refactor: implement delta add/subtract by actually adding and subtrac…

…ting weights (#4486)

Previously, subtraction is done by copying weights from the newer model, and addition is done by overwriting the older weights. The results are identical, but the new implementation is more intuitive. It also makes model merging with different base models easier to implement in the future.

vowpalwabbit/core/src/reductions/gd.cc

@@ -90,10 +90,17 @@ void merge_weights_with_save_resume(size_t length,
 }
 
 template <typename WeightsT>
-void copy_weights(WeightsT& dest, const WeightsT& source, size_t length)
+void add_weights(WeightsT& dest, const WeightsT& lhs, const WeightsT& rhs, size_t length)
 {
   const size_t full_weights_size = length << dest.stride_shift();
-  for (size_t i = 0; i < full_weights_size; i++) { dest[i] = source[i]; }
+  for (size_t i = 0; i < full_weights_size; i++) { dest[i] = lhs[i] + rhs[i]; }
+}
+
+template <typename WeightsT>
+void subtract_weights(WeightsT& dest, const WeightsT& lhs, const WeightsT& rhs, size_t length)
+{
+  const size_t full_weights_size = length << dest.stride_shift();
+  for (size_t i = 0; i < full_weights_size; i++) { dest[i] = lhs[i] - rhs[i]; }
 }
 
 void sync_weights(VW::workspace& all)
@@ -274,13 +281,15 @@ void merge(const std::vector<float>& per_model_weighting, const std::vector<cons
   }
 }
 
-void add(const VW::workspace& /* ws1 */, const VW::reductions::gd& data1, const VW::workspace& ws2,
-    VW::reductions::gd& data2, VW::workspace& ws_out, VW::reductions::gd& data_out)
+void add(const VW::workspace& ws1, const VW::reductions::gd& data1, const VW::workspace& ws2, VW::reductions::gd& data2,
+    VW::workspace& ws_out, VW::reductions::gd& data_out)
 {
   const size_t length = static_cast<size_t>(1) << ws_out.num_bits;
-  // When adding, output the weights from the model delta (2nd arugment to addition)
-  if (ws_out.weights.sparse) { copy_weights(ws_out.weights.sparse_weights, ws2.weights.sparse_weights, length); }
-  else { copy_weights(ws_out.weights.dense_weights, ws2.weights.dense_weights, length); }
+  if (ws_out.weights.sparse)
+  {
+    add_weights(ws_out.weights.sparse_weights, ws1.weights.sparse_weights, ws2.weights.sparse_weights, length);
+  }
+  else { add_weights(ws_out.weights.dense_weights, ws1.weights.dense_weights, ws2.weights.dense_weights, length); }
 
   for (size_t i = 0; i < data_out.per_model_states.size(); i++)
   {
@@ -293,13 +302,15 @@ void add(const VW::workspace& /* ws1 */, const VW::reductions::gd& data1, const
   }
 }
 
-void subtract(const VW::workspace& ws1, const VW::reductions::gd& data1, const VW::workspace& /* ws2 */,
+void subtract(const VW::workspace& ws1, const VW::reductions::gd& data1, const VW::workspace& ws2,
     VW::reductions::gd& data2, VW::workspace& ws_out, VW::reductions::gd& data_out)
 {
   const size_t length = static_cast<size_t>(1) << ws_out.num_bits;
-  // When subtracting, output the weights from the newer model (1st arugment to subtraction)
-  if (ws_out.weights.sparse) { copy_weights(ws_out.weights.sparse_weights, ws1.weights.sparse_weights, length); }
-  else { copy_weights(ws_out.weights.dense_weights, ws1.weights.dense_weights, length); }
+  if (ws_out.weights.sparse)
+  {
+    subtract_weights(ws_out.weights.sparse_weights, ws1.weights.sparse_weights, ws2.weights.sparse_weights, length);
+  }
+  else { subtract_weights(ws_out.weights.dense_weights, ws1.weights.dense_weights, ws2.weights.dense_weights, length); }
 
   for (size_t i = 0; i < data_out.per_model_states.size(); i++)
   {