diff --git a/extra_tests/regression_checks.py b/extra_tests/regression_checks.py
index c5679bf4f9..ceb04cd475 100644
--- a/extra_tests/regression_checks.py
+++ b/extra_tests/regression_checks.py
@@ -27,7 +27,7 @@
     "no_lagrange": 27,
     "no_csr": 613,
     "polarized_evol": 34,
-    "single_dense": 316,
+    "multi_dense": 316,
 }
 
 
diff --git a/extra_tests/regression_fits/central_16.json b/extra_tests/regression_fits/central_16.json
index 44ae30e28b..d70a76c075 100644
--- a/extra_tests/regression_fits/central_16.json
+++ b/extra_tests/regression_fits/central_16.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 11.068717002868652,
+      "Total": 10.047237396240234,
       "start": 0.0,
-      "replica_set": 0.23674464225769043,
-      "replica_fitted": 11.06860899925232,
-      "replica_set_to_replica_fitted": 10.831864356994629
+      "replica_set": 0.210205078125,
+      "replica_fitted": 10.047173023223877,
+      "replica_set_to_replica_fitted": 9.836967945098877
     },
     "cputime": {
-      "Total": 12.634108122999999,
+      "Total": 11.469310126,
       "start": 0.0,
-      "replica_set": 0.23454409999999992,
-      "replica_fitted": 12.633997697,
-      "replica_set_to_replica_fitted": 12.399453597
+      "replica_set": 0.2088275399999997,
+      "replica_fitted": 11.469243942000002,
+      "replica_set_to_replica_fitted": 11.260416402
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/diagonal_45.json b/extra_tests/regression_fits/diagonal_45.json
index dbdff72a05..abbfa81d84 100644
--- a/extra_tests/regression_fits/diagonal_45.json
+++ b/extra_tests/regression_fits/diagonal_45.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 11.215790271759033,
+      "Total": 9.477155923843384,
       "start": 0.0,
-      "replica_set": 0.23657774925231934,
-      "replica_fitted": 11.215726852416992,
-      "replica_set_to_replica_fitted": 10.979149103164673
+      "replica_set": 0.21604132652282715,
+      "replica_fitted": 9.477098941802979,
+      "replica_set_to_replica_fitted": 9.261057615280151
     },
     "cputime": {
-      "Total": 12.762100954,
+      "Total": 10.790387835,
       "start": 0.0,
-      "replica_set": 0.23547829999999959,
-      "replica_fitted": 12.762035623000001,
-      "replica_set_to_replica_fitted": 12.526557323000002
+      "replica_set": 0.21436629899999993,
+      "replica_fitted": 10.790329496999998,
+      "replica_set_to_replica_fitted": 10.575963198
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/feature_scaling_81.json b/extra_tests/regression_fits/feature_scaling_81.json
index 4c1c1e5a52..00865ddf03 100644
--- a/extra_tests/regression_fits/feature_scaling_81.json
+++ b/extra_tests/regression_fits/feature_scaling_81.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 11.622541427612305,
+      "Total": 9.83653473854065,
       "start": 0.0,
-      "replica_set": 0.23537468910217285,
-      "replica_fitted": 11.62245488166809,
-      "replica_set_to_replica_fitted": 11.387080192565918
+      "replica_set": 0.22139739990234375,
+      "replica_fitted": 9.836406946182251,
+      "replica_set_to_replica_fitted": 9.615009546279907
     },
     "cputime": {
-      "Total": 13.069087044,
+      "Total": 11.082168318,
       "start": 0.0,
-      "replica_set": 0.2290513789999995,
-      "replica_fitted": 13.068997967000001,
-      "replica_set_to_replica_fitted": 12.839946588000002
+      "replica_set": 0.2204650259999994,
+      "replica_fitted": 11.082038816,
+      "replica_set_to_replica_fitted": 10.861573790000001
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/flavour_29.exportgrid b/extra_tests/regression_fits/flavour_29.exportgrid
index 5afbabf453..b15eb1cfe6 100644
--- a/extra_tests/regression_fits/flavour_29.exportgrid
+++ b/extra_tests/regression_fits/flavour_29.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, -0.08641043305397034, 0.25056973099708557, 0.2924432158470154, 0.11987581849098206,
-  -2.82051157951355, 0.1887914389371872, 0.3841733932495117, 0.2434862107038498, -0.08641044795513153,
+- [0.0, 0.0, -0.08658803999423981, 0.25055211782455444, 0.2923639714717865, 0.11981478333473206,
+  -2.819662094116211, 0.1887313276529312, 0.384093314409256, 0.24346855282783508,
+  -0.086588054895401, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.08807513862848282, 0.2504374384880066, 0.2942172586917877, 0.11954109370708466,
+  -2.7913472652435303, 0.18830379843711853, 0.38618505001068115, 0.24350543320178986,
+  -0.08807512372732162, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -0.08960243314504623, 0.2503203749656677, 0.2961156666278839, 0.1192501112818718,
+  -2.7622592449188232, 0.18785460293293, 0.3883271813392639, 0.24354287981987, -0.08960244804620743,
   0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.08789772540330887, 0.25045499205589294, 0.29429635405540466, 0.1196020171046257,
-  -2.792196750640869, 0.18836380541324615, 0.3862648904323578, 0.24352306127548218,
-  -0.08789772540330887, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.08942512422800064, 0.25033801794052124, 0.2961946725845337, 0.11931098997592926,
-  -2.7631096839904785, 0.18791460990905762, 0.38840705156326294, 0.2435605674982071,
-  -0.08942513912916183, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.09099400043487549, 0.25021862983703613, 0.2981396019458771, 0.119001604616642,
-  -2.7332210540771484, 0.18744246661663055, 0.390601247549057, 0.24359850585460663,
-  -0.09099400043487549, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.09260577708482742, 0.25009670853614807, 0.3001326024532318, 0.11867332458496094,
-  -2.7025108337402344, 0.18694667518138885, 0.3928491175174713, 0.24363677203655243,
-  -0.09260577708482742, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0942620113492012, 0.2499721795320511, 0.30217549204826355, 0.11832532286643982,
-  -2.6709492206573486, 0.1864262968301773, 0.395152747631073, 0.2436753660440445,
-  -0.0942620113492012, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.09596388041973114, 0.24984478950500488, 0.3042697012424469, 0.11795663088560104,
-  -2.6385116577148438, 0.1858801394701004, 0.3975136876106262, 0.24371415376663208,
-  -0.09596386551856995, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.09771310538053513, 0.24971447885036469, 0.3064172863960266, 0.1175665408372879,
-  -2.605170726776123, 0.1853073537349701, 0.39993393421173096, 0.24375300109386444,
-  -0.09771310538053513, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.0995110273361206, 0.2495809942483902, 0.30862006545066833, 0.11715418845415115,
-  -2.570897102355957, 0.18470686674118042, 0.40241554379463196, 0.24379174411296844,
-  -0.09951101243495941, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.10135960578918457, 0.24944418668746948, 0.31088003516197205, 0.11671856790781021,
-  -2.535662889480591, 0.18407750129699707, 0.404960572719574, 0.24383027851581573,
-  -0.10135960578918457, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.10326065123081207, 0.24930380284786224, 0.3131992220878601, 0.11625876277685165,
-  -2.4994349479675293, 0.1834181249141693, 0.40757128596305847, 0.24386842548847198,
-  -0.10326063632965088, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.10521561652421951, 0.24915975332260132, 0.3155798316001892, 0.11577380448579788,
-  -2.4621851444244385, 0.18272750079631805, 0.4102499186992645, 0.24390608072280884,
-  -0.10521561652421951, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.10722628980875015, 0.24901176989078522, 0.3180241286754608, 0.11526293307542801,
-  -2.4238808155059814, 0.1820046752691269, 0.4129990339279175, 0.243942990899086,
-  -0.10722628980875015, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.10929523408412933, 0.24885964393615723, 0.3205345571041107, 0.11472507566213608,
-  -2.384488105773926, 0.18124829232692719, 0.41582098603248596, 0.24397902190685272,
-  -0.10929523408412933, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.11142383515834808, 0.2487030327320099, 0.3231135904788971, 0.11415909230709076,
-  -2.3439712524414062, 0.18045710027217865, 0.41871848702430725, 0.24401387572288513,
-  -0.11142382025718689, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.11361441016197205, 0.24854186177253723, 0.3257639706134796, 0.11356449872255325,
-  -2.302298069000244, 0.17963023483753204, 0.42169442772865295, 0.24404750764369965,
-  -0.11361441016197205, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.11586930602788925, 0.24837586283683777, 0.32848837971687317, 0.11293963342905045,
-  -2.2594311237335205, 0.17876578867435455, 0.4247516393661499, 0.24407958984375,
-  -0.11586932092905045, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.11819062381982803, 0.24820470809936523, 0.3312898874282837, 0.1122841164469719,
-  -2.2153351306915283, 0.17786309123039246, 0.4278932809829712, 0.24410994350910187,
-  -0.11819063872098923, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.12058115750551224, 0.24802802503108978, 0.3341716229915619, 0.1115967333316803,
-  -2.169969081878662, 0.17692062258720398, 0.4311225116252899, 0.24413824081420898,
-  -0.12058115750551224, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.12304273992776871, 0.24784573912620544, 0.3371365964412689, 0.11087649315595627,
-  -2.123293876647949, 0.17593711614608765, 0.4344426989555359, 0.24416427314281464,
-  -0.12304273992776871, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.12557834386825562, 0.24765734374523163, 0.34018829464912415, 0.11012255400419235,
-  -2.075272560119629, 0.17491133511066437, 0.4378573000431061, 0.24418772757053375,
-  -0.1255783587694168, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.12819083034992218, 0.247462660074234, 0.34333041310310364, 0.10933419317007065,
-  -2.0258617401123047, 0.17384222149848938, 0.4413701593875885, 0.24420827627182007,
-  -0.12819083034992218, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.13088293373584747, 0.24726125597953796, 0.34656673669815063, 0.10850997269153595,
-  -1.9750192165374756, 0.1727280467748642, 0.44498518109321594, 0.24422571063041687,
-  -0.13088291883468628, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.13365742564201355, 0.24705281853675842, 0.3499010503292084, 0.10764973610639572,
-  -1.9227015972137451, 0.1715681105852127, 0.44870641827583313, 0.24423953890800476,
-  -0.13365744054317474, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.13651761412620544, 0.24683697521686554, 0.3533375859260559, 0.10675247758626938,
-  -1.868868112564087, 0.17036117613315582, 0.4525378942489624, 0.2442495971918106,
-  -0.13651758432388306, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.1394667625427246, 0.24661342799663544, 0.35688087344169617, 0.10581755638122559,
-  -1.8134703636169434, 0.16910602152347565, 0.45648452639579773, 0.24425536394119263,
-  -0.1394667774438858, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.14250804483890533, 0.24638159573078156, 0.36053532361984253, 0.10484427958726883,
-  -1.7564631700515747, 0.16780158877372742, 0.4605507254600525, 0.24425646662712097,
-  -0.14250805974006653, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.14564520120620728, 0.2461412250995636, 0.3643057942390442, 0.10383249074220657,
-  -1.697803258895874, 0.1664472073316574, 0.4647414982318878, 0.2442525029182434,
-  -0.14564523100852966, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.14888176321983337, 0.2458917498588562, 0.368197500705719, 0.10278157144784927,
-  -1.6374417543411255, 0.1650417596101761, 0.4690619707107544, 0.24424304068088531,
-  -0.148881733417511, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.1522216498851776, 0.2456328272819519, 0.3722159266471863, 0.10169164091348648,
-  -1.5753288269042969, 0.16358478367328644, 0.4735177159309387, 0.2442275881767273,
-  -0.1522216498851776, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.15566881000995636, 0.24536384642124176, 0.3763660788536072, 0.10056263953447342,
-  -1.5114225149154663, 0.16207575798034668, 0.4781140387058258, 0.24420560896396637,
-  -0.15566881000995636, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.15922734141349792, 0.24508437514305115, 0.3806544840335846, 0.09939448535442352,
-  -1.4456686973571777, 0.16051390767097473, 0.4828571677207947, 0.24417661130428314,
-  -0.15922731161117554, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.1629015952348709, 0.24479378759860992, 0.3850869834423065, 0.09818801283836365,
-  -1.3780204057693481, 0.15889939665794373, 0.4877530038356781, 0.2441399097442627,
-  -0.1629015952348709, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.16669607162475586, 0.24449153244495392, 0.3896700441837311, 0.09694384038448334,
-  -1.3084297180175781, 0.15723225474357605, 0.4928082227706909, 0.24409495294094086,
-  -0.16669607162475586, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.17061544954776764, 0.2441769689321518, 0.3944106101989746, 0.09566308557987213,
-  -1.2368502616882324, 0.15551288425922394, 0.4980294108390808, 0.24404114484786987,
-  -0.17061544954776764, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.17466424405574799, 0.2438494712114334, 0.39931556582450867, 0.09434706717729568,
-  -1.1632311344146729, 0.1537417471408844, 0.5034236311912537, 0.24397757649421692,
-  -0.17466424405574799, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.17884768545627594, 0.24350810050964355, 0.4043923020362854, 0.0929974839091301,
-  -1.0875259637832642, 0.15191979706287384, 0.5089977383613586, 0.24390345811843872,
-  -0.17884764075279236, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.18317081034183502, 0.24315223097801208, 0.40964868664741516, 0.09161665290594101,
-  -1.0096875429153442, 0.15004844963550568, 0.5147597789764404, 0.24381794035434723,
-  -0.18317081034183502, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.18763846158981323, 0.2427809238433838, 0.4150926470756531, 0.09020735323429108,
-  -0.9296711683273315, 0.14812955260276794, 0.5207173228263855, 0.24371998012065887,
-  -0.18763846158981323, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.19225606322288513, 0.24239303171634674, 0.4207325875759125, 0.08877278119325638,
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-  -0.19225606322288513, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.19702887535095215, 0.24198751151561737, 0.42657679319381714, 0.08731688559055328,
-  -0.7629334330558777, 0.14415861666202545, 0.5332505106925964, 0.24348172545433044,
-  -0.19702887535095215, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.2019619345664978, 0.24156291782855988, 0.4326343238353729, 0.08584422618150711,
-  -0.6761321425437927, 0.1421128660440445, 0.5398426651954651, 0.24333862960338593,
-  -0.2019619345664978, 0.0, 0.0, 0.0]
-- [0.0, 0.0, -0.20706012845039368, 0.24111786484718323, 0.4389139711856842, 0.08435989916324615,
-  -0.586993396282196, 0.14003197848796844, 0.5466629862785339, 0.2431773543357849,
-  -0.20706015825271606, 0.0, 0.0, 0.0]
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+  0.0017721605254337192, 0.00028425041818991303, 0.011777210980653763, -7.952356827445328e-05,
+  -7.594209455419332e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.07182300882414e-05, 6.785560253774747e-05, 0.009378260932862759, 0.00037066172808408737,
+  0.0014402825618162751, 0.0002389741421211511, 0.010484847240149975, -7.156915671657771e-05,
+  -6.0718222812283784e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -4.810402970178984e-05, 5.953448635409586e-05, 0.008309719152748585,
+  0.00031706769368611276, 0.0011604375904425979, 0.0001992984616663307, 0.0092895133420825,
+  -6.397459947038442e-05, -4.810401514987461e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -3.773392381845042e-05, 5.2044739277334884e-05, 0.00732460105791688,
+  0.0002695043513085693, 0.0009262051898986101, 0.00016474620497319847, 0.00818763580173254,
+  -5.6786102504702285e-05, -3.773393473238684e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.9281274692039005e-05, 4.5309123379411176e-05, 0.006419702433049679,
+  0.00022750496282242239, 0.0007317152922041714, 0.00013486124225892127, 0.0071756006218492985,
+  -5.0036516768159345e-05, -2.9281278330017813e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.2455211365013383e-05, 3.9257978642126545e-05, 0.0055917841382324696,
+  0.00019061822968069464, 0.000571629439946264, 0.00010920592467300594, 0.00624976446852088,
+  -4.374980926513672e-05, -2.2455211365013383e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.6998685168800876e-05, 3.3829608582891524e-05, 0.004837585147470236,
+  0.00015841332788113505, 0.0004411150293890387, 8.736542804399505e-05, 0.005406456533819437,
+  -3.794096483034082e-05, -1.6998685168800876e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.268554842681624e-05, 2.8969843697268516e-05, 0.004153817426413298,
+  0.00013047615357208997, 0.00033582179457880557, 6.894434773130342e-05, 0.004641979932785034,
+  -3.261628080508672e-05, -1.2685544788837433e-05, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -9.318094271293376e-06, 2.4631357518956065e-05, 0.003537160577252507,
+  0.00010641096014296636, 0.00025185555568896234, 5.356810288503766e-05, 0.003952605649828911,
+  -2.7774432965088636e-05, -9.318089723819867e-06, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.724824743287172e-06, 2.0770992705365643e-05, 0.0029842799995094538,
+  8.584267197875306e-05, 0.00018575371359474957, 4.088525747647509e-05, 0.0033345867414027452,
+  -2.3408978449879214e-05, -6.72482383379247e-06, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -4.758323029818712e-06, 1.7350868802168407e-05, 0.0024918122217059135,
+  6.841296271886677e-05, 0.00013445891090668738, 3.0563391192117706e-05, 0.0027841494884341955,
+  -1.95075790543342e-05, -4.758318937092554e-06, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -3.2924349397944752e-06, 1.433669422112871e-05, 0.002056362573057413,
+  5.378412242862396e-05, 9.529229282634333e-05, 2.229327401437331e-05, 0.0022974866442382336,
+  -1.6053540093707852e-05, -3.2924349397944752e-06, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.2210188035387546e-06, 1.1697499758156482e-05, 0.0016745271859690547,
+  4.163706398685463e-05, 6.592922727577388e-05, 1.5786299627507105e-05, 0.0018707785056903958,
+  -1.302643522649305e-05, -2.221017439296702e-06, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.4551807225871016e-06, 9.4046990852803e-06, 0.001342872972600162, 3.1673054763814434e-05,
+  4.437140887603164e-05, 1.0776680028357077e-05, 0.0015001785941421986, -1.0402898624306545e-05,
+  -1.4551790172845358e-06, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -9.217027923114074e-07, 7.431756330333883e-06, 0.00105794589035213, 2.3611826691194437e-05,
+  2.892098927986808e-05, 7.019209533609683e-06, 0.0011818183120340109, -8.157077900250442e-06,
+  -9.217027923114074e-07, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -5.610388029708702e-07, 5.753626282967161e-06, 0.0008162750746123493,
+  1.7193600797327235e-05, 1.815466384869069e-05, 4.291383902454982e-06, 0.000911808863747865,
+  -6.261387625272619e-06, -5.61038064006425e-07, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -3.2571449537499575e-07, 4.346356490714243e-06, 0.0006143652717582881,
+  1.2177710232208483e-05, 1.0897146239585709e-05, 2.391984708083328e-06, 0.0006862387526780367,
+  -4.686762622441165e-06, -3.2571460906183347e-07, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.785674612619914e-07, 3.186516323694377e-06, 0.0004487043188419193,
+  8.343234185304027e-06, 6.195625246618874e-06, 1.141648226621328e-06, 0.0005011771572753787,
+  -3.40344081450894e-06, -1.7856758915968385e-07, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -9.120164179421408e-08, 2.2510901089844992e-06, 0.00031576078617945313,
+  5.4884294513612986e-06, 3.2942095913313096e-06, 3.8231016219469893e-07, 0.0003526735818013549,
+  -2.3810484890418593e-06, -9.120176258647916e-08, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -4.257741892388367e-08, 1.517022155894665e-06, 0.0002119835844496265,
+  3.4310885439481353e-06, 1.6088690699689323e-06, -2.243714369853933e-08, 0.00023675641568843275,
+  -1.5890958593445248e-06, -4.257747932001621e-08, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.76723613520835e-08, 9.610358802092378e-07, 0.0001338044530712068,
+  2.008093815675238e-06, 7.030557185316866e-07, -1.878481583617031e-07, 0.0001494363823439926,
+  -9.972342240871512e-07, -1.767230095595096e-08, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.2493201724578284e-09, 5.594854997070797e-07, 7.763502071611583e-05,
+  1.075209866030491e-06, 2.6391822416371724e-07, -2.0818079349282925e-07, 8.670240640640259e-05,
+  -5.753737468694453e-07, -6.2493201724578284e-09, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.749371425496804e-09, 2.881840259760793e-07, 3.986963929492049e-05,
+  5.069004487268103e-07, 7.949425651077036e-08, -1.5692151578150515e-07, 4.4525120756588876e-05,
+  -2.939296166459826e-07, -1.7493940740465064e-09, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -3.3942909594131265e-10, 1.2233303436914866e-07, 1.688258271315135e-05,
+  1.9590990518736362e-07, 1.6906387401149914e-08, -8.716900623539914e-08, 1.8853525034501217e-05,
+  -1.2386657033403026e-07, -3.3941774391088586e-10, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -3.360724892820244e-11, 3.649518731663193e-08, 5.0271773943677545e-06,
+  5.2918192494644245e-08, 1.9050836463918586e-09, -3.195922104737292e-08, 5.61397928322549e-06,
+  -3.673035209317277e-08, -3.360440745114879e-11, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -6.419753509172288e-13, 4.603964320892828e-09, 6.335218358799466e-07,
+  6.013532338755567e-09, 4.550571724992736e-11, -4.7546970805001365e-09, 7.07462788795965e-07,
+  -4.613359028127206e-09, -6.426858828109672e-13, 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: 29
diff --git a/extra_tests/regression_fits/flavour_29.json b/extra_tests/regression_fits/flavour_29.json
index 7721988ce9..e67c032558 100644
--- a/extra_tests/regression_fits/flavour_29.json
+++ b/extra_tests/regression_fits/flavour_29.json
@@ -49,47 +49,47 @@
       "trainable": false
     }
   ],
-  "stop_epoch": 181,
-  "best_epoch": 69,
-  "erf_tr": 4.977453231811523,
-  "erf_vl": 5.5623860359191895,
-  "chi2": 3.8969779014587402,
+  "stop_epoch": 141,
+  "best_epoch": 29,
+  "erf_tr": 4.978306293487549,
+  "erf_vl": 5.562335014343262,
+  "chi2": 3.8961379528045654,
   "pos_state": "POS_PASS",
   "arc_lengths": [
-    1.1047281768455546,
-    1.2121895138128305,
-    0.9906464943638001,
-    0.9904916210719534,
-    0.9907080933270742
+    1.1046950323223816,
+    1.2122357294523425,
+    0.9906464880057816,
+    0.9904916575857023,
+    0.9907080733680326
   ],
   "integrability": [
-    0.46764490008354204,
-    0.4676449000835418,
-    0.08091166429221643,
-    0.10038149356842034,
-    0.5176680088043213
+    0.46764521300792666,
+    0.46764521300792683,
+    0.0809073969721795,
+    0.10018515586853038,
+    0.5176685005426407
   ],
   "timing": {
     "walltime": {
-      "Total": 4.9544456005096436,
+      "Total": 4.027747869491577,
       "start": 0.0,
-      "replica_set": 0.24539613723754883,
-      "replica_fitted": 4.954279899597168,
-      "replica_set_to_replica_fitted": 4.708883762359619
+      "replica_set": 0.21877336502075195,
+      "replica_fitted": 4.027618646621704,
+      "replica_set_to_replica_fitted": 3.808845281600952
     },
     "cputime": {
-      "Total": 5.150289656,
+      "Total": 4.170468237,
       "start": 0.0,
-      "replica_set": 0.23985466799999955,
-      "replica_fitted": 5.150120960999999,
-      "replica_set_to_replica_fitted": 4.910266292999999
+      "replica_set": 0.2169810080000003,
+      "replica_fitted": 4.170337463000001,
+      "replica_set_to_replica_fitted": 3.9533564550000007
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/single_dense.weights.h5 b/extra_tests/regression_fits/multi_dense.weights.h5
similarity index 66%
rename from extra_tests/regression_fits/single_dense.weights.h5
rename to extra_tests/regression_fits/multi_dense.weights.h5
index 4daf8e08f2..219dbdce8b 100644
Binary files a/extra_tests/regression_fits/single_dense.weights.h5 and b/extra_tests/regression_fits/multi_dense.weights.h5 differ
diff --git a/extra_tests/regression_fits/single_dense.yml b/extra_tests/regression_fits/multi_dense.yml
similarity index 96%
rename from extra_tests/regression_fits/single_dense.yml
rename to extra_tests/regression_fits/multi_dense.yml
index 8c9165597e..b1a1f1ab75 100644
--- a/extra_tests/regression_fits/single_dense.yml
+++ b/extra_tests/regression_fits/multi_dense.yml
@@ -34,8 +34,8 @@ nnseed: 2
 mcseed: 1
 
 # checks both that can be loaded and saved
-save: "single_dense.weights.h5"
-load: "single_dense.weights.h5"
+save: "multi_dense.weights.h5"
+load: "multi_dense.weights.h5"
 
 parameters: # This defines the parameter dictionary that is passed to the Model Trainer
   nodes_per_layer: [15, 10, 8]
@@ -50,7 +50,7 @@ parameters: # This defines the parameter dictionary that is passed to the Model
     multiplier: 1.05
     initial: 1.5
   stopping_patience: 0.10 # percentage of the number of epochs
-  layer_type: 'single_dense'
+  layer_type: 'multidense'
   dropout: 0.0
   threshold_chi2: 10.0
 
diff --git a/extra_tests/regression_fits/multi_dense_316.exportgrid b/extra_tests/regression_fits/multi_dense_316.exportgrid
new file mode 100644
index 0000000000..268093483f
--- /dev/null
+++ b/extra_tests/regression_fits/multi_dense_316.exportgrid
@@ -0,0 +1,633 @@
+labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
+pdfgrid:
+- [0.0, 0.0, -2.414682626724243, 0.032906413078308105, 0.00648618396371603, 0.006533617153763771,
+  -16.949392318725586, 0.006687344517558813, 0.006641445215791464, 0.03265798091888428,
+  -2.414682626724243, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.3386027812957764, 0.03612871840596199, 0.00865098461508751, 0.008704930543899536,
+  -16.960304260253906, 0.008874863386154175, 0.008822760544717312, 0.03585616126656532,
+  -2.338602304458618, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.2649240493774414, 0.039499178528785706, 0.010920420289039612, 0.01098173949867487,
+  -16.96973991394043, 0.011169618926942348, 0.011110520921647549, 0.03920017182826996,
+  -2.2649240493774414, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.1935720443725586, 0.04302005097270012, 0.013294789008796215, 0.013364536687731743,
+  -16.977588653564453, 0.013572296127676964, 0.013505223207175732, 0.04269205033779144,
+  -2.1935715675354004, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.1244704723358154, 0.0466928705573082, 0.015773674473166466, 0.015852976590394974,
+  -16.983747482299805, 0.01608276180922985, 0.016006680205464363, 0.046333082020282745,
+  -2.1244702339172363, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -2.057549238204956, 0.05052153021097183, 0.018358789384365082, 0.018448911607265472,
+  -16.988086700439453, 0.01870310865342617, 0.01861686445772648, 0.05012689158320427,
+  -2.057549476623535, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.992738962173462, 0.054507434368133545, 0.021049322560429573, 0.021151790395379066,
+  -16.990489959716797, 0.021433057263493538, 0.02133525349199772, 0.05407460033893585,
+  -1.992738962173462, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.9299731254577637, 0.05865481123328209, 0.02384714037179947, 0.023963691666722298,
+  -16.99082374572754, 0.024274958297610283, 0.024164026603102684, 0.058180104941129684,
+  -1.9299731254577637, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.8691858053207397, 0.06296699494123459, 0.026753094047307968, 0.02688560262322426,
+  -16.988929748535156, 0.02723015286028385, 0.02710440754890442, 0.06244640424847603,
+  -1.8691858053207397, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.8103145360946655, 0.0674474686384201, 0.029768045991659164, 0.029918726533651352,
+  -16.984663009643555, 0.030300196260213852, 0.030157653614878654, 0.06687658280134201,
+  -1.8103147745132446, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.7532986402511597, 0.07210055738687515, 0.0328935906291008, 0.03306487202644348,
+  -16.97785758972168, 0.033487312495708466, 0.03332582488656044, 0.07147450745105743,
+  -1.7532986402511597, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.6980786323547363, 0.07693096995353699, 0.03613148629665375, 0.03632623329758644,
+  -16.968332290649414, 0.03679414466023445, 0.036611177027225494, 0.07624451071023941,
+  -1.6980788707733154, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.6445977687835693, 0.0819433182477951, 0.03948323801159859, 0.03970468044281006,
+  -16.95589828491211, 0.04022308066487312, 0.0400158166885376, 0.08119065314531326,
+  -1.6445977687835693, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.592800259590149, 0.08714254945516586, 0.04295060411095619, 0.04320234805345535,
+  -16.940353393554688, 0.04377681016921997, 0.04354212060570717, 0.08631733059883118,
+  -1.592800259590149, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.5426323413848877, 0.09253472834825516, 0.04653608426451683, 0.04682227224111557,
+  -16.92147445678711, 0.04745902493596077, 0.04719335585832596, 0.09162995964288712,
+  -1.5426323413848877, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.4940425157546997, 0.09812494367361069, 0.05024115368723869, 0.05056653171777725,
+  -16.899038314819336, 0.051272470504045486, 0.05097179487347603, 0.09713304042816162,
+  -1.4940427541732788, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.4469798803329468, 0.10391977429389954, 0.05406849458813667, 0.05443836748600006,
+  -16.872793197631836, 0.05522121489048004, 0.05488104745745659, 0.1028323620557785,
+  -1.4469796419143677, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.4013957977294922, 0.10992558300495148, 0.05802030488848686, 0.05844071879982948,
+  -16.842470169067383, 0.05930905416607857, 0.05892437323927879, 0.10873351991176605,
+  -1.4013960361480713, 0.0, 0.0, 0.0]
+- [0.0, 0.0, -1.3572425842285156, 0.11614957451820374, 0.06209934130311012, 0.06257722526788712,
+  -16.807777404785156, 0.06354065239429474, 0.0631057471036911, 0.11484281718730927,
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+  0.841028750298844, 0.8493704095226, 0.857715163684985, 0.866062956202683, 0.874413732009721,
+  0.882767437504206, 0.891124020497459, 0.899483430165226, 0.907845617001021, 0.916210532771399,
+  0.924578130473112, 0.932948364292029, 0.941321189563734, 0.949696562735755, 0.958074441331298,
+  0.966454783914439, 0.974837550056705, 0.983222700304978, 0.991610196150662, 1.0]
diff --git a/extra_tests/regression_fits/multi_dense_316.json b/extra_tests/regression_fits/multi_dense_316.json
new file mode 100644
index 0000000000..7ea0671429
--- /dev/null
+++ b/extra_tests/regression_fits/multi_dense_316.json
@@ -0,0 +1,95 @@
+{
+  "preprocessing": [
+    {
+      "fl": "sng",
+      "smallx": 1.1168484687805176,
+      "largex": 1.4932247400283813,
+      "trainable": false
+    },
+    {
+      "fl": "g",
+      "smallx": 0.9923287034034729,
+      "largex": 3.7714877128601074,
+      "trainable": false
+    },
+    {
+      "fl": "v",
+      "smallx": 0.4898352324962616,
+      "largex": 1.672149658203125,
+      "trainable": false
+    },
+    {
+      "fl": "v3",
+      "smallx": 0.28436920046806335,
+      "largex": 3.4038245677948,
+      "trainable": false
+    },
+    {
+      "fl": "v8",
+      "smallx": 0.635401725769043,
+      "largex": 1.9356087446212769,
+      "trainable": false
+    },
+    {
+      "fl": "t3",
+      "smallx": 0.5063296556472778,
+      "largex": 2.4878852367401123,
+      "trainable": false
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+    {
+      "fl": "t8",
+      "smallx": 0.8517391681671143,
+      "largex": 2.7349023818969727,
+      "trainable": false
+    },
+    {
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+      "smallx": 1.1255686283111572,
+      "largex": 1.68263578414917,
+      "trainable": false
+    }
+  ],
+  "stop_epoch": 1100,
+  "best_epoch": 1099,
+  "erf_tr": 2.4744553565979004,
+  "erf_vl": 2.9059481620788574,
+  "chi2": 2.118800401687622,
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+    1.488952866412567,
+    1.1794333655766738,
+    1.000696970195011,
+    1.2462031714666137
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+    0.0008942512758955967,
+    5.0144157625053865e-05,
+    0.46068396419286617,
+    0.007144219125619022
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+    "keras": "3.4.1",
+    "tensorflow": "2.17.0, mkl=False",
+    "numpy": "1.26.4",
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
+  }
+}
diff --git a/extra_tests/regression_fits/no_csr_613.json b/extra_tests/regression_fits/no_csr_613.json
index f2a7a525a0..e3f52ddeba 100644
--- a/extra_tests/regression_fits/no_csr_613.json
+++ b/extra_tests/regression_fits/no_csr_613.json
@@ -77,25 +77,25 @@
   ],
   "timing": {
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-      "Total": 9.365455150604248,
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-      "replica_fitted": 9.365368366241455,
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+      "replica_set": 0.22439932823181152,
+      "replica_fitted": 8.54661750793457,
+      "replica_set_to_replica_fitted": 8.322218179702759
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     "cputime": {
-      "Total": 10.445483985,
+      "Total": 9.500806777000001,
       "start": 0.0,
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-      "replica_fitted": 10.445394979,
-      "replica_set_to_replica_fitted": 10.214643918
+      "replica_set": 0.22265501399999987,
+      "replica_fitted": 9.500716870000002,
+      "replica_set_to_replica_fitted": 9.278061856
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   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/no_lagrange_27.json b/extra_tests/regression_fits/no_lagrange_27.json
index 545ba87df5..7d5e64604d 100644
--- a/extra_tests/regression_fits/no_lagrange_27.json
+++ b/extra_tests/regression_fits/no_lagrange_27.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 16.37596321105957,
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       "start": 0.0,
-      "replica_set": 0.23856806755065918,
-      "replica_fitted": 16.375898361206055,
-      "replica_set_to_replica_fitted": 16.137330293655396
+      "replica_set": 0.21603798866271973,
+      "replica_fitted": 14.253704071044922,
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     "cputime": {
-      "Total": 17.616454738,
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       "start": 0.0,
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-      "replica_set_to_replica_fitted": 17.378999702999998
+      "replica_set": 0.21512377100000002,
+      "replica_fitted": 15.377821143,
+      "replica_set_to_replica_fitted": 15.162697372
     }
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   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/no_msr_92.json b/extra_tests/regression_fits/no_msr_92.json
index 16a213aa8e..7488ad2d41 100644
--- a/extra_tests/regression_fits/no_msr_92.json
+++ b/extra_tests/regression_fits/no_msr_92.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 22.70932173728943,
+      "Total": 19.36279797554016,
       "start": 0.0,
-      "replica_set": 0.24144625663757324,
-      "replica_fitted": 22.70919704437256,
-      "replica_set_to_replica_fitted": 22.467750787734985
+      "replica_set": 0.22215056419372559,
+      "replica_fitted": 19.36264204978943,
+      "replica_set_to_replica_fitted": 19.140491485595703
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     "cputime": {
-      "Total": 24.311431295,
+      "Total": 20.82930143,
       "start": 0.0,
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-      "replica_fitted": 24.311304799,
-      "replica_set_to_replica_fitted": 24.077983007
+      "replica_set": 0.2209823669999995,
+      "replica_fitted": 20.829144176,
+      "replica_set_to_replica_fitted": 20.608161809
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/no_sumrules_18.json b/extra_tests/regression_fits/no_sumrules_18.json
index 074dc6e214..dd936dea86 100644
--- a/extra_tests/regression_fits/no_sumrules_18.json
+++ b/extra_tests/regression_fits/no_sumrules_18.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 19.123758792877197,
+      "Total": 15.640143632888794,
       "start": 0.0,
-      "replica_set": 0.23555827140808105,
-      "replica_fitted": 19.123591899871826,
-      "replica_set_to_replica_fitted": 18.888033628463745
+      "replica_set": 0.23237943649291992,
+      "replica_fitted": 15.640068531036377,
+      "replica_set_to_replica_fitted": 15.407689094543457
     },
     "cputime": {
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+      "Total": 16.991643305,
       "start": 0.0,
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-      "replica_set_to_replica_fitted": 20.385975520000002
+      "replica_set": 0.22577083200000025,
+      "replica_fitted": 16.991566942000002,
+      "replica_set_to_replica_fitted": 16.76579611
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/no_vsr_54.json b/extra_tests/regression_fits/no_vsr_54.json
index 932ccd4809..89d97ee36d 100644
--- a/extra_tests/regression_fits/no_vsr_54.json
+++ b/extra_tests/regression_fits/no_vsr_54.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
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+      "Total": 10.118329048156738,
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+      "replica_set": 0.22046351432800293,
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     "cputime": {
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+      "replica_set": 0.2187228000000001,
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   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
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 }
diff --git a/extra_tests/regression_fits/normal_fit_72.json b/extra_tests/regression_fits/normal_fit_72.json
index b5ac432328..a274d6da13 100644
--- a/extra_tests/regression_fits/normal_fit_72.json
+++ b/extra_tests/regression_fits/normal_fit_72.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 17.749327182769775,
+      "Total": 15.853733539581299,
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-      "replica_fitted": 17.749066591262817,
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     "cputime": {
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       "start": 0.0,
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-      "replica_set_to_replica_fitted": 20.025126646
+      "replica_set": 0.22598911499999907,
+      "replica_fitted": 18.056944325,
+      "replica_set_to_replica_fitted": 17.83095521
     }
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   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/polarized_evol_34.json b/extra_tests/regression_fits/polarized_evol_34.json
index c86165a711..937b10e891 100644
--- a/extra_tests/regression_fits/polarized_evol_34.json
+++ b/extra_tests/regression_fits/polarized_evol_34.json
@@ -47,25 +47,25 @@
   ],
   "timing": {
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   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
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 }
diff --git a/extra_tests/regression_fits/single_dense_316.exportgrid b/extra_tests/regression_fits/single_dense_316.exportgrid
deleted file mode 100644
index ee039f4e0d..0000000000
--- a/extra_tests/regression_fits/single_dense_316.exportgrid
+++ /dev/null
@@ -1,633 +0,0 @@
-labels: [TBAR, BBAR, CBAR, SBAR, UBAR, DBAR, GLUON, D, U, S, C, B, T, PHT]
-pdfgrid:
-- [0.0, 0.0, 0.624907374382019, 0.9272689819335938, 0.9285414814949036, 0.9285261034965515,
-  1.0354629755020142, 0.9288173317909241, 0.9288352131843567, 0.9272533655166626,
-  0.624907374382019, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.6072399616241455, 0.9036694765090942, 0.9050180912017822, 0.9050008058547974,
-  1.0520607233047485, 0.9053240418434143, 0.9053443670272827, 0.9036529660224915,
-  0.6072399616241455, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.590065062046051, 0.8806789517402649, 0.8821075558662415, 0.8820883631706238,
-  1.068817138671875, 0.8824471831321716, 0.8824701905250549, 0.88066166639328, 0.5900651812553406,
-  0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.5733710527420044, 0.8582808971405029, 0.8597937822341919, 0.8597723245620728,
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-  0.5733710527420044, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.5571458339691162, 0.8364583253860474, 0.8380599617958069, 0.8380358815193176,
-  1.1028027534484863, 0.8384779095649719, 0.8385072946548462, 0.8364391326904297,
-  0.5571458339691162, 0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.5413783192634583, 0.8151952624320984, 0.8168901205062866, 0.8168631792068481,
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-  0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.5260571837425232, 0.7944762110710144, 0.796268880367279, 0.7962389588356018,
-  1.137416958808899, 0.796783447265625, 0.7968209981918335, 0.7944557070732117, 0.5260571837425232,
-  0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.5111715793609619, 0.7742850184440613, 0.7761805057525635, 0.7761471271514893,
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-  0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.4967108964920044, 0.754607081413269, 0.7566105723381042, 0.7565733790397644,
-  1.172662615776062, 0.7572438716888428, 0.7572919726371765, 0.754585862159729, 0.4967108964920044,
-  0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.48266416788101196, 0.7354274392127991, 0.7375439405441284, 0.7375024557113647,
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-  0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.4690214991569519, 0.71673184633255, 0.7189667820930481, 0.7189206480979919,
-  1.2085503339767456, 0.7197458744049072, 0.7198075652122498, 0.71671062707901, 0.4690214991569519,
-  0.0, 0.0, 0.0]
-- [0.0, 0.0, 0.455772340297699, 0.6985060572624207, 0.7008650302886963, 0.7008136510848999,
-  1.226742148399353, 0.7017290592193604, 0.7017987370491028, 0.6984851956367493, 0.455772340297699,
-  0.0, 0.0, 0.0]
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-  0.271742695942783, 0.279477769504149, 0.287235730364833, 0.295015546847664, 0.302816252626866,
-  0.310636941519503, 0.318476762768082, 0.326334916761672, 0.334210651149156, 0.342103257303627,
-  0.350012067101685, 0.357936449985571, 0.365875810279643, 0.373829584735962, 0.381797240286494,
-  0.389778271981947, 0.397772201099286, 0.40577857340234, 0.413796957540671, 0.421826943574548,
-  0.429868141614175, 0.437920180563205, 0.44598270695699, 0.454055383887562, 0.462137890007651,
-  0.470229918607142, 0.478331176755675, 0.486441384506059, 0.494560274153348, 0.502687589545177,
-  0.510823085439086, 0.518966526903235, 0.527117688756998, 0.535276355048428, 0.543442318565661,
-  0.551615380379768, 0.559795349416641, 0.5679820420558, 0.576175281754088, 0.584374898692498,
-  0.59258072944444, 0.60079261666395, 0.609010408792398, 0.61723395978245, 0.625463128838069,
-  0.633697780169485, 0.641937782762089, 0.650183010158361, 0.658433340251944, 0.666688655093089,
-  0.674948840704708, 0.683213786908386, 0.691483387159697, 0.699757538392251, 0.708036140869916,
-  0.716319098046733, 0.724606316434025, 0.732897705474271, 0.741193177421404, 0.749492647227008,
-  0.757796032432224, 0.766103253064927, 0.774414231541921, 0.782728892575836, 0.791047163086478,
-  0.799368972116378, 0.807694250750291, 0.816022932038457, 0.824354950923382, 0.832690244169987,
-  0.841028750298844, 0.8493704095226, 0.857715163684985, 0.866062956202683, 0.874413732009721,
-  0.882767437504206, 0.891124020497459, 0.899483430165226, 0.907845617001021, 0.916210532771399,
-  0.924578130473112, 0.932948364292029, 0.941321189563734, 0.949696562735755, 0.958074441331298,
-  0.966454783914439, 0.974837550056705, 0.983222700304978, 0.991610196150662, 1.0]
diff --git a/extra_tests/regression_fits/single_dense_316.json b/extra_tests/regression_fits/single_dense_316.json
deleted file mode 100644
index ca641e37ee..0000000000
--- a/extra_tests/regression_fits/single_dense_316.json
+++ /dev/null
@@ -1,95 +0,0 @@
-{
-  "preprocessing": [
-    {
-      "fl": "sng",
-      "smallx": 1.0993791818618774,
-      "largex": 2.2761056423187256,
-      "trainable": false
-    },
-    {
-      "fl": "g",
-      "smallx": 0.9254842400550842,
-      "largex": 3.943401336669922,
-      "trainable": false
-    },
-    {
-      "fl": "v",
-      "smallx": 0.5844998955726624,
-      "largex": 1.7474256753921509,
-      "trainable": false
-    },
-    {
-      "fl": "v3",
-      "smallx": 0.31110942363739014,
-      "largex": 2.2980215549468994,
-      "trainable": false
-    },
-    {
-      "fl": "v8",
-      "smallx": 0.5919869542121887,
-      "largex": 1.7609920501708984,
-      "trainable": false
-    },
-    {
-      "fl": "t3",
-      "smallx": 0.5465919971466064,
-      "largex": 2.460597038269043,
-      "trainable": false
-    },
-    {
-      "fl": "t8",
-      "smallx": 0.7418460845947266,
-      "largex": 2.282687187194824,
-      "trainable": false
-    },
-    {
-      "fl": "t15",
-      "smallx": 1.1181368827819824,
-      "largex": 1.614270567893982,
-      "trainable": false
-    }
-  ],
-  "stop_epoch": 1100,
-  "best_epoch": 1099,
-  "erf_tr": 15.51508903503418,
-  "erf_vl": 16.14827537536621,
-  "chi2": 11.207615852355957,
-  "pos_state": "POS_VETO",
-  "arc_lengths": [
-    1.0478482082378506,
-    1.2771206199216336,
-    1.0363260020464442,
-    1.0001806126564081,
-    1.037880031773835
-  ],
-  "integrability": [
-    0.0057379395002511435,
-    0.0057379395002497,
-    7.455025911473623e-05,
-    0.032392028719186894,
-    0.005861893761903825
-  ],
-  "timing": {
-    "walltime": {
-      "Total": 10.993557214736938,
-      "start": 0.0,
-      "replica_set": 0.22788548469543457,
-      "replica_fitted": 10.993452787399292,
-      "replica_set_to_replica_fitted": 10.765567302703857
-    },
-    "cputime": {
-      "Total": 12.537273967,
-      "start": 0.0,
-      "replica_set": 0.2268365139999995,
-      "replica_fitted": 12.537167609,
-      "replica_set_to_replica_fitted": 12.310331095000002
-    }
-  },
-  "version": {
-    "keras": "3.4.1",
-    "tensorflow": "2.17.0, mkl=False",
-    "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
-  }
-}
diff --git a/extra_tests/regression_fits/trainable_prepro_61.json b/extra_tests/regression_fits/trainable_prepro_61.json
index e108f757f8..249bf27b65 100644
--- a/extra_tests/regression_fits/trainable_prepro_61.json
+++ b/extra_tests/regression_fits/trainable_prepro_61.json
@@ -71,25 +71,25 @@
   ],
   "timing": {
     "walltime": {
-      "Total": 12.758163213729858,
+      "Total": 11.157723665237427,
       "start": 0.0,
-      "replica_set": 0.23384833335876465,
-      "replica_fitted": 12.758097887039185,
-      "replica_set_to_replica_fitted": 12.52424955368042
+      "replica_set": 0.23775172233581543,
+      "replica_fitted": 11.15766978263855,
+      "replica_set_to_replica_fitted": 10.919918060302734
     },
     "cputime": {
-      "Total": 14.366323394000002,
+      "Total": 12.520099947000002,
       "start": 0.0,
-      "replica_set": 0.23262794400000075,
-      "replica_fitted": 14.366252531,
-      "replica_set_to_replica_fitted": 14.133624587
+      "replica_set": 0.23561744399999984,
+      "replica_fitted": 12.520044984000002,
+      "replica_set_to_replica_fitted": 12.284427540000001
     }
   },
   "version": {
     "keras": "3.4.1",
     "tensorflow": "2.17.0, mkl=False",
     "numpy": "1.26.4",
-    "nnpdf": "4.0.9.post1053.dev0+e72ce3cc8",
-    "validphys": "4.0.9.post1053.dev0+e72ce3cc8"
+    "nnpdf": "4.0.9.post1058.dev0+0a1b331ae",
+    "validphys": "4.0.9.post1058.dev0+0a1b331ae"
   }
 }
diff --git a/extra_tests/regression_fits/weights.weights.h5 b/extra_tests/regression_fits/weights.weights.h5
index 219dbdce8b..efe850dde2 100644
Binary files a/extra_tests/regression_fits/weights.weights.h5 and b/extra_tests/regression_fits/weights.weights.h5 differ
diff --git a/extra_tests/regression_fits/weights_feature.weights.h5 b/extra_tests/regression_fits/weights_feature.weights.h5
index 31bb6b47e5..15c100194f 100644
Binary files a/extra_tests/regression_fits/weights_feature.weights.h5 and b/extra_tests/regression_fits/weights_feature.weights.h5 differ
diff --git a/extra_tests/regression_fits/weights_flavour.weights.h5 b/extra_tests/regression_fits/weights_flavour.weights.h5
index 612c0df35b..e1df3d56f3 100644
Binary files a/extra_tests/regression_fits/weights_flavour.weights.h5 and b/extra_tests/regression_fits/weights_flavour.weights.h5 differ
diff --git a/extra_tests/regression_fits/weights_polevol.weights.h5 b/extra_tests/regression_fits/weights_polevol.weights.h5
index 351d53d501..4ff6fcafab 100644
Binary files a/extra_tests/regression_fits/weights_polevol.weights.h5 and b/extra_tests/regression_fits/weights_polevol.weights.h5 differ
diff --git a/n3fit/runcards/examples/nnpdf40-like.yml b/n3fit/runcards/examples/nnpdf40-like.yml
index 160e10e631..36e66b9dad 100644
--- a/n3fit/runcards/examples/nnpdf40-like.yml
+++ b/n3fit/runcards/examples/nnpdf40-like.yml
@@ -1,10 +1,10 @@
 #
 # Configuration file for n3fit
 #
-################################################################################
-description: NNLO baseline fit, NNPDF4.0 dataset
+######################################################################################
+description: NNLO baseline fit, NNPDF4.0 dataset, compare to NNPDF40_nnlo_as_01180_qcd
 
-################################################################################
+######################################################################################
 dataset_inputs:
 - {dataset: NMC_NC_NOTFIXED_DW_EM-F2, frac: 0.75, variant: legacy}
 - {dataset: NMC_NC_NOTFIXED_P_EM-SIGMARED, frac: 0.75, variant: legacy}
diff --git a/n3fit/src/n3fit/backends/keras_backend/base_layers.py b/n3fit/src/n3fit/backends/keras_backend/base_layers.py
index e6afc6c5c6..6a21a26480 100644
--- a/n3fit/src/n3fit/backends/keras_backend/base_layers.py
+++ b/n3fit/src/n3fit/backends/keras_backend/base_layers.py
@@ -102,7 +102,7 @@ def dense_per_flavour(basis_size=8, kernel_initializer="glorot_normal", **dense_
 
     # Need to generate a list of dense layers
     dense_basis = [
-        base_layer_selector("single_dense", kernel_initializer=initializer, **dense_kwargs)
+        base_layer_selector("dense", kernel_initializer=initializer, **dense_kwargs)
         for initializer in kernel_initializer
     ]
 
@@ -132,7 +132,7 @@ def apply_dense(xinput):
 
 
 layers = {
-    "dense": (
+    "multidense": (
         MultiDense,
         {
             "replica_seeds": None,
@@ -144,7 +144,7 @@ def apply_dense(xinput):
             "is_first_layer": False,
         },
     ),
-    "single_dense": (
+    "dense": (
         Dense,
         {
             "kernel_initializer": "glorot_normal",
diff --git a/n3fit/src/n3fit/checks.py b/n3fit/src/n3fit/checks.py
index 9aa05dfae8..1b92cc4875 100644
--- a/n3fit/src/n3fit/checks.py
+++ b/n3fit/src/n3fit/checks.py
@@ -135,7 +135,7 @@ def check_initializer(initializer):
 def check_layer_type_implemented(parameters):
     """Checks whether the layer_type is implemented"""
     layer_type = parameters.get("layer_type")
-    implemented_types = ["dense", "dense_per_flavour", "single_dense"]
+    implemented_types = ["dense", "dense_per_flavour", "multidense"]
     if layer_type not in implemented_types:
         raise CheckError(
             f"Layer type {layer_type} not implemented, must be one of {implemented_types}"
@@ -423,7 +423,7 @@ def check_consistent_parallel(parameters, parallel_models):
     """
     if not parallel_models:
         return
-    if parameters.get("layer_type") != "dense":
+    if parameters.get("layer_type") not in ("dense"):
         raise CheckError("Parallelization has only been tested with layer_type=='dense'")
 
 
diff --git a/n3fit/src/n3fit/model_gen.py b/n3fit/src/n3fit/model_gen.py
index e5a2cf55ba..ee88da1ad3 100644
--- a/n3fit/src/n3fit/model_gen.py
+++ b/n3fit/src/n3fit/model_gen.py
@@ -742,7 +742,7 @@ def layer_generator(i_layer, nodes_out, activation):
             """Generate the ``i_layer``-th dense_per_flavour layer for all replicas."""
             layers = []
             for replica_seed in replica_seeds:
-                seed = replica_seed + i_layer * basis_size
+                seed = int(replica_seed + i_layer * basis_size)
                 initializers = [
                     MetaLayer.select_initializer(initializer_name, seed=seed + b)
                     for b in range(basis_size)
@@ -758,25 +758,27 @@ def layer_generator(i_layer, nodes_out, activation):
 
             return layers
 
-    elif layer_type == "single_dense":
+    elif layer_type == "dense":
 
-        # The checks should've triggered, but better safe than sorry
-        if len(replica_seeds) > 1:
-            raise ValueError("`single_dense` only valid with one replica")
-        seed = replica_seeds[0]
+        def initializer_generator(seed, i_layer):
+            seed += i_layer
+            return MetaLayer.select_initializer(initializer_name, seed=int(seed))
 
         def layer_generator(i_layer, nodes_out, activation):
-            return base_layer_selector(
-                layer_type,
-                kernel_initializer=MetaLayer.select_initializer(
-                    initializer_name, seed=seed + i_layer
-                ),
-                units=nodes_out,
-                activation=activation,
-                regularizer=reg,
-            )
+            layers = []
+            for replica_seed in replica_seeds:
+                layers.append(
+                    base_layer_selector(
+                        layer_type,
+                        kernel_initializer=initializer_generator(replica_seed, i_layer),
+                        units=nodes_out,
+                        activation=activation,
+                        regularizer=reg,
+                    )
+                )
+            return layers
 
-    elif layer_type == "dense":
+    elif layer_type == "multidense":
 
         def layer_generator(i_layer, nodes_out, activation):
             """Generate the ``i_layer``-th MetaLayer.MultiDense layer for all replicas."""
@@ -813,8 +815,8 @@ def layer_generator(i_layer, nodes_out, activation):
         concat = base_layer_selector("concatenate")
         list_of_pdf_layers[-1] = [lambda x: concat(layer(x)) for layer in list_of_pdf_layers[-1]]
 
-    # Apply all layers to the input to create the models
-    if layer_type in ("dense", "single_dense"):
+    # In the `layer_type` multidense we have a `MultiDense` layer and we can get out here
+    if layer_type == "multidense":
         pdfs = x_input
         for layer in list_of_pdf_layers:
             pdfs = layer(pdfs)
diff --git a/n3fit/src/n3fit/tests/regressions/weights_1.weights.h5 b/n3fit/src/n3fit/tests/regressions/weights_1.weights.h5
index a18d7c37f2..7c549bfa51 100644
Binary files a/n3fit/src/n3fit/tests/regressions/weights_1.weights.h5 and b/n3fit/src/n3fit/tests/regressions/weights_1.weights.h5 differ
diff --git a/n3fit/src/n3fit/tests/regressions/weights_3.weights.h5 b/n3fit/src/n3fit/tests/regressions/weights_3.weights.h5
index 1232c0f746..f191c3e339 100644
Binary files a/n3fit/src/n3fit/tests/regressions/weights_3.weights.h5 and b/n3fit/src/n3fit/tests/regressions/weights_3.weights.h5 differ
diff --git a/n3fit/src/n3fit/tests/regressions/weights_pol_1.weights.h5 b/n3fit/src/n3fit/tests/regressions/weights_pol_1.weights.h5
index 5f7d2f80cb..9bd1a29260 100644
Binary files a/n3fit/src/n3fit/tests/regressions/weights_pol_1.weights.h5 and b/n3fit/src/n3fit/tests/regressions/weights_pol_1.weights.h5 differ
diff --git a/n3fit/src/n3fit/tests/regressions/weights_pol_3.weights.h5 b/n3fit/src/n3fit/tests/regressions/weights_pol_3.weights.h5
index 3912417844..10adb69011 100644
Binary files a/n3fit/src/n3fit/tests/regressions/weights_pol_3.weights.h5 and b/n3fit/src/n3fit/tests/regressions/weights_pol_3.weights.h5 differ
diff --git a/n3fit/src/n3fit/tests/test_modelgen.py b/n3fit/src/n3fit/tests/test_modelgen.py
index c87523f838..2e35441576 100644
--- a/n3fit/src/n3fit/tests/test_modelgen.py
+++ b/n3fit/src/n3fit/tests/test_modelgen.py
@@ -1,10 +1,11 @@
-""" 
+"""
     Test for the model generation
 
     These tests check that the generated NN are as expected
     It checks that both the number of layers and the shape
     of the weights of the layers are what is expected
 """
+
 from n3fit.backends import NN_PREFIX
 from n3fit.model_gen import generate_nn
 
@@ -28,6 +29,17 @@
 def test_generate_dense_network():
     nn = generate_nn("dense", **COMMON_ARGS)
 
+    # The number of layers should be input layer + len(OUT_SIZES)
+    assert len(nn.layers) == len(OUT_SIZES) + 1
+    # Check that the number of parameters is as expected
+    expected_sizes = [(INSIZE, OUT_SIZES[0]), (OUT_SIZES[0]), (*OUT_SIZES,), (OUT_SIZES[1])]
+    for weight, esize in zip(nn.weights, expected_sizes):
+        assert weight.shape == esize
+
+
+def test_generate_multi_dense_network():
+    nn = generate_nn("multidense", **COMMON_ARGS)
+
     # The number of layers should be input layer + len(OUT_SIZES)
     assert len(nn.layers) == len(OUT_SIZES) + 1
     # Check that the number of parameters is as expected