diff --git a/vowpalwabbit/core/src/reductions/eigen_memory_tree.cc b/vowpalwabbit/core/src/reductions/eigen_memory_tree.cc
index a496d8fc905..11da7bbb24b 100644
--- a/vowpalwabbit/core/src/reductions/eigen_memory_tree.cc
+++ b/vowpalwabbit/core/src/reductions/eigen_memory_tree.cc
@@ -489,15 +489,7 @@ void tree_bound(emt_tree& b, emt_example* ec)
   }
 }
 
-void scorer_features(const emt_feats& f1, VW::features& out)
-{
-  for (auto p : f1)
-  {
-    if (p.second != 0) { out.push_back(p.second, p.first); }
-  }
-}
-
-void scorer_features(const emt_feats& f1, const emt_feats& f2, VW::features& out)
+void scorer_features_sub(const emt_feats& f1, const emt_feats& f2, VW::features& out)
 {
   auto iter1 = f1.begin();
   auto iter2 = f2.begin();
@@ -535,15 +527,31 @@ void scorer_features(const emt_feats& f1, const emt_feats& f2, VW::features& out
   }
 }
 
+void scorer_features_mul(const emt_feats& f1, const emt_feats& f2, VW::features& out)
+{
+  auto iter1 = f1.begin();
+  auto iter2 = f2.begin();
+
+  while (iter1 != f1.end() && iter2 != f2.end())
+  {
+    if (iter1->first < iter2->first) { iter1++; }
+    else if (iter2->first < iter1->first) { iter2++; }
+    else
+    {
+      out.push_back(iter1->second * iter2->second, iter1->first);
+      iter1++;
+      iter2++;
+    }
+  }
+}
+
 void scorer_example(emt_tree& b, const emt_example& ex1, const emt_example& ex2)
 {
   VW::example& out = *b.ex;
 
   static constexpr VW::namespace_index X_NS = 'x';
-  static constexpr VW::namespace_index Z_NS = 'z';
 
   out.feature_space[X_NS].clear();
-  out.feature_space[Z_NS].clear();
 
   if (b.scorer_type == emt_scorer_type::SELF_CONSISTENT_RANK)
   {
@@ -552,7 +560,7 @@ void scorer_example(emt_tree& b, const emt_example& ex1, const emt_example& ex2)
 
     out.interactions->clear();
 
-    scorer_features(ex1.full, ex2.full, out.feature_space[X_NS]);
+    scorer_features_sub(ex1.full, ex2.full, out.feature_space[X_NS]);
 
     out.total_sum_feat_sq = out.feature_space[X_NS].sum_feat_sq;
     out.num_features = out.feature_space[X_NS].size();
@@ -565,26 +573,13 @@ void scorer_example(emt_tree& b, const emt_example& ex1, const emt_example& ex2)
   {
     out.indices.clear();
     out.indices.push_back(X_NS);
-    out.indices.push_back(Z_NS);
 
     out.interactions->clear();
-    out.interactions->push_back({X_NS, Z_NS});
-
-    b.all->feature_tweaks_config.ignore_some_linear = true;
-    b.all->feature_tweaks_config.ignore_linear[X_NS] = true;
-    b.all->feature_tweaks_config.ignore_linear[Z_NS] = true;
 
-    scorer_features(ex1.full, out.feature_space[X_NS]);
-    scorer_features(ex2.full, out.feature_space[Z_NS]);
+    scorer_features_mul(ex1.full, ex2.full, out.feature_space[X_NS]);
 
-    // when we receive ex1 and ex2 their features are indexed on top of eachother. In order
-    // to make sure VW recognizes the features from the two examples as separate features
-    // we apply a map of multiplying by 2 and then offseting by 1 on the second example.
-    for (auto& j : out.feature_space[X_NS].indices) { j = j * 2; }
-    for (auto& j : out.feature_space[Z_NS].indices) { j = j * 2 + 1; }
-
-    out.total_sum_feat_sq = out.feature_space[X_NS].sum_feat_sq + out.feature_space[Z_NS].sum_feat_sq;
-    out.num_features = out.feature_space[X_NS].size() + out.feature_space[Z_NS].size();
+    out.total_sum_feat_sq = out.feature_space[X_NS].sum_feat_sq;
+    out.num_features = out.feature_space[X_NS].size();
 
     auto initial = emt_initial(b.initial_type, ex1.full, ex2.full);
     out.ex_reduction_features.get<VW::simple_label_reduction_features>().initial = initial;