Fix BeamSearch T5 if initializers are on outer scope (microsoft#23044)

### Description
This PR adds the logic needed to consider only the needed implicit
inputs on BeamSearch op in case of T5 model (encoder/decoder, 2 graphs).
The logic added is similar to what happens in the _If_ kernel setup.


### Motivation and Context
Fixes microsoft#23043

onnxruntime/contrib_ops/cpu/transformers/subgraph_base.cc

@@ -31,6 +31,7 @@ Subgraph::Subgraph(
       allocator_(nullptr),
       is_output_float16_(false) {
   num_implicit_inputs = static_cast<int>(node.ImplicitInputDefs().size());
+  used_implicit_inputs = std::vector<bool>(num_implicit_inputs, true);
 
   auto& subgraph_inputs = subgraph.GetInputs();
   auto& subgraph_outputs = subgraph.GetOutputs();
@@ -73,8 +74,18 @@ Status Subgraph::Setup(const SessionState& session_state,
   // The position_ids, attention_mask, past_0, ... are created by this operator so the name doesn't matter.
   feed_names.insert(feed_names.end(), subgraph_input_names.begin(), subgraph_input_names.end());
 
-  for (auto& entry : node.ImplicitInputDefs()) {
-    feed_names.push_back(entry->Name());
+  const auto& subgraph_map = subgraph_session_state.GetOrtValueNameIdxMap();
+
+  const auto& implicit_input_defs = node.ImplicitInputDefs();
+  for (size_t i = 0, end = num_implicit_inputs; i < end; ++i) {
+    const auto* entry = implicit_input_defs[i];
+    int idx;
+    if (subgraph_map.GetIdx(entry->Name(), idx).IsOK()) {
+      feed_names.push_back(entry->Name());
+    } else {
+      --num_implicit_inputs;
+      used_implicit_inputs[i] = false;
+    }
   }
 
   InlinedVector<OrtDevice> feed_locations;

onnxruntime/contrib_ops/cpu/transformers/subgraph_base.h

@@ -31,6 +31,7 @@ class Subgraph {
   const GraphViewer& subgraph;    // The subgraph
 
   int num_implicit_inputs;
+  std::vector<bool> used_implicit_inputs;
 
   int num_subgraph_inputs;   // Same as subgraph_input_names.size(), keep it for convenience.
   int num_subgraph_outputs;  // Same as subgraph_output_names.size()

onnxruntime/contrib_ops/cpu/transformers/subgraph_t5_decoder.cc

@@ -281,8 +281,11 @@ Status T5DecoderSubgraph::CreateInitialFeeds(
   }
 
   // Pass through implicit inputs.
-  for (const auto* entry : implicit_inputs) {
-    decoder_feeds.push_back(*entry);
+  for (size_t i = 0; i < implicit_inputs.size(); ++i) {
+    const auto* entry = implicit_inputs[i];
+    if (used_implicit_inputs[i]) {
+      decoder_feeds.push_back(*entry);
+    }
   }
 
   return Status::OK();

onnxruntime/contrib_ops/cpu/transformers/subgraph_t5_encoder.cc

@@ -145,8 +145,11 @@ Status T5EncoderSubgraph::CreateInitialFeeds(
       pinned_allocator,
       location));
 
-  for (const auto* entry : implicit_inputs) {
-    feeds.push_back(*entry);
+  for (size_t i = 0; i < implicit_inputs.size(); ++i) {
+    const auto* entry = implicit_inputs[i];
+    if (used_implicit_inputs[i]) {
+      feeds.push_back(*entry);
+    }
   }
 
   return Status::OK();

onnxruntime/test/contrib_ops/beam_search_test.cc

@@ -7,6 +7,8 @@
 #include <gsl/gsl>
 #include "core/session/onnxruntime_cxx_api.h"
 #include "test/common/cuda_op_test_utils.h"
+#include "test/providers/model_tester.h"
+#include "test/util/include/current_test_name.h"
 
 #ifdef USE_CUDA
 #include "core/providers/cuda/cuda_provider_options.h"
@@ -394,5 +396,33 @@ TEST(BeamSearchTest, GptBeamSearchFp16_VocabPadded) {
   }
 }
 
+TEST(BeamSearchTest, DummyT5) {
+#if defined(USE_CUDA) && defined(USE_DML)
+  SKIP_CUDA_TEST_WITH_DML;
+#endif
+  ModelTester tester(CurrentTestName(), ORT_TSTR("testdata/dummy_t5.onnx"));
+  tester.ConfigEp(DefaultCpuExecutionProvider());
+  tester.AddInput("encoder_input_ids", {1, 5}, {14, 6, 13, 9, 7});
+  tester.AddOutput("sequences", {1, 3, 10}, {2, 16, 6, 14, 1, 15, 6, 14, 1, 15, 2, 3, 4, 15, 6, 14, 1, 15, 6, 14, 2, 16, 6, 14, 1, 15, 6, 14, 1, 14});
+#ifdef USE_CUDA
+  tester.ConfigEp(DefaultCudaExecutionProvider());
+#endif
+  tester.RunWithConfig();
+}
+
+TEST(BeamSearchTest, DummyT5WithOuterScopeInitializers) {
+#if defined(USE_CUDA) && defined(USE_DML)
+  SKIP_CUDA_TEST_WITH_DML;
+#endif
+  ModelTester tester(CurrentTestName(), ORT_TSTR("testdata/dummy_t5_with_outer_scope_initializers.onnx"));
+  tester.ConfigEp(DefaultCpuExecutionProvider());
+  tester.AddInput("encoder_input_ids", {1, 5}, {14, 6, 13, 9, 7});
+  tester.AddOutput("sequences", {1, 3, 10}, {2, 16, 6, 14, 1, 15, 6, 14, 1, 15, 2, 3, 4, 15, 6, 14, 1, 15, 6, 14, 2, 16, 6, 14, 1, 15, 6, 14, 1, 14});
+#ifdef USE_CUDA
+  tester.ConfigEp(DefaultCudaExecutionProvider());
+#endif
+  tester.RunWithConfig();
+}
+
 }  // namespace test
 }  // namespace onnxruntime