AbstractReversibleSolver + ReversibleAdjoint

add reversible

testing

testing

AbstractReversibleSolver + ReversibleAdjoint

allow arbitrary interpolation

unpacking over indexing

jax while loop

collapse saveat ValueErrors

remove statonovich solver condition

remove unused returns from AbstractReversibleSolver backward_step

add test and remove messy benchmark

add wrapped solver + tests

made_jump=True for both solver steps

improve docstrings

AbstractSolver and docstring note about SDEs

add AbstractReversibleSolver to public API

newline in docstrings

return RESULTS from reversible backward_step

restrict Reversible to AbstractERK and check result in adjoint

correct tprev and tnext of solver init

switch to linear interpolation and y0,y1 dense_info

name UReversible

various doc formatting changes

AbstractReversibleSolver check

add disable_fsal property to AbstractRungeKutta and use in UReversible

allow t0 != 0

Handle StepTo controller

t0==t1 branch

Author: Sam McCallum

diffrax/__init__.py

@@ -7,6 +7,7 @@
     ForwardMode as ForwardMode,
     ImplicitAdjoint as ImplicitAdjoint,
     RecursiveCheckpointAdjoint as RecursiveCheckpointAdjoint,
+    ReversibleAdjoint as ReversibleAdjoint,
 )
 from ._autocitation import citation as citation, citation_rules as citation_rules
 from ._brownian import (
@@ -75,6 +76,7 @@
     AbstractFosterLangevinSRK as AbstractFosterLangevinSRK,
     AbstractImplicitSolver as AbstractImplicitSolver,
     AbstractItoSolver as AbstractItoSolver,
+    AbstractReversibleSolver as AbstractReversibleSolver,
     AbstractRungeKutta as AbstractRungeKutta,
     AbstractSDIRK as AbstractSDIRK,
     AbstractSolver as AbstractSolver,
@@ -117,6 +119,7 @@
     StochasticButcherTableau as StochasticButcherTableau,
     StratonovichMilstein as StratonovichMilstein,
     Tsit5 as Tsit5,
+    UReversible as UReversible,
 )
 from ._step_size_controller import (
     AbstractAdaptiveStepSizeController as AbstractAdaptiveStepSizeController,

diffrax/_adjoint.py

@@ -16,8 +16,10 @@
 
 from ._heuristics import is_sde, is_unsafe_sde
 from ._saveat import save_y, SaveAt, SubSaveAt
+from ._solution import RESULTS
 from ._solver import (
     AbstractItoSolver,
+    AbstractReversibleSolver,
     AbstractRungeKutta,
     AbstractSRK,
     AbstractStratonovichSolver,
@@ -918,3 +920,307 @@ def loop(
 
 
 ForwardMode.__init__.__doc__ = """**Arguments:** None"""
+
+# Reversible Adjoint custom vjp computes gradients w.r.t.
+# - y, corresponding to the initial state;
+# - args, corresponding to explicit parameters;
+# - terms, corresponding to implicit parameters as part of the vector field.
+
+
+@eqx.filter_custom_vjp
+def _loop_reversible(y__args__terms, *, self, throw, max_steps, init_state, **kwargs):
+    del throw
+    y, args, terms = y__args__terms
+    init_state = eqx.tree_at(lambda s: s.y, init_state, y)
+    del y
+    return self._loop(
+        args=args,
+        terms=terms,
+        max_steps=max_steps,
+        init_state=init_state,
+        inner_while_loop=ft.partial(_inner_loop, kind="lax"),
+        outer_while_loop=ft.partial(_outer_loop, kind="lax"),
+        **kwargs,
+    )
+
+
+@_loop_reversible.def_fwd
+def _loop_reversible_fwd(perturbed, y__args__terms, **kwargs):
+    del perturbed
+    final_state, aux_stats = _loop_reversible(y__args__terms, **kwargs)
+    init_ts = final_state.reversible_init_ts
+    ts = final_state.reversible_ts
+    ts_final_index = final_state.reversible_save_index
+    y1 = final_state.y
+    save_state = final_state.save_state
+    solver_state = final_state.solver_state
+    return (final_state, aux_stats), (
+        init_ts,
+        ts,
+        ts_final_index,
+        y1,
+        save_state,
+        solver_state,
+    )
+
+
+@_loop_reversible.def_bwd
+def _loop_reversible_bwd(
+    residuals,
+    grad_final_state__aux_stats,
+    perturbed,
+    y__args__terms,
+    *,
+    self,
+    saveat,
+    init_state,
+    solver,
+    event,
+    **kwargs,
+):
+    assert event is None
+
+    del perturbed, self, init_state, kwargs
+    init_ts, ts, ts_final_index, y1, save_state, solver_state = residuals
+    del residuals
+
+    grad_final_state, _ = grad_final_state__aux_stats
+    saveat_ts = save_state.ts
+    ys = save_state.ys
+    saveat_ts_index = save_state.saveat_ts_index - 1
+    grad_ys = grad_final_state.save_state.ys
+    grad_ys = jtu.tree_map(_materialise_none, ys, grad_ys)
+
+    if saveat.subs.t1:
+        grad_y1 = (ω(grad_ys)[-1]).ω
+    else:
+        grad_y1 = jtu.tree_map(jnp.zeros_like, y1)
+
+    if saveat.subs.t0:
+        saveat_ts_index = saveat_ts_index + 1
+
+    del grad_final_state, grad_final_state__aux_stats
+
+    y, args, terms = y__args__terms
+    del y__args__terms
+
+    diff_state = eqx.filter(solver_state, eqx.is_inexact_array)
+    diff_args = eqx.filter(args, eqx.is_inexact_array)
+    diff_terms = eqx.filter(terms, eqx.is_inexact_array)
+    grad_state = jtu.tree_map(jnp.zeros_like, diff_state)
+    grad_args = jtu.tree_map(jnp.zeros_like, diff_args)
+    grad_terms = jtu.tree_map(jnp.zeros_like, diff_terms)
+    del diff_args, diff_terms
+
+    def grad_step(state):
+        def forward_step(y0, solver_state, args, terms):
+            y1, _, dense_info, new_solver_state, result = solver.step(
+                terms, t0, t1, y0, args, solver_state, False
+            )
+            assert result == RESULTS.successful
+            return y1, dense_info, new_solver_state
+
+        (
+            saveat_ts_index,
+            ts_index,
+            y1,
+            solver_state,
+            grad_y1,
+            grad_state,
+            grad_args,
+            grad_terms,
+        ) = state
+
+        t1 = ts[ts_index]
+        t0 = ts[ts_index - 1]
+
+        # Any ts state required to reverse the forward step
+        # e.g. LeapfrogMidpoint requires tm1
+        tm1_index = ts_index - 2
+        tm1 = ts[tm1_index]
+        tm1 = jnp.where(tm1_index >= 0, tm1, t0)
+        ts_state = (tm1,)
+
+        y0, dense_info, solver_state, result = solver.backward_step(
+            terms, t0, t1, y1, args, ts_state, solver_state, False
+        )
+        assert result == RESULTS.successful
+
+        # Pull gradients back through interpolation
+
+        def interpolate(t, t0, t1, dense_info):
+            interpolator = solver.interpolation_cls(t0=t0, t1=t1, **dense_info)
+            return interpolator.evaluate(t)
+
+        def _cond_fun(inner_state):
+            saveat_ts_index, _ = inner_state
+            return (saveat_ts[saveat_ts_index] >= t0) & (saveat_ts_index >= 0)
+
+        def _body_fun(inner_state):
+            saveat_ts_index, grad_dense_info = inner_state
+            t = saveat_ts[saveat_ts_index]
+            grad_y = (ω(grad_ys)[saveat_ts_index]).ω
+            _, interp_vjp = eqx.filter_vjp(interpolate, t, t0, t1, dense_info)
+            _, _, _, dgrad_dense_info = interp_vjp(grad_y)
+            grad_dense_info = eqx.apply_updates(grad_dense_info, dgrad_dense_info)
+            saveat_ts_index = saveat_ts_index - 1
+            return saveat_ts_index, grad_dense_info
+
+        grad_dense_info = jtu.tree_map(jnp.zeros_like, dense_info)
+        inner_state = (saveat_ts_index, grad_dense_info)
+        inner_state = eqxi.while_loop(_cond_fun, _body_fun, inner_state, kind="lax")
+        saveat_ts_index, grad_dense_info = inner_state
+
+        # Pull gradients back through forward step
+
+        _, vjp_fn = eqx.filter_vjp(forward_step, y0, solver_state, args, terms)
+        grad_y0, grad_state, dgrad_args, dgrad_terms = vjp_fn(
+            (grad_y1, grad_dense_info, grad_state)
+        )
+
+        grad_args = eqx.apply_updates(grad_args, dgrad_args)
+        grad_terms = eqx.apply_updates(grad_terms, dgrad_terms)
+
+        ts_index = ts_index - 1
+
+        return (
+            saveat_ts_index,
+            ts_index,
+            y0,
+            solver_state,
+            grad_y0,
+            grad_state,
+            grad_args,
+            grad_terms,
+        )
+
+    def cond_fun(state):
+        ts_index = state[1]
+        return ts_index > 0
+
+    state = (
+        saveat_ts_index,
+        ts_final_index,
+        y1,
+        solver_state,
+        grad_y1,
+        grad_state,
+        grad_args,
+        grad_terms,
+    )
+
+    state = jax.lax.while_loop(cond_fun, grad_step, state)
+    _, _, y0, _, grad_y0, grad_state, grad_args, grad_terms = state
+
+    # Pull solver_state gradients back onto y0, args, terms.
+
+    init_t0, init_t1 = init_ts
+    _, init_vjp = eqx.filter_vjp(solver.init, terms, init_t0, init_t1, y0, args)
+    dgrad_terms, _, _, dgrad_y0, dgrad_args = init_vjp(grad_state)
+    grad_y0 = eqx.apply_updates(grad_y0, dgrad_y0)
+    grad_terms = eqx.apply_updates(grad_terms, dgrad_terms)
+    grad_args = eqx.apply_updates(grad_args, dgrad_args)
+
+    return grad_y0, grad_args, grad_terms
+
+
+class ReversibleAdjoint(AbstractAdjoint):
+    """Backpropagate through [`diffrax.diffeqsolve`][] when using a reversible solver
+    [`diffrax.AbstractReversibleSolver`][].
+
+    Gradient calculation is exact (up to floating point errors) and backpropagation
+    becomes linear in time $O(n)$ and constant in memory $O(1)$, for $n$ time steps.
+
+    !!! note
+
+        This adjoint can be less numerically stable than
+        [`diffrax.RecursiveCheckpointAdjoint`][] and [`diffrax.DirectAdjoint`][].
+        Stability can be largely improved by using [double (64bit) precision](https://jax.readthedocs.io/en/latest/notebooks/Common_Gotchas_in_JAX.html#double-64bit-precision)
+        and [smaller/adaptive step sizes](https://docs.kidger.site/diffrax/api/stepsize_controller/).
+
+    ??? cite "References"
+
+        For an introduction to reversible backpropagation, see these references:
+
+        ```bibtex
+        @article{mccallum2024efficient,
+            title={Efficient, Accurate and Stable Gradients for Neural ODEs},
+            author={McCallum, Sam and Foster, James},
+            journal={arXiv preprint arXiv:2410.11648},
+            year={2024}
+        }
+
+        @phdthesis{kidger2021on,
+            title={{O}n {N}eural {D}ifferential {E}quations},
+            author={Patrick Kidger},
+            year={2021},
+            school={University of Oxford},
+        }
+        ```
+    """
+
+    def loop(
+        self,
+        *,
+        args,
+        terms,
+        solver,
+        saveat,
+        max_steps,
+        init_state,
+        passed_solver_state,
+        passed_controller_state,
+        event,
+        **kwargs,
+    ):
+        if not isinstance(solver, AbstractReversibleSolver):
+            raise ValueError(
+                "`ReversibleAdjoint` can only be used with an "
+                "`AbstractReversibleSolver`"
+            )
+        if max_steps is None:
+            raise ValueError(
+                "`max_steps=None` is incompatible with `ReversibleAdjoint`."
+            )
+
+        if (
+            jtu.tree_structure(saveat.subs, is_leaf=_is_subsaveat)
+            != jtu.tree_structure(0)
+            or saveat.dense
+            or saveat.subs.steps
+            or (saveat.subs.fn is not save_y)
+        ):
+            raise ValueError(
+                "`ReversibleAdjoint` is only compatible with the following `SaveAt` "
+                "properties: `t0`, `t1`, `ts`, `fn=save_y` (default)."
+            )
+
+        if event is not None:
+            raise NotImplementedError(
+                "`ReversibleAdjoint` is not compatible with events."
+            )
+
+        if is_unsafe_sde(terms):
+            raise ValueError(
+                "`ReversibleAdjoint` does not support `UnsafeBrownianPath`. "
+                "Consider using `VirtualBrownianTree` instead."
+            )
+
+        y = init_state.y
+        init_state = eqx.tree_at(lambda s: s.y, init_state, object())
+        init_state = _nondiff_solver_controller_state(
+            self, init_state, passed_solver_state, passed_controller_state
+        )
+
+        final_state, aux_stats = _loop_reversible(
+            (y, args, terms),
+            self=self,
+            saveat=saveat,
+            max_steps=max_steps,
+            init_state=init_state,
+            solver=solver,
+            event=event,
+            **kwargs,
+        )
+        final_state = _only_transpose_ys(final_state)
+        return final_state, aux_stats