diff --git a/imperative/src/impl/op_def.cpp b/imperative/src/impl/op_def.cpp
index ccc14ed5788f3075eb4d3096d041a41c41e5f9c6..6bf1cc4bc3d4668e3bc4db0bf1de9a55396b10a0 100644
--- a/imperative/src/impl/op_def.cpp
+++ b/imperative/src/impl/op_def.cpp
@@ -77,16 +77,16 @@ EncodedSubgraph OpDef::make_backward_graph(
         const SmallVector<bool>& output_has_grad) {
     using BackwardGraphCache =
             OpMethResultCache<EncodedSubgraph, SmallVector<bool>, SmallVector<bool>>;
-    thread_local BackwardGraphCache cache;
-    decltype(cache)::key_t cache_key{
+    thread_local auto cache = std::make_unique<BackwardGraphCache>();
+    BackwardGraphCache::key_t cache_key{
             const_cast<OpDef&>(def).shared_from_this(),
             inputs,
             {input_requires_grad, output_has_grad}};
-    auto iter = cache.find(cache_key);
-    if (iter == cache.end()) {
-        iter = cache.insert({cache_key, def.trait()->make_backward_graph(
-                                                def, inputs, input_requires_grad,
-                                                output_has_grad)})
+    auto iter = cache->find(cache_key);
+    if (iter == cache->end()) {
+        iter = cache->insert({cache_key, def.trait()->make_backward_graph(
+                                                 def, inputs, input_requires_grad,
+                                                 output_has_grad)})
                        .first;
     }
     return iter->second;
@@ -100,12 +100,12 @@ EncodedSubgraph OpDef::make_forward_graph(
         const OpDef& def, const SmallVector<LogicalTensorDesc>& inputs) {
     using ForwardGraphCache =
             OpMethResultCache<EncodedSubgraph, SmallVector<bool>, SmallVector<bool>>;
-    thread_local ForwardGraphCache cache;
-    decltype(cache)::key_t cache_key{
+    thread_local auto cache = std::make_unique<ForwardGraphCache>();
+    ForwardGraphCache::key_t cache_key{
             const_cast<OpDef&>(def).shared_from_this(), inputs};
-    auto iter = cache.find(cache_key);
-    if (iter == cache.end()) {
-        iter = cache.insert({cache_key, def.trait()->make_forward_graph(def, inputs)})
+    auto iter = cache->find(cache_key);
+    if (iter == cache->end()) {
+        iter = cache->insert({cache_key, def.trait()->make_forward_graph(def, inputs)})
                        .first;
     }
     return iter->second;
diff --git a/imperative/src/impl/ops/utility.cpp b/imperative/src/impl/ops/utility.cpp
index 89aa5f5a05263cb6d6afa824064236e1159f92c8..c67ceae605ed0b260f9686e0f2ad40c741357781 100644
--- a/imperative/src/impl/ops/utility.cpp
+++ b/imperative/src/impl/ops/utility.cpp
@@ -34,8 +34,20 @@ auto apply_on_var_node(const OpDef& def, const VarNodeArray& inputs) {
     return inputs;
 }
 
+auto make_backward_graph(
+        const OpDef& def, const SmallVector<LogicalTensorDesc>& inputs,
+        const SmallVector<bool>& input_requires_grad,
+        const SmallVector<bool>& output_has_grad) {
+    Subgraph graph;
+    graph.inputs = {1, 2, 3};
+    graph.outputs = {3};
+    graph.exprs = {};
+    return EncodedSubgraph::make(graph);
+}
+
 OP_TRAIT_REG(FastpathCopy, FastpathCopy)
         .apply_on_var_node(apply_on_var_node)
+        .make_backward_graph(make_backward_graph)
         .fallback();
 }  // namespace fastpathcopy
 }  // namespace
@@ -290,10 +302,10 @@ ComputingGraphHolder& get_computing_graph(
         std::shared_ptr<OpDef> compiled_op, SmallVector<LogicalTensorDesc> descs) {
     using ComputingGraphHolderCache =
             OpMethResultCache<std::queue<std::unique_ptr<ComputingGraphHolder>>>;
-    thread_local ComputingGraphHolderCache cache;
+    thread_local auto cache = std::make_unique<ComputingGraphHolderCache>();
     thread_local size_t nr_cg_holders = 0;
     ComputingGraphHolderCache::key_t cache_key = {compiled_op, descs};
-    auto& cg_holder_queue = cache[cache_key];
+    auto& cg_holder_queue = (*cache)[cache_key];
     std::unique_ptr<ComputingGraphHolder> holder;
     if (!cg_holder_queue.empty()) {
         // pick one