Question about BacksolveAdjoint through SemiImplicitEuler solver

I am testing the adjoint method to calculate the gradients from a SemiImplicitEuler solver. I met errors when calculate the gradients using BacksolveAdjoint method. Here is a working example. It would be great to have some suggestions.

Thank you in advance!

`
from diffrax import diffeqsolve, ODETerm, SemiImplicitEuler, SaveAt, BacksolveAdjoint
import jax.numpy as jnp
from jax import grad
from matplotlib import pyplot as plt

def drdt(t, v, args):
return v

def dvdt(t, r, args):
return -args[0]*(r-args[1])

terms =(ODETerm(drdt),ODETerm(dvdt))
solver = SemiImplicitEuler()
y0 = (jnp.array([1.0]),jnp.array([0.0]))
saveat = SaveAt(ts=jnp.arange(0,30,0.1))

def loss(y0):
solution = diffeqsolve(terms, solver, t0=0, t1=30, dt0=0.0001, y0=y0, args=[1.0,0.0], saveat=saveat,max_steps=10000000,adjoint=BacksolveAdjoint())
return jnp.sum(solution.ys[0])
grads = grad(loss)(y0)
print(grads)
`

here is the error message:

Traceback (most recent call last): File "test_harmonic.py", line 23, in <module> grads = grad(loss)(y0) File "/home/zwq2834/anaconda3/envs/diffsim_jax/lib/python3.8/site-packages/equinox-0.9.2-py3.8.egg/equinox/grad.py", line 482, in fn_bwd_wrapped out = fn_bwd(residuals, grad_diff_array_out, vjp_arg, *args, **kwargs) File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/adjoint.py", line 394, in _loop_backsolve_bwd state, _ = _scan_fun(state, val0, first=True) File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/adjoint.py", line 332, in _scan_fun _sol = diffeqsolve( File "/home/zwq2834/anaconda3/envs/diffsim_jax/lib/python3.8/site-packages/equinox-0.9.2-py3.8.egg/equinox/jit.py", line 82, in __call__ return __self._fun_wrapper(False, args, kwargs) File "/home/zwq2834/anaconda3/envs/diffsim_jax/lib/python3.8/site-packages/equinox-0.9.2-py3.8.egg/equinox/jit.py", line 78, in _fun_wrapper dynamic_out, static_out = self._cached(dynamic, static) File "/home/zwq2834/anaconda3/envs/diffsim_jax/lib/python3.8/site-packages/equinox-0.9.2-py3.8.egg/equinox/jit.py", line 30, in fun_wrapped out = fun(*args, **kwargs) File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/integrate.py", line 858, in diffeqsolve final_state, aux_stats = adjoint.loop( File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/adjoint.py", line 499, in loop final_state, aux_stats = _loop_backsolve( File "/home/zwq2834/anaconda3/envs/diffsim_jax/lib/python3.8/site-packages/equinox-0.9.2-py3.8.egg/equinox/grad.py", line 509, in __call__ out = self.fn_wrapped( File "/home/zwq2834/anaconda3/envs/diffsim_jax/lib/python3.8/site-packages/equinox-0.9.2-py3.8.egg/equinox/grad.py", line 443, in fn_wrapped out = self.fn(vjp_arg, *args, **kwargs) File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/adjoint.py", line 250, in _loop_backsolve return self._loop_fn( File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/integrate.py", line 497, in loop final_state = bounded_while_loop( File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/misc/bounded_while_loop.py", line 125, in bounded_while_loop return lax.while_loop(cond_fun, _body_fun, init_val) File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/misc/bounded_while_loop.py", line 118, in _body_fun _new_val = body_fun(_val, inplace) File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/integrate.py", line 137, in body_fun (y, y_error, dense_info, solver_state, solver_result) = solver.step( File "/home/zwq2834/development/DiffSim_Jax/diffrax/diffrax/solver/semi_implicit_euler.py", line 42, in step y0_1, y0_2 = y0 ValueError: too many values to unpack (expected 2)

Run the provided reproducer and start by reading diffrax/adjoint.py around _loop_backsolve and diffrax/solver/semi_implicit_euler.py around step, where the tuple-unpacking error occurs. Determine whether BacksolveAdjoint supports this tuple-valued state and establish a working gradient result or a documented limitation.