rematerialization.py

from dataclasses import dataclass, replace
from functools import partial
from itertools import chain, product, takewhile
from typing import Optional, Tuple, Union
from collections.abc import Callable
from collections.abc import Sequence
from collections import defaultdict
import time

from igraph import Graph

from thunder.core import prims, utils
from thunder.core.baseutils import BoundSymbolInterface, ProxyInterface
from thunder.core.prims import PrimIDs
from thunder.core.proxies import TensorProxy, variableify, NumberProxy
from thunder.core.pytree import tree_flatten, tree_unflatten
from thunder.core.symbol import has_tags
from thunder.core.trace import from_trace, TraceCtx, TraceProvenance
from thunder.core.transform_common import dce
from thunder.executors.passes import update_fusion_call_ctx


def find_external_producer_outputs(
    proxy_to_consumers: dict[ProxyInterface, tuple[BoundSymbolInterface, ...]],
    next_consumers: Sequence[BoundSymbolInterface],
    producer: BoundSymbolInterface,
    consumer: BoundSymbolInterface,
) -> tuple[ProxyInterface, ...]:
    """Find producer's outputs that must be included in the output of the
    producer because they are used by other consumers.

    Args:
        proxy_to_consumers (dict[ProxyInterface, tuple[BoundSymbolInterface, ...]]): A dictionary that maps a producer's
            output to the consumers that use it.
        next_consumers (Sequence[BoundSymbolInterface]): Other consumers that
            use the producer's output.
        producer (BoundSymbolInterface): Producer node.
        consumer (BoundSymbolInterface): Consumer node.

    Returns:
        Tuple[ProxyInterface, ...]: Producer's outputs that must be included in
        the output of the producer.
    """
    local_consumer_info = utils.consumers(list(chain((producer, consumer), next_consumers)))

    def is_rematerializable(out: ProxyInterface):
        # First check local information to see if the output is used by other
        # consumers.
        local_consumers = local_consumer_info.get(out, tuple())
        if len(local_consumers) > 1:
            return False

        # If the output is not used by fusion consumers, check global information
        # to see if the output is used by other consumers.
        global_consumers = proxy_to_consumers.get(out, tuple())
        global_consumers = tuple(
            x for x in global_consumers if x.sym.name != "del" and x not in chain((consumer,), next_consumers)
        )

        # If the output is used by other global consumers, it's not rematerializable.
        if len(global_consumers) > 0:
            return False

        if len(local_consumers) == 0:
            return True

        # If the output is used by a single local consumer, it's rematerializable
        return len(local_consumers) == 1 and out.name in (x.name for x in consumer.args)

    rematerializable_producer_outputs = tuple(filter(is_rematerializable, producer.output))

    return tuple(x for x in producer.output if x.name not in (y.name for y in rematerializable_producer_outputs))


def find_external_consumer_inputs(
    producer: BoundSymbolInterface,
    consumer: BoundSymbolInterface,
) -> tuple[ProxyInterface, ...]:
    """Find consumer's inputs that must be included in the input of the
    consumer because they are produced by other producers.

    Args:
        producer (BoundSymbolInterface): Producer node.
        consumer (BoundSymbolInterface): Consumer node.

    Returns:
        Tuple[ProxyInterface, ...]: Consumer's inputs that must be included in
        the input of the consumer.
    """
    all_produced_vars = tuple(chain.from_iterable((y for y in x.flat_proxy_outs) for x in producer.subsymbols))
    external_consumer_inputs_names = tuple(
        sorted(
            {x.name for x in consumer.args}
            - {x.name for x in producer.output}
            - {x.name for x in producer.args}
            - {x.name for x in all_produced_vars}
        )
    )
    return tuple(x for x in consumer.args if x.name in external_consumer_inputs_names)


def apply_rematerialization_for_producer(
    external_producer_outputs,
    producer: BoundSymbolInterface,
    cut: Sequence[ProxyInterface | str],
) -> BoundSymbolInterface:
    """Update the producer node with the cut information.

    Args:
        producer (BoundSymbolInterface): Producer node.
        cut (Sequence[Union[ProxyInterface, str]]): Cut information.

    Returns:
        BoundSymbolInterface: Updated producer node.
    """
    # It's simple to update the producer node, all we need to do is to update
    # the producer's output with the cut information and the external outputs.
    cut_names = tuple(map(lambda x: x.name, cut)) if isinstance(cut[0], ProxyInterface) else tuple(cut)
    new_producer_output_names = (
        tuple(x.name if isinstance(x, ProxyInterface) else x for x in external_producer_outputs) + cut_names
    )
    # Remove the producer's inputs from the new producer's output.
    new_producer_output_names = tuple(
        x for x in new_producer_output_names if x not in (y.name for y in producer.flat_args)
    )
    all_produced_vars = tuple(chain.from_iterable((y for y in x.flat_proxy_outs) for x in producer.subsymbols))
    # Choose the new producer's output from all the produced variables.
    new_producer_output = tuple(x for x in all_produced_vars if x.name in new_producer_output_names)
    new_producer_output = tuple(sorted(new_producer_output, key=lambda x: x.name))
    new_producer = replace(producer, output=new_producer_output)
    return new_producer


def apply_rematerialization_for_consumer(
    producer: BoundSymbolInterface,
    consumer: BoundSymbolInterface,
    cut: Sequence[ProxyInterface | str],
) -> BoundSymbolInterface:
    """Update the consumer node with the cut information.

    Args:
        producer (BoundSymbolInterface): Producer node.
        consumer (BoundSymbolInterface): Consumer node.
        cut (Sequence[Union[ProxyInterface, str]]): Cut information.

    Returns:
        BoundSymbolInterface: Updated consumer node.
    """
    # It's a bit more complicated to update the consumer node, we need to
    # update the consumer's input with the cut information.
    # We need to keep consumer's inputs that are not in the cut and are not
    # produced by the producer. We call these inputs "external inputs".
    external_inputs = find_external_consumer_inputs(producer, consumer)
    all_produced_vars = tuple(chain.from_iterable((y for y in x.flat_proxy_outs) for x in producer.subsymbols))
    cut_names = tuple(map(lambda x: x.name, cut)) if isinstance(cut[0], ProxyInterface) else tuple(cut)
    cut_inputs = tuple(filter(lambda x: x.name in cut_names, (*all_produced_vars, *producer.args)))
    new_consumer_args = cut_inputs + external_inputs

    # We need to rematerialize the consumer's inputs that are not in the new consumer's inputs.
    rematerialized_inputs = tuple(
        filter(lambda x: x.name not in map(lambda x: x.name, new_consumer_args), consumer.args)
    )

    # Construct a temporary Trace object with subsymbols from both the producer and the consumer.
    trace = TraceCtx(None)
    trace.bound_symbols = (*producer.subsymbols, *consumer.subsymbols)

    recomputing_symbols = utils.find_producer_symbols(trace, rematerialized_inputs, cut_inputs)
    new_subsymbols = recomputing_symbols + tuple(consumer.subsymbols)

    # Some recomputing_symbols might require producer's inputs, so we need to
    # add them to the consumer's inputs.
    # Probably find_min_cut should have returned this information.
    all_args = tuple(
        chain.from_iterable(
            (x.name for x in bsym.flat_args if isinstance(x, ProxyInterface)) for bsym in new_subsymbols
        )
    )
    new_consumer_args += tuple(
        x for x in producer.args if x.name in all_args and x.name not in (x.name for x in new_consumer_args)
    )
    new_consumer_args = tuple(sorted(new_consumer_args, key=lambda x: x.name))
    new_consumer = replace(consumer, args=new_consumer_args, subsymbols=new_subsymbols)
    return new_consumer


def find_filtered_producer_consumer_pairs(
    trace: TraceCtx,
    filter_func: Callable | None = None,
    *,
    proxy_to_consumers=None,
) -> tuple[tuple[BoundSymbolInterface, BoundSymbolInterface], ...]:
    """Find producer-consumer pairs among the filtered symbols.

    Args:
        trace (TraceCtx): Trace object.
        filter_func (Optional[Callable], optional): Filter function. Defaults to None.

    Returns:
        Tuple[Tuple[BoundSymbolInterface, BoundSymbolInterface], ...]: Producer-consumer bound symbol pairs.
    """
    filter_func = filter_func or (lambda x: True)
    proxy_to_consumers = utils.consumers(trace) if proxy_to_consumers is None else proxy_to_consumers
    producer_consumer_pairs = set()
    order_in_trace = {bsym: i for i, bsym in enumerate(filter(filter_func, trace.bound_symbols))}

    # We are looking for special producer-consumer pairs among the filtered symbols
    for producer in filter(filter_func, trace.bound_symbols):
        for out in producer.flat_outs:
            consumers = proxy_to_consumers.get(out, tuple())
            consumers = filter(filter_func, consumers)
            for consumer in consumers:
                producer_consumer_pairs.add((producer, consumer))
    return tuple(
        sorted(
            producer_consumer_pairs,
            key=lambda pair: (order_in_trace[pair[0]], order_in_trace[pair[1]]),
        )
    )


find_nvfuser_producer_consumer_pairs = partial(
    find_filtered_producer_consumer_pairs, filter_func=lambda x: x.sym.name.startswith("nvFusion")
)
find_fusion_producer_consumer_pairs = partial(
    find_filtered_producer_consumer_pairs, filter_func=lambda x: x.sym.is_fusion
)


def find_cut(
    external_producer_outputs: Sequence[ProxyInterface],
    producer: BoundSymbolInterface,
    consumer: BoundSymbolInterface,
) -> Sequence[ProxyInterface | str]:
    """Find the minimal cut between the producer and the consumer.

    Args:
        trace (TraceCtx): Trace object.
        producer (BoundSymbolInterface): Producer node.
        consumer (BoundSymbolInterface): Consumer node.

    Returns:
        Sequence[Union[ProxyInterface, str]]: Cut information.
    """
    # We are going to use the igraph library to find the minimal cut between the
    # producer and the consumer. Minimum cut is a set of edges that, if removed,
    # would disconnect the producer and the consumer. But we are not interested
    # in the edges, we are interested in the nodes that are connected by the
    # edges. These nodes are the cut nodes. So we need to reformulate our node
    # graph into an edge graph.

    # All the nodes from the producer that we connect to a "source" node will
    # not be in the cut. Similarly, all the nodes from the consumer that we
    # connect to a "sink" node will not be in the cut. So we need to add a
    # "source" node and a "sink" node to our graph. We also disallow the cut to
    # be in the consumer's part of the graph to avoid balancing the graph into
    # the producer from the consumer.

    # Required producer variables. These are the variables that are required to
    # be connected to the "source" node.
    required_producer_vars = tuple(x for x in producer.args)
    required_producer_vars += tuple(x for x in external_producer_outputs)

    # This is needed to avoid rematerializing random or reduction primitives.
    tags = {prims.OpTags.REDUCTION_OP, prims.OpTags.RANDOM_OP}
    required_producer_vars += tuple(
        chain.from_iterable((y for y in x.flat_outs) for x in producer.subsymbols if has_tags(x, tags))
    )

    # We can apply rematerialization for any pair of symbols with is_fusion=True
    # property. Currently this could be an nvFuser or a TorchCompile fusion.
    # These executors might have a different coverage of supported operators. So
    # we need to mark unsupported by consumer operators variables as required
    # producer variables. So that we don't move them to the consumer.
    if producer.sym.executor != consumer.sym.executor:
        required_producer_vars += tuple(
            chain.from_iterable(
                (y for y in x.flat_outs)
                for x in producer.subsymbols
                if not has_tags(x, tags) and not consumer.sym.executor.can_fuse(x)
            )
        )

    # Required consumer variables. These are the variables that are required to
    # be connected to the "sink" node.
    required_consumer_vars = tuple(x.name for x in consumer.output)
    external_consumer_inputs = find_external_consumer_inputs(producer, consumer)
    required_consumer_vars += tuple(x.name for x in external_consumer_inputs)

    # To the required consumer variables we also need to add the path from the
    # consumer's output to the external consumer's inputs. This is needed to
    # avoid balancing the graph into the producer from the consumer.
    consumer_trace = TraceCtx(None)
    consumer_trace.bound_symbols = consumer.subsymbols
    required_consumer_symbols = tuple(
        utils.find_producer_symbols(consumer_trace, consumer.output, external_consumer_inputs)
    )
    required_consumer_vars += tuple(
        chain.from_iterable((y.name for y in x.flat_outs) for x in required_consumer_symbols)
    )

    # TODO: Use TensorProxy properties to compute the weights
    WEIGHT = 1.0

    # Create a graph
    edges = []
    name_to_id = {}
    capacities = []

    def add_edge(src, dst, capacity):
        edges.append((name_to_id.setdefault(src, len(name_to_id)), name_to_id.setdefault(dst, len(name_to_id))))
        capacities.append(capacity)

    utils.check(
        len(required_consumer_vars) > 0,
        lambda: "The consumer has no outputs. This is not supported by the cut finding algorithm.",
    )
    for var_name in required_consumer_vars:
        add_edge(var_name + "_in", "sink", capacity=float("inf"))

    sym_skip_list = (
        prims.PrimIDs.UNPACK_SEQUENCE,
        prims.PrimIDs.UNPACK_TRIVIAL,
        prims.PrimIDs.UNPACK_KEY,
        prims.PrimIDs.RETURN,
    )

    combined_trace = TraceCtx(None)
    combined_trace.bound_symbols = (*producer.subsymbols, *consumer.subsymbols)
    combined_consumers = utils.consumers(combined_trace)

    def get_weight(var):
        if isinstance(var, TensorProxy):
            return WEIGHT * var.dtype.bytes
        elif isinstance(var, NumberProxy):
            return 0.0
        return WEIGHT

    def add_edges(var):
        var_name = var.name
        weight = get_weight(var)
        weight = weight / 2.0 if var_name in (x.name for x in producer.args) else weight
        add_edge(var_name + "_in", var_name + "_out", capacity=weight)
        for user in combined_consumers._dict.get(var_name, tuple()):
            if user.sym.id in sym_skip_list:
                continue
            for out in user.flat_proxy_outs:
                user_name = out.name
                add_edge(var_name + "_out", user_name + "_in", capacity=float("inf"))

    if not required_producer_vars:
        # If there are no required producer variables, we need to make sure that
        # the source node is added to the graph.
        add_edge("source", "source", capacity=float("inf"))

    for var in required_producer_vars:
        add_edge("source", var.name + "_in", capacity=float("inf"))
        add_edges(var)

    for symbol in chain(producer.subsymbols, consumer.subsymbols):
        for var in symbol.flat_proxy_outs:
            add_edges(var)

    g = Graph(
        n=len(name_to_id),
        edges=edges,
        directed=True,
        edge_attrs={"capacity": capacities},
    )
    source = name_to_id["source"]
    sink = name_to_id["sink"]

    id_to_name = dict(map(reversed, name_to_id.items()))

    g_edges = g.get_edgelist()
    cut = g.mincut(source, sink, "capacity").cut
    cut_nodes = set()
    for cut_edge_id in cut:
        u, v = g_edges[cut_edge_id]
        node_in, node_out = id_to_name[u], id_to_name[v]
        if node_out == "sink":
            continue
        assert node_in.endswith("_in"), node_in
        assert node_out.endswith("_out"), node_out
        assert node_in[:-3] == node_out[:-4]
        var_name = node_in[:-3]
        cut_nodes.add(var_name)
    return tuple(sorted(cut_nodes))


def rematerialize_all_gather(fw_trace: TraceCtx, bw_trace: TraceCtx) -> tuple[TraceCtx, TraceCtx]:
    """Insert new allgather+wait for backward trace and update the return statement for forward trace"""

    from thunder.core.proxies import FutureTensorProxy
    from thunder.core.trace import reset_tracectx, set_tracectx
    from thunder.distributed.prims import PrimIDs as distPrimIDs
    from thunder.executors.torchex import all_gather_prim_impl, wait_prim_impl

    new_bw_trace = from_trace(bw_trace)
    consumers = utils.consumers(fw_trace)

    # Find all waits that consume all_gather outputs
    all_gathers = tuple(
        x for x in fw_trace.bound_symbols if x.sym.id in {distPrimIDs.ALL_GATHER, all_gather_prim_impl.id}
    )
    all_gather_outputs = tuple(chain.from_iterable((y for y in x.flat_proxy_outs) for x in all_gathers))
    waits = tuple(consumers[o][0] for o in all_gather_outputs)
    assert all(x.sym.id in (distPrimIDs.WAIT, wait_prim_impl.id) for x in waits)
    wait_outputs = tuple(chain.from_iterable((y for y in x.flat_proxy_outs) for x in waits))

    visited_wait_output = set()
    # map the output of the original waitop to the output of the new waitop
    wait_output_replacement_map = {}
    wait_output_to_all_gather = utils.ProxyDict()
    wait_output_to_wait = utils.ProxyDict()
    for v, o in utils.safe_zip(wait_outputs, all_gathers):
        wait_output_to_all_gather[v] = o
    for v, w in utils.safe_zip(wait_outputs, waits):
        wait_output_to_wait[v] = w

    try:
        token = set_tracectx(new_bw_trace)
        new_symbols = []
        new_bw_trace.bound_symbols = new_symbols
        for bsym in bw_trace.bound_symbols:
            if bsym.sym.id in {distPrimIDs.ALL_GATHER, all_gather_prim_impl.id}:
                continue
            if bsym.sym.id in {distPrimIDs.WAIT, wait_prim_impl.id} and bsym in waits:
                continue
            # update the unpack operators in the joint_fn trace
            if bsym.sym.id in {
                PrimIDs.UNPACK_TRIVIAL,
                PrimIDs.UNPACK_SEQUENCE,
                PrimIDs.UNPACK_EMPTY_DICT,
                PrimIDs.UNPACK_KEY,
            }:
                new_symbols.append(bsym)
                continue

            used_wait_outputs = tuple(x for x in bsym.flat_proxy_args if x in wait_output_to_wait)
            if used_wait_outputs:
                for used_wait_output in used_wait_outputs:
                    # Skip inserting all_gather+wait if it's not the first consumer of the wait op
                    if used_wait_output.name in visited_wait_output:
                        continue
                    visited_wait_output.add(used_wait_output.name)
                    all_gather_bsym = wait_output_to_all_gather[used_wait_output]
                    all_gather_out = FutureTensorProxy(like=all_gather_bsym.output)
                    new_all_gather_bsym = replace(all_gather_bsym, output=all_gather_out)
                    new_symbols.append(new_all_gather_bsym)

                    wait_bsym = wait_output_to_wait[used_wait_output]
                    wait_out = TensorProxy(like=wait_bsym.output)
                    new_wait_bsym = replace(wait_bsym, output=wait_out, args=(all_gather_out,))
                    new_symbols.append(new_wait_bsym)
                    wait_output_replacement_map[variableify(used_wait_output)] = wait_out

                new_bsym = bsym.from_bsym_swap_proxies(wait_output_replacement_map)
                new_symbols.append(new_bsym)
                continue
            new_symbols.append(bsym)

    finally:
        reset_tracectx(token)

    new_bw_bsyms = list(
        bsym
        for bsym in new_bw_trace.bound_symbols
        if bsym.sym.id
        not in (
            PrimIDs.UNPACK_TRIVIAL,
            PrimIDs.UNPACK_SEQUENCE,
            PrimIDs.UNPACK_EMPTY_DICT,
            PrimIDs.UNPACK_KEY,
            PrimIDs.RETURN,
        )
    )
    all_args = tuple(
        chain.from_iterable((x for x in bsym.flat_args if isinstance(x, ProxyInterface)) for bsym in new_bw_bsyms)
    )
    producers = utils.producers(new_bw_bsyms)
    new_required_for_backward = tuple(
        a
        for a in all_args
        if producers.get(a, None) is None
        and a.name not in (y.name for y in tree_flatten(bw_trace.args[1])[0] if isinstance(y, ProxyInterface))
    )
    new_required_for_backward = tuple(
        sorted({x.name: x for x in new_required_for_backward}.values(), key=lambda a: a.name)
    )  # Removes duplicates and sorts by name
    # Now construct the updated backward and forward traces
    from thunder.core.transforms import (
        _update_backward_with_new_saved_for_backward,
        _update_forward_with_new_saved_for_backward,
    )

    _update_backward_with_new_saved_for_backward(new_bw_trace, new_required_for_backward)

    new_fw_trace = from_trace(fw_trace)
    new_fw_trace.bound_symbols = list(fw_trace.bound_symbols)
    _update_forward_with_new_saved_for_backward(new_fw_trace, new_required_for_backward)
    return new_fw_trace, new_bw_trace


def rematerialize(trace: TraceCtx) -> TraceCtx:
    """Rematerialize the trace.

    Args:
        trace (TraceCtx): Trace object.

    Returns:
        TraceCtx: Rematerialized trace and the list of
            rematerialized traces.
    """
    start_time_ns = time.time_ns()

    static_consumer_info = utils.consumers(trace)

    # Find all the producers and consumers
    pairs = find_fusion_producer_consumer_pairs(trace, proxy_to_consumers=static_consumer_info)

    # Pairs of producer and consumer are not unique. Each update to the producer
    # or consumer may affect the other. We need to update the producer and
    # consumer sequentially.
    producers = {producer for producer, _ in pairs}
    consumers = {consumer for _, consumer in pairs}
    new_bsyms = {bsym: bsym for bsym in producers | consumers}
    computed_cuts_for_producers = defaultdict(tuple)
    for i, (producer, consumer) in enumerate(pairs):
        current_producer = new_bsyms.get(producer, None) or producer
        current_consumer = new_bsyms.get(consumer, None) or consumer
        # Determine which producer's outputs cannot be rematerialized
        next_consumers = takewhile(lambda x: x[0] == producer, pairs[i + 1 :])
        next_consumers = tuple(consumer for _, consumer in next_consumers)
        next_consumers = tuple(new_bsyms.get(bsym, bsym) for bsym in next_consumers)
        external_producer_outputs = find_external_producer_outputs(
            static_consumer_info, next_consumers, current_producer, current_consumer
        )
        # Find the minimal cut between the producer and the consumer
        cut = find_cut(external_producer_outputs, current_producer, current_consumer)
        if cut:
            # If we have already computed the cut for the producer, we need to
            # update the external producer outputs with the previous cut
            # information.
            external_producer_outputs += computed_cuts_for_producers.get(producer, tuple())

            updated_producer = apply_rematerialization_for_producer(external_producer_outputs, current_producer, cut)
            updated_consumer = apply_rematerialization_for_consumer(current_producer, current_consumer, cut)
            # As we replace bound symbols of the input trace with updated ones every iteration,
            # we should keep track of the map of `current` to `updated` as well as `producer`/`consumer`
            # to `updated` ones.
            # ref: https://github.com/Lightning-AI/lightning-thunder/pull/868#discussion_r1305640813
            new_bsyms[producer] = new_bsyms[current_producer] = updated_producer
            new_bsyms[consumer] = new_bsyms[current_consumer] = updated_consumer

            computed_cuts_for_producers[producer] += cut

    rematerialized_trace = from_trace(trace)
    rematerialized_trace.bound_symbols = tuple(new_bsyms.get(bsym, bsym) for bsym in trace.bound_symbols)

    end_time_ns = time.time_ns()
    elapsed_time_ns = end_time_ns - start_time_ns
    elapsed_time_millis = elapsed_time_ns // 1000000

    rematerialized_trace.set_provenance(TraceProvenance(f"Rematerialization (took {elapsed_time_millis} milliseconds)"))
    return rematerialized_trace


def rematerialize_forward_and_backward(fw_trace: TraceCtx, bw_trace: TraceCtx) -> tuple[TraceCtx, TraceCtx]:
    """Apply rematerialization optimization to the forward and backward traces.

    Args:
        fw_trace (TraceCtx): Forward trace.
        bw_trace (TraceCtx): Backward trace.

    Returns:
        tuple[TraceCtx, TraceCtx]: Rematerialized forward and backward traces.
    """
    # Circular dependency
    from thunder.core.transforms import (
        _update_backward_with_new_saved_for_backward,
        _update_forward_with_new_saved_for_backward,
    )

    def joint_fn(args, kwargs, cotangents):
        pass

    joint_extrace = TraceCtx(joint_fn)
    joint_extrace.names = set.union(fw_trace.names, bw_trace.names)
    joint_extrace.args = (fw_trace.args, fw_trace.kwargs, bw_trace.args[1])
    assert fw_trace.bound_symbols[-1].sym.id == PrimIDs.RETURN
    assert bw_trace.bound_symbols[-1].sym.id == PrimIDs.RETURN
    # Omit the last RETURN symbol
    joint_extrace.bound_symbols = fw_trace.bound_symbols[:-1] + bw_trace.bound_symbols[:-1]
    # Add a new RETURN symbol
    joint_extrace.bound_symbols.append(
        replace(fw_trace.bound_symbols[-1], args=(fw_trace.bound_symbols[-1].args[0], bw_trace.bound_symbols[-1].args))
    )
    joint_extrace = rematerialize(joint_extrace)

    # We need to update "save_for_backward" sequence
    new_bw_bsyms = joint_extrace.bound_symbols[len(fw_trace.bound_symbols) :]
    new_bw_bsyms = list(
        bsym
        for bsym in new_bw_bsyms
        if bsym.sym.id
        not in (
            PrimIDs.UNPACK_TRIVIAL,
            PrimIDs.UNPACK_SEQUENCE,
            PrimIDs.UNPACK_EMPTY_DICT,
            PrimIDs.UNPACK_KEY,
            PrimIDs.DEL,
            PrimIDs.RETURN,
        )
    )
    all_args = tuple(
        chain.from_iterable((x for x in bsym.flat_args if isinstance(x, ProxyInterface)) for bsym in new_bw_bsyms)
    )
    producers = utils.producers(new_bw_bsyms)
    new_required_for_backward = tuple(
        a
        for a in all_args
        if producers.get(a, None) is None
        and a.name not in (y.name for y in tree_flatten(bw_trace.args[1])[0] if isinstance(y, ProxyInterface))
    )
    new_required_for_backward = tuple(
        sorted({x.name: x for x in new_required_for_backward}.values(), key=lambda a: a.name)
    )  # Removes duplicates and sorts by name

    # Now construct the updated backward and forward traces
    new_bw_trace = from_trace(bw_trace)
    new_bw_trace.set_provenance(TraceProvenance("Rematerialization"))
    new_bw_trace.bound_symbols = new_bw_bsyms
    new_bw_trace.bound_symbols.append(replace(bw_trace.bound_symbols[-1], args=bw_trace.bound_symbols[-1].args))
    _update_backward_with_new_saved_for_backward(new_bw_trace, new_required_for_backward)

    new_fw_trace = from_trace(fw_trace)
    new_fw_trace.set_provenance(TraceProvenance("Rematerialization"))
    new_fw_trace.bound_symbols = list(
        bsym for bsym in joint_extrace.bound_symbols[: len(fw_trace.bound_symbols) - 1] if bsym.sym.id != PrimIDs.DEL
    )
    new_fw_trace.bound_symbols.append(replace(fw_trace.bound_symbols[-1], args=fw_trace.bound_symbols[-1].args))
    _update_forward_with_new_saved_for_backward(new_fw_trace, new_required_for_backward)

    # prims.python_return was updated and now DCE can remove the unused
    # variables and symbols
    new_fw_trace = dce(new_fw_trace)
    new_bw_trace = dce(new_bw_trace)

    # Update the call context
    new_fw_trace = update_fusion_call_ctx(new_fw_trace)
    new_bw_trace = update_fusion_call_ctx(new_bw_trace)
    return new_fw_trace, new_bw_trace