diff --git a/include/onnxruntime/core/graph/graph.h b/include/onnxruntime/core/graph/graph.h
index 361047e8d8..be49b2add7 100644
--- a/include/onnxruntime/core/graph/graph.h
+++ b/include/onnxruntime/core/graph/graph.h
@@ -654,6 +654,14 @@ class Graph {
   */
   const ONNX_NAMESPACE::TensorProto* GetConstantInitializer(const std::string& name, bool check_outer_scope) const;
 
+  /** returns the initializer's TensorProto if 'name' is an initializer (both constant and overridable). 
+  If the initializer is not found, a nullptr is returned.
+  @param check_outer_scope If true and the graph is a subgraph,
+         check ancestor graph/s for 'name' if not found in 'graph'.
+  @remarks check_outer_scope of true is not supported in a minimal build
+  */
+  const ONNX_NAMESPACE::TensorProto* GetInitializer(const std::string& name, bool check_outer_scope) const;
+
   /** Gets the Graph inputs excluding initializers.
   These are the required inputs to the Graph as the initializers can be optionally overridden via graph inputs.
   @remarks Contains no nullptr values. */
diff --git a/onnxruntime/core/framework/fallback_cpu_capability.cc b/onnxruntime/core/framework/fallback_cpu_capability.cc
index 011eaf9edb..28e309f26d 100644
--- a/onnxruntime/core/framework/fallback_cpu_capability.cc
+++ b/onnxruntime/core/framework/fallback_cpu_capability.cc
@@ -16,10 +16,18 @@ namespace onnxruntime {
 namespace {
 const int64_t kSmallInitializerThreshold = 100;
 
-bool IsSmallInitializer(const onnxruntime::GraphViewer& graph, const NodeArg* arg) {
-  const ONNX_NAMESPACE::TensorProto* initializer_tensor;
-  if (!graph.GetInitializedTensor(arg->Name(), initializer_tensor))
+static bool IsSmallInitializer(const onnxruntime::GraphViewer& graph, const NodeArg* arg) {
+  // 'true' in the function call is to let the searching for the initializer
+  // continue in the outer scopes of the current (sub-)graph if applicable
+  const ONNX_NAMESPACE::TensorProto* initializer_tensor =
+      graph.GetGraph().GetInitializer(arg->Name(), true);
+
+  // Not an initializer at all
+  if (initializer_tensor == nullptr) {
     return false;
+  }
+
+  // Check if "small" enough
   int64_t size = 1;
   for (auto& dim : initializer_tensor->dims()) {
     size *= dim;
diff --git a/onnxruntime/core/graph/graph.cc b/onnxruntime/core/graph/graph.cc
index 59bca28e45..77174cde50 100644
--- a/onnxruntime/core/graph/graph.cc
+++ b/onnxruntime/core/graph/graph.cc
@@ -2787,6 +2787,21 @@ const ONNX_NAMESPACE::TensorProto* Graph::GetConstantInitializer(const std::stri
   return initializer;
 }
 
+const ONNX_NAMESPACE::TensorProto* Graph::GetInitializer(const std::string& initializer_name,
+                                                         bool check_outer_scope) const {
+  const ONNX_NAMESPACE::TensorProto* initializer = nullptr;
+  if (GetInitializedTensor(initializer_name, initializer)) {
+    return initializer;
+  } else if (check_outer_scope && IsSubgraph()) {
+    // make sure there's not a local value with the same name. if there is it shadows any initializer in outer scope.
+    if (IsOuterScopeValue(initializer_name)) {
+      initializer = parent_graph_->GetInitializer(initializer_name, check_outer_scope);
+    }
+  }
+
+  return initializer;
+}
+
 #if !defined(ORT_MINIMAL_BUILD)
 void Graph::AddValueInfo(const NodeArg* new_value_info) {
   NodeArg* node_arg = GetNodeArg(new_value_info->Name());