fit.backends import MetaModel, callbacks, clear_backend_state
+from n3fit.backends import NN_LAYER_ALL_REPLICAS, MetaModel, callbacks, clear_backend_state
 from n3fit.backends import operations as op
-from n3fit.backends import NN_LAYER_ALL_REPLICAS
 import n3fit.hyper_optimization.penalties
 import n3fit.hyper_optimization.rewards
 from n3fit.scaler import generate_scaler
@@ -143,15 +142,10 @@ class ModelTrainer:
                 list with the replicas ids to be fitted
         """
         # Save all input information
-        self.exp_info = exp_info
-        if pos_info is None:
-            pos_info = []
-        self.pos_info = pos_info
-        self.integ_info = integ_info
-        if self.integ_info is not None:
-            self.all_info = exp_info + pos_info + integ_info
-        else:
-            self.all_info = exp_info + pos_info
+        self.exp_info = list(exp_info)
+        self.pos_info = [] if pos_info is None else pos_info
+        self.integ_info = [] if integ_info is None else integ_info
+        self.all_info = self.exp_info[0] + self.pos_info + self.integ_info
         self.flavinfo = flavinfo
         self.fitbasis = fitbasis
         self._nn_seeds = nnseeds
@@ -219,6 +213,7 @@ class ModelTrainer:
             "posdatasets": [],
         }
         self.experimental = {"output": [], "expdata": [], "ndata": 0, "model": None, "folds": []}
+        self.tr_masks = []
 
         self._fill_the_dictionaries()
 
@@ -268,7 +263,7 @@ class ModelTrainer:
             - ``name``: names of the experiment
             - ``ndata``: number of experimental points
         """
-        for exp_dict in self.exp_info:
+        for exp_dict in self.exp_info[0]:
             self.training["expdata"].append(exp_dict["expdata"])
             self.validation["expdata"].append(exp_dict["expdata_vl"])
             self.experimental["expdata"].append(exp_dict["expdata_true"])
@@ -293,10 +288,10 @@ class ModelTrainer:
             self.training["posdatasets"].append(pos_dict["name"])
             self.validation["expdata"].append(pos_dict["expdata"])
             self.validation["posdatasets"].append(pos_dict["name"])
-        if self.integ_info is not None:
-            for integ_dict in self.integ_info:
-                self.training["expdata"].append(integ_dict["expdata"])
-                self.training["integdatasets"].append(integ_dict["name"])
+
+        for integ_dict in self.integ_info:
+            self.training["expdata"].append(integ_dict["expdata"])
+            self.training["integdatasets"].append(integ_dict["name"])
 
     def _xgrid_generation(self):
         """
@@ -483,7 +478,7 @@ class ModelTrainer:
             self.experimental[key] = []
 
     ############################################################################
-    # # Parametizable functions                                                #
+    # # Parameterizable functions                                                #
     #                                                                          #
     # The functions defined in this block accept a 'params' dictionary which   #
     # defines the fit and the behaviours of the Neural Networks                #
@@ -523,12 +518,44 @@ class ModelTrainer:
         self._reset_observables()
         log.info("Generating layers")
 
+        # We need to transpose Experimental data, stacking over replicas
+        experiment_data = {
+            "trmask": [],
+            "expdata": [],
+            "expdata_vl": [],
+            "invcovmat": [],
+            "invcovmat_vl": [],
+        }
+
+        # Loop over datasets
+        for i in range(len(self.exp_info[0])):
+            # Loop over data fields
+            for key, value in experiment_data.items():
+                replica_data = []
+                # Loop over replicas
+                for replica in self.exp_info:
+                    if key in ["expdata", "expdata_vl"]:
+                        # Save the data with shape (ndata) instead of (1, ndata)
+                        replica_data.append(replica[i][key][0])
+                    else:
+                        replica_data.append(replica[i][key])
+                # Stack
+                value.append(np.stack(replica_data))
+
         # Now we need to loop over all dictionaries (First exp_info, then pos_info and integ_info)
-        for exp_dict in self.exp_info:
+        for i, exp_dict in enumerate(self.exp_info[0]):
             if not self.mode_hyperopt:
                 log.info("Generating layers for experiment %s", exp_dict["name"])
 
-            exp_layer = model_gen.observable_generator(exp_dict)
+            # Stacked tr-vl mask array for all replicas for this dataset
+            exp_layer = model_gen.observable_generator(
+                exp_dict,
+                mask_array=experiment_data["trmask"][i],
+                training_data=experiment_data["expdata"][i],
+                validation_data=experiment_data["expdata_vl"][i],
+                invcovmat_tr=experiment_data["invcovmat"][i],
+                invcovmat_vl=experiment_data["invcovmat_vl"][i],
+            )
 
             # Save the input(s) corresponding to this experiment
             self.input_list.append(exp_layer["inputs"])
@@ -549,8 +576,17 @@ class ModelTrainer:
             pos_initial, pos_multiplier = _LM_initial_and_multiplier(
                 all_pos_initial, all_pos_multiplier, max_lambda, positivity_steps
             )
-
-            pos_layer = model_gen.observable_generator(pos_dict, positivity_initial=pos_initial)
+            num_experiments = len(self.exp_info)
+            replica_masks = np.stack([pos_dict["trmask"]] * num_experiments)
+            training_data = np.stack([pos_dict["expdata"].flatten()] * num_experiments)
+
+            pos_layer = model_gen.observable_generator(
+                pos_dict,
+                positivity_initial=pos_initial,
+                mask_array=replica_masks,
+                training_data=training_data,
+                validation_data=training_data,
+            )
             # The input list is still common
             self.input_list.append(pos_layer["inputs"])
 
@@ -562,28 +598,27 @@ class ModelTrainer:
             self.training["posinitials"].append(pos_initial)
 
         # Finally generate the integrability penalty
-        if self.integ_info is not None:
-            for integ_dict in self.integ_info:
-                if not self.mode_hyperopt:
-                    log.info("Generating integrability penalty for %s", integ_dict["name"])
-
-                integrability_steps = int(epochs / PUSH_INTEGRABILITY_EACH)
-                max_lambda = integ_dict["lambda"]
-
-                integ_initial, integ_multiplier = _LM_initial_and_multiplier(
-                    all_integ_initial, all_integ_multiplier, max_lambda, integrability_steps
-                )
-
-                integ_layer = model_gen.observable_generator(
-                    integ_dict, positivity_initial=integ_initial, integrability=True
-                )
-                # The input list is still common
-                self.input_list.append(integ_layer["inputs"])
-
-                # The integrability all falls to the training
-                self.training["output"].append(integ_layer["output_tr"])
-                self.training["integmultipliers"].append(integ_multiplier)
-                self.training["integinitials"].append(integ_initial)
+        for integ_dict in self.integ_info:
+            if not self.mode_hyperopt:
+                log.info("Generating integrability penalty for %s", integ_dict["name"])
+
+            integrability_steps = int(epochs / PUSH_INTEGRABILITY_EACH)
+            max_lambda = integ_dict["lambda"]
+
+            integ_initial, integ_multiplier = _LM_initial_and_multiplier(
+                all_integ_initial, all_integ_multiplier, max_lambda, integrability_steps
+            )
+
+            integ_layer = model_gen.observable_generator(
+                integ_dict, positivity_initial=integ_initial, integrability=True
+            )
+            # The input list is still common
+            self.input_list.append(integ_layer["inputs"])
+
+            # The integrability all falls to the training
+            self.training["output"].append(integ_layer["output_tr"])
+            self.training["integmultipliers"].append(integ_multiplier)
+            self.training["integinitials"].append(integ_initial)
 
         # Store a reference to the interpolator as self._scaler
         if interpolation_points:
diff --git a/n3fit/src/n3fit/performfit.py b/n3fit/src/n3fit/performfit.py
index ee38aad4ea401777ec1a2785370c13f76d85914b..6514029ca25f2d932e5fc2666de6e8c4c2a2df80 100644
--- a/n3fit/src/n3fit/performfit.py
+++ b/n3fit/src/n3fit/performfit.py
@@ -143,49 +143,40 @@ def performfit(
     from n3fit.io.writer import WriterWrapper
     from n3fit.model_trainer import ModelTrainer
 
-    # Note: there are three possible scenarios for the loop of replicas:
-    #   1.- Only one replica is being run, in this case the loop is only evaluated once
-    #   2.- Many replicas being run, in this case each will have a replica_number, seed, etc
-    #       and they will be fitted sequentially
-    #   3.- Many replicas being run in parallel. In this case the loop will be evaluated just once
-    #       but a model per replica will be generated
+    # Note that this can be run in sequence or in parallel
+    # To do both cases in the same loop, we uniformize the replica information as:
+    # - sequential: a list over replicas, each entry containing tuples of length 1
+    # - parallel: a list of length 1, containing tuples over replicas
     #
-    # In the main scenario (1) replicas_nnseed_fitting_data_dict is a list of just one element
-    # case (3) is similar but the one element of replicas_nnseed_fitting_data_dict will be modified
-    # to be (
-    #       [list of all replica idx],
-    #       one experiment with data=(replicas, ndata),
-    #       [list of all NN seeds]
-    #       )
-    #
-    n_models = len(replicas_nnseed_fitting_data_dict)
-    if parallel_models and n_models != 1:
-        replicas, replica_experiments, nnseeds = zip(*replicas_nnseed_fitting_data_dict)
-        # Parse the experiments so that the output data contain information for all replicas
-        # as the only different from replica to replica is the experimental training/validation data
-        all_experiments = copy.deepcopy(replica_experiments[0])
-        for i_exp in range(len(all_experiments)):
-            training_data = []
-            validation_data = []
-            for i_rep in range(n_models):
-                training_data.append(replica_experiments[i_rep][i_exp]['expdata'])
-                validation_data.append(replica_experiments[i_rep][i_exp]['expdata_vl'])
-            all_experiments[i_exp]['expdata'] = np.concatenate(training_data, axis=0)
-            all_experiments[i_exp]['expdata_vl'] = np.concatenate(validation_data, axis=0)
+    # Add inner tuples
+    replicas_info = [
+        ((replica,), (experiment,), (nnseed,))
+        for replica, experiment, nnseed in replicas_nnseed_fitting_data_dict
+    ]
+
+    n_models = len(replicas_info)
+    if parallel_models:
+        # Move replicas from outer list to inner tuples
+        replicas, experiments, nnseeds = [], [], []
+
+        for replica, experiment, nnseed in replicas_info:
+            replicas.extend(replica)
+            experiments.extend(experiment)
+            nnseeds.extend(nnseed)
+
+        replicas_info = [(tuple(replicas), tuple(experiments), tuple(nnseeds))]
         log.info(
             "Starting parallel fits from replica %d to %d", replicas[0], replicas[0] + n_models - 1
         )
-        replicas_info = [(replicas, all_experiments, nnseeds)]
     else:
-        replicas_info = replicas_nnseed_fitting_data_dict
+        log.info(
+            "Starting sequential fits from replica %d to %d",
+            replicas[0],
+            replicas[0] + n_models - 1,
+        )
 
     for replica_idxs, exp_info, nnseeds in replicas_info:
-        if not parallel_models or n_models == 1:
-            # Cases 1 and 2 above are a special case of 3 where the replica idx and the seed should
-            # be a list of just one element
-            replica_idxs = [replica_idxs]
-            nnseeds = [nnseeds]
-            log.info("Starting replica fit %d", replica_idxs[0])
+        log.info("Starting replica fit " + str(replica_idxs))
 
         # Generate a ModelTrainer object
         # this object holds all necessary information to train a PDF (up to the NN definition)
diff --git a/n3fit/src/n3fit/stopping.py b/n3fit/src/n3fit/stopping.py
index 8884e7f01b03a251d6dd6bb86a90d4128efcdee1..380c5445d7b321619c9b553bf40bd449d856ce96 100644
--- a/n3fit/src/n3fit/stopping.py
+++ b/n3fit/src/n3fit/stopping.py
@@ -384,7 +384,7 @@ class Stopping:
     @property
     def stop_epoch(self):
         """Epoch in which the fit is stopped"""
-        return self._history.final_epoch + 1
+        return -1 if self._history.final_epoch is None else self._history.final_epoch + 1
 
     @property
     def positivity_status(self):
diff --git a/n3fit/src/n3fit/tests/test_layers.py b/n3fit/src/n3fit/tests/test_layers.py
index 1cae6c6c6a4ac534c3973c9ba4b146e34ca69e80..6ff4887d64623e73e0d13a4dc4f331b87f1c955f 100644
--- a/n3fit/src/n3fit/tests/test_layers.py
+++ b/n3fit/src/n3fit/tests/test_layers.py
@@ -240,8 +240,9 @@ def test_rotation_evol():
 
 def test_mask():
     """Test the mask layer"""
-    SIZE = 100
-    fi = np.random.rand(SIZE)
+    batch_size, replicas, points = 1, 1, 100
+    shape = (batch_size, replicas, points)
+    fi = np.random.rand(*shape)
     # Check that the multiplier works
     vals = [0.0, 2.0, np.random.rand()]
     for val in vals:
@@ -249,10 +250,10 @@ def test_mask():
         ret = masker(fi)
         np.testing.assert_allclose(ret, val * fi, rtol=1e-5)
     # Check that the boolean works
-    np_mask = np.random.randint(0, 2, size=SIZE, dtype=bool)
+    np_mask = np.random.randint(0, 2, size=shape[1:], dtype=bool)
     masker = layers.Mask(bool_mask=np_mask)
     ret = masker(fi)
-    masked_fi = fi[np_mask]
+    masked_fi = fi[np.newaxis, :, np_mask]
     np.testing.assert_allclose(ret, masked_fi, rtol=1e-5)
     # Check that the combination works!
     rn_val = vals[-1]
diff --git a/validphys2/src/validphys/filters.py b/validphys2/src/validphys/filters.py
index 931d5b42146c557050efdf61a9acf90fce71dd6e..566b372c6d0959b9b5b9b5f6fcdd8fc04e49d811 100644
--- a/validphys2/src/validphys/filters.py
+++ b/validphys2/src/validphys/filters.py
@@ -180,9 +180,7 @@ def _filter_real_data(filter_path, data):
     return total_data_points, total_cut_data_points
 
 
-def _filter_closure_data(
-    filter_path, data, fakepdf, fakenoise, filterseed, data_index, sep_mult
-):
+def _filter_closure_data(filter_path, data, fakepdf, fakenoise, filterseed, data_index, sep_mult):
     """
     This function is accessed within a closure test only, that is, the fakedata
     namespace has to be True (If fakedata = False, the _filter_real_data function
@@ -395,14 +393,7 @@ class Rule:
 
     numpy_functions = {"sqrt": np.sqrt, "log": np.log, "fabs": np.fabs}
 
-    def __init__(
-        self,
-        initial_data: dict,
-        *,
-        defaults: dict,
-        theory_parameters: dict,
-        loader=None,
-    ):
+    def __init__(self, initial_data: dict, *, defaults: dict, theory_parameters: dict, loader=None):
         self.dataset = None
         self.process_type = None
         self._local_variables_code = {}
@@ -453,13 +444,7 @@ class Rule:
         self.rule_string = self.rule
         self.defaults = defaults
         self.theory_params = theory_parameters
-        ns = {
-            *self.numpy_functions,
-            *self.defaults,
-            *self.variables,
-            "idat",
-            "central_value",
-        }
+        ns = {*self.numpy_functions, *self.defaults, *self.variables, "idat", "central_value"}
         for k, v in self.local_variables.items():
             try:
                 self._local_variables_code[k] = lcode = compile(
@@ -536,11 +521,7 @@ class Rule:
             return eval(
                 self.rule,
                 self.numpy_functions,
-                {
-                    **{"idat": idat, "central_value": central_value},
-                    **self.defaults,
-                    **ns,
-                },
+                {**{"idat": idat, "central_value": central_value}, **self.defaults, **ns},
             )
         except Exception as e:  # pragma: no cover
             raise FatalRuleError(f"Error when applying rule {self.rule_string!r}: {e}") from e
diff --git a/validphys2/src/validphys/n3fit_data.py b/validphys2/src/validphys/n3fit_data.py
index 38f946248dae878ccbf6d8206c8fbba24e3681a1..ced700f98f6e62e4f24cb7e6c1b239211b224d9c 100644
--- a/validphys2/src/validphys/n3fit_data.py
+++ b/validphys2/src/validphys/n3fit_data.py
@@ -74,7 +74,7 @@ class _TrMasks(TupleComp):
             yield m
 
 
-def tr_masks(data, replica_trvlseed):
+def tr_masks(data, replica_trvlseed, parallel_models=False, replica=1, replicas=(1,)):
     """Generate the boolean masks used to split data into training and
     validation points. Returns a list of 1-D boolean arrays, one for each
     dataset. Each array has length equal to N_data, the datapoints which
@@ -97,8 +97,16 @@ def tr_masks(data, replica_trvlseed):
         # We do this so that a given dataset will always have the same number of points masked
         trmax = int(ndata * frac)
         if trmax == 0:
-            # If that number is 0, then get 1 point with probability frac
-            trmax = int(rng.random() < frac)
+            if parallel_models:
+                if replica == replicas[0]:
+                    log.warning(
+                        f'Single-datapoint dataset {dataset.name} encountered in parallel multi-replica fit: '
+                        'all replicas will include it in their training data'
+                    )
+                trmax = 1
+            else:
+                # If that number is 0, then get 1 point with probability frac
+                trmax = int(rng.random() < frac)
         mask = np.concatenate([np.ones(trmax, dtype=bool), np.zeros(ndata - trmax, dtype=bool)])
         rng.shuffle(mask)
         trmask_partial.append(mask)
@@ -311,6 +319,7 @@ def fitting_data_dict(
         "folds": folds,
         "data_transformation_tr": dt_trans_tr,
         "data_transformation_vl": dt_trans_vl,
+        "data_transformation": dt_trans,
     }
     return dict_out