fix(autodiff): fix some bugs in relation to 2nd order grad

1. implement double backward for batchnorm
2. fix grad attach in nested grad manager
3. pad empty tensor for unsatisfied output_has_grad
4. support double backward for jit subgraph
5. support double backward for autodiff.Function
6. readd debug flag MGE_LOG_OP_DISPATCH

GitOrigin-RevId: cd31ddc620a35e0582c9721df7290c972fa3c610

imperative/python/megengine/core/autodiff/grad.py

@@ -212,10 +212,7 @@ class Function:
 
         if self.__single_output:
             outputs = (outputs,)
-        for grad in reversed(group):
-            if grad._impl is None:
-                continue
-            outputs = core2.set_grad(grad._impl, normalized_backward, args, outputs)
+        outputs = core2.set_grad(normalized_backward, args, outputs)
         if self.__single_output:
             (outputs,) = outputs
         return outputs

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

@@ -209,7 +209,6 @@ def subgraph(
             outputs = gen.send(None)
             nr_outputs = len(outputs)
             forward_fn = build(builder, outputs, [False] * nr_outputs)
-
             output_grads = [builder.input() for _ in range(nr_outputs)]
             input_grads = gen.send(output_grads)
             assert len(input_grads) == nr_inputs
@@ -222,25 +221,49 @@ def subgraph(
             ]
             encoded_input_grads = [grad for grad in input_grads if grad is not None]
             backward_fn = build(
-                builder, encoded_input_grads, [False] * len(encoded_input_grads)
+                builder, encoded_input_grads, [True] * len(encoded_input_grads)
             )
 
             class SubgraphOp(Function):
                 def __init__(self):
                     self.inputs = None
+                    self.output_shapes = None
 
                 def forward(self, *inputs):
                     self.inputs = inputs
-                    return apply(forward_fn(), *inputs)
+                    outputs = apply(forward_fn(), *inputs)
+                    if len(outputs) > 1:
+                        self.output_shapes = [output.shape for output in outputs]
+                    return outputs
 
                 def backward(self, *output_grads):
                     inputs = self.inputs
-                    self.inputs = None
-                    encoded_input_grads = apply(backward_fn(), *inputs, *output_grads)
-                    input_grads = [
-                        encoded_input_grads[i] if i is not None else None
-                        for i in indices
-                    ]
+                    any_valid = False
+                    all_valid = True
+                    for output_grad in output_grads:
+                        if output_grad is None:
+                            all_valid = False
+                        else:
+                            any_valid = True
+                    if not any_valid:
+                        input_grads = [None] * len(indices)
+                    else:
+                        if not all_valid:
+                            assert self.output_shapes is not None
+                            from ...functional import zeros
+
+                            output_grads = [
+                                zeros(self.output_shapes[i]) if grad is None else grad
+                                for i, grad in enumerate(output_grads)
+                            ]
+                        self = None
+                        encoded_input_grads = apply(
+                            backward_fn(), *inputs, *output_grads
+                        )
+                        input_grads = [
+                            encoded_input_grads[i] if i is not None else None
+                            for i in indices
+                        ]
                     return input_grads
 
             gen.close()

imperative/python/megengine/functional/nn.py

@@ -896,7 +896,7 @@ def prelu(inp: Tensor, weight: Tensor) -> Tensor:
 
 
 @lru_cache(maxsize=None)
-def _get_leagk_relu_op(negative_slope, *, dtype=None, device=None):
+def _get_leaky_relu_op(negative_slope, *, dtype=None, device=None):
     @subgraph_fn(
         "LeakyReLU",
         dtype=dtype,
@@ -925,7 +925,7 @@ def leaky_relu(inp: Tensor, negative_slope: float = 0.01) -> Tensor:
 
     Refer to :class:`~.LeakyReLU` for more information.
     """
-    leakyReLU = _get_leagk_relu_op(negative_slope, dtype=inp.dtype, device=inp.device)
+    leakyReLU = _get_leaky_relu_op(negative_slope, dtype=inp.dtype, device=inp.device)
     (oup,) = leakyReLU(inp)
     return oup
 
@@ -1399,7 +1399,7 @@ def _get_sync_bn_ops(device, dtype, eps_mode, ndim, channels):
             f("fma3",  input, inv_var_wt,
                     f("+",  f("*", neg_channel_mean, inv_var_wt),
                             bias))
-        return (outvar, channel_mean, channel_var, inv_var_wt), (True, False, False, False)
+        return (outvar, channel_mean, channel_var), (True, True, True)
 
     @subgraph("SyncBnStage1Inference", dtype, device, 6)
     def syncbn_stage1_inference(inputs, f, c):
@@ -1509,7 +1509,7 @@ def sync_batch_norm(
     """
     _eps_mode = eps_mode.lower()
     assert _eps_mode in {"max", "additive"}, "unknown eps_mode: {}".format(eps_mode)
-    if _eps_mode == "additive" and not (is_distributed() and training):
+    if _eps_mode == "additive" and not (is_distributed() or training):
         return batch_norm(
             inp,
             running_mean,

imperative/python/src/grad.cpp

@@ -121,13 +121,13 @@ void GradKeyWrapper::enter() {
     m_key = m_transformation->key();
     m_key->name(m_name);
     grad_key_map[m_key] = this;
-    TransformationManager::get_instance().register_at<TransformationManager::Grad>(
-            m_transformation);
+    m_transformation_guard =
+            TransformationManager::get_instance()
+                    .register_at<TransformationManager::Grad>(m_transformation);
 }
 
 void GradKeyWrapper::exit() {
-    TransformationManager::get_instance().unregister<TransformationManager::Grad>(
-            m_transformation);
+    m_transformation_guard.reset();
     grad_key_map.erase(m_key);
     m_key = {};
     m_transformation.reset();

imperative/python/src/grad.h

@@ -29,6 +29,7 @@ struct GradKeyWrapper : NonCopyableObj {
     std::string m_name;
     std::shared_ptr<GradKey> m_key;
     std::shared_ptr<GradTransformation> m_transformation;
+    std::unique_ptr<CleanupGuard<>> m_transformation_guard;
 
     GradKeyWrapper();
 

imperative/python/src/tensor.cpp

@@ -449,15 +449,24 @@ void init_tensor(py::module m) {
                     interpreter::Interpreter::inst().create_channel())
                     ->get();
     interpreter_for_py = channel;
-    transformations.register_at<Segment::Eval>(
-            std::make_shared<InterpreterTransformation>(
-                    std::shared_ptr<Channel>(channel, [](Channel*) {})));
-    transformations.register_at<Segment::Scalar>(
-            std::make_shared<ScalarTransformation>());
-    transformations.register_at<Segment::DTypePromote>(
-            std::make_shared<DTypePromoteTransformation>());
-    transformations.register_at<Segment::DimExpansion>(
-            std::make_shared<DimExpansionTransformation>());
+    MGB_MARK_USED_VAR(
+            transformations
+                    .register_at<Segment::Eval>(
+                            std::make_shared<InterpreterTransformation>(
+                                    std::shared_ptr<Channel>(channel, [](Channel*) {})))
+                    .release());
+    MGB_MARK_USED_VAR(transformations
+                              .register_at<Segment::Scalar>(
+                                      std::make_shared<ScalarTransformation>())
+                              .release());
+    MGB_MARK_USED_VAR(transformations
+                              .register_at<Segment::DTypePromote>(
+                                      std::make_shared<DTypePromoteTransformation>())
+                              .release());
+    MGB_MARK_USED_VAR(transformations
+                              .register_at<Segment::DimExpansion>(
+                                      std::make_shared<DimExpansionTransformation>())
+                              .release());
 
     static py::exception<interpreter::AsyncError> py_async_error(
             m, "AsyncError", PyExc_RuntimeError);
@@ -681,6 +690,9 @@ void init_tensor(py::module m) {
         std::pair<size_t, std::shared_ptr<GraphProfiler>> profiler;
         std::optional<TraceResult> trace_result;
         std::function<bool(py::object, py::object)> array_comparator;
+        std::unique_ptr<CleanupGuard<>> tracing_guard;
+        std::unique_ptr<CleanupGuard<>> compiled_guard;
+        std::unique_ptr<CleanupGuard<>> lazy_eval_guard;
 
         bool compare_value(ValueRef lhs, ValueRef rhs) {
             auto lvalue = lhs.cast_ref<HostValue>();
@@ -730,13 +742,16 @@ void init_tensor(py::module m) {
                                 std::make_shared<GraphProfiler>(&current_graph));
                     }
                 }
-                transformations.register_at<Segment::Trace>(self.compiled);
+                compiled_guard =
+                        transformations.register_at<Segment::Trace>(self.compiled);
                 // start execute because InputCallback depends
                 self.compiled->execute();
             } else if (self.tracing) {
-                transformations.register_at<Segment::Trace>(self.tracing);
+                tracing_guard =
+                        transformations.register_at<Segment::Trace>(self.tracing);
                 if (self.lazy_eval) {
-                    transformations.register_at<Segment::Eval>(self.lazy_eval);
+                    lazy_eval_guard =
+                            transformations.register_at<Segment::Eval>(self.lazy_eval);
                 }
             } else {
                 mgb_throw(MegBrainError, "invalid state: neither tracing nor compiled");
@@ -746,16 +761,16 @@ void init_tensor(py::module m) {
         void exit() {
             auto& self = *this;
             if (self.tracing) {
-                transformations.unregister<Segment::Trace>(self.tracing);
+                tracing_guard.reset();
                 self.trace_result = self.tracing->get_result();
                 self.tracing.reset();
                 if (self.lazy_eval) {
                     auto lazy_eval = std::move(self.lazy_eval);
-                    transformations.unregister<Segment::Eval>(lazy_eval);
+                    lazy_eval_guard.reset();
                     lazy_eval->check_exception();
                 }
             } else if (self.compiled) {
-                transformations.unregister<Segment::Trace>(self.compiled);
+                compiled_guard.reset();
                 self.compiled->wait();
             } else {
                 mgb_throw(MegBrainError, "invalid state: neither tracing nor compiled");
@@ -829,17 +844,19 @@ void init_tensor(py::module m) {
                  [](Trace& self) {
                      mgb_assert(bool(self.tracing) ^ bool(self.compiled));
                      if (self.tracing) {
-                         transformations.unregister<Segment::Trace>(self.tracing);
+                         self.tracing_guard.reset();
                      } else if (self.compiled) {
-                         transformations.unregister<Segment::Trace>(self.compiled);
+                         self.compiled_guard.reset();
                      }
                  })
             .def("end_excluded_region", [](Trace& self) {
                 mgb_assert(bool(self.tracing) ^ bool(self.compiled));
                 if (self.tracing) {
-                    transformations.register_at<Segment::Trace>(self.tracing);
+                    self.tracing_guard =
+                            transformations.register_at<Segment::Trace>(self.tracing);
                 } else if (self.compiled) {
-                    transformations.register_at<Segment::Trace>(self.compiled);
+                    self.compiled_guard =
+                            transformations.register_at<Segment::Trace>(self.compiled);
                 }
             });
 
@@ -900,11 +917,8 @@ void init_tensor(py::module m) {
                 GradKeyWrapper::get(output.cast<GradKeyValue>())));
     });
 
-    m.def("set_grad", [](py::object py_key, py::function backward_fn,
-                         std::vector<py::object> inputs,
+    m.def("set_grad", [](py::function backward_fn, std::vector<py::object> inputs,
                          std::vector<py::object> outputs) {
-        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) -> ValueRefList {
             py::list output_grad_tws;
@@ -937,8 +951,8 @@ void init_tensor(py::module m) {
             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);
+        auto wrapped_output_values =
+                imperative::apply(SetGrad(generic_backward_fn, inputs.size()), values);
         std::vector<py::object> wrapped_outputs;
         mgb_assert(wrapped_output_values.size() == outputs.size());
         for (auto&& output_value : wrapped_output_values) {
@@ -956,8 +970,10 @@ void init_tensor(py::module m) {
             mgb_assert(module_trace_hook);
             module_trace_transformation =
                     std::make_shared<ModuleTraceTransformation>(module_trace_hook);
-            transformations.register_at<Segment::ModuleTrace>(
-                    module_trace_transformation);
+            MGB_MARK_USED_VAR(transformations
+                                      .register_at<Segment::ModuleTrace>(
+                                              module_trace_transformation)
+                                      .release());
         }
         return module_trace_transformation;
     };

imperative/python/src/transformation.h

@@ -18,11 +18,13 @@
 
 #include "megbrain/imperative/dispatch.h"
 #include "megbrain/imperative/transformation.h"
+#include "megbrain/imperative/utils/helper.h"
 #include "megbrain/imperative/value.h"
 #include "megbrain/utils/small_vector.h"
 
 namespace mgb::imperative::python {
 struct TransformationManager {
+public:
     enum Segment {
         ModuleTrace,
         DTypePromote,
@@ -35,8 +37,21 @@ struct TransformationManager {
 
     std::array<std::vector<std::shared_ptr<Transformation>>, 7> segments;
 
+private:
+    template <Segment segment>
+    void unregister(std::shared_ptr<Transformation> transformation) noexcept {
+        mgb_assert(segment < segments.size());
+        auto iter = std::find(
+                segments[segment].begin(), segments[segment].end(), transformation);
+        mgb_assert(iter != segments[segment].end());
+        transformation->unregister();
+        segments[segment].erase(iter);
+    }
+
+public:
     template <Segment segment>
-    void register_at(std::shared_ptr<Transformation> transformation) {
+    [[nodiscard]] std::unique_ptr<CleanupGuard<>> register_at(
+            std::shared_ptr<Transformation> transformation) {
         mgb_assert(segment < segments.size());
         std::shared_ptr<Transformation> next;
         for (size_t i = segment; i < segments.size(); ++i) {
@@ -51,16 +66,8 @@ struct TransformationManager {
             transformation->register_at(next->pos());
         }
         segments[segment].push_back(transformation);
-    }
-
-    template <Segment segment>
-    void unregister(std::shared_ptr<Transformation> transformation) noexcept {
-        mgb_assert(segment < segments.size());
-        auto iter = std::find(
-                segments[segment].begin(), segments[segment].end(), transformation);
-        mgb_assert(iter != segments[segment].end());
-        transformation->unregister();
-        segments[segment].erase(iter);
+        return std::make_unique<CleanupGuard<>>(
+                [this, transformation]() { unregister<segment>(transformation); });
     }
 
     static TransformationManager& get_instance() {

imperative/python/test/unit/autodiff/test_grad_manger.py

@@ -452,6 +452,8 @@ def test_2nd_grad_with_custom_gradient():
             return y
 
         def backward(self, dy):
+            if dy is None:
+                return None
             dx = -MySin()(self.inp) * dy
             return dx
 

imperative/python/test/unit/core/test_autodiff.py

@@ -14,6 +14,7 @@ import pytest
 import megengine as mge
 import megengine.distributed as dist
 import megengine.functional as F
+import megengine.module as M
 from megengine.core._imperative_rt import CompNode, TensorAttr, imperative
 from megengine.core._imperative_rt.core2 import TensorWeakRef, apply, sync
 from megengine.core.autodiff.grad import Grad

imperative/python/test/unit/core/test_function.py

@@ -318,3 +318,41 @@ def test_throw_on_non_tensor_argument():
     func = NonTensorArg()
     with pytest.raises(TypeError, match=r"op .* expect type Tensor as inputs"):
         func(x, 1)
+
+
+def test_multiple_grad():
+    data_shape = (9, 2, 6)
+    av = np.random.random(data_shape).astype(np.float32)
+
+    class MulFunc(Function):
+        def forward(self, a):
+            self.a = a
+            return a * 10
+
+        def backward(self, grad_o):
+            return grad_o * 20
+
+    class Simple(Module):
+        def __init__(self, a):
+            super().__init__()
+            self.a = Parameter(a, dtype=np.float32)
+            self.layer1 = MulFunc()
+
+        def forward(self):
+            x = self.layer1(self.a)
+            return x
+
+    net = Simple(av)
+    gm = ad.GradManager().attach(net.parameters())
+    gm2 = ad.GradManager().attach(net.parameters())
+    opt = optimizer.SGD(net.parameters(), lr=1.0)
+
+    opt.clear_grad()
+    with gm:
+        with gm2:
+            loss = net()
+        gm.backward(loss.sum())
+    opt.step()
+
+    np.testing.assert_almost_equal(loss.numpy(), (av * 10))
+    np.testing.assert_almost_equal(net.a.numpy(), (av - 20))

imperative/python/test/unit/core/test_subgraph.py

@@ -109,3 +109,46 @@ def test_subgraph(device, batch_size, channels, use_trace, symbolic, gopt_level,
 
         _assert_allclose(out1.numpy(), out2.numpy())
         _assert_allclose(grad1.numpy(), grad2.numpy())
+
+
+@functools.lru_cache(maxsize=None)
+def _get_mul_fn(dtype, device):
+    @subgraph_fn(
+        "Mul",
+        dtype=dtype,
+        device=device,
+        nr_inputs=2,
+        gopt_level=None,
+        jit_fusion=False,
+        custom_grad=True,
+    )
+    def mul(inputs, f, c):
+        x, y = inputs[0:2]
+        z = f("*", x, y)
+        (dz,) = yield (z,)
+        dx = f("*", dz, y)
+        dy = f("*", dz, x)
+        yield (dx, dy)
+
+    return mul
+
+
+def test_subgraph_jit_backward():
+    x_np = np.random.rand(3, 4, 5).astype("float32")
+    x1 = megengine.Tensor(x_np)
+    x2 = megengine.Tensor(x_np)
+    mul = _get_mul_fn(x1.dtype, x1.device)
+    gm = GradManager()
+    gm.attach([x1, x2])
+    with gm:
+        y1 = x1 * x1
+        y2 = mul(x2, x2)
+        gm.backward(y1)
+    with gm:
+        y1 = x1 * x1
+        y2 = mul(x2, x2)
+        gm.backward(y1 + y2)
+    with gm:
+        y1 = x1 * x1
+        y2 = mul(x2, x2)
+        gm.backward(y2)

imperative/src/impl/dispatch.cpp

@@ -18,18 +18,44 @@
 
 namespace mgb {
 namespace imperative {
+namespace {
 
-ValueRefList apply(const Operator& op, Span<ValueRef> inputs) {
+ValueRefList apply_release(const Operator& op, Span<ValueRef> inputs) {
+    auto& context = Transformation::get_context();
+    size_t& depth = context.next_transformation;
+    mgb_assert(depth < context.transformations.size());
+    auto& transformation = *context.transformations[depth++];
+    CleanupGuard _{[&] { --depth; }};
+    return transformation.apply_transformation(op, inputs);
+}
+
+MGB_NOINLINE ValueRefList apply_debug(const Operator& op, Span<ValueRef> inputs) {
     auto& context = Transformation::get_context();
     size_t& depth = context.next_transformation;
-    // TODO: add fallback transformation
-    bool fallback = depth >= context.transformations.size();
-    if (mgb_unlikely(fallback)) {
-        return op.fallback(inputs);
+    mgb_assert(depth < context.transformations.size());
+    static const char tabs[] = "\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t";
+    const char* prefix = tabs + (sizeof(tabs) / sizeof(char)) - depth - 1;
+    mgb_log_debug(
+            "%s apply %s to %s", prefix, op.to_string().c_str(),
+            imperative::to_string(inputs).c_str());
+    ValueRefList result;
+    auto& transformation = *context.transformations[depth++];
+    CleanupGuard _{[&] { --depth; }};
+    result = transformation.apply_transformation(op, inputs);
+    mgb_log_debug(
+            "%s returns %s", prefix,
+            imperative::to_string(Span<ValueRef>(result)).c_str());
+    return result;
+}
+
+}  // namespace
+
+ValueRefList apply(const Operator& op, Span<ValueRef> inputs) {
+    static bool debug = MGB_GETENV("MGE_LOG_OP_DISPATCH");
+    if (mgb_unlikely(debug)) {
+        return apply_debug(op, inputs);
     } else {
-        auto& transformation = *context.transformations[depth++];
-        CleanupGuard _{[&] { --depth; }};
-        return transformation.apply_transformation(op, inputs);
+        return apply_release(op, inputs);
     }
 }
 

imperative/src/impl/op_def.cpp

@@ -106,7 +106,8 @@ EncodedSubgraph OpDef::make_forward_graph(
 }
 
 std::string OpDef::to_string() const {
-    std::string builder = trait()->make_name(*this) + "{";
+    std::string builder = trait()->name;
+    builder += "{";
     for (auto&& [name, value] : props(*this)) {
         builder += name;
         builder += ": ";
@@ -196,7 +197,7 @@ std::string Subgraph::repr() const {
         if (auto* p = op->try_cast_final<OprAttr>()) {
             buf << p->type;
         } else {
-            buf << op->make_name();
+            buf << op->to_string();
         }
         for (size_t i : ins) {
             buf << " ";

imperative/src/impl/ops/batch_norm.cpp

@@ -11,13 +11,94 @@
 
 #include "megbrain/opr/dnn/batch_norm.h"
 #include "../op_trait.h"
+#include "megbrain/imperative/graph_builder.h"
 #include "megbrain/imperative/ops/autogen.h"
+#include "megbrain/imperative/ops/utility.h"
+#include "megbrain/imperative/proxy_graph_detail.h"
+#include "megbrain/imperative/subgraph_detail.h"
+#include "megbrain/tensor.h"
 
 namespace mgb {
 namespace imperative {
-
 namespace {
 
+EncodedSubgraph generate_batchnorm_backward_graph(DType dtype, CompNode device) {
+    Subgraph::Builder<LogicalTensorDesc> builder{
+            [](std::shared_ptr<OpDef> op, SmallVector<LogicalTensorDesc> inputs,
+               size_t nr_outputs) {
+                auto [outputs, validated] =
+                        OpDef::infer_output_attrs_fallible(*op, inputs);
+                mgb_assert(outputs.size() == nr_outputs, "nr_outputs mismatch");
+                return outputs;
+            }};
+    auto f = [&](auto&& op, auto... args) {
+        return builder.write_expr(
+                op, Subgraph::vars_t({(Subgraph::var_t)args...}), 1)[0];
+    };
+
+    auto prod = Reduce::make(megdnn::param::Reduce(Reduce::Mode::PRODUCT, 0));
+    auto sum = Reduce::make(megdnn::param::Reduce(Reduce::Mode::SUM));
+    auto sub = Elemwise::make(Elemwise::Mode::SUB);
+    auto mul = Elemwise::make(Elemwise::Mode::MUL);
+    auto div = Elemwise::make(Elemwise::Mode::TRUE_DIV);
+    auto floor_div = Elemwise::make(Elemwise::Mode::FLOOR_DIV);
+    auto broadcast = Broadcast::make();
+
+    auto c = [&](TensorPtr tensor, DType dtype) {
+        auto result = builder.write_constant(
+                tensor, {TensorLayout{tensor->dtype()}, tensor->comp_node()});
+        if (tensor->dtype() != dtype) {
+            result = f(TypeCvt::make(dtype), result);
+        }
+        return result;
+    };
+    auto ci = [&](megdnn::dt_int32 value) {
+        return c(Tensor::make_scalar(DTypeScalar(value), device), dtype::Int32());
+    };
+    auto cf = [&](megdnn::dt_float32 value) {
+        return c(Tensor::make_scalar(DTypeScalar(value), device), dtype);
+    };
+
+    auto desc = LogicalTensorDesc{TensorLayout{dtype}, device};
+    auto x = builder.write_input(desc);
+    auto y_grad = builder.write_input(desc);
+    auto save_mean = builder.write_input(desc);
+    auto save_invstd = builder.write_input(desc);
+    auto weight = builder.write_input(desc);
+    auto reserved = builder.write_input(desc);
+    MGB_MARK_USED_VAR(reserved);
+
+    // assert x.ndim == 4
+    auto input_shape = f(GetVarShape::make(), x);
+    auto channels = f(GetVarShape::make(1), x);
+    auto reduce_shape = f(Concat::make(0, device), ci(1), channels, ci(1), ci(1));
+    auto input_elems = f(prod, input_shape);
+    auto reduce_size = f(floor_div, input_elems, channels);
+    auto reduce_size_f = f(TypeCvt::make(dtype), reduce_size);
+    auto mean = f(broadcast, save_mean, input_shape);
+    auto invstd = save_invstd;
+    auto norm = f(div, cf(1), reduce_size_f);
+    auto output_grad_sum = f(sum, y_grad, reduce_shape);
+    auto dot_p = f(sum, f(mul, y_grad, f(sub, x, mean)), reduce_shape);
+    auto mean_grad = f(broadcast, f(mul, output_grad_sum, norm), input_shape);
+    auto proj_scale =
+            f(broadcast, f(mul, f(mul, dot_p, norm), f(mul, invstd, invstd)),
+              input_shape);
+    auto grad_scale = f(
+            mul, f(broadcast, invstd, input_shape), f(broadcast, weight, input_shape));
+    auto proj = f(mul, f(sub, x, mean), proj_scale);
+    auto x_grad = f(mul, f(sub, f(sub, y_grad, proj), mean_grad), grad_scale);
+    auto weight_grad = f(mul, dot_p, invstd);
+    auto bias_grad = output_grad_sum;
+
+    builder.add_outputs({weight_grad, bias_grad, x_grad});
+
+    auto bn_backward = builder.encode();
+    return bn_backward;
+}
+
+namespace bn {
+
 std::shared_ptr<OpDef> make_from_op_node(cg::OperatorNodeBase* node_) {
     auto* node = &node_->cast_final_safe<opr::BatchNorm>();
     return BatchNorm::make(node->param());
@@ -72,8 +153,60 @@ OP_TRAIT_REG(BatchNorm, BatchNorm, opr::BatchNorm)
         .apply_on_var_node(apply_on_var_node)
         .infer_output_attrs_fallible(infer_output_attrs_fallible)
         .fallback();
-}  // anonymous namespace
 
+}  // namespace bn
+
+namespace bn_backward {
+
+std::shared_ptr<OpDef> make_from_op_node(cg::OperatorNodeBase* node_) {
+    auto* node = &node_->cast_final_safe<opr::BatchNormBackward>();
+    return BatchNormBackward::make(node->param());
+}
+
+VarNodeArray apply_on_var_node(const OpDef& def, const VarNodeArray& inputs) {
+    auto& op = def.cast_final_safe<BatchNormBackward>();
+    cg::SymbolVar x, y_grad, save_mean, save_variance, weight, reserve;
+    x = inputs[0];
+    y_grad = inputs[1];
+    save_mean = inputs[2];
+    save_variance = inputs[3];
+    weight = inputs[4];
+    if (inputs.size() == 6) {
+        reserve = inputs[5];
+    }
+    return opr::BatchNormBackward::make(
+                   x, y_grad, save_mean, save_variance, weight, reserve, op.param())[0]
+            .node()
+            ->owner_opr()
+            ->usable_output();
+}
+
+EncodedSubgraph make_backward_graph(
+        const OpDef& def, const SmallVector<LogicalTensorDesc>& inputs,
+        const SmallVector<bool>& input_requires_grad,
+        const SmallVector<bool>& output_has_grad) {
+    def.cast_final_safe<BatchNormBackward>();
+    size_t nr_inputs = 6;
+    size_t nr_outputs = 3;
+    mgb_assert(inputs.size() == nr_inputs);
+    mgb_assert(input_requires_grad.size() == nr_inputs);
+    mgb_assert(output_has_grad.size() == nr_outputs);
+    auto dtype = inputs[0].layout.dtype;
+    auto device = inputs[0].comp_node;
+    auto bn_backward = generate_batchnorm_backward_graph(dtype, device);
+    auto bn_double_backward = subgraph_detail::make_backward_graph_from_forward(
+            bn_backward, inputs, input_requires_grad, output_has_grad);
+    return bn_double_backward;
+}
+
+OP_TRAIT_REG(BatchNormBackward, BatchNormBackward, opr::BatchNormBackward)
+        .make_from_op_node(make_from_op_node)
+        .apply_on_var_node(apply_on_var_node)
+        .make_backward_graph(make_backward_graph)
+        .fallback();
+}  // namespace bn_backward
+
+}  // anonymous namespace
 }  // namespace imperative
 }  // namespace mgb
 

imperative/src/impl/ops/utility.cpp

@@ -762,7 +762,9 @@ EncodedSubgraph make_backward_graph(
         const OpDef& def, const SmallVector<LogicalTensorDesc>& inputs,
         const SmallVector<bool>& input_requires_grad,
         const SmallVector<bool>& output_has_grad) {
-    return {};
+    return OpDef::make_backward_graph(
+            *def.cast_final_safe<JITFusionOp>().op, inputs, input_requires_grad,
+            output_has_grad);
 }
 
 OP_TRAIT_REG(JITFusionOp, JITFusionOp)

imperative/src/impl/subgraph_detail.cpp

@@ -96,10 +96,11 @@ SmallVector<LayoutConstraintCallback> get_input_layout_constraint(
     return res;
 }
 
-static EncodedSubgraph make_backward_graph_from_forward(
+EncodedSubgraph make_backward_graph_from_forward(
+        const EncodedSubgraph& forward_graph,
         const SmallVector<LogicalTensorDesc>& inputs,
         const SmallVector<bool>& input_requires_grad,
-        const SmallVector<bool>& output_has_grad, EncodedSubgraph forward_graph) {
+        const SmallVector<bool>& output_has_grad) {
     using namespace std::placeholders;
     using var_t = Subgraph::var_t;
     using vars_t = Subgraph::vars_t;
@@ -179,7 +180,7 @@ EncodedSubgraph make_backward_graph(
         const SmallVector<bool>& output_has_grad) {
     auto forward_graph = OpDef::make_forward_graph(def, inputs);
     return make_backward_graph_from_forward(
-            inputs, input_requires_grad, output_has_grad, forward_graph);
+            forward_graph, inputs, input_requires_grad, output_has_grad);
 }
 
 }  // namespace subgraph_detail

imperative/src/impl/transformations/eval.cpp

@@ -139,7 +139,7 @@ ValueRefList InterpreterTransformation::apply_transformation(
             return {ValueRef()};
         }
     } else {
-        return imperative::apply(op, inputs);
+        return op.fallback(inputs);
     }
 }
 

imperative/src/impl/transformations/grad.cpp

@@ -62,7 +62,8 @@ BackwardGraphWithClosure::BackwardGraphWithClosure(
         std::shared_ptr<OpDef> op, Span<ValueRef> inputs, Span<ValueRef> outputs)
         : backward_graph(backward_graph),
           output_mask_offset(inputs.size()),
-          grad_mask_offset(inputs.size() + outputs.size()) {
+          grad_mask_offset(inputs.size() + outputs.size()),
+          op(op) {
     auto& save_for_backward = backward_graph->save_for_backward;
     mgb_assert(save_for_backward.size() == inputs.size() + 2 * outputs.size());
     size_t count = std::count_if(
@@ -92,6 +93,13 @@ BackwardGraphWithClosure::BackwardGraphWithClosure(
             closure.push_back(outputs[i]);
         }
     }
+    if (outputs.size() > 1) {
+        output_descs.reserve(outputs.size());
+        for (auto&& output : outputs) {
+            auto symbolic_shape = imperative::apply(*GetVarShape::make(), output)[0];
+            output_descs.push_back({symbolic_shape, output.dtype(), output.device()});
+        }
+    }
 }
 void BackwardGraphWithClosure::operator()(
         Span<ValueRef> grads, std::function<void(size_t, ValueRef)> receiver) {
@@ -100,23 +108,46 @@ void BackwardGraphWithClosure::operator()(
     for (auto&& value : closure) {
         args[nargs++] = value;
     }
-    bool null_grad = false;
+    size_t null_grad = 0;
+    size_t valid_grad = 0;
     for (size_t i = 0; i < grads.size(); ++i) {
         if (backward_graph->save_for_backward[grad_mask_offset + i]) {
             if (grads[i]) {
-                mgb_assert(!null_grad, "null_grad");
+                valid_grad++;
                 args[nargs++] = grads[i];
             } else {
-                null_grad = true;
+                null_grad++;
+                nargs++;
             }
         }
     }
-    if (null_grad) {
+    if (valid_grad == 0) {
         return;
     }
-    auto igrads_ = imperative::apply(backward_graph->backward, Span(args, nargs));
-    SmallVector<ValueRef> igrads = {igrads_.begin(), igrads_.end()};
-    igrads_.clear();
+    if (null_grad > 0) {
+        auto zeros_like = [](const OutputDesc& desc) {
+            HostTensorStorage storage(*desc.device);
+            storage.ensure_size(desc.dtype->size());
+            std::memset(storage.ptr(), 0, desc.dtype->size());
+            auto t = imperative::apply(
+                    CreateTensor(
+                            CreateTensor::Unique, *desc.device, *desc.dtype,
+                            ValueShape()),
+                    HostStorage::make(storage))[0];
+            auto res = imperative::apply(*Broadcast::make(), t, desc.shape)[0];
+            return res;
+        };
+        nargs = closure.size();
+        for (size_t i = 0; i < grads.size(); ++i) {
+            if (backward_graph->save_for_backward[grad_mask_offset + i]) {
+                if (!grads[i]) {
+                    args[nargs] = zeros_like(output_descs[i]);
+                }
+                nargs++;
+            }
+        }
+    }
+    auto igrads = imperative::apply(backward_graph->backward, Span(args, nargs));
     auto&& iter = igrads.begin();
     for (auto [i, p] : ranges::views::enumerate(backward_graph->input_has_grad)) {
         if (p) {
@@ -221,9 +252,11 @@ void GradKey::backward() {
             if (!dest) {
                 continue;
             }
-            if (!dest.m_producer_record.next && dest->callback && dest->m_grad) {
+            if (!dest.m_producer_record.next && dest->callback) {
                 // I'm the last grad producer, invoke callback
-                dest->callback(dest->m_grad);
+                if (dest->m_grad) {
+                    dest->callback(dest->m_grad);
+                }
             }
         }
         grad_fn->clear();
@@ -394,16 +427,22 @@ ValueRefList GradTransformation::apply_transformation(
         return imperative::apply(op, inputs);
     }
     if (auto* attach_grad = op.as<AttachGrad>()) {
-        if (!has_key(attach_grad->key())) {
+        auto& tensor = inputs[0];
+        if (auto&& grad_value = tensor.as_ref(m_value_type)) {
+            mgb_assert(!has_key(attach_grad->key()));
+            auto output = fallback()[0];
+            return record_grad(m_value_type.make(output, m_key, grad_value->slot()));
+        } else if (!has_key(attach_grad->key())) {
             return fallback();
+        } else {
+            GenericFunction callback =
+                    (GenericFunction&)inputs[1].cast<FunctionValue>();
+            auto output = attach_grad->key()->attach(tensor, [callback](ValueRef grad) {
+                auto ret = callback({&grad, 1});
+                assert(ret.empty());
+            });
+            return {record_grad(output)};
         }
-        auto tensor = inputs[0];
-        GenericFunction callback = (GenericFunction&)inputs[1].cast<FunctionValue>();
-        auto output = attach_grad->key()->attach(tensor, [callback](ValueRef grad) {
-            auto ret = callback({&grad, 1});
-            assert(ret.empty());
-        });
-        return {record_grad(output)};
     } else if (auto* grad_backward = op.as<GradBackward>()) {
         if (!has_key(grad_backward->key())) {
             return fallback();
@@ -431,10 +470,10 @@ ValueRefList GradTransformation::apply_transformation(
         mgb_assert(inputs.size() > nr_inputs);
         size_t nr_outputs = inputs.size() - nr_inputs;
         Span<ValueRef> inputs_ = {inputs.data(), nr_inputs};
-        Span<ValueRef> outputs_ = {inputs.data() + nr_inputs, nr_outputs};
-        backward.m_input_has_grad = SmallVector(nr_inputs, true);
-        backward.m_output_attrs =
-                SmallVector(nr_outputs, CustomBackward::OutputAttr{true, true});
+        auto outputs_ = fallback();
+        backward.m_input_has_grad.resize(nr_inputs, true);
+        backward.m_output_attrs.resize(
+                nr_outputs, CustomBackward::OutputAttr{true, true});
         backward.m_backward = [fn = set_grad->grad_fn()](Span<ValueRef> inputs) {
             auto result = fn(inputs);
             return SmallVector<ValueRef>(result.begin(), result.end());

imperative/src/include/megbrain/imperative/graph_builder.h

@@ -31,6 +31,7 @@ class Subgraph::Builder {
     using infer_fn_t = std::function<descs_t(op_t, descs_t, size_t)>;
     using encoded_graph_t = EncodedSubgraph;
     using var_map_t = std::unordered_map<var_t, var_t>;
+    using mask_t = SmallVector<bool>;
     vars_t m_inputs;
     SmallVector<std::pair<var_t, TensorPtr>> m_constants;
     vars_t m_outputs;
@@ -94,6 +95,7 @@ public:
     descs_t get_descs(vars_t vars) {
         descs_t descs;
         for (auto&& var : vars) {
+            mgb_assert(var, "invalid var");
             descs.push_back(get_desc(var));
         }
         return descs;
@@ -128,4 +130,4 @@ public:
     expr_iter_t end() { return m_exprs.end(); }
 };
 }  // namespace imperative
-}  // namespace mgb
\ No newline at end of file
+}  // namespace mgb

imperative/src/include/megbrain/imperative/ops/utility.h

@@ -38,7 +38,6 @@ struct ShapeInfer final : OpDefImplBase<ShapeInfer> {
     std::shared_ptr<OpDef> op;
     SmallVector<CompNode> devices;
     SmallVector<DType> dtypes;
-    EncodedSubgraph graph;
     ShapeInfer() = default;
     ShapeInfer(
             std::shared_ptr<OpDef> op, SmallVector<CompNode> devices,

imperative/src/include/megbrain/imperative/subgraph_detail.h

@@ -39,6 +39,11 @@ EncodedSubgraph make_backward_graph(
 SmallVector<VarNode::LayoutConstraintCallback> get_input_layout_constraint(
         const OpDef& def, const SmallVector<TensorPtr>& inputs);
 
+EncodedSubgraph make_backward_graph_from_forward(
+        const EncodedSubgraph& forward, const SmallVector<LogicalTensorDesc>& inputs,
+        const SmallVector<bool>& input_requires_grad,
+        const SmallVector<bool>& output_has_grad);
+
 }  // namespace subgraph_detail
 }  // namespace imperative
-}  // namespace mgb
\ No newline at end of file
+}  // namespace mgb

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

@@ -29,6 +29,15 @@ struct BackwardGraphWithClosure {
     SmallVector<ValueRef> closure;
     size_t output_mask_offset;
     size_t grad_mask_offset;
+    std::shared_ptr<OpDef> op;
+
+    struct OutputDesc {
+        ValueRef shape;
+        DTypeValue::ref_t dtype;
+        CompNodeValue::ref_t device;
+    };
+
+    SmallVector<OutputDesc> output_descs;
 
     BackwardGraphWithClosure(
             std::shared_ptr<OptimizedBackwardGraphResult> backward_graph,
@@ -356,20 +365,22 @@ public:
 
 class SetGrad : public OperatorImpl<SetGrad> {
 private:
-    std::shared_ptr<GradKey> m_key;
     GenericFunction m_grad_fn;
     size_t m_nr_inputs;
 
 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) {}
+    SetGrad(GenericFunction grad_fn, size_t nr_inputs)
+            : m_grad_fn(grad_fn), m_nr_inputs(nr_inputs) {}
 
     GenericFunction grad_fn() const { return m_grad_fn; }
 
     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());
+    std::string to_string() const override { return ssprintf("SetGradValue{}"); }
+
+    ValueRefList fallback(Span<ValueRef> inputs) const override {
+        auto outputs = inputs.sub(m_nr_inputs, inputs.size() - m_nr_inputs);
+        return {outputs.begin(), outputs.end()};
     }
 };
 

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

@@ -15,12 +15,14 @@
 #include <memory>
 #include <sstream>
 
+#include "megbrain/utils/metahelper.h"
+
 namespace mgb {
 
 namespace imperative {
 
-template <typename T>
-class CleanupGuard {
+template <typename T = std::function<void()>>
+class CleanupGuard : public NonCopyableObj {
 private:
     T m_callback;
 
@@ -37,4 +39,4 @@ inline std::string quoted(std::string str) {
 
 }  // namespace imperative
 
-}  // namespace mgb
\ No newline at end of file
+}  // namespace mgb

src/core/include/megbrain/ir/ops.td

@@ -89,6 +89,8 @@ def SlidingWindowTranspose : MgbHashableOp<"SlidingWindowTranspose", [SlidingWin
 
 def BatchNorm : MgbHashableOp<"BatchNorm", [BNParam]>;
 
+def BatchNormBackward : MgbHashableOp<"BatchNormBackward", [BNParam]>;
+
 def ROIAlign: MgbHashableOp<"ROIAlign", [ROIAlignParam]>;
 def Correlation: MgbHashableOp<"Correlation", [CorrelationParam]>;