diff --git a/imperative/src/impl/interpreter/interpreter_impl.cpp b/imperative/src/impl/interpreter/interpreter_impl.cpp
index 45fda4dbfe218f74da72236ce5e378a681c424cc..960512a48d200bbc1e218a5282ab0f1873039119 100644
--- a/imperative/src/impl/interpreter/interpreter_impl.cpp
+++ b/imperative/src/impl/interpreter/interpreter_impl.cpp
@@ -149,9 +149,13 @@ TensorInfo* ChannelImpl::put_impl(const HostTensorND& value, bool no_cache) {
         const_cast<HostTensorND&>(value).reset(value.storage(), layout);
     }
     auto info = alloc();
-    init(info, {value.layout(), value.comp_node(), value.proxy_to_default_cpu()});
+    constexpr int size_threshold = TensorShape::MAX_NDIM;
+    init(info, {value.layout(), value.comp_node()});
+    if (value.layout().total_nr_elems() <= size_threshold) {
+        info->h_value = value;
+        info->desc.value = value.proxy_to_default_cpu();
+    }
     info->mem_desc.id = StorageIdentifier::make(++m_storage_id);
-    info->h_value = value;
     m_buffer.enqueue(Put{info, value, no_cache});
     if (m_async_level == 0) {
         sync_impl();
diff --git a/imperative/src/impl/physical_tensor.cpp b/imperative/src/impl/physical_tensor.cpp
index 12df60bf472cb405ffe3db1ee13d278372d89326..84035f85817029b5632ea78670e8a4c75268457b 100644
--- a/imperative/src/impl/physical_tensor.cpp
+++ b/imperative/src/impl/physical_tensor.cpp
@@ -130,7 +130,10 @@ Tensor::Tensor(
         : m_layout(layout), m_blob(std::move(blob)), m_offset(offset), m_value(hv) {}
 
 Tensor::Tensor(const HostTensorND& hv) : Tensor(hv.layout(), hv.comp_node()) {
-    m_value = hv;
+    constexpr int size_threshold = TensorShape::MAX_NDIM;
+    if (hv.layout().total_nr_elems() <= size_threshold) {
+        m_value = hv;
+    }
     MGB_RECORD_EVENT(
             profiler::HostToDeviceEvent, hv.layout(), hv.comp_node(), hv.raw_ptr(),
             dev_tensor().raw_ptr());