refactor(dispatch): implement grad

GitOrigin-RevId: d8367f9587093919c4dcb40361c7f91a9589f6c7

imperative/src/impl/transformations/grad.cpp

+/**
+ * \file imperative/src/impl/transformations/grad.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/grad.h"
+
+#include "megbrain/imperative/graph_cache.h"
+
+#include <range/v3/all.hpp>
+
+namespace mgb {
+namespace imperative {
+
+static std::shared_ptr<OptimizedBackwardGraphResult> make_optimized_backward_graph(
+        std::shared_ptr<OpDef> op, Span<ValueRef> inputs, Span<ValueRef> outputs,
+        Span<bool> inputs_require_grad) {
+    // hash
+    using OptimizedBackwardGraphCache = OpMethResultCache<
+            std::shared_ptr<OptimizedBackwardGraphResult>, SmallVector<bool>>;
+    thread_local auto cache = std::make_unique<OptimizedBackwardGraphCache>();
+    OptimizedBackwardGraphCache::key_t cache_key{op};
+    SmallVector<LogicalTensorDesc>& input_descs = cache_key.inputs;
+    std::get<0>(cache_key.extras) = inputs_require_grad.copy_into<SmallVector<bool>>();
+    input_descs.resize(inputs.size());
+    for (size_t i = 0; i < inputs.size(); ++i) {
+        input_descs[i].layout.dtype = inputs[i].dtype().cast<DTypeValue>();
+        input_descs[i].comp_node = inputs[i].device().cast<CompNodeValue>();
+    }
+
+    auto iter = cache->find(cache_key);
+    if (iter != cache->end()) {
+        return iter->second;
+    }
+
+    // slow path
+    SmallVector<bool> output_has_grad(outputs.size(), true);
+    std::shared_ptr<OptimizedBackwardGraphResult> ret;
+    auto bg = OpDef::make_backward_graph(
+            *op, input_descs, std::get<0>(cache_key.extras), output_has_grad);
+    if (!bg.graph.empty()) {
+        ret = std::make_shared<OptimizedBackwardGraphResult>(bg);
+    }
+    cache->emplace(cache_key, ret);
+    return ret;
+}
+
+BackwardGraphWithClosure::BackwardGraphWithClosure(
+        std::shared_ptr<OptimizedBackwardGraphResult> backward_graph,
+        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()) {
+    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(
+            save_for_backward.begin(), save_for_backward.end(), ranges::identity{});
+    if (!backward_graph->precomp.empty()) {
+        SmallVector<ValueRef> inputs_and_outputs;
+        for (auto&& input : inputs) {
+            inputs_and_outputs.push_back(input);
+        }
+        for (auto&& output : outputs) {
+            inputs_and_outputs.push_back(output);
+        }
+        auto precomp = imperative::apply(backward_graph->precomp, inputs_and_outputs);
+        closure.reserve(precomp.size() + count);
+        std::copy(precomp.begin(), precomp.end(), std::back_inserter(closure));
+    } else {
+        closure.reserve(count);
+    }
+    for (size_t i = 0; i < inputs.size(); ++i) {
+        if (save_for_backward[i]) {
+            closure.push_back(inputs[i]);
+        }
+    }
+    for (size_t i = 0; i < outputs.size(); ++i) {
+        if (save_for_backward[inputs.size() + i]) {
+            closure.push_back(outputs[i]);
+        }
+    }
+}
+void BackwardGraphWithClosure::operator()(
+        std::vector<ValueRef> grads, std::function<void(size_t, ValueRef)> receiver) {
+    ValueRef args[closure.size() + grads.size()];
+    size_t nargs = 0;
+    for (auto&& value : closure) {
+        args[nargs++] = value;
+    }
+    bool null_grad = false;
+    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");
+                args[nargs++] = grads[i];
+            } else {
+                null_grad = true;
+            }
+        }
+    }
+    if (null_grad) {
+        return;
+    }
+    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) {
+            receiver(i, std::move(*iter));
+            ++iter;
+        }
+    }
+}
+
+void CustomBackward::operator()(
+        std::vector<ValueRef> grads, std::function<void(size_t, ValueRef)> receiver) {
+    size_t nargs = grads.size();
+    ValueRef args[nargs];
+    for (size_t i = 0; i < nargs; ++i) {
+        args[i] = grads[i];
+    }
+    auto ret = m_backward({args, nargs});
+    for (size_t i = 0; i < ret.size(); ++i) {
+        if (auto&& t = ret[i]) {
+            receiver(i, std::move(t));
+        }
+    }
+}
+
+std::string GradSlot::to_string() const {
+    bool has_callback = bool(callback);
+    return ssprintf(
+            "GradSlot{grad=%s, has_callback=%d}", m_grad.to_string().c_str(),
+            (int)has_callback);
+}
+
+std::string GradFn::to_string() const {
+    return ssprintf("GradFn{dests=%s}", imperative::to_string(m_dests).c_str());
+}
+
+std::string GradSlotPtr::to_string() const {
+    if (!m_fn) {
+        return "<empty>";
+    }
+    return (*this)->to_string();
+}
+
+std::string GradValue::to_string() const {
+    return ssprintf(
+            "GradValue{key=\"%s\", slot=%s, value=%s}", m_key->name().c_str(),
+            m_slot.to_string().c_str(), m_value.to_string().c_str());
+}
+
+static std::unordered_map<Typeinfo*, CustomBackward::BackwardRule>&
+get_backward_rule_storage() {
+    static std::unordered_map<Typeinfo*, CustomBackward::BackwardRule> sl_storage;
+    return sl_storage;
+}
+
+bool CustomBackward::register_grad_rule(Typeinfo* typeinfo, BackwardRule rule) {
+    return get_backward_rule_storage().insert({typeinfo, rule}).second;
+}
+
+auto CustomBackward::lookup_grad_rule(Typeinfo* typeinfo) -> BackwardRule {
+    auto iter = get_backward_rule_storage().find(typeinfo);
+    if (iter == get_backward_rule_storage().end()) {
+        return {};
+    }
+    return iter->second;
+}
+
+void GradKey::backward() {
+    mgb_assert(m_frozen);
+    auto& tape = m_frozen_tape;
+    for (std::ptrdiff_t k = tape.size() - 1; k >= 0; --k) {
+        auto& [grad_fn, op] = tape[k];
+        auto grad_receiver = [&, grad_fn = grad_fn](size_t i, ValueRef grad) {
+            auto& dest = grad_fn->m_dests[i];
+            if (dest) {
+                auto& existing_grad = dest->m_grad;
+                if (!existing_grad) {
+                    existing_grad = grad;
+                } else {
+                    existing_grad = imperative::apply(
+                            ApplyOp(*Elemwise::make(Elemwise::Mode::ADD)),
+                            existing_grad, grad)[0];
+                }
+            }
+        };
+        // clang-format off
+        std::visit([&, grad_fn = grad_fn, op = op](auto&& backward) {
+            using T = std::decay_t<decltype(backward)>;
+            if constexpr (std::is_same_v<T, std::monostate>) {
+                mgb_throw(AssertionError, "invalid backward");
+            } else {
+                mgb_assert(grad_fn->m_slots.size() > 0);
+                std::vector<ValueRef> grads;
+                for (auto&& slot : grad_fn->m_slots) {
+                    grads.push_back(slot.m_grad);
+                }
+                backward(grads, grad_receiver);
+            }
+        }, grad_fn->m_backward);
+        // clang-format on
+        for (auto&& dest : grad_fn->m_dests) {
+            if (!dest) {
+                continue;
+            }
+            if (!dest.m_producer_record.next && dest->callback && dest->m_grad) {
+                // I'm the last grad producer, invoke callback
+                dest->callback(dest->m_grad);
+            }
+        }
+        grad_fn->clear();
+    }
+    tape.clear();
+}
+
+GradValue::ref_t GradKey::attach(
+        ValueRef tensor, std::function<void(ValueRef)> callback) {
+    auto grad_value = tensor.as_ref<GradValue>();
+    if (grad_value && grad_value->has_key(shared_from_this())) {
+        mgb_assert(
+                !tensor.cast<GradValue>().slot_for(shared_from_this())->callback,
+                "callback exists");
+    } else {
+        GradSlotPtr grad_slot;
+        auto& grad_fn = grad_slot.m_fn;
+        grad_fn = std::make_shared<GradFn>();
+        grad_fn->m_key = shared_from_this();
+        grad_fn->m_slots.resize(1);
+        grad_slot.m_index = 0;
+        grad_value = GradValue::make(tensor, shared_from_this(), grad_slot);
+    }
+    grad_value->slot_for(shared_from_this()).m_fn->m_slots[0].callback = callback;
+    return grad_value;
+}
+
+void GradKey::freeze() {
+    mgb_assert(m_frozen_tape.empty() && !m_frozen);
+    for (auto&& [grad_fn, op] : m_tape) {
+        if (auto valid_grad_fn = grad_fn.lock()) {
+            m_frozen_tape.push_back({valid_grad_fn, op});
+        }
+    }
+    m_tape.clear();
+    m_frozen = true;
+}
+
+std::vector<ValueRef> 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);
+            } else {
+                unwrapped_inputs.push_back(input);
+            }
+        }
+        return unwrapped_inputs;
+    };
+    if (m_suppressed) {
+        return imperative::apply(op, unwrap_inputs(inputs));
+    }
+    if (auto* op_val = op.as<ApplyOp>()) {
+        size_t nr_require_grad = 0;
+        SmallVector<bool> require_grads;
+        for (auto&& input : inputs) {
+            if (is_grad_value(input)) {
+                nr_require_grad++;
+                require_grads.push_back(true);
+            } else {
+                require_grads.push_back(false);
+            }
+        }
+        if (nr_require_grad == 0) {
+            return imperative::apply(op, inputs);
+        }
+        SmallVector<ValueRef> captured_inputs;
+        SmallVector<bool> inputs_require_grad;
+        // 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) {
+            if (auto grad_value = as_grad_value(input)) {
+                captured_inputs.push_back(capture_value(grad_value->m_value));
+                inputs_require_grad.push_back(true);
+            } else {
+                captured_inputs.push_back(capture_value(input));
+                inputs_require_grad.push_back(false);
+            }
+        }
+        decltype(std::declval<GradFn>().m_backward) backward_storage;
+        auto outputs = [&] {
+            auto backward_rule =
+                    CustomBackward::lookup_grad_rule(op_val->op().dyn_typeinfo());
+            if (backward_rule) {
+                CustomBackward backward;
+                auto optional_outputs = backward_rule(
+                        op_val->op(), {captured_inputs.data(), captured_inputs.size()},
+                        {inputs_require_grad.data(), inputs_require_grad.size()},
+                        backward);
+                if (optional_outputs) {
+                    backward_storage = backward;
+                    // backward by rule
+                    return *optional_outputs;
+                }
+            }
+            auto outputs = imperative::apply(
+                    op, {captured_inputs.begin(), captured_inputs.end()});
+            auto backward_graph = make_optimized_backward_graph(
+                    op.cast<ApplyOp>().op().shared_from_this(),
+                    {captured_inputs.begin(), captured_inputs.end()},
+                    {outputs.data(), outputs.size()},
+                    {inputs_require_grad.data(), inputs_require_grad.size()});
+            if (backward_graph) {
+                backward_storage = BackwardGraphWithClosure(
+                        backward_graph, op.cast<ApplyOp>().op().shared_from_this(),
+                        {captured_inputs.begin(), captured_inputs.end()},
+                        {outputs.data(), outputs.size()});
+                // backward by make_backward_graph
+                return outputs;
+            } else {
+                // no backward
+                return outputs;
+            }
+        }();
+        if (std::holds_alternative<std::monostate>(backward_storage)) {
+            return outputs;
+        }
+        auto grad_fn = std::make_shared<GradFn>();
+        grad_fn->m_key = m_key;
+        grad_fn->m_slots.resize(outputs.size());
+        grad_fn->m_backward = backward_storage;
+        mgb_assert(!outputs.empty());
+        grad_fn->m_dests.reserve(inputs.size());
+        // clang-format off
+        std::visit([&](auto& backward) {
+            using T = std::decay_t<decltype(backward)>;
+            if constexpr (std::is_same_v<T, std::monostate>) {
+                mgb_throw(AssertionError, "invalid backward");
+            } else {
+                for (size_t i = 0; i < inputs.size(); ++i) {
+                    if (backward.input_has_grad(i) && require_grads[i]) {
+                        auto& input_grad_slot =
+                                inputs[i].cast<GradValue>().slot_for(m_key);
+                        grad_fn->m_dests.emplace_back(input_grad_slot);
+                        grad_fn->m_dests.back().m_producer_record.insert_after(
+                                input_grad_slot->m_producer_head);
+                    } else {
+                        grad_fn->m_dests.emplace_back();
+                    }
+                }
+                for (size_t i = 0; i < outputs.size(); ++i) {
+                    if (backward.output_requires_grad(i)) {
+                        auto grad_value = GradValue::make(outputs[i], m_key, GradSlotPtr{grad_fn, i});
+                        outputs[i] = record_grad(grad_value);
+                    }
+                }
+            }
+        }, grad_fn->m_backward);
+        // clang-format on
+        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 (auto* attach_grad = op.as<AttachGrad>()) {
+        if (!has_key(attach_grad->key())) {
+            return imperative::apply(op, unwrap_inputs(inputs));
+        }
+        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 imperative::apply(op, unwrap_inputs(inputs));
+        }
+        size_t nr_grads = inputs.size() / 2;
+        mgb_assert(nr_grads * 2 == inputs.size());
+        auto values = inputs.sub(0, nr_grads);
+        auto grads = inputs.sub(nr_grads, nr_grads);
+        make_backward_closure(values)(grads);
+        return {};
+    } else if (auto* is_attached_to = op.as<IsAttachedTo>()) {
+        if (has_key(is_attached_to->key())) {
+            if (auto grad_value = as_grad_value(inputs[0])) {
+                // TODO: assert grad_fn
+                return {BoolValue::make(true)};
+            }
+        }
+        return {BoolValue::make(false)};
+    } else if (auto* set_grad = op.as<SetGrad>()) {
+        // TODO: merge SetGrad and ApplyOp
+        auto grad_fn = std::make_shared<GradFn>();
+        auto& backward =
+                std::get<CustomBackward>(grad_fn->m_backward = CustomBackward());
+        size_t nr_inputs = set_grad->nr_inputs();
+        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});
+        backward.m_backward = set_grad->grad_fn();
+        std::vector<ValueRef> outputs;
+        grad_fn->m_key = m_key;
+        grad_fn->m_slots.resize(nr_outputs);
+        grad_fn->m_dests.reserve(nr_inputs);
+        for (size_t i = 0; i < nr_inputs; ++i) {
+            if (auto grad_value = as_grad_value(inputs_[i])) {
+                auto& input_grad_slot = grad_value->m_slot;
+                grad_fn->m_dests.emplace_back(grad_value->m_slot);
+                grad_fn->m_dests.back().m_producer_record.insert_after(
+                        input_grad_slot->m_producer_head);
+            } else {
+                grad_fn->m_dests.emplace_back();
+            }
+        }
+        for (size_t i = 0; i < nr_outputs; ++i) {
+            auto& output = outputs_[i];
+            auto grad_value = as_grad_value(output);
+            if (grad_value) {
+                grad_value = GradValue::make(
+                        grad_value->m_value, m_key, GradSlotPtr(grad_fn, i));
+            } else {
+                grad_value = GradValue::make(output, m_key, GradSlotPtr(grad_fn, i));
+            }
+            outputs.push_back(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 {FunctionValue::make(make_backward_closure(inputs))};
+    } else if (op.is<DetachGrad>()) {
+        if (auto grad_value = as_grad_value(inputs[0])) {
+            return {grad_value->m_value};
+        } else {
+            return {inputs[0]};
+        }
+    } else if (op.is<GetGradKey>()) {
+        for (auto&& input : inputs) {
+            if (auto grad_value = as_grad_value(input)) {
+                return {GradKeyValue::make(grad_value->m_key)};
+            }
+        }
+        return imperative::apply(op, inputs);
+    } else if (op.kind() == Operator::IdentityLike) {
+        mgb_assert(inputs.size() == 1);
+        if (auto grad_value = as_grad_value(inputs[0])) {
+            auto output = imperative::apply(op, grad_value->m_value)[0];
+            auto grad_output = GradValue::make(
+                    output, grad_value->key(), grad_value->slot_for(m_key));
+            return {record_grad(grad_output)};
+        } 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;
+    }
+}
+
+GenericFunction GradTransformation::make_backward_closure(Span<ValueRef> ys) {
+    // reset GradKey
+    auto grad_key = m_key;
+    std::vector<GradSlotPtr> y_slots;
+    for (auto&& y : ys) {
+        if (auto grad_value = as_grad_value(y)) {
+            y_slots.push_back(grad_value->slot_for(grad_key));
+        } else {
+            y_slots.emplace_back();
+        }
+    }
+    GenericFunction closure = [grad_key,
+                               y_slots](Span<ValueRef> dys) -> std::vector<ValueRef> {
+        size_t nr_grads = y_slots.size();
+        mgb_assert(dys.size() == nr_grads);
+        for (size_t i = 0; i < nr_grads; ++i) {
+            if (y_slots[i]) {
+                y_slots[i]->m_grad = dys[i];
+            }
+        }
+        grad_key->backward();
+        return {};
+    };
+    grad_key->freeze();
+    cleanup();
+    return closure;
+}
+
+void GradTransformation::on_unregister() noexcept {
+    cleanup();
+}
+
+void GradTransformation::cleanup() {
+    for (auto&& weak_value : m_weak_values) {
+        auto grad_value = weak_value.lock();
+        if (grad_value) {
+            mgb_assert(grad_value->m_key == m_key);
+            grad_value.reset(grad_value->m_value);
+        }
+    }
+    m_weak_values.clear();
+    m_key = {};
+}
+
+void GradTransformation::suppress() {
+    m_suppressed++;
+}
+
+void GradTransformation::resume() {
+    m_suppressed--;
+}
+
+}  // namespace imperative
+}  // namespace mgb

imperative/src/include/megbrain/imperative/transformations/grad.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 <variant>
+
+#include "megbrain/imperative/backward_graph_opt.h"
+#include "megbrain/imperative/dispatch.h"
+#include "megbrain/imperative/interpreter.h"
+#include "megbrain/imperative/opr_utility.h"
+#include "megbrain/imperative/ops/autogen.h"
+#include "megbrain/imperative/utils/helper.h"
+#include "megbrain/imperative/utils/intrusive_list.h"
+#include "megbrain/imperative/utils/to_string.h"
+
+namespace mgb::imperative {
+
+struct BackwardGraphWithClosure {
+    std::shared_ptr<OptimizedBackwardGraphResult> backward_graph;
+    SmallVector<ValueRef> closure;
+    size_t output_mask_offset;
+    size_t grad_mask_offset;
+
+    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);
+
+    bool input_has_grad(size_t i) { return backward_graph->input_has_grad[i]; }
+
+    bool output_requires_grad(size_t i) {
+        return backward_graph->save_for_backward[grad_mask_offset + i];
+    }
+    bool output_captured(size_t i) {
+        return backward_graph->save_for_backward[output_mask_offset + i];
+    }
+};
+
+struct CustomBackward;
+
+using GradRuleFn =
+        std::function<std::vector<ValueRef>(Span<ValueRef> inputs, CustomBackward&)>;
+
+struct CustomBackward {
+    using BackwardFn = std::function<std::vector<ValueRef>(Span<ValueRef>)>;
+    using BackwardRule = std::function<std::optional<std::vector<ValueRef>>(
+            const OpDef&, Span<ValueRef>, Span<bool>, CustomBackward&)>;
+    BackwardFn m_backward;
+    SmallVector<bool, 8> m_input_has_grad;
+    struct OutputAttr {
+        bool requires_grad = true, captured = true;
+    };
+    SmallVector<OutputAttr> m_output_attrs;
+
+public:
+    void operator()(
+            std::vector<ValueRef> 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; }
+    bool output_captured(size_t i) { return m_output_attrs[i].captured; }
+
+    static bool register_grad_rule(Typeinfo* typeinfo, BackwardRule rule);
+    static BackwardRule lookup_grad_rule(Typeinfo* typeinfo);
+};
+
+class GradSlot;
+class GradSlotPtr;
+class GradSlotProducerPtr;
+class GradFn;
+class GradKey;
+
+struct GradProducerRecord : utils::intrusive_list::Node<GradProducerRecord> {
+    using Node = utils::intrusive_list::Node<GradProducerRecord>;
+
+    GradProducerRecord() = default;
+    GradProducerRecord(head_t& head) : Node(utils::intrusive_list::after_t{}, head) {}
+};
+
+class GradSlot {
+private:
+    ValueRef m_grad;
+    GradProducerRecord::head_t m_producer_head;
+    std::function<void(ValueRef)> callback;
+
+public:
+    std::string to_string() const;
+
+    friend class GradKey;
+    friend class GradSlotProducerPtr;
+    friend class GradTransformation;
+};
+
+template <>
+struct ToStringTrait<GradSlot> {
+    std::string operator()(const GradSlot& value) const { return value.to_string(); }
+};
+
+class GradFn {
+private:
+    std::weak_ptr<GradKey> m_key;
+    std::vector<GradSlot> m_slots;
+    std::vector<GradSlotProducerPtr> m_dests;
+    std::variant<std::monostate, BackwardGraphWithClosure, CustomBackward> m_backward;
+
+public:
+    void clear() {
+        m_key.reset();
+        m_slots.clear();
+        m_dests.clear();
+        m_backward.emplace<std::monostate>();
+    }
+
+    std::string to_string() const;
+
+    friend class GradSlotPtr;
+    friend class GradKey;
+    friend class GradTransformation;
+};
+
+class GradSlotPtr {
+private:
+    std::shared_ptr<GradFn> m_fn;
+    size_t m_index = 0;
+
+public:
+    GradSlotPtr(std::shared_ptr<GradFn> fn, size_t index) : m_fn(fn), m_index(index) {}
+    GradSlotPtr() = default;
+    GradSlot* operator->() const { return &m_fn->m_slots[m_index]; }
+
+    operator bool() const { return bool(m_fn); }
+
+    std::string to_string() const;
+
+    friend class GradKey;
+    friend class GradTransformation;
+};
+
+template <>
+struct ToStringTrait<GradSlotPtr> {
+    std::string operator()(const GradSlotPtr& value) const { return value.to_string(); }
+};
+
+class GradSlotProducerPtr : public GradSlotPtr {
+private:
+    GradProducerRecord m_producer_record;
+    bool dirty = false;
+
+public:
+    GradSlotProducerPtr(const GradSlotPtr& info)
+            : GradSlotPtr(info), m_producer_record(info->m_producer_head) {}
+    GradSlotProducerPtr() = default;
+    GradSlotProducerPtr(GradSlotProducerPtr&&) = default;
+    ~GradSlotProducerPtr() { dirty = true; }
+    friend class GradKey;
+    friend class GradTransformation;
+};
+
+template <>
+struct ToStringTrait<GradSlotProducerPtr> {
+    std::string operator()(const GradSlotProducerPtr& value) const {
+        return value.to_string();
+    }
+};
+
+class GradValue final : public ValueImpl<GradValue> {
+private:
+    ValueRef m_value;
+    std::shared_ptr<GradKey> m_key;
+    GradSlotPtr m_slot;
+
+public:
+    GradValue(ValueRef value, std::shared_ptr<GradKey> key, GradSlotPtr slot = {})
+            : m_value(value), m_key(key), m_slot(slot) {}
+
+    std::string to_string() const override;
+
+    bool has_key(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);
+        return m_slot;
+    }
+
+    std::shared_ptr<GradKey> key() const { return m_key; }
+
+    void clear() override {
+        m_slot = {};
+        m_value = {};
+        m_key = nullptr;
+    }
+
+    void on_watch() override { m_value.watch(); }
+
+    void on_unwatch() override { m_value.unwatch(); }
+
+    friend class GradKey;
+    friend class GradTransformation;
+};
+
+class GradKey : public std::enable_shared_from_this<GradKey> {
+private:
+    std::string m_name;
+    std::vector<std::pair<std::weak_ptr<GradFn>, std::shared_ptr<OpDef>>> m_tape;
+    std::vector<std::pair<std::shared_ptr<GradFn>, std::shared_ptr<OpDef>>>
+            m_frozen_tape;
+    bool m_frozen = false;
+
+public:
+    void backward();
+    GradValue::ref_t attach(ValueRef tensor, std::function<void(ValueRef)> callback);
+    const std::string& name() const { return m_name; }
+    void name(std::string name) { m_name = std::move(name); }
+    void freeze();
+
+    friend class GradTransformation;
+};
+
+class GradKeyValue final
+        : public MixinValueImpl<GradKeyValue, std::shared_ptr<GradKey>> {
+public:
+    using MixinValueImpl::MixinValueImpl;
+
+    std::string to_string() const override {
+        return ssprintf("GradKey{%s}", (*this)->name().c_str());
+    }
+};
+
+class GradTransformation final : public Transformation {
+private:
+    std::shared_ptr<GradKey> m_key;
+    std::vector<GradValue::weak_ref_t> m_weak_values;
+    size_t m_suppressed = 0;
+
+public:
+    GradTransformation(std::shared_ptr<GradKey> key) : m_key(key) {}
+
+    auto record_grad(GradValue::ref_t tensor) {
+        m_weak_values.push_back(tensor);
+        return tensor;
+    }
+
+    bool is_grad_value(ValueRef value) {
+        if (auto* grad_value = value.as<GradValue>()) {
+            if (grad_value->has_key(m_key)) {
+                return true;
+            }
+        }
+        return false;
+    }
+
+    /**
+     * \brief test whether value is related to this GradTransformation
+     *
+     * there may be multiple grad transformations, so simply using value.is<GradValue>()
+     * is unsafe
+     *
+     * \param value
+     * \return GradValue::ref_t
+     */
+    GradValue::ref_t as_grad_value(ValueRef value) {
+        if (auto grad_value = value.as_ref<GradValue>()) {
+            if (grad_value->has_key(m_key)) {
+                return grad_value;
+            }
+        }
+        return {};
+    }
+
+    bool has_key(std::shared_ptr<GradKey> key) {
+        if (key == m_key) {
+            return true;
+        }
+        return false;
+    }
+
+    std::vector<ValueRef> apply_transformation(
+            const Operator& op, Span<ValueRef> inputs) override;
+
+    ValueRef unwrap(ValueRef value) override {
+        if (auto grad_val = as_grad_value(value)) {
+            return grad_val->m_value;
+        }
+        return value;
+    }
+
+    std::string name() const override { return "GradTransformation"; }
+
+    GenericFunction make_backward_closure(Span<ValueRef> ys);
+
+    void on_unregister() noexcept override;
+
+    void cleanup();
+    void suppress();
+    void resume();
+};
+
+class DetachGrad : public OperatorImpl<DetachGrad, Operator::IdentityLike> {
+private:
+    // TODO: identified by GradKey
+public:
+    std::string to_string() const override { return "DetachValue"; }
+
+    std::vector<ValueRef> fallback(Span<ValueRef> inputs) const override {
+        return {inputs.as_array<1>()[0]};
+    }
+};
+
+class AttachGrad : public OperatorImpl<AttachGrad> {
+private:
+    std::shared_ptr<GradKey> m_key;
+
+public:
+    AttachGrad(std::shared_ptr<GradKey> key) : m_key(key) {}
+    std::shared_ptr<GradKey> key() { return m_key; }
+
+    std::string to_string() const override {
+        return ssprintf("AttachGradValue{key=%s}", m_key->name().c_str());
+    }
+};
+
+class GradBackward : public OperatorImpl<GradBackward, Operator::GetAttrLike> {
+private:
+    std::shared_ptr<GradKey> m_key;
+
+public:
+    GradBackward(std::shared_ptr<GradKey> key) : m_key(key) {}
+
+    std::shared_ptr<GradKey> key() { return m_key; }
+
+    std::string to_string() const override {
+        return ssprintf("GradBackwardValue{key=%s}", m_key->name().c_str());
+    }
+};
+
+class IsAttachedTo : public OperatorImpl<IsAttachedTo, Operator::GetAttrLike> {
+private:
+    std::shared_ptr<GradKey> m_key;
+
+public:
+    IsAttachedTo(std::shared_ptr<GradKey> key) : m_key(key) {}
+    std::shared_ptr<GradKey> key() { 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 {
+        return {BoolValue::make(false)};
+    }
+};
+
+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) {}
+
+    GenericFunction grad_fn() { return m_grad_fn; }
+
+    size_t nr_inputs() { return m_nr_inputs; }
+
+    std::string to_string() const override {
+        return ssprintf("SetGradValue{key=%s}", m_key->name().c_str());
+    }
+};
+
+class GetGradKey : public OperatorImpl<GetGradKey, Operator::GetAttrLike> {
+public:
+    GetGradKey() = default;
+
+    std::string to_string() const override { return ssprintf("GetGradKeyValue{}"); }
+
+    std::vector<ValueRef> fallback(Span<ValueRef> inputs) const override {
+        return {ValueRef()};
+    }
+};
+
+class GetBackwardColsure
+        : public OperatorImpl<GetBackwardColsure, Operator::GetAttrLike> {
+private:
+    std::shared_ptr<GradKey> m_key;
+
+public:
+    GetBackwardColsure(std::shared_ptr<GradKey> key) : m_key(key) {}
+
+    std::shared_ptr<GradKey> key() { return m_key; }
+
+    std::string to_string() const override {
+        return ssprintf("GetBackwardClosure{key=%s}", m_key->name().c_str());
+    }
+};
+
+}  // namespace mgb::imperative