perf(dispatch): speed up dispatch system

GitOrigin-RevId: eabbe3e0219ff989801751c726eb0828b1b7a740

imperative/python/megengine/core/tensor/array_method.py

@@ -16,6 +16,7 @@ import numpy as np
 from .. import _config
 from .._imperative_rt.common import CompNode
 from .._imperative_rt.core2 import SymbolVar, Tensor, apply, dtype_promotion
+from .._imperative_rt.core2 import reduce_to_scalar as _reduce_to_scalar
 from ..ops import builtin
 from . import amp
 from .indexing import getitem, setitem
@@ -508,12 +509,8 @@ def _reduce(mode):
         elif self.dtype == np.bool_:
             data = data.astype("int32")
         if axis is None:
-            data = data.reshape(-1)
             assert not keepdims, "can not set axis=None and keepdims=True"
-
-            op = builtin.Reduce(mode=mode, axis=0)
-            (result,) = apply(op, data)
-            result = _remove_axis(result, 0)
+            result = _reduce_to_scalar(builtin.Reduce(mode=mode), data)
         elif isinstance(axis, collections.abc.Iterable):
             axis = _normalize_axis(self.ndim, axis, reverse=True)
             for ai in axis:

imperative/python/megengine/optimizer/sgd.py

@@ -69,7 +69,7 @@ class SGD(Optimizer):
         inplace_mode = int(os.getenv("MEGENGINE_INPLACE_UPDATE", "0"))
         if inplace_mode:
             _neg_lr = tensor(-lr, dtype="float32")
-            c1 = tensor([1.0])
+            c1 = tensor(1.0)
 
         for param in param_group["params"]:
             if param.grad is None:

imperative/python/megengine/tensor.py

@@ -84,14 +84,15 @@ class Tensor(_Tensor, ArrayMethodMixin):
         device: str = None,
         is_const: bool = False,
         no_cache: bool = False,
-        name: str = "",
+        name: str = None,
     ):
         if name is None:
             name = ""
+        else:
+            self._set_name(name)
         self._custom_name = name
         self._name = name
         self._short_name = name
-        self._set_name(self._name)
         self._prefix = None
 
     @property

imperative/python/src/grad.cpp

@@ -46,17 +46,17 @@ void GradKeyWrapper::attach(PyObject* const* args, size_t nargs) {
     if (args[1] != Py_None) {
         callback = py::reinterpret_borrow<py::object>(args[1]);
     }
-    GenericFunction generic_callback =
-            [=](Span<ValueRef> inputs) -> std::vector<ValueRef> {
+    GenericFunction generic_callback = [=](Span<ValueRef> inputs) -> ValueRefList {
         mgb_assert(inputs.size() == 1);
         if (callback) {
             callback(TensorWrapper::make(py_tensor_type, inputs[0]));
         }
         return {};
     };
-    tw->m_tensor->reset(imperative::apply(
+    auto attached_value = imperative::apply(
             AttachGrad(m_key), tw->m_tensor->data(),
-            FunctionValue::make(generic_callback))[0]);
+            FunctionValue::make(generic_callback))[0];
+    tw->m_tensor->reset(attached_value);
 }
 
 void GradKeyWrapper::backward(GradKeyWrapper* self, py::list tensors, py::list grads) {

imperative/python/src/grad_override.cpp

@@ -98,7 +98,7 @@ ValueRef make_empty_tensor(
     return res;
 }
 
-std::optional<std::vector<ValueRef>> elemwise_grad_rule(
+std::optional<ValueRefList> elemwise_grad_rule(
         const OpDef& op, Span<ValueRef> inputs, Span<bool> inputs_require_grad,
         CustomBackward& backward) {
     auto& elemwise = op.cast_final_safe<Elemwise>();
@@ -117,7 +117,7 @@ std::optional<std::vector<ValueRef>> elemwise_grad_rule(
     maker.backward([shapes = std::move(input_shapes)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        std::vector<ValueRef> ret(2);
+        ValueRefList ret(2);
         if (!grad) {
             return ret;
         }
@@ -132,7 +132,7 @@ std::optional<std::vector<ValueRef>> elemwise_grad_rule(
     return imperative::apply(ApplyOp(op), inputs);
 }
 
-std::optional<std::vector<ValueRef>> reshape_grad_rule(
+std::optional<ValueRefList> reshape_grad_rule(
         const OpDef& op, Span<ValueRef> inputs, Span<bool> inputs_require_grad,
         CustomBackward& backward) {
     mgb_assert(inputs.size() == 2);
@@ -147,7 +147,7 @@ std::optional<std::vector<ValueRef>> reshape_grad_rule(
     maker.backward([shapes = std::move(input_shapes)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        std::vector<ValueRef> ret(2);
+        ValueRefList ret(2);
         if (!grad) {
             return ret;
         }
@@ -162,7 +162,7 @@ std::optional<std::vector<ValueRef>> reshape_grad_rule(
     return imperative::apply(ApplyOp(op), inputs);
 }
 
-std::optional<std::vector<ValueRef>> subtensor_grad_rule(
+std::optional<ValueRefList> subtensor_grad_rule(
         const OpDef& op, Span<ValueRef> inputs, Span<bool> inputs_require_grad,
         CustomBackward& backward) {
     auto&& subtensor = op.cast_final_safe<Subtensor>();
@@ -180,9 +180,9 @@ std::optional<std::vector<ValueRef>> subtensor_grad_rule(
                     grad_op_ = std::move(grad_op)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        std::vector<ValueRef> ret(1);
+        ValueRefList ret(1);
         if (grad && inputs[0]) {
-            SmallVector<ValueRef> args_(inputs.size() + 1);
+            ValueRefList args_(inputs.size() + 1);
             auto&& zeros = make_empty_tensor(grad.device(), inputs[0], grad.dtype());
             args_[0] = zeros;
             args_[1] = grad;
@@ -197,7 +197,7 @@ std::optional<std::vector<ValueRef>> subtensor_grad_rule(
     return imperative::apply(ApplyOp(op), inputs);
 }
 
-std::optional<std::vector<ValueRef>> indexingMultiAxisVec_grad_rule(
+std::optional<ValueRefList> indexingMultiAxisVec_grad_rule(
         const OpDef& op, Span<ValueRef> inputs, Span<bool> inputs_require_grad,
         CustomBackward& backward) {
     auto&& indexingMultiAxisVec = op.cast_final_safe<IndexingMultiAxisVec>();
@@ -215,9 +215,9 @@ std::optional<std::vector<ValueRef>> indexingMultiAxisVec_grad_rule(
                     grad_op_ = std::move(grad_op)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        std::vector<ValueRef> ret(1);
+        ValueRefList ret(1);
         if (grad && inputs[0]) {
-            SmallVector<ValueRef> args_(inputs.size() + 1);
+            ValueRefList args_(inputs.size() + 1);
             auto&& zeros = make_empty_tensor(grad.device(), inputs[0], grad.dtype());
             args_[0] = zeros;
             args_[1] = grad;
@@ -232,7 +232,7 @@ std::optional<std::vector<ValueRef>> indexingMultiAxisVec_grad_rule(
     return imperative::apply(ApplyOp(op), inputs);
 }
 
-std::optional<std::vector<ValueRef>> reduce_grad_rule(
+std::optional<ValueRefList> reduce_grad_rule(
         const OpDef& op, Span<ValueRef> inputs, Span<bool> inputs_require_grad,
         CustomBackward& backward) {
     auto& reduce = op.cast_final_safe<Reduce>();
@@ -251,7 +251,7 @@ std::optional<std::vector<ValueRef>> reduce_grad_rule(
     maker.backward([shapes = std::move(input_shapes)](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        std::vector<ValueRef> ret(1);
+        ValueRefList ret(1);
         if (grad && shapes[0]) {
             ret[0] = broadcast_to(grad, shapes[0]);
         }
@@ -261,7 +261,7 @@ std::optional<std::vector<ValueRef>> reduce_grad_rule(
     return imperative::apply(ApplyOp(op), inputs);
 }
 
-std::optional<std::vector<ValueRef>> addAxis_grad_rule(
+std::optional<ValueRefList> addAxis_grad_rule(
         const OpDef& op, Span<ValueRef> inputs, Span<bool> inputs_require_grad,
         CustomBackward& backward) {
     auto&& addAxis = op.cast_final_safe<AddAxis>();
@@ -274,7 +274,7 @@ std::optional<std::vector<ValueRef>> addAxis_grad_rule(
     maker.backward([grad_op_ = std::move(grad_op), flag_ = flag](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        std::vector<ValueRef> ret(1);
+        ValueRefList ret(1);
         if (grad && flag_) {
             ret[0] = imperative::apply(*grad_op_, grad)[0];
         }
@@ -284,7 +284,7 @@ std::optional<std::vector<ValueRef>> addAxis_grad_rule(
     return imperative::apply(op, inputs);
 }
 
-std::optional<std::vector<ValueRef>> removeAxis_grad_rule(
+std::optional<ValueRefList> removeAxis_grad_rule(
         const OpDef& op, Span<ValueRef> inputs, Span<bool> inputs_require_grad,
         CustomBackward& backward) {
     auto&& removeAxis = op.cast_final_safe<RemoveAxis>();
@@ -297,7 +297,7 @@ std::optional<std::vector<ValueRef>> removeAxis_grad_rule(
     maker.backward([grad_op_ = std::move(grad_op), flag_ = flag](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        std::vector<ValueRef> ret(1);
+        ValueRefList ret(1);
         if (grad && flag_) {
             ret[0] = imperative::apply(*grad_op_, grad)[0];
         }
@@ -307,7 +307,7 @@ std::optional<std::vector<ValueRef>> removeAxis_grad_rule(
     return imperative::apply(op, inputs);
 }
 
-std::optional<std::vector<ValueRef>> fastpathcopy_grad_rule(
+std::optional<ValueRefList> fastpathcopy_grad_rule(
         const OpDef& op, Span<ValueRef> inputs, Span<bool> inputs_require_grad,
         CustomBackward& backward) {
     mgb_assert(inputs.size() == 1);
@@ -316,7 +316,7 @@ std::optional<std::vector<ValueRef>> fastpathcopy_grad_rule(
     maker.backward([](Span<ValueRef> grads) {
         mgb_assert(grads.size() == 1);
         ValueRef grad = grads[0];
-        std::vector<ValueRef> ret(1);
+        ValueRefList ret(1);
         if (grad) {
             ret[0] = grad;
         }

imperative/python/src/module_trace.h

@@ -25,24 +25,23 @@ private:
     py::function m_hook_fn;
     int m_enabled = 0;
 
-    std::vector<ValueRef> apply_module_trace_hook(
-            const OpDef& op, Span<ValueRef> input_values) {
+    ValueRefList apply_module_trace_hook(const OpDef& op, Span<ValueRef> input_values) {
         py::list input_tws;
         for (auto&& input_value : input_values) {
             input_tws.append(TensorWrapper::make(py_tensor_type, input_value));
         }
         py::list output_tws = m_hook_fn(py::cast(op.shared_from_this()), *input_tws);
-        std::vector<ValueRef> outputs;
+        ValueRefList outputs(output_tws.size());
+        auto it = outputs.begin();
         for (auto&& output_tw : output_tws) {
-            outputs.push_back(
-                    TensorWrapper::try_cast(output_tw.ptr())->m_tensor->data());
+            *(it++) = TensorWrapper::try_cast(output_tw.ptr())->m_tensor->data();
         }
         return outputs;
     }
 
 public:
     ModuleTraceTransformation(py::function hook_fn) : m_hook_fn(hook_fn) {}
-    std::vector<ValueRef> apply_transformation(
+    ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) override {
         if (op.is<ApplyOp>() && m_enabled > 0) {
             auto outputs = apply_module_trace_hook(op.cast<ApplyOp>().op(), inputs);

imperative/python/src/tensor.cpp

@@ -87,7 +87,7 @@ PyObject* py_apply(
         --nargs;
 
         auto op = py::handle(py_op).cast<std::shared_ptr<OpDef>>();
-        SmallVector<ValueRef, 64> tensors(nargs);
+        SmallVector<ValueRef, 8> tensors(nargs);
 
         if (py::isinstance<PySymbolVar>(py::handle(args[0]))) {
             // swap to a special context to reuse scalar handle
@@ -100,16 +100,15 @@ PyObject* py_apply(
                     Transformation::top());
             std::make_shared<ScalarTransformation>()->register_at(
                     Transformation::top());
-            SmallVector<ValueRef> inputs(nargs);
             for (size_t i = 0; i < nargs; ++i) {
                 auto* py_input = py::handle(args[i]).cast<PySymbolVar*>();
                 ValueRef input = SymbolValue::make(py_input->m_node);
                 if (py_input->is_scalar) {
                     input = ScalarValue::make(input);
                 }
-                inputs[i] = input;
+                tensors[i] = input;
             }
-            auto outputs = imperative::apply(*op, inputs);
+            auto outputs = imperative::apply(*op, tensors);
             auto ret = pybind11::tuple(outputs.size());
             auto typeobj = py::handle(args[0]).get_type();
             for (size_t i = 0; i < outputs.size(); ++i) {
@@ -140,7 +139,7 @@ PyObject* py_apply(
             }
         }
 
-        auto outputs = imperative::apply(ApplyOp(*op), {tensors.data(), nargs});
+        auto outputs = imperative::apply(*op, tensors);
         size_t nout = outputs.size();
         auto ret = py::tuple(nout);
         for (size_t i = 0; i < nout; ++i) {
@@ -214,16 +213,10 @@ TensorWrapper::TensorWrapper(PyObject* args, PyObject* kwargs) {
             if (!name.empty()) {
                 m_tensor->reset(
                         imperative::apply(RenameValue(name), m_tensor->data())[0]);
-                mgb_assert(
-                        ((std::string&)*m_tensor->data().name()) == name,
-                        "result name incorrect");
-            }
-
-            if (data.ndim() == 0) {
-                mgb_assert(m_tensor->is_scalar(), "result should be scalar");
             }
         }
     }
+    mgb_assert(m_tensor->data());
 }
 
 PyObject* TensorWrapper::module_trace_info() {
@@ -1384,15 +1377,20 @@ void init_tensor(py::module m) {
         std::function<bool(py::object, py::object)> array_comparator;
 
         bool compare_value(ValueRef lhs, ValueRef rhs) {
-            if (!lhs.shape()->eq(*rhs.shape())) {
+            auto lvalue = lhs.numpy();
+            auto rvalue = rhs.numpy();
+            if (lvalue->shape() != rvalue->shape()) {
                 return false;
             }
-            HostTensorND lvalue = lhs.numpy()->as_nd(true);
-            HostTensorND rvalue = rhs.numpy()->as_nd(true);
+            if (lvalue->shape().is_scalar()) {
+                return lvalue->item() == rvalue->item();
+            }
+            HostTensorND lnd = lvalue->as_nd(true);
+            HostTensorND rnd = rvalue->as_nd(true);
             auto larr = py::reinterpret_steal<py::array>(
-                    npy::ndarray_from_tensor(lvalue, npy::ShareType::TRY_SHARE));
+                    npy::ndarray_from_tensor(lnd, npy::ShareType::TRY_SHARE));
             auto rarr = py::reinterpret_steal<py::array>(
-                    npy::ndarray_from_tensor(rvalue, npy::ShareType::TRY_SHARE));
+                    npy::ndarray_from_tensor(rnd, npy::ShareType::TRY_SHARE));
             return array_comparator(larr, rarr);
         }
 
@@ -1539,6 +1537,19 @@ void init_tensor(py::module m) {
                 }
             });
 
+    m.def("reduce_to_scalar", [](py::object op, py::object tensor) {
+        auto* tw = TensorWrapper::try_cast(tensor.ptr());
+        auto make_scalar_shape = [&](CompNode device) {
+            return imperative::apply(
+                    CreateTensor(CreateTensor::Const, device, dtype::Int32(), {0}),
+                    HostStorage::make(device))[0];
+        };
+        auto output = imperative::apply(
+                *op.cast<std::shared_ptr<OpDef>>(), tw->m_tensor->data(),
+                make_scalar_shape(tw->m_tensor->comp_node()))[0];
+        return TensorWrapper::make(py_tensor_type, output);
+    });
+
     m.def("name_tensor", [](std::string name, py::object tensor) {
         auto* tw = TensorWrapper::try_cast(tensor.ptr());
         auto output = imperative::apply(TraceMarkVar(name), tw->m_tensor->data())[0];
@@ -1546,9 +1557,9 @@ void init_tensor(py::module m) {
     });
 
     m.def("is_grad_attached", [](std::vector<py::object> tensors) -> bool {
-        SmallVector<ValueRef> values;
-        for (auto&& tensor : tensors) {
-            values.push_back(tensor.cast<TensorWrapper>().m_tensor->data());
+        ValueRefList values(tensors.size());
+        for (size_t i = 0; i < tensors.size(); ++i) {
+            values[i] = tensors[i].cast<TensorWrapper>().m_tensor->data();
         }
         auto outputs = imperative::apply(GetGradKey(), values);
         if (outputs[0].is<GradKeyValue>()) {
@@ -1559,9 +1570,9 @@ void init_tensor(py::module m) {
     });
 
     m.def("get_grad_key", [](std::vector<py::object> tensors) -> py::object {
-        SmallVector<ValueRef> values;
-        for (auto&& tensor : tensors) {
-            values.push_back(tensor.cast<TensorWrapper>().m_tensor->data());
+        ValueRefList values(tensors.size());
+        for (size_t i = 0; i < tensors.size(); ++i) {
+            values[i] = tensors[i].cast<TensorWrapper>().m_tensor->data();
         }
         auto outputs = imperative::apply(GetGradKey(), values);
         if (auto* grad_key_val = outputs[0].as<GradKeyValue>()) {
@@ -1578,7 +1589,7 @@ void init_tensor(py::module m) {
         mgb_assert(GradKeyWrapper::wrap_t::type().isinstance(py_key.ptr()));
         auto* key = reinterpret_cast<GradKeyWrapper::wrap_t*>(py_key.ptr())->inst();
         GenericFunction generic_backward_fn =
-                [backward_fn](Span<ValueRef> output_grads) -> std::vector<ValueRef> {
+                [backward_fn](Span<ValueRef> output_grads) -> ValueRefList {
             py::list output_grad_tws;
             for (auto&& output_grad : output_grads) {
                 if (output_grad) {
@@ -1589,23 +1600,25 @@ void init_tensor(py::module m) {
                 }
             }
             py::tuple input_grad_tws = backward_fn(*output_grad_tws);
-            std::vector<ValueRef> input_grads;
-            for (auto&& input_grad_tw : input_grad_tws) {
+            ValueRefList input_grads(input_grad_tws.size());
+            for (size_t i = 0; i < input_grad_tws.size(); ++i) {
+                auto input_grad_tw = input_grad_tws[i];
                 if (!input_grad_tw.is_none()) {
-                    input_grads.push_back(
-                            py::cast<TensorWrapper>(input_grad_tw).m_tensor->data());
+                    input_grads[i] =
+                            py::cast<TensorWrapper>(input_grad_tw).m_tensor->data();
                 } else {
-                    input_grads.push_back({});
+                    input_grads[i] = {};
                 }
             }
             return input_grads;
         };
-        SmallVector<ValueRef> values;
-        for (auto&& input : inputs) {
-            values.push_back(input.cast<TensorWrapper>().m_tensor->data());
+        ValueRefList values(inputs.size() + outputs.size());
+        for (size_t i = 0; i < inputs.size(); ++i) {
+            values[i] = inputs[i].cast<TensorWrapper>().m_tensor->data();
         }
-        for (auto&& output : outputs) {
-            values.push_back(output.cast<TensorWrapper>().m_tensor->data());
+        for (size_t i = 0; i < outputs.size(); ++i) {
+            values[i + inputs.size()] =
+                    outputs[i].cast<TensorWrapper>().m_tensor->data();
         }
         auto wrapped_output_values = imperative::apply(
                 SetGrad(key->m_key, generic_backward_fn, inputs.size()), values);

imperative/python/src/tensor.h

@@ -39,7 +39,7 @@ namespace mgb::imperative::python {
 extern interpreter::Interpreter::Channel* interpreter_for_py;
 extern PyTypeObject* py_tensor_type;
 
-struct Tensor : std::enable_shared_from_this<Tensor>, NonCopyableObj {
+struct Tensor : NonCopyableObj {
 private:
     std::string m_name;
     ValueRef m_data;
@@ -52,7 +52,7 @@ public:
     ~Tensor() = default;
 
     inline std::shared_ptr<Tensor> copy() {
-        auto ret = std::make_shared<Tensor>(m_data.unwrap());
+        auto ret = std::make_shared<Tensor>(m_data);
         ret->m_name = m_name;
         return ret;
     }

imperative/python/src/transformation.h

@@ -11,7 +11,15 @@
 
 #pragma once
 
+#include <optional>
+#include <string>
+
+#include "pybind11/pybind11.h"
+
+#include "megbrain/imperative/dispatch.h"
 #include "megbrain/imperative/transformation.h"
+#include "megbrain/imperative/value.h"
+#include "megbrain/utils/small_vector.h"
 
 namespace mgb::imperative::python {
 struct TransformationManager {
@@ -58,4 +66,14 @@ struct TransformationManager {
         return sl_instance;
     }
 };
+
+class PyValue final : public MixinValueImpl<PyValue, pybind11::object> {
+public:
+    using MixinValueImpl::MixinValueImpl;
+
+    std::string to_string() const {
+        return pybind11::str((const pybind11::object&)*this).cast<std::string>();
+    }
+};
+
 }  // namespace mgb::imperative::python

imperative/src/impl/basic_operators.cpp

@@ -45,7 +45,7 @@ CreateTensor::CreateTensor(Kind kind, CompNode device, TensorLayout layout)
             layout.is_contiguous() || layout.is_empty(), "layout should be contiguous");
 }
 
-auto CreateTensor::parse(Span<ValueRef> inputs) -> Args {
+auto CreateTensor::parse(Span<ValueRef> inputs) const -> Args {
     Args result;
     for (auto&& input : inputs) {
         if (auto host_storage = input.as_ref<HostStorage>()) {

imperative/src/impl/dispatch.cpp

@@ -16,70 +16,67 @@
 #include "megbrain/imperative/utils/map.h"
 
 namespace mgb {
+
+void imperative_log_profile_begin(const char* message);
+void imperative_log_profile(const char* message);
+void imperative_log_profile_end(const char* message);
+
 namespace imperative {
 
-std::vector<ValueRef> apply(const Operator& op, Span<ValueRef> inputs) {
-    static bool log_dispatch = MGB_GETENV("MGE_LOG_OP_DISPATCH");
-    bool enable_watch = ValueRef::any_watching();
-    auto& context = Transformation::get_context();
-    size_t& depth = context.next_transformation;
-    static const char tabs_storage[] = "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t";
-    const char* tabs = tabs_storage + sizeof(tabs_storage) / sizeof(char) - depth - 1;
-    bool log_current_dispatch = log_dispatch;
-    if (enable_watch) {
-        for (size_t i = 0; i < inputs.size(); ++i) {
-            auto& input = inputs[i];
-            if (input.watching()) {
-                log_current_dispatch = true;
-                mgb_log_debug("%sinput[%zu] is %s", tabs, i, input.to_string().c_str());
-                debug::notify_event("apply");
-            }
-        }
-    }
-    // entrance
-    std::vector<ValueRef> outputs;
-    if (depth >= context.transformations.size()) {
-        // fallback
-        if (log_current_dispatch) {
-            mgb_log_debug(
-                    "%sfallback apply %s in %s", tabs, op.to_string().c_str(),
-                    imperative::to_string(inputs).c_str());
+namespace {
+MGB_NOINLINE void copy_outputs(
+        ForwardAllocator<ValueRef>& allocator, ValueRefList& outputs) {
+    size_t nr_outputs = outputs.size();
+    if (mgb_likely(nr_outputs == 1)) {
+        ValueRef output_copy;
+        output_copy = outputs[0];
+        allocator.clear();
+        outputs = ValueRefList({output_copy});
+    } else if (!outputs.empty()) {
+        SmallVector<ValueRef> outputs_copy(nr_outputs);
+        for (size_t i = 0; i < nr_outputs; ++i) {
+            outputs_copy[i] = outputs[i];
         }
-        outputs = op.fallback(inputs);
+        outputs.clear();
+        allocator.clear();
+        outputs = {outputs_copy.begin(), outputs_copy.end()};
     } else {
-        // dispatch to stack top
-        auto& transformation = *context.transformations[depth];
-        ++depth;
-        context.frames.push_back({op, inputs});
-        CleanupGuard _{[&] {
-            context.frames.pop_back();
-            --depth;
-        }};
-        if (log_current_dispatch) {
-            mgb_log_debug(
-                    "%s%s apply %s in %s", tabs, transformation.name().c_str(),
-                    op.to_string().c_str(), imperative::to_string(inputs).c_str());
-        }
-        outputs = transformation.apply_transformation(op, inputs);
+        allocator.clear();
     }
-    if (log_current_dispatch) {
-        mgb_log_debug("%sreturn %s", tabs, imperative::to_string(outputs).c_str());
+}
+}  // namespace
+
+ValueRefList apply(const Operator& op, Span<ValueRef> inputs) {
+    auto& context = Transformation::get_context();
+    size_t& depth = context.next_transformation;
+    bool top = depth == 0;
+    auto outputs = ([&] {
+        if (mgb_unlikely(depth >= context.transformations.size())) {
+            return op.fallback(inputs);
+        } else {
+            auto& transformation = *context.transformations[depth++];
+            CleanupGuard _{[&] { --depth; }};
+            return transformation.apply_transformation(op, inputs);
+        }
+    })();
+    if (mgb_unlikely(top)) {
+        copy_outputs(context.allocator, outputs);
     }
     return outputs;
 }
 
-std::vector<ValueRef> apply(const OpDef& def, Span<ValueRef> inputs) {
+ValueRefList apply(const OpDef& def, Span<ValueRef> inputs) {
     return imperative::apply(ApplyOp{def}, inputs);
 }
 
-std::vector<ValueRef> apply(Subgraph graph, Span<ValueRef> inputs) {
+ValueRefList apply(const Subgraph& graph, Span<ValueRef> inputs) {
     SmallVector<ValueRef> inputs_storage;
     for (size_t i = 0; i < inputs.size(); ++i) {
         inputs_storage.push_back(inputs[i]);
     }
     auto apply_functor = [](std::shared_ptr<OpDef> op, SmallVector<ValueRef> inputs,
                             size_t) {
-        auto outputs = imperative::apply(ApplyOp(*op), inputs);
+        auto outputs = imperative::apply(*op, inputs);
         return SmallVector<ValueRef>(outputs.begin(), outputs.end());
     };
     auto make_const = [](TensorPtr constant) -> ValueRef {
@@ -101,7 +98,7 @@ std::vector<ValueRef> apply(Subgraph graph, Span<ValueRef> inputs) {
                 DeviceStorage::make(device_value.storage()))[0];
     };
     auto outputs = graph.apply(inputs_storage, apply_functor, make_const);
-    return {outputs.begin(), outputs.end()};
+    return ValueRefList{outputs.begin(), outputs.end()};
 }
 
 }  // namespace imperative

imperative/src/impl/interpreter/stack_manager.h

@@ -126,7 +126,7 @@ public:
             m_frames[m_frames.size() - 1 - i] = {node, node->version()};
             node = node->parent();
         }
-        mgb_assert(node->is_root(), "");
+        mgb_assert(node->is_root());
     }
     Trace() = default;
     std::string to_string() const {

imperative/src/impl/operator.cpp

@@ -3,7 +3,7 @@
 namespace mgb {
 namespace imperative {
 
-std::vector<ValueRef> Operator::fallback(Span<ValueRef> inputs) const {
+ValueRefList Operator::fallback(Span<ValueRef> inputs) const {
     mgb_throw(MegBrainError, "no fallback implementation for %s", to_string().c_str());
 }
 

imperative/src/impl/physical_tensor.cpp

@@ -99,19 +99,22 @@ Tensor::Tensor(
 
 Tensor::Tensor(const HostTensorND& hv) : Tensor(hv.layout(), hv.comp_node()) {
     constexpr int size_threshold = TensorShape::MAX_NDIM;
-    if (hv.layout().total_nr_elems() <= size_threshold) {
+    size_t nr_elems = hv.layout().total_nr_elems();
+    if (nr_elems <= size_threshold) {
         m_value = hv;
     }
-    MGB_RECORD_EVENT(
-            profiler::HostToDeviceEvent, hv.layout(), hv.comp_node(), hv.raw_ptr(),
-            dev_tensor().raw_ptr());
-    dev_tensor().copy_from_fixlayout(hv);
-    // even though hv is saved in m_value, Tensor itself could be
-    // released before copy completes
-    MGB_RECORD_EVENT(
-            profiler::HostToDeviceFinishEvent, hv.layout(), hv.comp_node(),
-            hv.raw_ptr(), dev_tensor().raw_ptr());
-    AsyncReleaser::inst()->add(hv);
+    if (nr_elems) {
+        MGB_RECORD_EVENT(
+                profiler::HostToDeviceEvent, hv.layout(), hv.comp_node(), hv.raw_ptr(),
+                dev_tensor().raw_ptr());
+        dev_tensor().copy_from_fixlayout(hv);
+        // even though hv is saved in m_value, Tensor itself could be
+        // released before copy completes
+        MGB_RECORD_EVENT(
+                profiler::HostToDeviceFinishEvent, hv.layout(), hv.comp_node(),
+                hv.raw_ptr(), dev_tensor().raw_ptr());
+        AsyncReleaser::inst()->add(hv);
+    }
 }
 
 Tensor::Tensor(const DeviceTensorND& dv, const HostTensorND& hv) {

imperative/src/impl/profiler/chrome_timeline.cpp

@@ -310,7 +310,8 @@ struct ChromeTimelineEventVisitor : EventVisitor<ChromeTimelineEventVisitor> {
         } else if constexpr (std::is_same_v<TEvent, TensorGetPropEvent>) {
             new_host_event("TensorGetProp", 'X')
                     .dur(0)
-                    .args(current_tensor->detail(current->time));
+                    .args(current_tensor->detail(current->time))
+                    .arg("kind", imperative::to_string(event.prop));
         } else if constexpr (std::is_same_v<TEvent, TensorWaitPropEvent>) {
             new_host_event("TensorWaitProp", 'B');
         } else if constexpr (std::is_same_v<TEvent, TensorWaitPropFinishEvent>) {

imperative/src/impl/transformations/eval.cpp

@@ -15,71 +15,109 @@
 namespace mgb {
 namespace imperative {
 
-std::vector<ValueRef> InterpreterTransformation::apply_transformation(
-        const Operator& op, Span<ValueRef> inputs) {
-    if (auto* op_val = op.as<ApplyOp>()) {
-        if (op_val->op().same_type<FastpathCopy>()) {
-            return {inputs[0]};
-        }
-        SmallVector<Handle> input_handles;
-        SmallVector<Handle> output_handles;
-        CleanupGuard _{[&] {
-            for (auto handle : output_handles) {
-                if (handle) {
-                    m_channel->del(handle);
-                }
+DTypeValue::ref_t InterpreterInfo::dtype() const {
+    if (!m_dtype) {
+        m_dtype = DTypeValue::make(handle()->channel()->get_dtype(handle()->handle()));
+    }
+    return m_dtype;
+}
+
+CompNodeValue::ref_t InterpreterInfo::comp_node() const {
+    if (!m_comp_node) {
+        m_comp_node = CompNodeValue::make(
+                handle()->channel()->get_device(handle()->handle()));
+    }
+    return m_comp_node;
+}
+
+ShapeValue::ref_t InterpreterInfo::shape() const {
+    if (!m_shape) {
+        m_shape = ShapeValue::make(
+                ValueShape::from(handle()->channel()->get_shape(handle()->handle())));
+    }
+    return m_shape;
+}
+
+ValueRefList InterpreterTransformation::apply_op(
+        const ApplyOp& apply_op, Span<ValueRef> inputs) {
+    if (apply_op.op().same_type<FastpathCopy>()) {
+        return {inputs[0]};
+    }
+    SmallVector<Handle> input_handles;
+    SmallVector<Handle> output_handles;
+    CleanupGuard _{[&] {
+        for (auto handle : output_handles) {
+            if (handle) {
+                m_channel->del(handle);
             }
-        }};
-        for (auto input : inputs) {
-            input_handles.push_back(*input.cast<InterpreterValue>().handle());
-        }
-        output_handles =
-                m_channel->apply_op(op_val->op().shared_from_this(), input_handles);
-        std::vector<ValueRef> outputs;
-        for (auto& handle : output_handles) {
-            outputs.push_back(InterpreterValue::make(share_handle(handle)));
-            handle = nullptr;
         }
-        return outputs;
+    }};
+    for (auto input : inputs) {
+        input_handles.push_back(input.cast<InterpreterValue>().handle()->handle());
+    }
+    output_handles =
+            m_channel->apply_op(apply_op.op().shared_from_this(), input_handles);
+    ValueRefList outputs(output_handles.size());
+    for (size_t i = 0; i < output_handles.size(); ++i) {
+        outputs[i] = InterpreterValue::make(share_handle(output_handles[i]));
+        output_handles[i] = nullptr;
+    }
+    return outputs;
+}
+
+ValueRefList InterpreterTransformation::apply_get_attr(
+        const GetAttr& get_attr, Span<ValueRef> inputs) {
+    auto& input = inputs.item().cast<InterpreterValue>();
+    ValueRef output;
+    switch (get_attr.attr()) {
+        case GetAttr::DType:
+            output = input.dtype();
+            break;
+        case GetAttr::Shape:
+            output = input.shape();
+            break;
+        case GetAttr::Device:
+            output = input.comp_node();
+            break;
+        case GetAttr::Value:
+            output = HostValue::make(m_channel->get_value(input.handle()->handle()));
+            break;
+        case GetAttr::Data:
+            output = DeviceValue::make(
+                    m_channel->get_dev_tensor(input.handle()->handle()));
+            break;
+        default:
+            mgb_throw(
+                    MegBrainError, "Interpreter: malformed GetAttr: %s",
+                    get_attr.to_string().c_str());
+    }
+    return {output};
+}
+
+ValueRefList InterpreterTransformation::apply_create_tensor(
+        const CreateTensor& create_tensor, Span<ValueRef> inputs) {
+    auto args = create_tensor.parse(inputs);
+    if (!args.device) {
+        // implies H2D
+        mgb_assert(args.host, "neither host and device value is valid");
+        return {InterpreterValue::make(share_handle(
+                m_channel->put(*args.host, args.kind == CreateTensor::Unique)))};
+    } else {
+        return {InterpreterValue::make(share_handle(m_channel->put(
+                *args.device, args.host ? *args.host : HostTensorND())))};
+    }
+}
+
+ValueRefList InterpreterTransformation::apply_transformation(
+        const Operator& op, Span<ValueRef> inputs) {
+    if (auto* op_val = op.as<ApplyOp>()) {
+        return apply_op(*op_val, inputs);
     } else if (auto* get_attr = op.as<GetAttr>()) {
-        Handle handle = *inputs[0].cast<InterpreterValue>().handle();
-        ValueRef output;
-        switch (get_attr->attr()) {
-            case GetAttr::DType:
-                output = DTypeValue::make(m_channel->get_dtype(handle));
-                break;
-            case GetAttr::Shape:
-                output = ShapeValue::make(
-                        ValueShape::from(m_channel->get_shape(handle)));
-                break;
-            case GetAttr::Device:
-                output = CompNodeValue::make(m_channel->get_device(handle));
-                break;
-            case GetAttr::Value:
-                output = HostValue::make(m_channel->get_value(handle));
-                break;
-            case GetAttr::Data:
-                output = DeviceValue::make(m_channel->get_dev_tensor(handle));
-                break;
-            default:
-                mgb_throw(
-                        MegBrainError, "Interpreter: malformed GetAttr: %s",
-                        op.to_string().c_str());
-        }
-        return {output};
+        return apply_get_attr(*get_attr, inputs);
     } else if (auto* create_tensor = op.as<CreateTensor>()) {
-        auto args = create_tensor->parse(inputs);
-        if (!args.device) {
-            // implies H2D
-            mgb_assert(args.host, "neither host and device value is valid");
-            return {InterpreterValue::make(share_handle(
-                    m_channel->put(*args.host, args.kind == CreateTensor::Unique)))};
-        } else {
-            return {InterpreterValue::make(share_handle(m_channel->put(
-                    *args.device, args.host ? *args.host : HostTensorND())))};
-        }
+        return apply_create_tensor(*create_tensor, inputs);
     } else if (auto* dtr_command = op.as<DTRCommand>()) {
-        auto handle = *inputs[0].cast<InterpreterValue>().handle();
+        auto handle = inputs[0].cast<InterpreterValue>().handle()->handle();
         switch (dtr_command->kind()) {
             case DTRCommand::Drop:
                 m_channel->drop(handle);

imperative/src/impl/transformations/grad.cpp

@@ -64,12 +64,13 @@ BackwardGraphWithClosure::BackwardGraphWithClosure(
     size_t count = std::count_if(
             save_for_backward.begin(), save_for_backward.end(), ranges::identity{});
     if (!backward_graph->precomp.empty()) {
-        SmallVector<ValueRef> inputs_and_outputs;
+        ValueRefList inputs_and_outputs(inputs.size() + outputs.size());
+        auto it = inputs_and_outputs.begin();
         for (auto&& input : inputs) {
-            inputs_and_outputs.push_back(input);
+            *it++ = input;
         }
         for (auto&& output : outputs) {
-            inputs_and_outputs.push_back(output);
+            *it++ = output;
         }
         auto precomp = imperative::apply(backward_graph->precomp, inputs_and_outputs);
         closure.reserve(precomp.size() + count);
@@ -89,7 +90,7 @@ BackwardGraphWithClosure::BackwardGraphWithClosure(
     }
 }
 void BackwardGraphWithClosure::operator()(
-        std::vector<ValueRef> grads, std::function<void(size_t, ValueRef)> receiver) {
+        ValueRefList grads, std::function<void(size_t, ValueRef)> receiver) {
     ValueRef args[closure.size() + grads.size()];
     size_t nargs = 0;
     for (auto&& value : closure) {
@@ -120,7 +121,7 @@ void BackwardGraphWithClosure::operator()(
 }
 
 void CustomBackward::operator()(
-        std::vector<ValueRef> grads, std::function<void(size_t, ValueRef)> receiver) {
+        ValueRefList grads, std::function<void(size_t, ValueRef)> receiver) {
     size_t nargs = grads.size();
     ValueRef args[nargs];
     for (size_t i = 0; i < nargs; ++i) {
@@ -201,9 +202,10 @@ void GradKey::backward() {
                 mgb_throw(AssertionError, "invalid backward");
             } else {
                 mgb_assert(grad_fn->m_slots.size() > 0);
-                std::vector<ValueRef> grads;
+                ValueRefList grads (grad_fn->m_slots.size());
+                auto iter = grads.begin();
                 for (auto&& slot : grad_fn->m_slots) {
-                    grads.push_back(slot.m_grad);
+                    *iter++ = slot.m_grad;
                 }
                 backward(grads, grad_receiver);
             }
@@ -254,21 +256,28 @@ void GradKey::freeze() {
     m_frozen = true;
 }
 
-std::vector<ValueRef> GradTransformation::apply_transformation(
+ValueRefList GradTransformation::apply_transformation(
         const Operator& op, Span<ValueRef> inputs) {
-    auto unwrap_inputs = [this](Span<ValueRef> inputs) -> SmallVector<ValueRef> {
-        SmallVector<ValueRef> unwrapped_inputs;
-        for (auto&& input : inputs) {
-            if (auto grad_value = as_grad_value(input)) {
-                unwrapped_inputs.push_back(grad_value->m_value);
+    auto fallback = [&] {
+        ValueRefList unwrapped_inputs(inputs.size());
+        for (size_t i = 0; i < inputs.size(); ++i) {
+            if (auto grad_value = as_grad_value(inputs[i])) {
+                unwrapped_inputs[i] = grad_value->m_value;
             } else {
-                unwrapped_inputs.push_back(input);
+                unwrapped_inputs[i] = inputs[i];
             }
         }
-        return unwrapped_inputs;
+        return imperative::apply(op, unwrapped_inputs);
     };
+    if (auto* get_attr = op.as<GetAttr>()) {
+        if (auto grad_value = as_grad_value(inputs.item())) {
+            return imperative::apply(op, grad_value->m_value);
+        } else {
+            return imperative::apply(op, inputs);
+        }
+    }
     if (m_suppressed) {
-        return imperative::apply(op, unwrap_inputs(inputs));
+        return fallback();
     }
     if (auto* op_val = op.as<ApplyOp>()) {
         size_t nr_require_grad = 0;
@@ -284,20 +293,21 @@ std::vector<ValueRef> GradTransformation::apply_transformation(
         if (nr_require_grad == 0) {
             return imperative::apply(op, inputs);
         }
-        SmallVector<ValueRef> captured_inputs;
-        SmallVector<bool> inputs_require_grad;
+        ValueRefList captured_inputs(inputs.size());
+        SmallVector<bool> inputs_require_grad(inputs.size());
         // capture value so that trace could assume input as same
         auto capture_value = [](ValueRef value) {
             // TODO: fastpath copy shouldn't be an OpDef
             return imperative::apply(ApplyOp(*FastpathCopy::make()), {&value, 1})[0];
         };
-        for (auto& input : inputs) {
+        for (size_t i = 0; i < inputs.size(); ++i) {
+            auto& input = inputs[i];
             if (auto grad_value = as_grad_value(input)) {
-                captured_inputs.push_back(capture_value(grad_value->m_value));
-                inputs_require_grad.push_back(true);
+                captured_inputs[i] = capture_value(grad_value->m_value);
+                inputs_require_grad[i] = true;
             } else {
-                captured_inputs.push_back(capture_value(input));
-                inputs_require_grad.push_back(false);
+                captured_inputs[i] = capture_value(input);
+                inputs_require_grad[i] = false;
             }
         }
         decltype(std::declval<GradFn>().m_backward) backward_storage;
@@ -373,9 +383,11 @@ std::vector<ValueRef> GradTransformation::apply_transformation(
         mgb_assert(!grad_fn->m_slots.empty());
         m_key->m_tape.push_back({grad_fn, op_val->op().shared_from_this()});
         return outputs;
+    } else if (op.is<CreateTensor>()) {
+        return imperative::apply(op, inputs);
     } else if (auto* attach_grad = op.as<AttachGrad>()) {
         if (!has_key(attach_grad->key())) {
-            return imperative::apply(op, unwrap_inputs(inputs));
+            return fallback();
         }
         auto tensor = inputs[0];
         GenericFunction callback = (GenericFunction&)inputs[1].cast<FunctionValue>();
@@ -386,7 +398,7 @@ std::vector<ValueRef> GradTransformation::apply_transformation(
         return {record_grad(output)};
     } else if (auto* grad_backward = op.as<GradBackward>()) {
         if (!has_key(grad_backward->key())) {
-            return imperative::apply(op, unwrap_inputs(inputs));
+            return fallback();
         }
         size_t nr_grads = inputs.size() / 2;
         mgb_assert(nr_grads * 2 == inputs.size());
@@ -416,7 +428,7 @@ std::vector<ValueRef> GradTransformation::apply_transformation(
         backward.m_output_attrs =
                 SmallVector(nr_outputs, CustomBackward::OutputAttr{true, true});
         backward.m_backward = set_grad->grad_fn();
-        std::vector<ValueRef> outputs;
+        ValueRefList outputs(nr_outputs);
         grad_fn->m_key = m_key;
         grad_fn->m_slots.resize(nr_outputs);
         grad_fn->m_dests.reserve(nr_inputs);
@@ -439,13 +451,13 @@ std::vector<ValueRef> GradTransformation::apply_transformation(
             } else {
                 grad_value = GradValue::make(output, m_key, GradSlotPtr(grad_fn, i));
             }
-            outputs.push_back(record_grad(grad_value));
+            outputs[i] = record_grad(grad_value);
         }
         m_key->m_tape.push_back({grad_fn, nullptr});
         return outputs;
     } else if (auto* gbc = op.as<GetBackwardColsure>()) {
         if (gbc->key() != m_key) {
-            return imperative::apply(op, unwrap_inputs(inputs));
+            return fallback();
         }
         return {FunctionValue::make(make_backward_closure(inputs))};
     } else if (op.is<DetachGrad>()) {
@@ -471,21 +483,8 @@ std::vector<ValueRef> GradTransformation::apply_transformation(
         } else {
             return imperative::apply(op, inputs);
         }
-    } else if (op.is<CreateTensor>()) {
-        return imperative::apply(op, inputs);
     } else {
-        SmallVector<ValueRef> unwrapped_inputs;
-        for (auto&& input : inputs) {
-            if (auto grad_value = as_grad_value(input)) {
-                unwrapped_inputs.push_back(grad_value->m_value);
-            } else {
-                unwrapped_inputs.push_back(input);
-            }
-        }
-        auto outputs = imperative::apply(
-                op, {unwrapped_inputs.data(), unwrapped_inputs.size()});
-        mgb_assert(op.kind() == Operator::GetAttrLike || outputs.empty());
-        return outputs;
+        return fallback();
     }
 }
 
@@ -500,8 +499,7 @@ GenericFunction GradTransformation::make_backward_closure(Span<ValueRef> ys) {
             y_slots.emplace_back();
         }
     }
-    GenericFunction closure = [grad_key,
-                               y_slots](Span<ValueRef> dys) -> std::vector<ValueRef> {
+    GenericFunction closure = [grad_key, y_slots](Span<ValueRef> dys) -> ValueRefList {
         size_t nr_grads = y_slots.size();
         mgb_assert(dys.size() == nr_grads);
         for (size_t i = 0; i < nr_grads; ++i) {

imperative/src/impl/transformations/lazy.cpp

@@ -21,7 +21,7 @@
 namespace mgb {
 namespace imperative {
 
-std::vector<ValueRef> LazyEvalTransformation::apply_transformation(
+ValueRefList LazyEvalTransformation::apply_transformation(
         const Operator& op, Span<ValueRef> inputs) {
     if (auto* op_val = op.as<ApplyOp>()) {
         static std::unordered_set<Typeinfo*> mm_io_ops = {
@@ -59,9 +59,9 @@ std::vector<ValueRef> LazyEvalTransformation::apply_transformation(
             mgb_assert(!output_nodes.empty());
             m_io_link = SymbolVar(output_nodes[0]);
         }
-        std::vector<ValueRef> outputs;
-        for (auto&& output_node : output_nodes) {
-            outputs.push_back(record_var(output_node));
+        ValueRefList outputs(output_nodes.size());
+        for (size_t i = 0; i < output_nodes.size(); ++i) {
+            outputs[i] = record_var(output_nodes[i]);
         }
         return outputs;
     } else if (auto* create_tensor = op.as<CreateTensor>()) {

imperative/src/impl/transformations/scalar.cpp

@@ -19,26 +19,8 @@ namespace imperative {
 
 namespace {
 
-using ScalarRule = std::function<std::vector<ValueRef>(const OpDef&, Span<ValueRef>)>;
-static std::unordered_map<
-        Typeinfo*, std::function<std::vector<ValueRef>(const OpDef&, Span<ValueRef>)>>
-        scalar_rules;
-
-ValueRef unwrap_input(ValueRef input) {
-    if (auto scalar_input = input.as_ref<ScalarValue>()) {
-        return scalar_input->value();
-    } else {
-        return input;
-    }
-}
-
-std::vector<ValueRef> unwrap_inputs(Span<ValueRef> inputs) {
-    std::vector<ValueRef> unwrapped_inputs;
-    for (auto&& input : inputs) {
-        unwrapped_inputs.push_back(unwrap_input(input));
-    }
-    return unwrapped_inputs;
-}
+using ScalarRule = ValueRefList (*)(const OpDef&, Span<ValueRef>, Span<bool>);
+static std::unordered_map<Typeinfo*, ScalarRule> scalar_rules;
 
 ValueRef make_scalar_shape(CompNode device) {
     HostTensorND scalar_shape(device, {1}, dtype::Int32());
@@ -49,9 +31,6 @@ ValueRef make_scalar_shape(CompNode device) {
 }
 
 bool is_scalar_shape(ValueRef shape) {
-    if (shape.is<ScalarValue>()) {
-        return false;
-    }
     // may have performance issue
     auto shape_of_shape = shape.shape();
     if (!shape_of_shape) {
@@ -61,74 +40,65 @@ bool is_scalar_shape(ValueRef shape) {
     return *shape_of_shape == ValueShape{0};
 }
 
-template <typename T>
-void register_scalar_rule(std::vector<ValueRef> (*rule)(const T&, Span<ValueRef>)) {
-    scalar_rules[T::typeinfo()] = [rule](const OpDef& def, Span<ValueRef> inputs) {
-        return (*rule)(def.cast_final_safe<T>(), inputs);
+template <typename T, ValueRefList (*rule)(const T&, Span<ValueRef>, Span<bool>)>
+void register_scalar_rule() {
+    scalar_rules[T::typeinfo()] = [](const OpDef& def, Span<ValueRef> inputs,
+                                     Span<bool> inputs_mask) {
+        return (*rule)(def.cast_final_safe<T>(), inputs, inputs_mask);
     };
 }
 
-std::vector<ValueRef> elemwise_rule(const Elemwise& elem, Span<ValueRef> inputs) {
+template <typename TOpDef, size_t nr_inputs>
+ValueRefList elemwise_rule(
+        const TOpDef& op_def, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+    if constexpr (nr_inputs != 0) {
+        mgb_assert(inputs.size() == inputs.size(), "inputs size mismatch");
+    }
     bool all_scalar = true;
-    for (auto&& input : inputs) {
-        if (!input.is<ScalarValue>()) {
+    for (auto&& input_mask : inputs_mask) {
+        if (!input_mask) {
             all_scalar = false;
-            break;
         }
     }
-    auto output = imperative::apply(elem, unwrap_inputs(inputs))[0];
+    auto outputs = imperative::apply(op_def, inputs);
     if (all_scalar) {
-        return {ScalarValue::make(output)};
-    } else {
-        return {output};
+        outputs[0] = ScalarValue::make(outputs[0]);
     }
+    return outputs;
 }
 
-std::vector<ValueRef> remove_axis_rule(
-        const RemoveAxis& remove_axis, Span<ValueRef> inputs) {
-    mgb_assert(inputs.size() == 1);
-    mgb_assert(!inputs[0].is<ScalarValue>());
-    auto output = imperative::apply(remove_axis, inputs)[0];
-    bool is_scalar = inputs[0].shape()->ndim == remove_axis.axis.size();
+ValueRefList remove_axis_rule(
+        const RemoveAxis& remove_axis, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+    mgb_assert(!inputs_mask.item());
+    bool is_scalar = inputs.item().shape()->ndim == remove_axis.axis.size();
+    if (is_scalar && remove_axis.axis.size() == 1) {
+        return {ScalarValue::make(inputs.item())};
+    }
+    auto outputs = imperative::apply(remove_axis, inputs);
     if (is_scalar) {
-        return {ScalarValue::make(output)};
-    } else {
-        return {output};
+        outputs[0] = ScalarValue::make(outputs[0]);
     }
+    return outputs;
 }
 
-std::vector<ValueRef> reduce_rule(const Reduce& reduce, Span<ValueRef> inputs) {
+ValueRefList reduce_rule(
+        const Reduce& reduce, Span<ValueRef> inputs, Span<bool> inputs_mask) {
     if (inputs.size() == 1) {
-        return imperative::apply(reduce, unwrap_inputs(inputs));
+        return imperative::apply(reduce, inputs);
     }
     mgb_assert(inputs.size() == 2);
     bool is_scalar = is_scalar_shape(inputs[1]);
     if (is_scalar) {
-        auto unwrapped_input = unwrap_input(inputs[0]);
-        CompNode device = *unwrapped_input.device();
-        return {ScalarValue::make(imperative::apply(
-                reduce, unwrapped_input, make_scalar_shape(device))[0])};
-    }
-    auto output = imperative::apply(reduce, unwrap_inputs(inputs))[0];
-    if (is_scalar) {
-        return {ScalarValue::make(output)};
-    } else {
-        return {output};
-    }
-}
-
-std::vector<ValueRef> typecvt_rule(const TypeCvt& typecvt, Span<ValueRef> inputs) {
-    mgb_assert(inputs.size() == 1);
-    if (auto scalar_input = inputs[0].as_ref<ScalarValue>()) {
+        CompNode device = *inputs[0].device();
         return {ScalarValue::make(
-                imperative::apply(typecvt, scalar_input->value())[0])};
-    } else {
-        return imperative::apply(typecvt, inputs);
+                imperative::apply(reduce, inputs[0], make_scalar_shape(device))[0])};
     }
+    return imperative::apply(reduce, inputs);
 }
 
-std::vector<ValueRef> collective_comm_rule(
-        const CollectiveComm& collective_comm, Span<ValueRef> inputs) {
+ValueRefList collective_comm_rule(
+        const CollectiveComm& collective_comm, Span<ValueRef> inputs,
+        Span<bool> inputs_mask) {
     mgb_assert(inputs.size() == 1);
     static std::unordered_set<CollectiveComm::Mode> modes = {
             CollectiveComm::Mode::ALL_REDUCE_MAX, CollectiveComm::Mode::ALL_REDUCE_MIN,
@@ -138,17 +108,17 @@ std::vector<ValueRef> collective_comm_rule(
     if (modes.count(collective_comm.mode) == 0) {
         return imperative::apply(collective_comm, inputs);
     }
-    if (auto scalar_input = inputs[0].as_ref<ScalarValue>()) {
-        return {ScalarValue::make(
-                imperative::apply(collective_comm, scalar_input->value())[0])};
+    if (inputs_mask.item()) {
+        return {ScalarValue::make(imperative::apply(collective_comm, inputs[0])[0])};
     } else {
         return imperative::apply(collective_comm, inputs);
     }
 }
 
-std::vector<ValueRef> param_pack_split_rule(
-        const ParamPackSplit& param_pack_split, Span<ValueRef> inputs) {
-    auto outputs = imperative::apply(param_pack_split, unwrap_inputs(inputs));
+ValueRefList param_pack_split_rule(
+        const ParamPackSplit& param_pack_split, Span<ValueRef> inputs,
+        Span<bool> inputs_mask) {
+    auto outputs = imperative::apply(param_pack_split, inputs);
     size_t nr_outputs = outputs.size();
     mgb_assert(nr_outputs == param_pack_split.shapes.size());
     for (size_t i = 0; i < nr_outputs; ++i) {
@@ -159,29 +129,28 @@ std::vector<ValueRef> param_pack_split_rule(
     return outputs;
 }
 
-std::vector<ValueRef> dot_rule(const Dot& dot, Span<ValueRef> inputs) {
-    return {ScalarValue::make(imperative::apply(dot, unwrap_inputs(inputs))[0])};
+ValueRefList dot_rule(const Dot& dot, Span<ValueRef> inputs, Span<bool> inputs_mask) {
+    return {ScalarValue::make(imperative::apply(dot, inputs)[0])};
 }
 
-std::vector<ValueRef> add_axis_rule(const AddAxis& add_axis, Span<ValueRef> inputs) {
+ValueRefList add_axis_rule(
+        const AddAxis& add_axis, Span<ValueRef> inputs, Span<bool> inputs_mask) {
     mgb_assert(inputs.size() == 1);
-    if (auto scalar_input = inputs[0].as_ref<ScalarValue>()) {
+    if (inputs_mask.item()) {
         mgb_assert(add_axis.axis[0] == 0);
         if (add_axis.axis.size() == 1) {
-            return {scalar_input->value()};
+            return {inputs[0]};
         } else {
             std::vector<int32_t> axis(add_axis.axis.begin() + 1, add_axis.axis.end());
-            return imperative::apply(
-                    ApplyOp(*AddAxis::make(axis, add_axis.scope())),
-                    scalar_input->value());
+            return imperative::apply(*AddAxis::make(axis, add_axis.scope()), inputs[0]);
         }
     } else {
         return imperative::apply(add_axis, inputs);
     }
 }
 
-std::vector<ValueRef> remote_recv_rule(
-        const RemoteRecv& remote_recv, Span<ValueRef> inputs) {
+ValueRefList remote_recv_rule(
+        const RemoteRecv& remote_recv, Span<ValueRef> inputs, Span<bool> inputs_mask) {
     if (remote_recv.shape.empty()) {
         std::vector<int32_t> shape = {1};
         auto remote_recv_no_scalar = RemoteRecv::make(
@@ -189,32 +158,32 @@ std::vector<ValueRef> remote_recv_rule(
                 remote_recv.rank_from, remote_recv.cn, shape, remote_recv.dtype,
                 remote_recv.backend);
         remote_recv_no_scalar->set_scope(remote_recv.scope());
-        return imperative::apply(
-                ApplyOp(*remote_recv_no_scalar), unwrap_inputs(inputs));
+        return imperative::apply(ApplyOp(*remote_recv_no_scalar), inputs);
     } else {
-        return imperative::apply(remote_recv, unwrap_inputs(inputs));
+        return imperative::apply(remote_recv, inputs);
     }
 }
 
-std::vector<ValueRef> check_no_finite_rule(
-        const CheckNonFinite& check_no_finite, Span<ValueRef> inputs) {
-    auto outputs = imperative::apply(check_no_finite, unwrap_inputs(inputs));
+ValueRefList check_no_finite_rule(
+        const CheckNonFinite& check_no_finite, Span<ValueRef> inputs,
+        Span<bool> inputs_mask) {
+    auto outputs = imperative::apply(check_no_finite, inputs);
     mgb_assert(outputs.size() == inputs.size() + 1, "output size mismatch");
     outputs.back() = ScalarValue::make(outputs.back());
     for (size_t i = 0; i < inputs.size(); ++i) {
-        if (inputs[i].is<ScalarValue>()) {
+        if (inputs_mask[i]) {
             outputs[i] = ScalarValue::make(outputs[i]);
         }
     }
     return outputs;
 }
 
-std::vector<ValueRef> subtensor_rule(
-        const Subtensor& subtensor, Span<ValueRef> inputs) {
+ValueRefList subtensor_rule(
+        const Subtensor& subtensor, Span<ValueRef> inputs, Span<bool> inputs_mask) {
     mgb_assert(inputs.size() >= 1);
     auto input = inputs[0];
     bool is_scalar;
-    mgb_assert(!input.is<ScalarValue>(), "subtensor shouldn't have scalar input");
+    mgb_assert(!inputs_mask[0], "subtensor shouldn't have scalar input");
     if (auto shape = input.shape()) {
         size_t ndim = input.shape()->ndim;
         for (auto&& [axis, begin, end, step, idx] : subtensor.items) {
@@ -226,25 +195,25 @@ std::vector<ValueRef> subtensor_rule(
     } else {
         is_scalar = false;
     }
-    auto output = imperative::apply(subtensor, unwrap_inputs(inputs))[0];
+    auto outputs = imperative::apply(subtensor, inputs);
     if (is_scalar) {
-        return {ScalarValue::make(output)};
-    } else {
-        return {output};
+        outputs[0] = ScalarValue::make(outputs[0]);
     }
+    return outputs;
 }
 
-std::vector<ValueRef> get_var_shape_rule(
-        const GetVarShape& get_var_shape, Span<ValueRef> inputs) {
+ValueRefList get_var_shape_rule(
+        const GetVarShape& get_var_shape, Span<ValueRef> inputs,
+        Span<bool> inputs_mask) {
     bool all_scalar = true;
     mgb_assert(inputs.size() >= 1);
-    for (auto&& input : inputs) {
-        if (!input.is<ScalarValue>()) {
+    for (auto&& input_mask : inputs_mask) {
+        if (!input_mask) {
             all_scalar = false;
         }
     }
     if (all_scalar) {
-        auto device = inputs[0].cast<ScalarValue>().value().device();
+        auto device = inputs[0].device();
         auto storage = HostStorage::make(*device);
         // storage->ensure_size(1);
         return imperative::apply(
@@ -252,88 +221,49 @@ std::vector<ValueRef> get_var_shape_rule(
                         CreateTensor::Const, *device, dtype::Int32(), ValueShape{0}),
                 storage);
     } else {
-        return imperative::apply(get_var_shape, unwrap_inputs(inputs));
-    }
-}
-
-std::vector<ValueRef> fastpath_copy_rule(
-        const FastpathCopy& fastpath_copy, Span<ValueRef> inputs) {
-    mgb_assert(inputs.size() == 1);
-    bool is_scalar = inputs[0].is<ScalarValue>();
-    auto output = imperative::apply(fastpath_copy, unwrap_inputs(inputs))[0];
-    if (is_scalar) {
-        return {ScalarValue::make(output)};
-    } else {
-        return {output};
+        return imperative::apply(get_var_shape, inputs);
     }
 }
 
-std::vector<ValueRef> reshape_rule(const Reshape& reshape, Span<ValueRef> inputs) {
+ValueRefList reshape_rule(
+        const Reshape& reshape, Span<ValueRef> inputs, Span<bool> inputs_mask) {
     mgb_assert(inputs.size() == 2);
     bool is_scalar = is_scalar_shape(inputs[1]);
-    auto unwrapped_input = inputs[0].is<ScalarValue>()
-                                 ? inputs[0].cast<ScalarValue>().value()
-                                 : inputs[0];
     if (is_scalar) {
         return {ScalarValue::make(imperative::apply(
-                reshape, unwrapped_input,
-                make_scalar_shape(*unwrapped_input.device()))[0])};
+                reshape, inputs[0], make_scalar_shape(*inputs[0].device()))[0])};
     } else {
-        return imperative::apply(reshape, unwrap_inputs(inputs));
+        return imperative::apply(reshape, inputs);
     }
 }
 
-std::vector<ValueRef> broadcast_rule(
-        const Broadcast& broadcast, Span<ValueRef> inputs) {
+ValueRefList broadcast_rule(
+        const Broadcast& broadcast, Span<ValueRef> inputs, Span<bool> inputs_mask) {
     mgb_assert(inputs.size() == 2);
     bool is_scalar = is_scalar_shape(inputs[1]);
-    auto unwrapped_input = inputs[0].is<ScalarValue>()
-                                 ? inputs[0].cast<ScalarValue>().value()
-                                 : inputs[0];
     if (is_scalar) {
         return {ScalarValue::make(imperative::apply(
-                broadcast, unwrapped_input,
-                make_scalar_shape(*unwrapped_input.device()))[0])};
-    } else {
-        return imperative::apply(broadcast, unwrap_inputs(inputs));
-    }
-}
-
-std::vector<ValueRef> copy_rule(const Copy& copy, Span<ValueRef> inputs) {
-    mgb_assert(inputs.size() == 1);
-    bool is_scalar = inputs[0].is<ScalarValue>();
-    if (is_scalar) {
-        return {ScalarValue::make(imperative::apply(copy, unwrap_inputs(inputs))[0])};
-    } else {
-        return imperative::apply(copy, unwrap_inputs(inputs));
-    }
-}
-
-std::vector<ValueRef> inplace_add_rule(
-        const InplaceAdd& inplace_add, Span<ValueRef> inputs) {
-    mgb_assert(inputs.size() == 4);
-    bool is_scalar = inputs[0].is<ScalarValue>();
-    if (is_scalar) {
-        return {ScalarValue::make(
-                imperative::apply(inplace_add, unwrap_inputs(inputs))[0])};
+                broadcast, inputs[0], make_scalar_shape(*inputs[0].device()))[0])};
     } else {
-        return imperative::apply(inplace_add, unwrap_inputs(inputs));
+        return imperative::apply(broadcast, inputs);
     }
 }
 
 template <typename T>
-std::vector<ValueRef> subgraph_op_rule(const T& op, Span<ValueRef> inputs) {
+ValueRefList subgraph_op_rule(
+        const T& op, Span<ValueRef> inputs, Span<bool> inputs_mask,
+        const Type<ScalarValue>& scalar_type) {
     // TODO: add flag instead of assume
     bool all_scalar = true;
-    for (auto&& input : inputs) {
-        if (!input.is<ScalarValue>()) {
+    for (auto&& input_mask : inputs_mask) {
+        if (!input_mask) {
             all_scalar = false;
         }
     }
-    auto outputs = imperative::apply(op, unwrap_inputs(inputs));
+    auto outputs = imperative::apply(op, inputs);
     if (all_scalar) {
         for (auto& output : outputs) {
-            output = ScalarValue::make(output);
+            output = scalar_type.make(output);
         }
     }
     return outputs;
@@ -341,67 +271,54 @@ std::vector<ValueRef> subgraph_op_rule(const T& op, Span<ValueRef> inputs) {
 
 struct ScalarRuleRegistry {
     ScalarRuleRegistry() {
-        register_scalar_rule(elemwise_rule);
-        register_scalar_rule(remove_axis_rule);
-        register_scalar_rule(reduce_rule);
-        register_scalar_rule(typecvt_rule);
-        register_scalar_rule(collective_comm_rule);
-        register_scalar_rule(param_pack_split_rule);
-        register_scalar_rule(dot_rule);
-        register_scalar_rule(add_axis_rule);
-        register_scalar_rule(remote_recv_rule);
-        register_scalar_rule(check_no_finite_rule);
-        register_scalar_rule(subtensor_rule);
-        register_scalar_rule(get_var_shape_rule);
-        register_scalar_rule(fastpath_copy_rule);
-        register_scalar_rule(reshape_rule);
-        register_scalar_rule(broadcast_rule);
-        register_scalar_rule(copy_rule);
-        register_scalar_rule(inplace_add_rule);
-        register_scalar_rule(subgraph_op_rule<SubgraphOp>);
-        register_scalar_rule(subgraph_op_rule<CompiledOp>);
+        register_scalar_rule<Elemwise, elemwise_rule<Elemwise, 0>>();
+        register_scalar_rule<RemoveAxis, remove_axis_rule>();
+        register_scalar_rule<Reduce, reduce_rule>();
+        register_scalar_rule<TypeCvt, elemwise_rule<TypeCvt, 1>>();
+        register_scalar_rule<CollectiveComm, collective_comm_rule>();
+        register_scalar_rule<ParamPackSplit, param_pack_split_rule>();
+        register_scalar_rule<Dot, dot_rule>();
+        register_scalar_rule<AddAxis, add_axis_rule>();
+        register_scalar_rule<RemoteRecv, remote_recv_rule>();
+        register_scalar_rule<CheckNonFinite, check_no_finite_rule>();
+        register_scalar_rule<Subtensor, subtensor_rule>();
+        register_scalar_rule<GetVarShape, get_var_shape_rule>();
+        register_scalar_rule<FastpathCopy, elemwise_rule<FastpathCopy, 1>>();
+        register_scalar_rule<Reshape, reshape_rule>();
+        register_scalar_rule<Broadcast, broadcast_rule>();
+        register_scalar_rule<Copy, elemwise_rule<Copy, 1>>();
+        register_scalar_rule<InplaceAdd, elemwise_rule<InplaceAdd, 4>>();
+        register_scalar_rule<SubgraphOp, subgraph_op_rule<SubgraphOp>>();
+        register_scalar_rule<CompiledOp, subgraph_op_rule<CompiledOp>>();
     }
 } _;
 }  // namespace
 
-std::vector<ValueRef> ScalarTransformation::apply_transformation(
-        const Operator& op, Span<ValueRef> inputs) {
-    if (auto apply_op = op.as<ApplyOp>()) {
-        auto iter = scalar_rules.find(apply_op->op().dyn_typeinfo());
-        if (iter != scalar_rules.end()) {
-            return iter->second(apply_op->op(), inputs);
-        } else {
-            // TODO: repeat op
-            return imperative::apply(op, unwrap_inputs(inputs));
-        }
-    } else if (auto* create_tensor = op.as<CreateTensor>()) {
-        if (create_tensor->shape().is_scalar()) {
-            ValueShape scalar_shape = {1};
-            CreateTensor scalar_op(
-                    create_tensor->kind(), create_tensor->device(),
-                    create_tensor->dtype(), scalar_shape);
-            return {ScalarValue::make(imperative::apply(scalar_op, inputs)[0])};
-        } else {
-            return imperative::apply(op, inputs);
-        }
-    } else if (auto* get_attr = op.as<GetAttr>()) {
-        bool is_scalar = inputs.as_array<1>()[0].is<ScalarValue>();
-        auto output = imperative::apply(op, unwrap_inputs(inputs))[0];
-        if (!is_scalar) {
-            return {output};
+ValueRefList ScalarTransformation::apply_get_attr(
+        const GetAttr& get_attr, Span<ValueRef> inputs) {
+    auto&& input = inputs.item();
+    bool is_scalar = input.is<ScalarValue>();
+    if (!is_scalar) {
+        return imperative::apply(get_attr, input);
+    }
+    auto unwrapped_input = input.cast<ScalarValue>().value();
+    if (get_attr.attr() == GetAttr::Shape) {
+        if (!m_empty_shape) {
+            m_empty_shape = ShapeValue::make();
         }
-        switch (get_attr->attr()) {
-            case GetAttr::Shape: {
-                // Scalar Shape
-                return {ShapeValue::make()};
-            }
+        return {m_empty_shape};
+    } else {
+        auto outputs = imperative::apply(get_attr, unwrapped_input);
+        auto& output = outputs[0];
+        switch (get_attr.attr()) {
             case GetAttr::Value: {
                 auto& hv = output.cast<HostValue>();
                 mgb_assert(
                         hv.shape() == ValueShape({1}),
                         "underlying value should has shape {1}, got %s",
                         hv.shape().to_string().c_str());
-                return {HostValue::make(hv.dtype(), ValueShape(), hv.storage())};
+                output = HostValue::make(hv.dtype(), ValueShape(), hv.storage());
+                break;
             }
             case GetAttr::Data: {
                 auto& dv = output.cast<DeviceValue>();
@@ -409,22 +326,67 @@ std::vector<ValueRef> ScalarTransformation::apply_transformation(
                         dv.shape() == ValueShape({1}),
                         "underlying value should has shape {1}, got %s",
                         dv.shape().to_string().c_str());
-                return {DeviceValue::make(dv.dtype(), ValueShape(), dv.storage())};
+                output = DeviceValue::make(dv.dtype(), ValueShape(), dv.storage());
+                break;
             }
             default:
-                return {output};
+                break;
+        }
+        return outputs;
+    }
+}
+
+ValueRefList ScalarTransformation::apply_transformation(
+        const Operator& op, Span<ValueRef> inputs) {
+    if (auto* get_attr = op.as<GetAttr>()) {
+        // fastpath for GetAttr
+        return apply_get_attr(*get_attr, inputs);
+    }
+    size_t nr_inputs = inputs.size();
+    ValueRefList unwrapped_inputs(nr_inputs);
+    bool inputs_mask[nr_inputs];
+    for (size_t i = 0; i < inputs.size(); ++i) {
+        if (auto scalar_value = inputs[i].as_ref<ScalarValue>()) {
+            unwrapped_inputs[i] = scalar_value->value();
+            inputs_mask[i] = true;
+        } else {
+            unwrapped_inputs[i] = inputs[i];
+            inputs_mask[i] = false;
+        }
+    }
+    auto fallback = [&] { return imperative::apply(op, unwrapped_inputs); };
+    if (auto apply_op = op.as<ApplyOp>()) {
+        auto iter = scalar_rules.find(apply_op->op().dyn_typeinfo());
+        if (iter != scalar_rules.end()) {
+            return iter->second(
+                    apply_op->op(), unwrapped_inputs, {inputs_mask, nr_inputs});
+        } else {
+            // TODO: repeat op
+            return fallback();
+        }
+    } else if (auto* create_tensor = op.as<CreateTensor>()) {
+        if (create_tensor->shape().is_scalar()) {
+            ValueShape scalar_shape = {1};
+            CreateTensor scalar_op(
+                    create_tensor->kind(), create_tensor->device(),
+                    create_tensor->dtype(), scalar_shape);
+            return {ScalarValue::make(imperative::apply(scalar_op, inputs)[0])};
+        } else {
+            return imperative::apply(op, inputs);
         }
     } else if (op.as<IsScalar>()) {
-        return {BoolValue::make(inputs.as_array<1>()[0].is<ScalarValue>())};
+        mgb_assert(nr_inputs == 1);
+        return {BoolValue::make(inputs_mask[0])};
     } else if (op.is<Operator::IdentityLike>()) {
-        bool is_scalar = inputs.as_array<1>()[0].is<ScalarValue>();
+        mgb_assert(nr_inputs == 1);
+        bool is_scalar = inputs_mask[0];
+        auto outputs = fallback();
         if (is_scalar) {
-            return {ScalarValue::make(imperative::apply(op, unwrap_inputs(inputs))[0])};
-        } else {
-            return imperative::apply(op, inputs);
+            outputs[0] = ScalarValue::make(outputs[0]);
         }
+        return outputs;
     } else {
-        return imperative::apply(op, unwrap_inputs(inputs));
+        return fallback();
     }
 };
 

imperative/src/impl/transformations/tangent.cpp

+/**
+ * \file imperative/src/impl/transformations/tangent.cpp
+ * MegEngine is Licensed under the Apache License, Version 2.0 (the "License")
+ *
+ * Copyright (c) 2014-2021 Megvii Inc. All rights reserved.
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT ARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ */
+
+#include "megbrain/imperative/transformations/tangent.h"
+
+namespace mgb {
+namespace imperative {
+
+ValueRefList TangentTransformation::apply_transformation(
+        const Operator& op, Span<ValueRef> inputs) {
+    if (auto* apply_op = op.as<ApplyOp>()) {
+    }
+    mgb_assert(false);
+}
+
+}  // namespace imperative
+}  // namespace mgb

imperative/src/impl/transformations/trace.cpp

@@ -153,7 +153,7 @@ VarNodeArray TraceResult::dump(
     return output_nodes;
 }
 
-std::vector<ValueRef> TracingTransformation::apply_transformation(
+ValueRefList TracingTransformation::apply_transformation(
         const Operator& op, Span<ValueRef> inputs) {
     if (auto* op_value = op.as<ApplyOp>()) {
         SmallVector<ValueRef> unwrapped_inputs;
@@ -180,11 +180,12 @@ std::vector<ValueRef> TracingTransformation::apply_transformation(
         }
         const_cast<OpDef&>(op_value->op()).set_scope(scopes_join);
         auto unwrapped_outputs = imperative::apply(op, unwrapped_inputs);
-        std::vector<ValueRef> wrapped_outputs;
+        ValueRefList wrapped_outputs(unwrapped_outputs.size());
         SmallVector<size_t> output_ids;
-        for (auto&& output : unwrapped_outputs) {
+        for (size_t i = 0; i < unwrapped_outputs.size(); ++i) {
+            auto&& output = unwrapped_outputs[i];
             auto wrapped_output = record_var(output, false, VarKind::Internal);
-            wrapped_outputs.push_back(wrapped_output);
+            wrapped_outputs[i] = wrapped_output;
             output_ids.push_back(wrapped_output->id());
         }
         m_seq.push_back({op_value->op().shared_from_this(), input_ids, output_ids});
@@ -375,6 +376,11 @@ void CompiledTransformation::compile() {
         return accessor;
     };
     std::vector<VarAccessor> var_accessors(m_vars.size());
+    auto exc_setter = std::bind(
+            &CompiledTransformation::set_exception, this, std::placeholders::_1);
+    for (auto&& accessor : var_accessors) {
+        accessor.exc_setter = exc_setter;
+    }
     for (auto&& item : m_seq) {
         bool require_link = bool(item.op) && mm_io_ops.count(item.op->dyn_typeinfo());
         VarNodeArray input_vars;
@@ -509,8 +515,8 @@ void CompiledTransformation::trace_input(size_t id, ValueRef value) {
     }
 }
 
-TracedValue::ref_t CompiledTransformation::trace_output(size_t id) {
-    auto traced_value = TracedValue::make(id);
+auto CompiledTransformation::trace_output(size_t id) -> TracedValue::ref_t {
+    auto traced_value = TracedValue::make(id, &m_vars[id], &m_var_accessors[id]);
     m_weak_values.push_back(traced_value);
     return traced_value;
 }
@@ -520,64 +526,99 @@ TraceResult::SeqItem& CompiledTransformation::next_instruction() {
     return m_seq[m_pc++];
 }
 
-std::vector<ValueRef> CompiledTransformation::apply_transformation(
+ShapeValue::ref_t CompiledTransformation::TracedInfo::shape() const {
+    if (!m_shape) {
+        trace_assert(m_accessor->shape_getter, "shape unreadable");
+        m_shape = ShapeValue::make(ValueShape::from(m_accessor->shape_getter()));
+    }
+    return m_shape;
+}
+
+DTypeValue::ref_t CompiledTransformation::TracedInfo::dtype() const {
+    if (!m_dtype) {
+        m_dtype = DTypeValue::make(m_var->dtype);
+    }
+    return m_dtype;
+}
+
+CompNodeValue::ref_t CompiledTransformation::TracedInfo::comp_node() const {
+    if (!m_comp_node) {
+        m_comp_node = CompNodeValue::make(m_var->device);
+    }
+    return m_comp_node;
+}
+auto CompiledTransformation::TracedInfo::accessor() const -> const VarAccessor& {
+    return *m_accessor;
+}
+
+ValueRefList CompiledTransformation::apply_op(
+        const ApplyOp& apply_op, Span<ValueRef> inputs) {
+    auto& item = next_instruction();
+    trace_assert(inputs.size() == item.inputs.size(), "input size mismatch");
+    trace_assert(apply_op.op().is_same(*item.op), "operator mismatch");
+    for (size_t i = 0; i < inputs.size(); ++i) {
+        trace_input(item.inputs[i], inputs[i]);
+    }
+    ValueRefList outputs(item.outputs.size());
+    for (size_t i = 0; i < item.outputs.size(); ++i) {
+        outputs[i] = trace_output(item.outputs[i]);
+    }
+    return outputs;
+}
+
+ValueRefList CompiledTransformation::apply_get_attr(
+        const GetAttr& get_attr, Span<ValueRef> inputs) {
+    if (auto* traced_value = inputs[0].as<TracedValue>()) {
+        ValueRef output;
+        auto& var_accessor = traced_value->accessor();
+        switch (get_attr.attr()) {
+            case GetAttr::Shape:
+                output = traced_value->shape();
+                break;
+            case GetAttr::Data:
+                trace_assert(var_accessor.data_getter, "data unreadable");
+                output = DeviceValue::make(var_accessor.data_getter());
+                break;
+            case GetAttr::Value:
+                trace_assert(var_accessor.value_getter, "value unreadable");
+                output = HostValue::make(var_accessor.value_getter());
+                break;
+            case GetAttr::DType:
+                output = traced_value->dtype();
+                break;
+            case GetAttr::Device:
+                output = traced_value->comp_node();
+            default:
+                break;
+        }
+        return {output};
+    } else {
+        return imperative::apply(get_attr, inputs);
+    }
+}
+
+ValueRefList CompiledTransformation::apply_create_tensor(
+        const CreateTensor& create_tensor, Span<ValueRef> inputs) {
+    if (create_tensor.kind() == CreateTensor::NoTrace) {
+        return imperative::apply(create_tensor, inputs);
+    }
+    auto& item = next_instruction();
+    trace_assert(item.op == nullptr, "operator mismatch");
+    auto input_id = item.inputs[0];
+    auto output_id = item.outputs[0];
+    auto tensor = imperative::apply(create_tensor, inputs)[0];
+    trace_input(input_id, tensor);
+    return {trace_output(output_id)};
+}
+
+ValueRefList CompiledTransformation::apply_transformation(
         const Operator& op, Span<ValueRef> inputs) {
     if (auto* op_value = op.as<ApplyOp>()) {
-        auto& item = next_instruction();
-        SmallVector<ValueRef> unwrapped_inputs;
-        SmallVector<ValueRef> wrapped_inputs;
-        trace_assert(inputs.size() == item.inputs.size(), "input size mismatch");
-        trace_assert(op_value->op().is_same(*item.op), "operator mismatch");
-        for (size_t i = 0; i < inputs.size(); ++i) {
-            trace_input(item.inputs[i], inputs[i]);
-        }
-        std::vector<ValueRef> outputs;
-        for (auto&& output_id : item.outputs) {
-            outputs.push_back(trace_output(output_id));
-        }
-        return outputs;
+        return apply_op(*op_value, inputs);
     } else if (auto* create_tensor = op.as<CreateTensor>()) {
-        if (create_tensor->kind() == CreateTensor::NoTrace) {
-            return imperative::apply(op, inputs);
-        }
-        auto& item = next_instruction();
-        trace_assert(item.op == nullptr, "operator mismatch");
-        auto input_id = item.inputs[0];
-        auto output_id = item.outputs[0];
-        auto tensor = imperative::apply(op, inputs)[0];
-        trace_input(input_id, tensor);
-        return {trace_output(output_id)};
+        return apply_create_tensor(*create_tensor, inputs);
     } else if (auto* get_attr = op.as<GetAttr>()) {
-        if (auto* traced_value = inputs[0].as<TracedValue>()) {
-            ValueRef output;
-            auto& var = m_vars[traced_value->id()];
-            auto& var_accessor = m_var_accessors[traced_value->id()];
-            switch (get_attr->attr()) {
-                case GetAttr::Shape:
-                    trace_assert(var_accessor.shape_getter, "shape unreadable");
-                    output = ShapeValue::make(
-                            ValueShape::from(var_accessor.shape_getter()));
-                    break;
-                case GetAttr::Data:
-                    trace_assert(var_accessor.data_getter, "data unreadable");
-                    output = DeviceValue::make(var_accessor.data_getter());
-                    break;
-                case GetAttr::Value:
-                    trace_assert(var_accessor.value_getter, "value unreadable");
-                    output = HostValue::make(var_accessor.value_getter());
-                    break;
-                case GetAttr::DType:
-                    output = DTypeValue::make(var.dtype);
-                    break;
-                case GetAttr::Device:
-                    output = CompNodeValue::make(var.device);
-                default:
-                    break;
-            }
-            return {output};
-        } else {
-            return imperative::apply(op, inputs);
-        }
+        return apply_get_attr(*get_attr, inputs);
     } else if (auto* trace_mark_var = op.as<TraceMarkVar>()) {
         auto& item = next_instruction();
         trace_assert(item.op == nullptr, "operator mismatch");

imperative/src/impl/value.cpp

@@ -8,50 +8,58 @@ namespace mgb {
 namespace imperative {
 
 namespace {
-static thread_local size_t nr_watched_values = 0;
-static thread_local uint64_t nr_values = 0;
-static thread_local bool recording_values = false;
-static thread_local std::vector<ValueWeakRef> recorded_values;
+static /*thread_local*/ size_t nr_watched_values = 0;
+static /*thread_local*/ uint64_t nr_values = 0;
+static /*thread_local*/ bool recording_values = false;
+static /*thread_local*/ std::vector<ValueWeakRef> recorded_values;
 static WeakValueMap<uint64_t, ValueWeakRef> registered_values;
 }  // namespace
 
 ValueRef::storage_t& ValueRef::storage() const {
-    if (!m_storage) {
+    if (mgb_likely(!m_storage->m_successor.m_storage)) {
         return m_storage;
     }
-    if (auto& storage = m_storage->m_successor.m_storage) {
-        while (storage->m_successor.m_storage) {
-            storage = storage->m_successor.m_storage;
-        }
-        return storage;
-    } else {
-        return m_storage;
+    while (m_storage->m_successor.m_storage) {
+        m_storage = m_storage->m_successor.m_storage;
+    }
+    return m_storage;
+}
+
+const Value* ValueRef::as(size_t typecode) const {
+    auto&& storage = this->storage();
+    if (storage->m_typecode != typecode) {
+        return nullptr;
     }
+    return static_cast<Value*>(storage.get());
+}
+
+bool ValueRef::is(size_t typecode) const {
+    return this->storage()->m_typecode == typecode;
 }
 
 TypedValueRef<DeviceValue> ValueRef::dev_tensor() const {
-    return imperative::apply(GetAttr(GetAttr::Data), *this)[0].as_ref<DeviceValue>();
+    return imperative::apply(GetAttr(GetAttr::Data), *this)[0].cast_ref<DeviceValue>();
 }
 
 TypedValueRef<HostValue> ValueRef::numpy() const {
-    return imperative::apply(GetAttr(GetAttr::Value), *this)[0].as_ref<HostValue>();
+    return imperative::apply(GetAttr(GetAttr::Value), *this)[0].cast_ref<HostValue>();
 }
 
 TypedValueRef<CompNodeValue> ValueRef::device() const {
     return imperative::apply(GetAttr(GetAttr::Device), *this)[0]
-            .as_ref<CompNodeValue>();
+            .cast_ref<CompNodeValue>();
 }
 
 TypedValueRef<ShapeValue> ValueRef::shape() const {
-    return imperative::apply(GetAttr(GetAttr::Shape), *this)[0].as_ref<ShapeValue>();
+    return imperative::apply(GetAttr(GetAttr::Shape), *this)[0].cast_ref<ShapeValue>();
 }
 
 TypedValueRef<DTypeValue> ValueRef::dtype() const {
-    return imperative::apply(GetAttr(GetAttr::DType), *this)[0].as_ref<DTypeValue>();
+    return imperative::apply(GetAttr(GetAttr::DType), *this)[0].cast_ref<DTypeValue>();
 }
 
 TypedValueRef<StringValue> ValueRef::name() const {
-    return imperative::apply(GetName(), *this)[0].as_ref<StringValue>();
+    return imperative::apply(GetName(), *this)[0].cast_ref<StringValue>();
 }
 
 bool ValueRef::is_scalar() const {
@@ -75,13 +83,15 @@ void ValueRef::unwatch() const {
 }
 
 ValueRef ValueRef::unwrap() const {
-    ValueRef value = *this;
     auto& context = Transformation::get_context();
-    for (size_t i = 0; i < context.next_transformation; ++i) {
-        value = context.transformations[i]->unwrap(value);
+    if (mgb_unlikely(context.next_transformation)) {
+        ValueRef value = *this;
+        for (size_t i = 0; i < context.next_transformation; ++i) {
+            value = context.transformations[i]->unwrap(value);
+        }
+        return value;
     }
-    mgb_assert(value);
-    return value;
+    return *this;
 }
 
 std::string ValueRef::to_string() const {
@@ -101,13 +111,11 @@ std::string ValueRef::raw_type() const {
     return types[m_storage->m_typecode].name();
 }
 
-uint64_t ValueRef::id() const {
-    return m_storage ? m_storage->m_id : std::numeric_limits<uint64_t>::max();
-}
-
 bool ValueRef::watching() const {
-    auto storage = this->storage();
-    return storage && storage->m_watching;
+    if (!m_storage) {
+        return false;
+    }
+    return this->storage()->m_watching;
 }
 
 ValueRef ValueRef::make(ValueRef::storage_t storage) {
@@ -186,5 +194,96 @@ void Value::try_rethrow() {
     }
 }
 
+inline void ValueRefList::init(size_t nr_elems) {
+    m_size = nr_elems;
+    if (m_size > 0) {
+        if (m_size == 1) {
+            m_data = inline_storage();
+        } else {
+            auto& context = Transformation::get_context();
+            m_data = context.allocator.allocate(m_size);
+        }
+        for (size_t i = 0; i < m_size; ++i) {
+            new (m_data + i) ValueRef();
+        }
+    } else {
+        m_data = nullptr;
+    }
+}
+
+ValueRefList::ValueRefList(size_t nr_elems) {
+    init(nr_elems);
+}
+
+ValueRefList::ValueRefList(std::initializer_list<ValueRef> values)
+        : ValueRefList(values.begin(), values.end()) {}
+
+ValueRefList::ValueRefList(const ValueRefList& rhs)
+        : ValueRefList(rhs.cbegin(), rhs.cend()) {}
+
+ValueRefList::ValueRefList(ValueRefList&& rhs) : ValueRefList() {
+    m_size = rhs.m_size;
+    if (rhs.m_data == rhs.inline_storage()) {
+        m_data = inline_storage();
+        new (m_data) ValueRef();
+        m_data[0] = std::move(rhs.m_data[0]);
+    } else {
+        m_data = rhs.m_data;
+        rhs.m_data = nullptr;
+        rhs.m_size = 0;
+    }
+}
+
+ValueRefList& ValueRefList::operator=(const ValueRefList& rhs) {
+    if (this == &rhs) {
+        return *this;
+    }
+    clear();
+    init(rhs.m_size);
+    for (size_t i = 0; i < m_size; ++i) {
+        m_data[i] = rhs.m_data[i];
+    }
+    return *this;
+}
+
+ValueRefList& ValueRefList::operator=(ValueRefList&& rhs) {
+    if (this == &rhs) {
+        return *this;
+    }
+    clear();
+    if (rhs.m_data == rhs.inline_storage()) {
+        m_data = inline_storage();
+        new (m_data) ValueRef();
+        m_data[0] = rhs.m_data[0];
+        m_size = 1;
+        rhs.clear();
+    } else {
+        m_data = rhs.m_data;
+        m_size = rhs.m_size;
+        rhs.m_data = nullptr;
+        rhs.m_size = 0;
+    }
+    return *this;
+}
+
+ValueRefList::~ValueRefList() {
+    clear();
+}
+
+void ValueRefList::clear() {
+    for (size_t i = 0; i < m_size; ++i) {
+        m_data[i].~ValueRef();
+    }
+    if (m_data) {
+        if (m_size != 1) {
+            Transformation::get_context().allocator.deallocate(m_data, m_size);
+        } else {
+            mgb_assert(m_data == inline_storage());
+        }
+    }
+    m_data = nullptr;
+    m_size = 0;
+}
+
 }  // namespace imperative
 }  // namespace mgb

imperative/src/include/megbrain/imperative/basic_operators.h

@@ -24,8 +24,6 @@ namespace imperative {
 
 class GradKey;
 
-using GenericFunction = std::function<std::vector<ValueRef>(Span<ValueRef>)>;
-
 /**
  * \brief apply an OpDef to values
  *
@@ -37,7 +35,7 @@ private:
 public:
     ApplyOp(const OpDef& op) : m_op(op) {}
 
-    const OpDef& op() { return m_op; }
+    const OpDef& op() const { return m_op; }
 
     std::string to_string() const override;
 };
@@ -106,7 +104,7 @@ public:
      * \param inputs contains host_storage and device_storage
      * \return Args unpacked args
      */
-    Args parse(Span<ValueRef> inputs);
+    Args parse(Span<ValueRef> inputs) const;
 
     Kind kind() const { return m_kind; }
     CompNode device() const { return m_device; }
@@ -129,11 +127,11 @@ private:
 public:
     DTRCommand(Kind kind) : m_kind(kind) {}
 
-    Kind kind() { return m_kind; }
+    Kind kind() const { return m_kind; }
 
     std::string to_string() const override;
 
-    std::vector<ValueRef> fallback(Span<ValueRef> inputs) const override { return {}; }
+    ValueRefList fallback(Span<ValueRef> inputs) const override { return {}; }
 };
 
 // deprecated
@@ -141,9 +139,7 @@ class GetName final : public OperatorImpl<GetName, Operator::GetAttrLike> {
 public:
     std::string to_string() const override;
 
-    std::vector<ValueRef> fallback(Span<ValueRef> inputs) const override {
-        return {ValueRef()};
-    }
+    ValueRefList fallback(Span<ValueRef> inputs) const override { return {ValueRef()}; }
 };
 
 /**
@@ -161,7 +157,7 @@ public:
 
     std::string to_string() const override;
 
-    std::vector<ValueRef> fallback(Span<ValueRef> inputs) const override {
+    ValueRefList fallback(Span<ValueRef> inputs) const override {
         return {inputs.as_array<1>()[0]};
     }
 };

imperative/src/include/megbrain/imperative/basic_values.h

@@ -23,7 +23,7 @@ namespace imperative {
 
 class GradKey;
 
-using GenericFunction = std::function<std::vector<ValueRef>(Span<ValueRef>)>;
+using GenericFunction = std::function<ValueRefList(Span<ValueRef>)>;
 
 class ShapeValue final : public MixinValueImpl<ShapeValue, ValueShape> {
 public:
@@ -97,6 +97,10 @@ public:
     ValueShape shape() const { return m_shape; }
     CompNode device() const { return m_storage.comp_node(); }
     HostTensorStorage storage() const { return m_storage; }
+    DTypeScalar item() const {
+        mgb_assert(m_shape.is_scalar());
+        return DTypeScalar::make_from_raw(m_dtype, m_storage.ptr());
+    }
 
     HostTensorND as_nd(bool allow_scalar = false) const;
 };

imperative/src/include/megbrain/imperative/dispatch.h

@@ -36,11 +36,11 @@ namespace imperative {
  *
  * \param op
  * \param inputs
- * \return std::vector<ValueRef>
+ * \return ValueRefList
  */
-std::vector<ValueRef> apply(const Operator& op, Span<ValueRef> inputs);
-std::vector<ValueRef> apply(const OpDef& def, Span<ValueRef> inputs);
-std::vector<ValueRef> apply(Subgraph graph, Span<ValueRef> inputs);
+ValueRefList apply(const Operator& op, Span<ValueRef> inputs);
+ValueRefList apply(const OpDef& def, Span<ValueRef> inputs);
+ValueRefList apply(const Subgraph& graph, Span<ValueRef> inputs);
 
 template <typename... TArgs>
 constexpr bool is_all_value_ref_v =
@@ -49,7 +49,7 @@ constexpr bool is_all_value_ref_v =
 
 template <typename T, typename... TArgs>
 static auto apply(T&& op, TArgs&&... args)
-        -> std::enable_if_t<is_all_value_ref_v<TArgs...>, std::vector<ValueRef>> {
+        -> std::enable_if_t<is_all_value_ref_v<TArgs...>, ValueRefList> {
     ValueRef args_arr[sizeof...(TArgs)] = {std::forward<TArgs&&>(args)...};
     return imperative::apply(
             std::forward<T&&>(op),
@@ -63,7 +63,7 @@ static auto apply(T&& op, TContainer&& container) -> std::enable_if_t<
                 ValueRef> &&
                 std::is_same_v<decltype(container.size()), size_t> &&
                 !std::is_same_v<std::decay_t<TContainer>, Span<ValueRef>>,
-        std::vector<ValueRef>> {
+        ValueRefList> {
     return imperative::apply(
             std::forward<T&&>(op), Span<ValueRef>(container.data(), container.size()));
 }

imperative/src/include/megbrain/imperative/operator.h

@@ -25,6 +25,8 @@
 namespace mgb {
 namespace imperative {
 
+using GenericFunction = std::function<ValueRefList(Span<ValueRef>)>;
+
 /**
  * \brief base class for all operators
  *
@@ -49,25 +51,24 @@ public:
     Kind kind() const { return m_kind; }
 
     template <typename U>
-    U* as() const {
+    const U* as() const {
         if (m_typecode != U::TYPE_CODE) {
             return nullptr;
         }
-        return static_cast<U*>(const_cast<Operator*>(this));
+        return static_cast<const U*>(this);
     }
     template <typename U>
     bool is() const {
-        return as<U>() != nullptr;
+        return m_typecode == U::TYPE_CODE;
     }
     template <Kind kKind>
     bool is() const {
         return kind() == kKind;
     }
     template <typename U>
-    U& cast() const {
-        U* ptr = as<U>();
-        mgb_assert(ptr);
-        return *ptr;
+    const U& cast() const {
+        mgb_assert(m_typecode == U::TYPE_CODE);
+        return static_cast<const U&>(*this);
     }
 
     virtual std::string to_string() const = 0;
@@ -77,9 +78,9 @@ public:
      * implementation.
      *
      * \param inputs
-     * \return std::vector<ValueRef>
+     * \return ValueRefList
      */
-    virtual std::vector<ValueRef> fallback(Span<ValueRef> inputs) const;
+    virtual ValueRefList fallback(Span<ValueRef> inputs) const;
 
     std::type_index type() const { return registered_types()[m_typecode]; }
 

imperative/src/include/megbrain/imperative/profiler.h

@@ -123,7 +123,6 @@ public:
     template <typename T, typename... TArgs>
     static uint64_t record(TArgs&&... args) {
         auto& profiler = get_instance();
-        // auto& mem_pool = get_mem_pool<T>();
         if constexpr (sm_debug) {
             Status expected = Running;
             mgb_assert(profiler.m_status.compare_exchange_strong(expected, Recording));

imperative/src/include/megbrain/imperative/transformation.h

@@ -18,6 +18,7 @@
 
 #include "megbrain/common.h"
 #include "megbrain/imperative/subgraph.h"
+#include "megbrain/imperative/utils/allocator.h"
 #include "megbrain/imperative/utils/local_ptr.h"
 #include "megbrain/imperative/utils/span.h"
 
@@ -25,6 +26,7 @@ namespace mgb {
 namespace imperative {
 
 class ValueRef;
+class ValueRefList;
 class Operator;
 class Transformation;
 
@@ -43,6 +45,7 @@ struct TransformationContext {
     // TODO: deprecate TransformationGuard, let next_transformation == frames.size()
     size_t next_transformation = 0;
     std::vector<TransformationFrame> frames;
+    ForwardAllocator<ValueRef> allocator;
 };
 
 /**
@@ -86,9 +89,9 @@ public:
      *
      * \param op
      * \param inputs
-     * \return std::vector<ValueRef>
+     * \return ValueRefList
      */
-    virtual std::vector<ValueRef> apply_transformation(
+    virtual ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) = 0;
 
     virtual ValueRef unwrap(ValueRef value) = 0;
@@ -187,11 +190,12 @@ public:
         std::swap(context.transformations, current_context.transformations);
         std::swap(context.scopes, current_context.scopes);
         std::swap(context.next_transformation, current_context.next_transformation);
+        std::swap(context.allocator, current_context.allocator);
     }
 
     static TransformationContext& get_context();
 
-    friend std::vector<ValueRef> apply(const Operator& op, Span<ValueRef> inputs);
+    friend ValueRefList apply(const Operator& op, Span<ValueRef> inputs);
     friend class ValueRef;
 };
 

imperative/src/include/megbrain/imperative/transformations/eval.h

@@ -23,16 +23,38 @@ public:
     using Handle = interpreter::Interpreter::Handle;
     using Channel = interpreter::Interpreter::Channel;
 
+    class RAIIHandle : public NonCopyableObj {
+    private:
+        Handle m_handle = nullptr;
+        Channel* m_channel = nullptr;
+
+    public:
+        RAIIHandle(Handle handle, Channel* channel)
+                : m_handle(handle), m_channel(channel) {}
+        ~RAIIHandle() { m_channel->del(m_handle); }
+
+        Handle handle() const { return m_handle; }
+
+        Channel* channel() const { return m_channel; }
+    };
+
 private:
-    std::shared_ptr<Handle> m_handle = nullptr;
+    LocalPtr<RAIIHandle> m_handle;
     std::string m_name;
+    mutable DTypeValue::ref_t m_dtype;
+    mutable CompNodeValue::ref_t m_comp_node;
+    mutable ShapeValue::ref_t m_shape;
 
 public:
     InterpreterInfo() = default;
-    InterpreterInfo(std::shared_ptr<Handle> handle, std::string name = {})
+    InterpreterInfo(LocalPtr<RAIIHandle> handle, std::string name = {})
             : m_handle(handle), m_name(name) {}
 
-    std::shared_ptr<Handle> handle() const { return m_handle; }
+    const LocalPtr<RAIIHandle>& handle() const { return m_handle; }
+
+    DTypeValue::ref_t dtype() const;
+    CompNodeValue::ref_t comp_node() const;
+    ShapeValue::ref_t shape() const;
 
     std::string name() const { return m_name; }
 };
@@ -60,6 +82,7 @@ class InterpreterTransformation final : public Transformation {
 public:
     using Interpreter = interpreter::Interpreter;
     using Handle = Interpreter::Handle;
+    using SharedHandle = LocalPtr<InterpreterInfo::RAIIHandle>;
     using Channel = Interpreter::Channel;
 
 private:
@@ -71,7 +94,14 @@ public:
 
     Channel* channel() { return m_channel.get(); }
 
-    std::vector<ValueRef> apply_transformation(
+    ValueRefList apply_op(const ApplyOp& apply_op, Span<ValueRef> inputs);
+
+    ValueRefList apply_get_attr(const GetAttr& get_attr, Span<ValueRef> inputs);
+
+    ValueRefList apply_create_tensor(
+            const CreateTensor& create_tensor, Span<ValueRef> inputs);
+
+    ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) override;
 
     ValueRef unwrap(ValueRef value) override {
@@ -81,14 +111,8 @@ public:
 
     std::string name() const override { return "InterpreterTransformation"; }
 
-    std::shared_ptr<Handle> share_handle(Handle handle) {
-        return std::shared_ptr<Handle>(
-                new Handle(handle), [channel = m_channel.get()](Handle* ptr) {
-                    if (ptr) {
-                        channel->del(*ptr);
-                        delete ptr;
-                    }
-                });
+    SharedHandle share_handle(Handle handle) {
+        return SharedHandle::make(handle, m_channel.get());
     }
 };
 

imperative/src/include/megbrain/imperative/transformations/grad.h

@@ -34,9 +34,7 @@ struct BackwardGraphWithClosure {
             std::shared_ptr<OptimizedBackwardGraphResult> backward_graph,
             std::shared_ptr<OpDef> op, Span<ValueRef> inputs, Span<ValueRef> outputs);
 
-    void operator()(
-            std::vector<ValueRef> grads,
-            std::function<void(size_t, ValueRef)> receiver);
+    void operator()(ValueRefList grads, std::function<void(size_t, ValueRef)> receiver);
 
     bool input_has_grad(size_t i) { return backward_graph->input_has_grad[i]; }
 
@@ -50,12 +48,11 @@ struct BackwardGraphWithClosure {
 
 struct CustomBackward;
 
-using GradRuleFn =
-        std::function<std::vector<ValueRef>(Span<ValueRef> inputs, CustomBackward&)>;
+using GradRuleFn = std::function<ValueRefList(Span<ValueRef> inputs, CustomBackward&)>;
 
 struct CustomBackward {
-    using BackwardFn = std::function<std::vector<ValueRef>(Span<ValueRef>)>;
-    using BackwardRule = std::function<std::optional<std::vector<ValueRef>>(
+    using BackwardFn = std::function<ValueRefList(Span<ValueRef>)>;
+    using BackwardRule = std::function<std::optional<ValueRefList>(
             const OpDef&, Span<ValueRef>, Span<bool>, CustomBackward&)>;
     BackwardFn m_backward;
     SmallVector<bool, 8> m_input_has_grad;
@@ -65,9 +62,7 @@ struct CustomBackward {
     SmallVector<OutputAttr> m_output_attrs;
 
 public:
-    void operator()(
-            std::vector<ValueRef> grads,
-            std::function<void(size_t, ValueRef)> receiver);
+    void operator()(ValueRefList grads, std::function<void(size_t, ValueRef)> receiver);
 
     bool input_has_grad(size_t i) { return m_input_has_grad[i]; }
     bool output_requires_grad(size_t i) { return m_output_attrs[i].requires_grad; }
@@ -188,7 +183,7 @@ public:
 
     std::string to_string() const override;
 
-    bool has_key(std::shared_ptr<GradKey> key) const { return m_key == key; }
+    bool has_key(const std::shared_ptr<GradKey>& key) const { return m_key == key; }
 
     const GradSlotPtr& slot_for(std::shared_ptr<GradKey> key) const {
         mgb_assert(m_key == key);
@@ -287,7 +282,7 @@ public:
         return false;
     }
 
-    std::vector<ValueRef> apply_transformation(
+    ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) override;
 
     ValueRef unwrap(ValueRef value) override {
@@ -314,7 +309,7 @@ private:
 public:
     std::string to_string() const override { return "DetachValue"; }
 
-    std::vector<ValueRef> fallback(Span<ValueRef> inputs) const override {
+    ValueRefList fallback(Span<ValueRef> inputs) const override {
         return {inputs.as_array<1>()[0]};
     }
 };
@@ -325,7 +320,7 @@ private:
 
 public:
     AttachGrad(std::shared_ptr<GradKey> key) : m_key(key) {}
-    std::shared_ptr<GradKey> key() { return m_key; }
+    std::shared_ptr<GradKey> key() const { return m_key; }
 
     std::string to_string() const override {
         return ssprintf("AttachGradValue{key=%s}", m_key->name().c_str());
@@ -339,7 +334,7 @@ private:
 public:
     GradBackward(std::shared_ptr<GradKey> key) : m_key(key) {}
 
-    std::shared_ptr<GradKey> key() { return m_key; }
+    std::shared_ptr<GradKey> key() const { return m_key; }
 
     std::string to_string() const override {
         return ssprintf("GradBackwardValue{key=%s}", m_key->name().c_str());
@@ -352,13 +347,13 @@ private:
 
 public:
     IsAttachedTo(std::shared_ptr<GradKey> key) : m_key(key) {}
-    std::shared_ptr<GradKey> key() { return m_key; }
+    std::shared_ptr<GradKey> key() const { return m_key; }
 
     std::string to_string() const override {
         return ssprintf("IsAttachedToValue{key=%s}", m_key->name().c_str());
     }
 
-    std::vector<ValueRef> fallback(Span<ValueRef> inputs) const override {
+    ValueRefList fallback(Span<ValueRef> inputs) const override {
         return {BoolValue::make(false)};
     }
 };
@@ -373,9 +368,9 @@ public:
     SetGrad(std::shared_ptr<GradKey> key, GenericFunction grad_fn, size_t nr_inputs)
             : m_key(key), m_grad_fn(grad_fn), m_nr_inputs(nr_inputs) {}
 
-    GenericFunction grad_fn() { return m_grad_fn; }
+    GenericFunction grad_fn() const { return m_grad_fn; }
 
-    size_t nr_inputs() { return m_nr_inputs; }
+    size_t nr_inputs() const { return m_nr_inputs; }
 
     std::string to_string() const override {
         return ssprintf("SetGradValue{key=%s}", m_key->name().c_str());
@@ -388,9 +383,7 @@ public:
 
     std::string to_string() const override { return ssprintf("GetGradKeyValue{}"); }
 
-    std::vector<ValueRef> fallback(Span<ValueRef> inputs) const override {
-        return {ValueRef()};
-    }
+    ValueRefList fallback(Span<ValueRef> inputs) const override { return {ValueRef()}; }
 };
 
 class GetBackwardColsure
@@ -401,7 +394,7 @@ private:
 public:
     GetBackwardColsure(std::shared_ptr<GradKey> key) : m_key(key) {}
 
-    std::shared_ptr<GradKey> key() { return m_key; }
+    std::shared_ptr<GradKey> key() const { return m_key; }
 
     std::string to_string() const override {
         return ssprintf("GetBackwardClosure{key=%s}", m_key->name().c_str());

imperative/src/include/megbrain/imperative/transformations/lazy.h

@@ -81,7 +81,7 @@ public:
 
     ComputingGraph::Options& options() { return m_graph->options(); }
 
-    std::vector<ValueRef> apply_transformation(
+    ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) override;
 
     ValueRef unwrap(ValueRef value) override {

imperative/src/include/megbrain/imperative/transformations/scalar.h

@@ -11,6 +11,7 @@
 
 #pragma once
 
+#include "megbrain/imperative/basic_operators.h"
 #include "megbrain/imperative/dispatch.h"
 #include "megbrain/imperative/ops/autogen.h"
 
@@ -45,8 +46,10 @@ public:
  */
 class ScalarTransformation final : public Transformation {
 private:
+    ShapeValue::ref_t m_empty_shape;  // []
 public:
-    std::vector<ValueRef> apply_transformation(
+    ValueRefList apply_get_attr(const GetAttr& get_attr, Span<ValueRef> inputs);
+    ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) override;
 
     ValueRef unwrap(ValueRef value) override {

imperative/src/include/megbrain/imperative/transformations/symbol.h

@@ -50,7 +50,7 @@ private:
 
 public:
     SymbolTransformation(ComputingGraph* graph) : m_graph(graph) {}
-    std::vector<ValueRef> apply_transformation(
+    ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) override {
         if (auto* apply_op = op.as<ApplyOp>()) {
             SmallVector<VarNode*> input_nodes;
@@ -58,9 +58,9 @@ public:
                 input_nodes.push_back(input.cast<SymbolValue>().node());
             }
             auto output_nodes = OpDef::apply_on_var_node(apply_op->op(), input_nodes);
-            std::vector<ValueRef> outputs;
-            for (auto&& output_node : output_nodes) {
-                outputs.push_back(SymbolValue::make(output_node));
+            ValueRefList outputs(output_nodes.size());
+            for (size_t i = 0; i < output_nodes.size(); ++i) {
+                outputs[i] = SymbolValue::make(output_nodes[i]);
             }
             return outputs;
         } else if (auto* create_tensor = op.as<CreateTensor>()) {

imperative/src/include/megbrain/imperative/transformations/tangent.h

+/**
+ * \file imperative/src/include/megbrain/imperative/grad.h
+ * MegEngine is Licensed under the Apache License, Version 2.0 (the "License")
+ *
+ * Copyright (c) 2014-2021 Megvii Inc. All rights reserved.
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT ARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ */
+
+#pragma once
+
+#include "megbrain/imperative/basic_operators.h"
+#include "megbrain/imperative/operator.h"
+#include "megbrain/imperative/transformation.h"
+#include "megbrain/imperative/value.h"
+
+namespace mgb::imperative {
+
+struct TangentInfo {
+    ValueRef value;
+    ValueRef tangent;
+};
+
+class TangentTransformation final : public Transformation {
+public:
+    ValueRefList apply_transformation(
+            const Operator& op, Span<ValueRef> inputs) override;
+
+    ValueRef unwrap(ValueRef value) override { mgb_assert(false); }
+
+    std::string name() const override { return "Tangent"; }
+};
+
+}  // namespace mgb::imperative

imperative/src/include/megbrain/imperative/transformations/trace.h

@@ -126,25 +126,6 @@ public:
     void on_unwatch() override { value().unwatch(); }
 };
 
-class TracedInfo {
-private:
-    size_t m_id = 0;
-
-public:
-    TracedInfo() = default;
-    TracedInfo(size_t id) : m_id(id) {}
-    size_t id() const { return m_id; }
-};
-
-class TracedValue final : public MixinValueImpl<TracedValue, TracedInfo> {
-public:
-    using MixinValueImpl::MixinValueImpl;
-
-    std::string to_string() const override {
-        return ssprintf("TracedValue{\"id\"=%zu}", id());
-    }
-};
-
 /**
  * \brief trace operation sequence to TraceResult
  *
@@ -202,7 +183,7 @@ public:
         return value;
     }
 
-    std::vector<ValueRef> apply_transformation(
+    ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) override;
 
     ValueRef unwrap(ValueRef value) override {
@@ -248,6 +229,40 @@ public:
         std::function<DeviceTensorND()> data_getter;
         std::function<HostTensorND()> value_getter;
         std::function<void(DeviceTensorND)> data_setter;
+        std::function<void(std::exception_ptr)> exc_setter;
+    };
+
+    class TracedInfo {
+    private:
+        size_t m_id = 0;
+        VarInfo* m_var = nullptr;
+        VarAccessor* m_accessor = nullptr;
+        mutable ShapeValue::ref_t m_shape;
+        mutable DTypeValue::ref_t m_dtype;
+        mutable CompNodeValue::ref_t m_comp_node;
+
+    public:
+        TracedInfo() = default;
+        TracedInfo(size_t id, VarInfo* var, VarAccessor* accessor)
+                : m_id(id), m_var(var), m_accessor(accessor) {}
+        size_t id() const { return m_id; }
+        ShapeValue::ref_t shape() const;
+        DTypeValue::ref_t dtype() const;
+        CompNodeValue::ref_t comp_node() const;
+        const VarAccessor& accessor() const;
+
+        void set_exception(std::exception_ptr exc) const {
+            m_accessor->exc_setter(exc);
+        }
+    };
+
+    class TracedValue final : public MixinValueImpl<TracedValue, TracedInfo> {
+    public:
+        using MixinValueImpl::MixinValueImpl;
+
+        std::string to_string() const override {
+            return ssprintf("TracedValue{\"id\"=%zu}", id());
+        }
     };
 
 private:
@@ -319,7 +334,14 @@ public:
 
     TraceResult::SeqItem& next_instruction();
 
-    std::vector<ValueRef> apply_transformation(
+    ValueRefList apply_op(const ApplyOp& apply_op, Span<ValueRef> inputs);
+
+    ValueRefList apply_get_attr(const GetAttr& get_attr, Span<ValueRef> inputs);
+
+    ValueRefList apply_create_tensor(
+            const CreateTensor& create_tensor, Span<ValueRef> inputs);
+
+    ValueRefList apply_transformation(
             const Operator& op, Span<ValueRef> inputs) override;
 
     void on_unregister() noexcept override;

imperative/src/include/megbrain/imperative/utils/allocator.h

@@ -36,12 +36,12 @@ private:
 public:
     Allocator(pool_type* pool) : m_pool(pool) {}
 
-    T* allocate(size_type n) {
+    pointer allocate(size_type n) {
         mgb_assert(n == 1);
         return m_pool->alloc(sizeof(T));
     }
 
-    void deallocate(pointer* p, size_type n) {
+    void deallocate(pointer p, size_type n) {
         mgb_assert(n == 1);
         m_pool->free(p);
     }
@@ -68,4 +68,114 @@ public:
     bool operator!=(const ThreadLocalAllocatorAdapter& rhs) const { return false; }
 };
 
-}  // namespace mgb::imperative
\ No newline at end of file
+template <typename T>
+class ForwardAllocator {
+public:
+    using value_type = T;
+    using size_type = std::size_t;
+    using pointer = T*;
+
+    static constexpr size_t alignment = alignof(T);
+    static constexpr size_t element_offset =
+            sizeof(T) +
+            ((sizeof(T) % alignment) ? 0 : (alignment - sizeof(T) % alignment));
+
+private:
+    struct Block {
+        std::unique_ptr<std::byte[]> data;
+        size_t size = 0;
+        size_t capacity = 0;
+
+        T* allocate(size_type n) {
+            static_assert(element_offset > std::max(alignment, sizeof(T)));
+            size_t begin = size;
+            size_t end = begin + element_offset * n;
+            if (end > capacity) {
+                return nullptr;
+            }
+            size = end;
+            return reinterpret_cast<T*>(data.get() + begin);
+        }
+
+        void reset() { size = 0; }
+    };
+    std::vector<Block> m_used;
+    std::optional<Block> m_current;
+    size_t block_size = 16 * 1024 * 1024;
+    size_t nr_allocated = 0;
+
+private:
+    Block allocate_block() {
+        block_size *= 2;
+        return Block{std::make_unique<std::byte[]>(block_size), 0, block_size};
+    }
+
+public:
+    pointer allocate(size_type n) {
+        if (!m_current) {
+            m_current.emplace(allocate_block());
+        }
+        pointer pointer = m_current->allocate(n);
+        while (pointer == nullptr) {
+            m_used.push_back(allocate_block());
+            std::swap(m_used.back(), *m_current);
+            pointer = m_current->allocate(n);
+        }
+        nr_allocated++;
+        return pointer;
+    }
+
+    void deallocate(pointer p, size_type n) {
+        mgb_assert(nr_allocated > 0);
+        nr_allocated--;
+    }
+
+    void clear() {
+        if (mgb_likely(m_used.empty())) {
+            // fastpath
+            if (m_current) {
+                m_current->reset();
+            }
+        } else {
+            // trim
+            *m_current = allocate_block();
+            m_used.clear();
+        }
+        mgb_assert(nr_allocated == 0);
+    }
+
+    bool operator==(const ForwardAllocator& rhs) const { return &rhs == this; }
+    bool operator!=(const ForwardAllocator& rhs) const { return &rhs != this; }
+};
+
+template <typename T, template <typename> typename TAllocator>
+class ProxyAllocator {
+public:
+    using value_type = T;
+    using size_type = typename TAllocator<T>::size_type;
+    using pointer = typename TAllocator<T>::pointer;
+
+private:
+    TAllocator<T>* m_impl;
+
+public:
+    T* allocate(size_type n) { return m_impl->allocate(n); }
+
+    void deallocate(pointer* p, size_type n) { return m_impl->deallocate(p, n); }
+
+    bool operator==(const ProxyAllocator<T, TAllocator>& rhs) const {
+        if (m_impl == rhs.m_impl) {
+            return true;
+        } else if (bool(m_impl) ^ bool(rhs.m_impl)) {
+            return false;
+        } else {
+            return *m_impl == *rhs.m_impl;
+        }
+    }
+
+    bool operator!=(const ProxyAllocator<T, TAllocator>& rhs) const {
+        return !((*this) == rhs);
+    }
+};
+
+}  // namespace mgb::imperative

imperative/src/include/megbrain/imperative/utils/local_ptr.h

@@ -16,6 +16,8 @@
 #include "megbrain/imperative/utils/mempool.h"
 #include "megbrain/utils/metahelper.h"
 
+#define MGB_FAT_LOCAL_PTR 0
+
 namespace mgb::imperative {
 
 template <typename T>
@@ -52,6 +54,8 @@ private:
         }
     }
 
+    size_t ref_count() const { return m_ref_count; }
+
     template <typename U>
     friend class LocalPtr;
 
@@ -88,14 +92,24 @@ public:
     using storage_t = LocalPtrStorage<T>;
     using pool_t = MemPool<storage_t>;
     using weak_type = LocalWeakPtr<T>;
+    using pointer_t = T*;
 
 private:
     storage_t* m_storage = nullptr;
 
+#if MGB_FAT_LOCAL_PTR
+    pointer_t m_pointer = nullptr;
+#endif
+
+    // (m_storage == nullptr) == (m_pointer == nullptr)
+
     void emplace(storage_t* ptr) {
         if (ptr) {
             ptr->inc_ref();
             m_storage = ptr;
+#if MGB_FAT_LOCAL_PTR
+            m_pointer = ptr->m_pointer;
+#endif
         }
     }
 
@@ -103,8 +117,22 @@ private:
 
 public:
     LocalPtr() = default;
-    LocalPtr(const LocalPtr& rhs) { (*this) = rhs; }
-    LocalPtr(LocalPtr&& rhs) { (*this) = std::move(rhs); }
+    LocalPtr(const LocalPtr& rhs) {
+        auto storage = rhs.m_storage;
+        if (storage) {
+            storage->inc_ref();
+        }
+        m_storage = storage;
+#if MGB_FAT_LOCAL_PTR
+        m_pointer = rhs.m_pointer;
+#endif
+    }
+    LocalPtr(LocalPtr&& rhs) {
+        std::swap(m_storage, rhs.m_storage);
+#if MGB_FAT_LOCAL_PTR
+        std::swap(m_pointer, rhs.m_pointer);
+#endif
+    }
     LocalPtr& operator=(const LocalPtr& rhs) {
         if (this == &rhs) {
             return *this;
@@ -115,9 +143,11 @@ public:
         }
         if (m_storage) {
             m_storage->dec_ref();
-            // rhs.m_storage may be invalid here
         }
         m_storage = storage;
+#if MGB_FAT_LOCAL_PTR
+        m_pointer = rhs.m_pointer;
+#endif
         return *this;
     }
     LocalPtr& operator=(LocalPtr&& rhs) {
@@ -125,6 +155,9 @@ public:
             return *this;
         }
         std::swap(m_storage, rhs.m_storage);
+#if MGB_FAT_LOCAL_PTR
+        std::swap(m_pointer, rhs.m_pointer);
+#endif
         rhs.reset();
         return *this;
     }
@@ -186,10 +219,11 @@ public:
     T& operator*() const { return *get(); }
 
     T* get() const {
-        if ((!m_storage) || !m_storage->m_pointer) {
-            return nullptr;
-        }
-        return m_storage->m_pointer;
+#if MGB_FAT_LOCAL_PTR
+        return m_pointer;
+#else
+        return m_storage ? m_storage->m_pointer : nullptr;
+#endif
     }
 
     T* operator->() const { return get(); }
@@ -202,6 +236,9 @@ public:
         if (m_storage) {
             m_storage->dec_ref();
             m_storage = nullptr;
+#if MGB_FAT_LOCAL_PTR
+            m_pointer = nullptr;
+#endif
         }
     }
 

imperative/src/include/megbrain/imperative/utils/mempool.h

@@ -49,8 +49,8 @@ public:
                 instance = std::make_unique<MemPool<T>>();
                 sm_instance = instance.get();
             }
-            mgb_assert(sm_instance);
         }
+        return *sm_instance;
     }
 };
 
@@ -62,9 +62,9 @@ std::unordered_map<std::thread::id, std::unique_ptr<MemPool<T>>>
         MemPoolUtils<T>::sm_instances;
 
 template <typename T>
-thread_local MemPool<T>* MemPoolUtils<T>::tm_instance;
+thread_local MemPool<T>* MemPoolUtils<T>::tm_instance = nullptr;
 
 template <typename T>
-MemPool<T>* MemPoolUtils<T>::sm_instance;
+MemPool<T>* MemPoolUtils<T>::sm_instance = nullptr;
 
-}  // namespace mgb::imperative
\ No newline at end of file
+}  // namespace mgb::imperative

imperative/src/include/megbrain/imperative/utils/value_shape.h

@@ -95,6 +95,8 @@ struct ValueShape {
         }
         return true;
     }
+
+    bool operator!=(const ValueShape& rhs) const { return !operator==(rhs); }
 };
 
 static_assert(sizeof(size_t) >= sizeof(int));

imperative/src/include/megbrain/imperative/value.h

@@ -47,6 +47,17 @@ class StringValue;
 
 class Operator;
 
+class ValueRefList;
+
+template <typename T>
+class Type {
+private:
+    const size_t m_code = T::TYPE_CODE;
+
+public:
+    inline size_t code() const { return m_code; }
+};
+
 /**
  * \brief an smart reference of value
  *
@@ -64,8 +75,9 @@ public:
 
 protected:
     mutable storage_t m_storage;
+    size_t m_id = std::numeric_limits<size_t>::max();
 
-    ValueRef(storage_t storage) { m_storage = storage; }
+    inline ValueRef(storage_t storage);
 
 private:
     /**
@@ -75,6 +87,10 @@ private:
      */
     storage_t& storage() const;
 
+    const Value* as(size_t typecode) const;
+
+    bool is(size_t typecode) const;
+
 public:
     ValueRef() = default;
 
@@ -86,7 +102,7 @@ public:
      * \return false if empty or type of value is not TValue
      */
     template <typename TValue>
-    bool is() const;
+    inline bool is(Type<TValue> type = {}) const;
 
     /**
      * \brief try cast value as target type
@@ -95,7 +111,7 @@ public:
      * \return TValue* raw pointer if success, otherwise nullptr
      */
     template <typename TValue>
-    const TValue* as() const;
+    inline const TValue* as(Type<TValue> type = {}) const;
 
     /**
      * \brief cast value to target type
@@ -104,7 +120,7 @@ public:
      * \return TValue& reference of value
      */
     template <typename TValue>
-    const TValue& cast() const;
+    inline const TValue& cast(Type<TValue> type = {}) const;
 
     /**
      * \brief like as(), but returns TypedValueRef instead
@@ -113,7 +129,13 @@ public:
      * \return TypedValueRef<TValue> reference if success, otherwise empty reference
      */
     template <typename TValue>
-    inline TypedValueRef<TValue> as_ref() const;
+    inline TypedValueRef<TValue> as_ref(Type<TValue> type = {}) const;
+
+    template <typename TValue>
+    inline TypedValueRef<TValue> cast_ref(Type<TValue> type = {}) const;
+
+    template <typename TValue>
+    void on_cast_failure() const;
 
     operator bool() const { return bool(m_storage); }
 
@@ -132,7 +154,7 @@ public:
     ValueRef unwrap() const;
     std::string to_string() const;
     std::string raw_type() const;
-    uint64_t id() const;
+    uint64_t id() const { return m_id; }
     size_t hash() const { return id(); }
 
     static ValueRef make(storage_t storage);
@@ -144,7 +166,7 @@ public:
     friend class TypedValueRef;
     template <typename T>
     friend class ValueImpl;
-    friend std::vector<ValueRef> apply(const Operator& op, Span<ValueRef> inputs);
+    friend ValueRefList apply(const Operator& op, Span<ValueRef> inputs);
 };
 
 template <>
@@ -244,7 +266,7 @@ public:
     using ref_t = TypedValueRef<T>;
     using weak_ref_t = TypedValueWeakRef<T>;
 
-    static inline size_t TYPE_CODE = [] { return register_type(typeid(T)); }();
+    static inline const size_t TYPE_CODE = [] { return register_type(typeid(T)); }();
 
     /**
      * \brief helper function for construct a value
@@ -254,7 +276,7 @@ public:
      * \return TypedValueRef<T> reference of value
      */
     template <typename... TArgs>
-    static TypedValueRef<T> make(TArgs&&... args) {
+    static MGB_NOINLINE TypedValueRef<T> make(TArgs&&... args) {
         static_assert(std::is_final_v<T>);
         return ValueRef::make(LocalPtr<Value>::make<T>(std::forward<TArgs&&>(args)...));
     }
@@ -279,46 +301,60 @@ public:
     bool eq(const TMixin& value) const { return ((const TMixin&)*this) == value; }
 };
 
+inline ValueRef::ValueRef(storage_t storage) {
+    // mgb_assert(storage);
+    m_storage = storage;
+    m_id = m_storage->m_id;
+}
+
 template <typename TValue>
-const TValue* ValueRef::as() const {
+inline const TValue* ValueRef::as(Type<TValue> type) const {
     static_assert(std::is_base_of_v<ValueImpl<TValue>, TValue>);
-    auto storage = this->storage();
-    if (!storage) {
-        return nullptr;
-    }
-    if (storage->m_typecode != TValue::TYPE_CODE) {
-        return nullptr;
-    }
-    return static_cast<TValue*>(storage.get());
+    return static_cast<const TValue*>(as(type.code()));
 }
 
 template <typename TValue>
-const TValue& ValueRef::cast() const {
-    auto* ptr = as<TValue>();
-    if (!ptr) {
-        // if this is ErrorValue, rethrow directly
-        storage()->try_rethrow();
-        mgb_assert(
-                ptr, "expect type %s, got %s", typeid(TValue).name(),
-                to_string().c_str());
+inline const TValue& ValueRef::cast(Type<TValue> type) const {
+    auto* ptr = as<TValue>(type);
+    if (mgb_unlikely(!ptr)) {
+        on_cast_failure<TValue>();
     }
-    return *ptr;
+    return static_cast<const TValue&>(*ptr);
+}
+
+template <typename TValue>
+inline bool ValueRef::is(Type<TValue> type) const {
+    return is(type.code());
 }
 
 template <typename TValue>
-bool ValueRef::is() const {
-    auto* ptr = as<TValue>();
-    return ptr != nullptr;
+inline TypedValueRef<TValue> ValueRef::as_ref(Type<TValue> type) const {
+    if (!is<TValue>(type)) {
+        return {};
+    }
+    return TypedValueRef<TValue>(*this);
 }
 
 template <typename TValue>
-TypedValueRef<TValue> ValueRef::as_ref() const {
-    if (!is<TValue>()) {
+inline TypedValueRef<TValue> ValueRef::cast_ref(Type<TValue> type) const {
+    if (!m_storage) {
         return {};
     }
+    if (mgb_unlikely(!is<TValue>(type))) {
+        on_cast_failure<TValue>();
+    }
     return TypedValueRef<TValue>(*this);
 }
 
+template <typename TValue>
+void ValueRef::on_cast_failure() const {
+    // if this is ErrorValue, rethrow directly
+    storage()->try_rethrow();
+    mgb_assert(
+            storage()->m_typecode != TValue::TYPE_CODE, "expect type %s, got %s",
+            typeid(TValue).name(), to_string().c_str());
+}
+
 /**
  * \brief ValueRef with concrete type, convenient for dereference
  *
@@ -361,11 +397,87 @@ private:
 public:
     TypedValueWeakRef(ValueRef value) : ValueWeakRef(value) {}
     TypedValueWeakRef(ValueWeakRef value) : ValueWeakRef(value) {}
-    TypedValueRef<T> lock() { return ValueWeakRef::lock().template as_ref<T>(); }
+    TypedValueRef<T> lock() {
+        auto value = ValueWeakRef::lock();
+        if (value) {
+            return value.template as_ref<T>();
+        } else {
+            return {};
+        }
+    }
 };
 
 // TODO: add proxy value type, which is meant to be reset in the end
 
+class ValueRefList {
+private:
+    ValueRef* m_data = nullptr;
+    size_t m_size = 0;
+    std::aligned_storage_t<sizeof(ValueRef), alignof(ValueRef)> m_storage;
+
+private:
+    void init(size_t nr_elems);
+    ValueRef* inline_storage() { return reinterpret_cast<ValueRef*>(&m_storage); }
+
+public:
+    ValueRefList() = default;
+    ValueRefList(size_t nr_elems);
+    ValueRefList(ValueRef item);
+    ValueRefList(std::initializer_list<ValueRef> values);
+    template <typename TIterator>
+    ValueRefList(TIterator begin, TIterator end);
+    ValueRefList(const ValueRefList& rhs);
+    ValueRefList(ValueRefList&& rhs);
+    ValueRefList& operator=(const ValueRefList& rhs);
+    ValueRefList& operator=(ValueRefList&& rhs);
+    ~ValueRefList();
+    void clear();
+
+    ValueRef* begin() { return m_data; }
+    ValueRef* end() { return m_data + m_size; }
+    const ValueRef* cbegin() const { return m_data; }
+    const ValueRef* cend() const { return m_data + m_size; }
+    size_t size() const { return m_size; }
+    ValueRef& at(size_t idx) {
+        mgb_assert(idx < m_size);
+        return m_data[idx];
+    }
+    const ValueRef& at(size_t idx) const {
+        mgb_assert(idx < m_size);
+        return m_data[idx];
+    }
+    ValueRef& operator[](size_t idx) { return m_data[idx]; }
+    const ValueRef& operator[](size_t idx) const { return m_data[idx]; }
+    ValueRef* data() { return m_data; }
+    const ValueRef* data() const { return m_data; }
+    bool empty() const { return m_size == 0; }
+    ValueRef& front() {
+        mgb_assert(m_size > 1);
+        return m_data[0];
+    }
+    ValueRef& back() {
+        mgb_assert(m_size > 1);
+        return m_data[m_size - 1];
+    }
+};
+
+template <typename TIterator>
+ValueRefList::ValueRefList(TIterator begin, TIterator end) : ValueRefList(end - begin) {
+    for (size_t i = 0; i < m_size; ++i) {
+        m_data[i] = *(begin + i);
+    }
+}
+
+inline ValueRefList::ValueRefList(ValueRef item) : m_data(inline_storage()), m_size(1) {
+    new (m_data) ValueRef();
+    m_data[0] = std::move(item);
+}
+
+/*class ValueRefList : public SmallVector<ValueRef, 1> {
+public:
+    using SmallVector::SmallVector;
+};*/
+
 }  // namespace imperative
 }  // namespace mgb