diff --git a/test/core.vwtest.json b/test/core.vwtest.json
index f2114237c0f..547167e4146 100644
--- a/test/core.vwtest.json
+++ b/test/core.vwtest.json
@@ -5766,5 +5766,44 @@
     "depends_on": [
       441, 443
     ]
+  },
+  {
+    "id": 446,
+    "desc": "large action spaces with cb_explore_adf epsilon greedy",
+    "vw_command": "--cb_explore_adf -d train-sets/las_100_actions.txt --noconstant --large_action_space --extra_metrics metrics_las_e.json",
+    "diff_files": {
+      "stderr": "train-sets/ref/las_egreedy.stderr",
+      "metrics_las_e.json": "test-sets/ref/metrics_las_e.json"
+    },
+    "input_files": [
+      "train-sets/las_100_actions.txt"
+    ]
+  },
+  {
+    "id": 447,
+    "desc": "large action spaces with cb_explore_adf squarecb",
+    "vw_command": "--cb_explore_adf -d train-sets/las_100_actions.txt --squarecb --noconstant --large_action_space --extra_metrics metrics_las_sqcb.json",
+    "diff_files": {
+      "stderr": "train-sets/ref/las_sqcb.stderr",
+      "metrics_las_sqcb.json": "test-sets/ref/metrics_las_sqcb.json"
+    },
+    "input_files": [
+      "train-sets/las_100_actions.txt"
+    ]
+  },
+  {
+    "id": 448,
+    "desc": "transition from squarecb model to las + squarecb",
+    "vw_command": "-d train-sets/cb_load.dat --cb_explore_adf -q UA --squarecb -i models/sqcb_ld.model --large_action_space --max_actions 2",
+    "diff_files": {
+      "stderr": "train-sets/ref/sqcb_to_las.stderr"
+    },
+    "input_files": [
+      "train-sets/cb_load.dat",
+      "models/sqcb_ld.model"
+    ],
+    "depends_on": [
+      314
+    ]
   }
 ]
\ No newline at end of file
diff --git a/test/test-sets/ref/metrics_las_e.json b/test/test-sets/ref/metrics_las_e.json
new file mode 100644
index 00000000000..a0635fbb994
--- /dev/null
+++ b/test/test-sets/ref/metrics_las_e.json
@@ -0,0 +1 @@
+{"cb_las_filtering_factor":15,"cbea_label_first_action":0,"cbea_label_not_first":2,"cbea_labeled_ex":2,"cbea_max_actions":99,"cbea_min_actions":99,"cbea_non_zero_cost":2,"cbea_predict_in_learn":0,"sfm_count_learn_example_with_shared":2,"total_learn_calls":2,"total_log_calls":0,"total_predict_calls":2,"cbea_avg_actions_per_event":99.0,"cbea_avg_feat_per_action":48.0,"cbea_avg_feat_per_event":4761.0,"cbea_avg_ns_per_action":2.0,"cbea_avg_ns_per_event":198.0,"cbea_sum_cost":-2.0,"cbea_sum_cost_baseline":0.0}
\ No newline at end of file
diff --git a/test/test-sets/ref/metrics_las_sqcb.json b/test/test-sets/ref/metrics_las_sqcb.json
new file mode 100644
index 00000000000..a0635fbb994
--- /dev/null
+++ b/test/test-sets/ref/metrics_las_sqcb.json
@@ -0,0 +1 @@
+{"cb_las_filtering_factor":15,"cbea_label_first_action":0,"cbea_label_not_first":2,"cbea_labeled_ex":2,"cbea_max_actions":99,"cbea_min_actions":99,"cbea_non_zero_cost":2,"cbea_predict_in_learn":0,"sfm_count_learn_example_with_shared":2,"total_learn_calls":2,"total_log_calls":0,"total_predict_calls":2,"cbea_avg_actions_per_event":99.0,"cbea_avg_feat_per_action":48.0,"cbea_avg_feat_per_event":4761.0,"cbea_avg_ns_per_action":2.0,"cbea_avg_ns_per_event":198.0,"cbea_sum_cost":-2.0,"cbea_sum_cost_baseline":0.0}
\ No newline at end of file
diff --git a/test/train-sets/las_100_actions.txt b/test/train-sets/las_100_actions.txt
new file mode 100644
index 00000000000..fb0e0dabc77
--- /dev/null
+++ b/test/train-sets/las_100_actions.txt
@@ -0,0 +1,202 @@
+shared |User user=Anna time_of_day=morning
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+|Action politics:33 sports:51 music:15 food:36 math:31 science:17 computers:15 literature:53 social_media:54 dancing:29 news:36 celebrities:23 coffee:20 baking:26 ai:27 taxes:13 technology:11 pandemic:53 world_war_i:48 world_war_ii:6 religion:29 vaccination:0 the_queen:21 immigration:18 economics:25 fashion:5 NYC:31 LA:53 elections:29 brunch:9 space_exploration:9 climate_change:50 dogs:19 cats:12 inflation:28 sourdough:12 vegan:26 vacation:20 asteroid:12 eyewear:15 stationary:44 movies:12 oscars:53 acupuncture:50 hiking:33 swimming:16 barrys:55 
+|Action politics:66 sports:102 music:30 food:72 math:62 science:34 computers:30 literature:106 social_media:108 dancing:58 news:72 celebrities:46 coffee:40 baking:52 ai:54 taxes:26 technology:22 pandemic:106 world_war_i:96 world_war_ii:12 religion:58 vaccination:0 the_queen:42 immigration:36 economics:50 fashion:10 NYC:62 LA:106 elections:58 brunch:18 space_exploration:18 climate_change:100 dogs:38 cats:24 inflation:56 sourdough:24 vegan:52 vacation:40 asteroid:24 eyewear:30 stationary:88 movies:24 oscars:106 acupuncture:100 hiking:66 swimming:32 barrys:110 
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+|Action politics:37 sports:27 music:30 food:33 math:45 science:51 computers:31 literature:43 social_media:14 dancing:50 news:8 celebrities:3 coffee:53 baking:14 ai:40 taxes:16 technology:2 pandemic:36 world_war_i:24 world_war_ii:30 religion:23 vaccination:47 the_queen:20 immigration:14 economics:21 fashion:46 NYC:29 LA:50 elections:38 brunch:36 space_exploration:43 climate_change:35 dogs:32 cats:20 inflation:21 sourdough:11 vegan:28 vacation:46 asteroid:51 eyewear:41 stationary:50 movies:52 oscars:25 acupuncture:13 hiking:5 swimming:28 barrys:19 
+|Action politics:74 sports:54 music:60 food:66 math:90 science:102 computers:62 literature:86 social_media:28 dancing:100 news:16 celebrities:6 coffee:106 baking:28 ai:80 taxes:32 technology:4 pandemic:72 world_war_i:48 world_war_ii:60 religion:46 vaccination:94 the_queen:40 immigration:28 economics:42 fashion:92 NYC:58 LA:100 elections:76 brunch:72 space_exploration:86 climate_change:70 dogs:64 cats:40 inflation:42 sourdough:22 vegan:56 vacation:92 asteroid:102 eyewear:82 stationary:100 movies:104 oscars:50 acupuncture:26 hiking:10 swimming:56 barrys:38 
+|Action politics:111 sports:81 music:90 food:99 math:135 science:153 computers:93 literature:129 social_media:42 dancing:150 news:24 celebrities:9 coffee:159 baking:42 ai:120 taxes:48 technology:6 pandemic:108 world_war_i:72 world_war_ii:90 religion:69 vaccination:141 the_queen:60 immigration:42 economics:63 fashion:138 NYC:87 LA:150 elections:114 brunch:108 space_exploration:129 climate_change:105 dogs:96 cats:60 inflation:63 sourdough:33 vegan:84 vacation:138 asteroid:153 eyewear:123 stationary:150 movies:156 oscars:75 acupuncture:39 hiking:15 swimming:84 barrys:57 
+|Action politics:20 sports:11 music:30 food:6 math:33 science:39 computers:0 literature:7 social_media:23 dancing:20 news:26 celebrities:21 coffee:16 baking:10 ai:34 taxes:6 technology:11 pandemic:21 world_war_i:38 world_war_ii:48 religion:15 vaccination:19 the_queen:52 immigration:47 economics:18 fashion:34 NYC:48 LA:24 elections:46 brunch:39 space_exploration:36 climate_change:20 dogs:29 cats:51 inflation:14 sourdough:40 vegan:6 vacation:33 asteroid:32 eyewear:53 stationary:22 movies:20 oscars:54 acupuncture:36 hiking:7 swimming:46 barrys:5 
+|Action politics:40 sports:22 music:60 food:12 math:66 science:78 computers:0 literature:14 social_media:46 dancing:40 news:52 celebrities:42 coffee:32 baking:20 ai:68 taxes:12 technology:22 pandemic:42 world_war_i:76 world_war_ii:96 religion:30 vaccination:38 the_queen:104 immigration:94 economics:36 fashion:68 NYC:96 LA:48 elections:92 brunch:78 space_exploration:72 climate_change:40 dogs:58 cats:102 inflation:28 sourdough:80 vegan:12 vacation:66 asteroid:64 eyewear:106 stationary:44 movies:40 oscars:108 acupuncture:72 hiking:14 swimming:92 barrys:10 
+|Action politics:60 sports:33 music:90 food:18 math:99 science:117 computers:0 literature:21 social_media:69 dancing:60 news:78 celebrities:63 coffee:48 baking:30 ai:102 taxes:18 technology:33 pandemic:63 world_war_i:114 world_war_ii:144 religion:45 vaccination:57 the_queen:156 immigration:141 economics:54 fashion:102 NYC:144 LA:72 elections:138 brunch:117 space_exploration:108 climate_change:60 dogs:87 cats:153 inflation:42 sourdough:120 vegan:18 vacation:99 asteroid:96 eyewear:159 stationary:66 movies:60 oscars:162 acupuncture:108 hiking:21 swimming:138 barrys:15 
+|Action politics:13 sports:21 music:35 food:17 math:47 science:5 computers:40 literature:29 social_media:16 dancing:18 news:5 celebrities:37 coffee:42 baking:40 ai:7 taxes:11 technology:50 pandemic:1 world_war_i:39 world_war_ii:7 religion:41 vaccination:28 the_queen:15 immigration:29 economics:47 fashion:40 NYC:43 LA:6 elections:22 brunch:54 space_exploration:30 climate_change:38 dogs:32 cats:44 inflation:17 sourdough:4 vegan:17 vacation:55 asteroid:9 eyewear:42 stationary:20 movies:26 oscars:24 acupuncture:55 hiking:12 swimming:30 barrys:18 
+|Action politics:26 sports:42 music:70 food:34 math:94 science:10 computers:80 literature:58 social_media:32 dancing:36 news:10 celebrities:74 coffee:84 baking:80 ai:14 taxes:22 technology:100 pandemic:2 world_war_i:78 world_war_ii:14 religion:82 vaccination:56 the_queen:30 immigration:58 economics:94 fashion:80 NYC:86 LA:12 elections:44 brunch:108 space_exploration:60 climate_change:76 dogs:64 cats:88 inflation:34 sourdough:8 vegan:34 vacation:110 asteroid:18 eyewear:84 stationary:40 movies:52 oscars:48 acupuncture:110 hiking:24 swimming:60 barrys:36 
+|Action politics:39 sports:63 music:105 food:51 math:141 science:15 computers:120 literature:87 social_media:48 dancing:54 news:15 celebrities:111 coffee:126 baking:120 ai:21 taxes:33 technology:150 pandemic:3 world_war_i:117 world_war_ii:21 religion:123 vaccination:84 the_queen:45 immigration:87 economics:141 fashion:120 NYC:129 LA:18 elections:66 brunch:162 space_exploration:90 climate_change:114 dogs:96 cats:132 inflation:51 sourdough:12 vegan:51 vacation:165 asteroid:27 eyewear:126 stationary:60 movies:78 oscars:72 acupuncture:165 hiking:36 swimming:90 barrys:54 
+|Action politics:36 sports:26 music:6 food:26 math:25 science:4 computers:1 literature:43 social_media:55 dancing:31 news:18 celebrities:13 coffee:2 baking:48 ai:1 taxes:19 technology:10 pandemic:34 world_war_i:53 world_war_ii:54 religion:32 vaccination:21 the_queen:8 immigration:30 economics:22 fashion:13 NYC:35 LA:16 elections:0 brunch:44 space_exploration:36 climate_change:50 dogs:43 cats:35 inflation:32 sourdough:22 vegan:21 vacation:43 asteroid:27 eyewear:25 stationary:27 movies:19 oscars:27 acupuncture:1 hiking:51 swimming:55 barrys:15 
+|Action politics:72 sports:52 music:12 food:52 math:50 science:8 computers:2 literature:86 social_media:110 dancing:62 news:36 celebrities:26 coffee:4 baking:96 ai:2 taxes:38 technology:20 pandemic:68 world_war_i:106 world_war_ii:108 religion:64 vaccination:42 the_queen:16 immigration:60 economics:44 fashion:26 NYC:70 LA:32 elections:0 brunch:88 space_exploration:72 climate_change:100 dogs:86 cats:70 inflation:64 sourdough:44 vegan:42 vacation:86 asteroid:54 eyewear:50 stationary:54 movies:38 oscars:54 acupuncture:2 hiking:102 swimming:110 barrys:30 
+|Action politics:108 sports:78 music:18 food:78 math:75 science:12 computers:3 literature:129 social_media:165 dancing:93 news:54 celebrities:39 coffee:6 baking:144 ai:3 taxes:57 technology:30 pandemic:102 world_war_i:159 world_war_ii:162 religion:96 vaccination:63 the_queen:24 immigration:90 economics:66 fashion:39 NYC:105 LA:48 elections:0 brunch:132 space_exploration:108 climate_change:150 dogs:129 cats:105 inflation:96 sourdough:66 vegan:63 vacation:129 asteroid:81 eyewear:75 stationary:81 movies:57 oscars:81 acupuncture:3 hiking:153 swimming:165 barrys:45 
+|Action politics:4 sports:18 music:42 food:38 math:0 science:18 computers:41 literature:30 social_media:24 dancing:31 news:41 celebrities:30 coffee:7 baking:22 ai:54 taxes:22 technology:36 pandemic:45 world_war_i:32 world_war_ii:14 religion:43 vaccination:22 the_queen:7 immigration:52 economics:8 fashion:41 NYC:25 LA:39 elections:22 brunch:40 space_exploration:30 climate_change:2 dogs:35 cats:18 inflation:5 sourdough:10 vegan:18 vacation:32 asteroid:52 eyewear:47 stationary:11 movies:40 oscars:8 acupuncture:3 hiking:10 swimming:42 barrys:42 
+|Action politics:8 sports:36 music:84 food:76 math:0 science:36 computers:82 literature:60 social_media:48 dancing:62 news:82 celebrities:60 coffee:14 baking:44 ai:108 taxes:44 technology:72 pandemic:90 world_war_i:64 world_war_ii:28 religion:86 vaccination:44 the_queen:14 immigration:104 economics:16 fashion:82 NYC:50 LA:78 elections:44 brunch:80 space_exploration:60 climate_change:4 dogs:70 cats:36 inflation:10 sourdough:20 vegan:36 vacation:64 asteroid:104 eyewear:94 stationary:22 movies:80 oscars:16 acupuncture:6 hiking:20 swimming:84 barrys:84 
+|Action politics:12 sports:54 music:126 food:114 math:0 science:54 computers:123 literature:90 social_media:72 dancing:93 news:123 celebrities:90 coffee:21 baking:66 ai:162 taxes:66 technology:108 pandemic:135 world_war_i:96 world_war_ii:42 religion:129 vaccination:66 the_queen:21 immigration:156 economics:24 fashion:123 NYC:75 LA:117 elections:66 brunch:120 space_exploration:90 climate_change:6 dogs:105 cats:54 inflation:15 sourdough:30 vegan:54 vacation:96 asteroid:156 eyewear:141 stationary:33 movies:120 oscars:24 acupuncture:9 hiking:30 swimming:126 barrys:126 
+|Action politics:5 sports:13 music:0 food:16 math:34 science:41 computers:22 literature:2 social_media:19 dancing:4 news:6 celebrities:16 coffee:26 baking:51 ai:50 taxes:21 technology:13 pandemic:27 world_war_i:7 world_war_ii:49 religion:10 vaccination:54 the_queen:7 immigration:2 economics:53 fashion:31 NYC:54 LA:9 elections:30 brunch:36 space_exploration:18 climate_change:25 dogs:31 cats:44 inflation:6 sourdough:14 vegan:24 vacation:22 asteroid:2 eyewear:46 stationary:45 movies:22 oscars:18 acupuncture:43 hiking:29 swimming:45 barrys:0 
+|Action politics:10 sports:26 music:0 food:32 math:68 science:82 computers:44 literature:4 social_media:38 dancing:8 news:12 celebrities:32 coffee:52 baking:102 ai:100 taxes:42 technology:26 pandemic:54 world_war_i:14 world_war_ii:98 religion:20 vaccination:108 the_queen:14 immigration:4 economics:106 fashion:62 NYC:108 LA:18 elections:60 brunch:72 space_exploration:36 climate_change:50 dogs:62 cats:88 inflation:12 sourdough:28 vegan:48 vacation:44 asteroid:4 eyewear:92 stationary:90 movies:44 oscars:36 acupuncture:86 hiking:58 swimming:90 barrys:0 
+|Action politics:15 sports:39 music:0 food:48 math:102 science:123 computers:66 literature:6 social_media:57 dancing:12 news:18 celebrities:48 coffee:78 baking:153 ai:150 taxes:63 technology:39 pandemic:81 world_war_i:21 world_war_ii:147 religion:30 vaccination:162 the_queen:21 immigration:6 economics:159 fashion:93 NYC:162 LA:27 elections:90 brunch:108 space_exploration:54 climate_change:75 dogs:93 cats:132 inflation:18 sourdough:42 vegan:72 vacation:66 asteroid:6 eyewear:138 stationary:135 movies:66 oscars:54 acupuncture:129 hiking:87 swimming:135 barrys:0 
+|Action politics:1 sports:31 music:6 food:55 math:47 science:11 computers:31 literature:28 social_media:51 dancing:35 news:27 celebrities:0 coffee:15 baking:46 ai:3 taxes:5 technology:40 pandemic:45 world_war_i:31 world_war_ii:49 religion:40 vaccination:47 the_queen:1 immigration:17 economics:39 fashion:30 NYC:17 LA:15 elections:27 brunch:6 space_exploration:15 climate_change:43 dogs:47 cats:15 inflation:46 sourdough:34 vegan:39 vacation:38 asteroid:49 eyewear:49 stationary:7 movies:12 oscars:4 acupuncture:2 hiking:33 swimming:52 barrys:37 
+|Action politics:2 sports:62 music:12 food:110 math:94 science:22 computers:62 literature:56 social_media:102 dancing:70 news:54 celebrities:0 coffee:30 baking:92 ai:6 taxes:10 technology:80 pandemic:90 world_war_i:62 world_war_ii:98 religion:80 vaccination:94 the_queen:2 immigration:34 economics:78 fashion:60 NYC:34 LA:30 elections:54 brunch:12 space_exploration:30 climate_change:86 dogs:94 cats:30 inflation:92 sourdough:68 vegan:78 vacation:76 asteroid:98 eyewear:98 stationary:14 movies:24 oscars:8 acupuncture:4 hiking:66 swimming:104 barrys:74 
+|Action politics:3 sports:93 music:18 food:165 math:141 science:33 computers:93 literature:84 social_media:153 dancing:105 news:81 celebrities:0 coffee:45 baking:138 ai:9 taxes:15 technology:120 pandemic:135 world_war_i:93 world_war_ii:147 religion:120 vaccination:141 the_queen:3 immigration:51 economics:117 fashion:90 NYC:51 LA:45 elections:81 brunch:18 space_exploration:45 climate_change:129 dogs:141 cats:45 inflation:138 sourdough:102 vegan:117 vacation:114 asteroid:147 eyewear:147 stationary:21 movies:36 oscars:12 acupuncture:6 hiking:99 swimming:156 barrys:111 
+
diff --git a/test/train-sets/ref/las_egreedy.stderr b/test/train-sets/ref/las_egreedy.stderr
new file mode 100644
index 00000000000..753188c331a
--- /dev/null
+++ b/test/train-sets/ref/las_egreedy.stderr
@@ -0,0 +1,22 @@
+using no cache
+Reading datafile = train-sets/las_100_actions.txt
+num sources = 1
+Num weight bits = 18
+learning rate = 0.5
+initial_t = 0
+power_t = 0.5
+cb_type = mtr
+Enabled reductions: gd, scorer-identity, csoaa_ldf-rank, cb_adf, cb_explore_adf_large_action_space, cb_explore_adf_greedy, cb_actions_mask, shared_feature_merger, extra_metrics
+Input label = CB
+Output pred = ACTION_PROBS
+average  since         example        example        current        current  current
+loss     last          counter         weight          label        predict features
+0.000000 0.000000            1            1.0     47:-1:0.17         0:0.06     4761
+-0.00153 -0.00306            2            2.0     14:-1:0.96        65:0.95     4761
+
+finished run
+number of examples = 2
+weighted example sum = 2.000000
+weighted label sum = 0.000000
+average loss = -0.001535
+total feature number = 9522
diff --git a/test/train-sets/ref/las_sqcb.stderr b/test/train-sets/ref/las_sqcb.stderr
new file mode 100644
index 00000000000..e52a5af6db6
--- /dev/null
+++ b/test/train-sets/ref/las_sqcb.stderr
@@ -0,0 +1,22 @@
+using no cache
+Reading datafile = train-sets/las_100_actions.txt
+num sources = 1
+Num weight bits = 18
+learning rate = 0.5
+initial_t = 0
+power_t = 0.5
+cb_type = mtr
+Enabled reductions: gd, scorer-identity, csoaa_ldf-rank, cb_adf, cb_explore_adf_large_action_space, cb_explore_adf_squarecb, cb_actions_mask, shared_feature_merger, extra_metrics
+Input label = CB
+Output pred = ACTION_PROBS
+average  since         example        example        current        current  current
+loss     last          counter         weight          label        predict features
+0.000000 0.000000            1            1.0     47:-1:0.17         0:0.06     4761
+-0.02926 -0.05853            2            2.0     14:-1:0.96        65:0.17     4761
+
+finished run
+number of examples = 2
+weighted example sum = 2.000000
+weighted label sum = 0.000000
+average loss = -0.029265
+total feature number = 9522
diff --git a/test/train-sets/ref/sqcb_to_las.stderr b/test/train-sets/ref/sqcb_to_las.stderr
new file mode 100644
index 00000000000..03ea74ccc7a
--- /dev/null
+++ b/test/train-sets/ref/sqcb_to_las.stderr
@@ -0,0 +1,28 @@
+creating quadratic features for pairs: UA
+using no cache
+Reading datafile = train-sets/cb_load.dat
+num sources = 1
+Num weight bits = 18
+learning rate = 0.5
+initial_t = 113
+power_t = 0.5
+cb_type = mtr
+Enabled reductions: gd, scorer-identity, csoaa_ldf-rank, cb_adf, cb_explore_adf_large_action_space, cb_explore_adf_squarecb, cb_actions_mask, shared_feature_merger
+Input label = CB
+Output pred = ACTION_PROBS
+average  since         example        example        current        current  current
+loss     last          counter         weight          label        predict features
+0.000000 0.000000            1            1.0       4:0:0.14         0:0.97       42
+0.000000 0.000000            2            2.0       0:0:0.14         0:0.94       42
+0.000000 0.000000            4            4.0       1:0:0.14         2:0.97       42
+0.000000 0.000000            8            8.0       3:0:0.14         2:0.87       42
+0.000000 0.000000           16           16.0       3:0:0.14         2:0.88       42
+0.000000 0.000000           32           32.0       3:0:0.14         2:0.98       42
+-0.58935 -1.17870           64           64.0       0:0:0.77         0:0.97       42
+
+finished run
+number of examples = 113
+weighted example sum = 113.000000
+weighted label sum = 0.000000
+average loss = -0.581254
+total feature number = 4746
diff --git a/vowpalwabbit/core/include/vw/core/large_action_space_reduction_features.h b/vowpalwabbit/core/include/vw/core/large_action_space_reduction_features.h
index 6cbac00d8ac..a79aacfbd2b 100644
--- a/vowpalwabbit/core/include/vw/core/large_action_space_reduction_features.h
+++ b/vowpalwabbit/core/include/vw/core/large_action_space_reduction_features.h
@@ -20,6 +20,7 @@ class las_reduction_features
   std::vector<std::vector<VW::namespace_index>>* generated_interactions = nullptr;
   std::vector<std::vector<extent_term>>* generated_extent_interactions = nullptr;
   VW::multi_ex::value_type shared_example = nullptr;
+  float squarecb_gamma = 1.f;
 
   las_reduction_features() = default;
 
@@ -28,6 +29,7 @@ class las_reduction_features
     generated_interactions = nullptr;
     generated_extent_interactions = nullptr;
     shared_example = nullptr;
+    squarecb_gamma = 1.f;
   }
 };
 
diff --git a/vowpalwabbit/core/src/reductions/cb/cb_explore_adf_large_action_space.cc b/vowpalwabbit/core/src/reductions/cb/cb_explore_adf_large_action_space.cc
index 400c4722981..b81c0e5c9fa 100644
--- a/vowpalwabbit/core/src/reductions/cb/cb_explore_adf_large_action_space.cc
+++ b/vowpalwabbit/core/src/reductions/cb/cb_explore_adf_large_action_space.cc
@@ -112,15 +112,6 @@ bool _test_only_generate_A(VW::workspace* _all, const multi_ex& examples, std::v
   return (_A.cols() != 0 && _A.rows() != 0);
 }
 
-template <typename randomized_svd_impl, typename spanner_impl>
-void cb_explore_adf_large_action_space<randomized_svd_impl, spanner_impl>::save_load(io_buf& io, bool read, bool text)
-{
-  if (io.num_files() == 0) { return; }
-
-  if (read) { model_utils::read_model_field(io, _counter); }
-  else { model_utils::write_model_field(io, _counter, "cb large action space storing example counter", text); }
-}
-
 template <typename randomized_svd_impl, typename spanner_impl>
 void cb_explore_adf_large_action_space<randomized_svd_impl, spanner_impl>::randomized_SVD(const multi_ex& examples)
 {
@@ -157,7 +148,10 @@ void cb_explore_adf_large_action_space<randomized_svd_impl, spanner_impl>::updat
 
   if (_d < preds.size())
   {
-    shrink_fact_config.calculate_shrink_factor(_counter, _d, preds, shrink_factors);
+    auto& red_features =
+        examples[0]->ex_reduction_features.template get<VW::large_action_space::las_reduction_features>();
+
+    shrink_fact_config.calculate_shrink_factor(red_features.squarecb_gamma, _d, preds, shrink_factors);
     randomized_SVD(examples);
 
     // The U matrix is empty before learning anything.
@@ -205,9 +199,9 @@ template <typename randomized_svd_impl, typename spanner_impl>
 void cb_explore_adf_large_action_space<randomized_svd_impl, spanner_impl>::learn(
     VW::LEARNER::multi_learner& base, multi_ex& examples)
 {
+  VW::v_array<VW::action_score> preds = std::move(examples[0]->pred.a_s);
+  auto restore_guard = VW::scope_exit([&preds, &examples] { examples[0]->pred.a_s = std::move(preds); });
   base.learn(examples);
-  if (base.learn_returns_prediction) { update_example_prediction(examples); }
-  ++_counter;
 }
 
 void generate_Z(const multi_ex& examples, Eigen::MatrixXf& Z, Eigen::MatrixXf& B, uint64_t d, uint64_t seed)
@@ -235,33 +229,28 @@ void generate_Z(const multi_ex& examples, Eigen::MatrixXf& Z, Eigen::MatrixXf& B
 }
 
 template <typename T, typename S>
-cb_explore_adf_large_action_space<T, S>::cb_explore_adf_large_action_space(uint64_t d, float gamma_scale,
-    float gamma_exponent, float c, bool apply_shrink_factor, VW::workspace* all, uint64_t seed, size_t total_size,
-    size_t thread_pool_size, size_t block_size, bool use_explicit_simd, implementation_type impl_type)
+cb_explore_adf_large_action_space<T, S>::cb_explore_adf_large_action_space(uint64_t d, float c,
+    bool apply_shrink_factor, VW::workspace* all, uint64_t seed, size_t total_size, size_t thread_pool_size,
+    size_t block_size, bool use_explicit_simd, implementation_type impl_type)
     : _d(d)
     , _all(all)
-    , _counter(0)
     , _seed(seed)
     , _impl_type(impl_type)
     , spanner_state(c, d)
-    , shrink_fact_config(gamma_scale, gamma_exponent, apply_shrink_factor)
+    , shrink_fact_config(apply_shrink_factor)
     , impl(all, d, _seed, total_size, thread_pool_size, block_size, use_explicit_simd)
 {
 }
 
-shrink_factor_config::shrink_factor_config(float gamma_scale, float gamma_exponent, bool apply_shrink_factor)
-    : _gamma_scale(gamma_scale), _gamma_exponent(gamma_exponent), _apply_shrink_factor(apply_shrink_factor)
-{
-}
+shrink_factor_config::shrink_factor_config(bool apply_shrink_factor) : _apply_shrink_factor(apply_shrink_factor) {}
 
 void shrink_factor_config::calculate_shrink_factor(
-    size_t counter, size_t max_actions, const VW::action_scores& preds, std::vector<float>& shrink_factors)
+    float gamma, size_t max_actions, const VW::action_scores& preds, std::vector<float>& shrink_factors)
 {
   if (_apply_shrink_factor)
   {
     shrink_factors.clear();
     float min_ck = std::min_element(preds.begin(), preds.end())->score;
-    float gamma = _gamma_scale * static_cast<float>(std::pow(counter, _gamma_exponent));
     for (size_t i = 0; i < preds.size(); i++)
     {
       shrink_factors.push_back(std::sqrt(1 + max_actions + gamma / (4.0f * max_actions) * (preds[i].score - min_ck)));
@@ -283,12 +272,6 @@ void persist_metrics(cb_explore_adf_large_action_space<T, S>& data, VW::metric_s
   metrics.set_uint("cb_las_filtering_factor", data.number_of_non_degenerate_singular_values());
 }
 
-template <typename T, typename S>
-void save_load(cb_explore_adf_large_action_space<T, S>& data, VW::io_buf& io, bool read, bool text)
-{
-  data.save_load(io, read, text);
-}
-
 template <typename T, typename S>
 void predict(cb_explore_adf_large_action_space<T, S>& data, VW::LEARNER::multi_learner& base, VW::multi_ex& examples)
 {
@@ -303,15 +286,15 @@ void learn(cb_explore_adf_large_action_space<T, S>& data, VW::LEARNER::multi_lea
 
 template <typename T, typename S>
 VW::LEARNER::base_learner* make_las_with_impl(VW::setup_base_i& stack_builder, VW::LEARNER::multi_learner* base,
-    implementation_type& impl_type, VW::workspace& all, uint64_t d, float gamma_scale, float gamma_exponent, float c,
-    bool apply_shrink_factor, size_t thread_pool_size, size_t block_size, bool use_explicit_simd)
+    implementation_type& impl_type, VW::workspace& all, uint64_t d, float c, bool apply_shrink_factor,
+    size_t thread_pool_size, size_t block_size, bool use_explicit_simd)
 {
   size_t problem_multiplier = 1;
 
   float seed = (all.get_random_state()->get_random() + 1) * 10.f;
 
-  auto data = VW::make_unique<cb_explore_adf_large_action_space<T, S>>(d, gamma_scale, gamma_exponent, c,
-      apply_shrink_factor, &all, seed, 1 << all.num_bits, thread_pool_size, block_size, use_explicit_simd, impl_type);
+  auto data = VW::make_unique<cb_explore_adf_large_action_space<T, S>>(d, c, apply_shrink_factor, &all, seed,
+      1 << all.num_bits, thread_pool_size, block_size, use_explicit_simd, impl_type);
 
   auto* l = make_reduction_learner(std::move(data), base, learn<T, S>, predict<T, S>,
       stack_builder.get_setupfn_name(VW::reductions::cb_explore_adf_large_action_space_setup))
@@ -321,8 +304,7 @@ VW::LEARNER::base_learner* make_las_with_impl(VW::setup_base_i& stack_builder, V
                 .set_output_prediction_type(VW::prediction_type_t::ACTION_SCORES)
                 .set_params_per_weight(problem_multiplier)
                 .set_persist_metrics(persist_metrics<T, S>)
-                .set_save_load(save_load<T, S>)
-                .set_learn_returns_prediction(base->learn_returns_prediction)
+                .set_learn_returns_prediction(false)
                 .build();
   return VW::LEARNER::make_base(*l);
 }
@@ -336,8 +318,6 @@ VW::LEARNER::base_learner* VW::reductions::cb_explore_adf_large_action_space_set
   bool cb_explore_adf_option = false;
   bool large_action_space = false;
   uint64_t d;
-  float gamma_scale = 1.f;
-  float gamma_exponent = 0.f;
   float c;
   bool apply_shrink_factor = false;
   bool use_two_pass_svd_impl = false;
@@ -389,12 +369,7 @@ VW::LEARNER::base_learner* VW::reductions::cb_explore_adf_large_action_space_set
   auto enabled = options.add_parse_and_check_necessary(new_options) && large_action_space;
   if (!enabled) { return nullptr; }
 
-  if (options.was_supplied("squarecb"))
-  {
-    apply_shrink_factor = true;
-    gamma_scale = options.get_typed_option<float>("gamma_scale").value();
-    gamma_exponent = options.get_typed_option<float>("gamma_exponent").value();
-  }
+  if (options.was_supplied("squarecb")) { apply_shrink_factor = true; }
 
   if (options.was_supplied("cb_type"))
   {
@@ -414,15 +389,14 @@ VW::LEARNER::base_learner* VW::reductions::cb_explore_adf_large_action_space_set
   if (use_two_pass_svd_impl)
   {
     auto impl_type = implementation_type::two_pass_svd;
-    return make_las_with_impl<two_pass_svd_impl, one_rank_spanner_state>(stack_builder, base, impl_type, all, d,
-        gamma_scale, gamma_exponent, c, apply_shrink_factor, thread_pool_size, block_size,
+    return make_las_with_impl<two_pass_svd_impl, one_rank_spanner_state>(stack_builder, base, impl_type, all, d, c,
+        apply_shrink_factor, thread_pool_size, block_size,
         /*use_explicit_simd=*/false);
   }
   else
   {
     auto impl_type = implementation_type::one_pass_svd;
-    return make_las_with_impl<one_pass_svd_impl, one_rank_spanner_state>(stack_builder, base, impl_type, all, d,
-        gamma_scale, gamma_exponent, c, apply_shrink_factor, thread_pool_size, block_size,
-        use_simd_in_one_pass_svd_impl);
+    return make_las_with_impl<one_pass_svd_impl, one_rank_spanner_state>(stack_builder, base, impl_type, all, d, c,
+        apply_shrink_factor, thread_pool_size, block_size, use_simd_in_one_pass_svd_impl);
   }
 }
diff --git a/vowpalwabbit/core/src/reductions/cb/cb_explore_adf_squarecb.cc b/vowpalwabbit/core/src/reductions/cb/cb_explore_adf_squarecb.cc
index fe0e4e1b404..f976e78f4c1 100644
--- a/vowpalwabbit/core/src/reductions/cb/cb_explore_adf_squarecb.cc
+++ b/vowpalwabbit/core/src/reductions/cb/cb_explore_adf_squarecb.cc
@@ -43,7 +43,7 @@ class cb_explore_adf_squarecb
 {
 public:
   cb_explore_adf_squarecb(float gamma_scale, float gamma_exponent, bool elim, float c0, float min_cb_cost,
-      float max_cb_cost, VW::version_struct model_file_version, float epsilon);
+      float max_cb_cost, VW::version_struct model_file_version, float epsilon, bool store_gamma_in_reduction_features);
   ~cb_explore_adf_squarecb() = default;
 
   // Should be called through cb_explore_adf_base for pre/post-processing
@@ -68,6 +68,8 @@ class cb_explore_adf_squarecb
 
   VW::version_struct _model_file_version;
 
+  bool _store_gamma_in_reduction_features;
+
   // for backing up cb example data when computing sensitivities
   std::vector<VW::action_scores> _ex_as;
   std::vector<std::vector<VW::cb_class>> _ex_costs;
@@ -76,7 +78,8 @@ class cb_explore_adf_squarecb
 };
 
 cb_explore_adf_squarecb::cb_explore_adf_squarecb(float gamma_scale, float gamma_exponent, bool elim, float c0,
-    float min_cb_cost, float max_cb_cost, VW::version_struct model_file_version, float epsilon)
+    float min_cb_cost, float max_cb_cost, VW::version_struct model_file_version, float epsilon,
+    bool store_gamma_in_reduction_features)
     : _counter(0)
     , _gamma_scale(gamma_scale)
     , _gamma_exponent(gamma_exponent)
@@ -86,6 +89,7 @@ cb_explore_adf_squarecb::cb_explore_adf_squarecb(float gamma_scale, float gamma_
     , _max_cb_cost(max_cb_cost)
     , _epsilon(epsilon)
     , _model_file_version(model_file_version)
+    , _store_gamma_in_reduction_features(store_gamma_in_reduction_features)
 {
 }
 
@@ -186,14 +190,20 @@ void cb_explore_adf_squarecb::get_cost_ranges(float delta, multi_learner& base,
 
 void cb_explore_adf_squarecb::predict(multi_learner& base, VW::multi_ex& examples)
 {
+  // The actual parameter $\gamma$ used in the SquareCB.
+  const float gamma = _gamma_scale * static_cast<float>(std::pow(_counter, _gamma_exponent));
+  if (_store_gamma_in_reduction_features)
+  {
+    auto& red_features =
+        examples[0]->ex_reduction_features.template get<VW::large_action_space::las_reduction_features>();
+    red_features.squarecb_gamma = gamma;
+  }
+
   multiline_learn_or_predict<false>(base, examples, examples[0]->ft_offset);
 
   VW::v_array<VW::action_score>& preds = examples[0]->pred.a_s;
   uint32_t num_actions = static_cast<uint32_t>(preds.size());
 
-  // The actual parameter $\gamma$ used in the SquareCB.
-  const float gamma = _gamma_scale * static_cast<float>(std::pow(_counter, _gamma_exponent));
-
   // RegCB action set parameters
   const float max_range = _max_cb_cost - _min_cb_cost;
   // threshold on empirical loss difference
@@ -374,6 +384,9 @@ VW::LEARNER::base_learner* VW::reductions::cb_explore_adf_squarecb_setup(VW::set
   // Ensure serialization of cb_adf in all cases.
   if (!options.was_supplied("cb_adf")) { options.insert("cb_adf", ""); }
 
+  bool store_gamma_in_reduction_features = false;
+  if (options.was_supplied("large_action_space")) { store_gamma_in_reduction_features = true; }
+
   // Set explore_type
   size_t problem_multiplier = 1;
 
@@ -384,7 +397,7 @@ VW::LEARNER::base_learner* VW::reductions::cb_explore_adf_squarecb_setup(VW::set
 
   using explore_type = cb_explore_adf_base<cb_explore_adf_squarecb>;
   auto data = VW::make_unique<explore_type>(all.global_metrics.are_metrics_enabled(), gamma_scale, gamma_exponent, elim,
-      c0, min_cb_cost, max_cb_cost, all.model_file_ver, epsilon);
+      c0, min_cb_cost, max_cb_cost, all.model_file_ver, epsilon, store_gamma_in_reduction_features);
   auto* l = make_reduction_learner(std::move(data), base, explore_type::learn, explore_type::predict,
       stack_builder.get_setupfn_name(cb_explore_adf_squarecb_setup))
                 .set_input_label_type(VW::label_type_t::CB)
diff --git a/vowpalwabbit/core/src/reductions/cb/details/large_action_space.h b/vowpalwabbit/core/src/reductions/cb/details/large_action_space.h
index aa465a5fe00..103a459e140 100644
--- a/vowpalwabbit/core/src/reductions/cb/details/large_action_space.h
+++ b/vowpalwabbit/core/src/reductions/cb/details/large_action_space.h
@@ -95,13 +95,11 @@ class one_pass_svd_impl
 class shrink_factor_config
 {
 public:
-  const float _gamma_scale;
-  const float _gamma_exponent;
   const bool _apply_shrink_factor;
-  shrink_factor_config(float gamma_scale, float gamma_exponent, bool apply_shrink_factor);
+  shrink_factor_config(bool apply_shrink_factor);
 
   void calculate_shrink_factor(
-      size_t counter, size_t max_actions, const VW::action_scores& preds, std::vector<float>& shrink_factors);
+      float gamma, size_t max_actions, const VW::action_scores& preds, std::vector<float>& shrink_factors);
 };
 
 class one_rank_spanner_state
@@ -135,7 +133,6 @@ class cb_explore_adf_large_action_space
 private:
   uint64_t _d;
   VW::workspace* _all;
-  size_t _counter;
   uint64_t _seed;
   implementation_type _impl_type;
   size_t _non_degenerate_singular_values;
@@ -153,9 +150,9 @@ class cb_explore_adf_large_action_space
   Eigen::SparseMatrix<float> _A;
   Eigen::MatrixXf _V;
 
-  cb_explore_adf_large_action_space(uint64_t d, float gamma_scale, float gamma_exponent, float c,
-      bool apply_shrink_factor, VW::workspace* all, uint64_t seed, size_t total_size, size_t thread_pool_size,
-      size_t block_size, bool use_explicit_simd, implementation_type impl_type);
+  cb_explore_adf_large_action_space(uint64_t d, float c, bool apply_shrink_factor, VW::workspace* all, uint64_t seed,
+      size_t total_size, size_t thread_pool_size, size_t block_size, bool use_explicit_simd,
+      implementation_type impl_type);
 
   ~cb_explore_adf_large_action_space() = default;
 
diff --git a/vowpalwabbit/core/tests/cb_las_spanner_test.cc b/vowpalwabbit/core/tests/cb_las_spanner_test.cc
index 6b484204baa..3088d449aab 100644
--- a/vowpalwabbit/core/tests/cb_las_spanner_test.cc
+++ b/vowpalwabbit/core/tests/cb_las_spanner_test.cc
@@ -35,7 +35,7 @@ TEST(Las, CheckFindingMaxVolume)
     VW::cb_explore_adf::cb_explore_adf_large_action_space<VW::cb_explore_adf::one_pass_svd_impl,
         VW::cb_explore_adf::one_rank_spanner_state>
         largecb(
-            /*d=*/0, /*gamma_scale=*/1.f, /*gamma_exponent=*/0.f, /*c=*/2, false, vw.get(), seed, 1 << vw->num_bits,
+            /*d=*/0, /*c=*/2, false, vw.get(), seed, 1 << vw->num_bits,
             /*thread_pool_size*/ 0, /*block_size*/ 0, /*use_explicit_simd=*/use_simd,
             VW::cb_explore_adf::implementation_type::one_pass_svd);
     largecb.U = Eigen::MatrixXf{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {0, 0, 0}, {7, 5, 3}, {6, 4, 8}};