re_dense = ravel(re)
im_dense = ravel(im)
res = jnp.stack([re_dense, im_dense], axis=0)
return res
def ravel(x: PyTree) -> Array:
"""
shorthand for tree_ravel
"""
dense, _ = nkjax.tree_ravel(x)
return dense
dense_jacobian_real_holo = nkjax.compose(ravel, jacobian_real_holo)
dense_jacobian_cplx = nkjax.compose(
stack_jacobian_tuple, partial(jacobian_cplx, _build_fn=lambda *x: x)
)
def _rescale(centered_oks):
"""
compute ΔOₖ/√Sₖₖ and √Sₖₖ
to do scale-invariant regularization (Becca & Sorella 2017, pp. 143)
Sₖₗ/(√Sₖₖ√Sₗₗ) = ΔOₖᴴΔOₗ/(√Sₖₖ√Sₗₗ) = (ΔOₖ/√Sₖₖ)ᴴ(ΔOₗ/√Sₗₗ)
"""
scale = (
mpi.mpi_sum_jax(
jnp.sum((centered_oks * centered_oks.conj()).real, axis=0, keepdims=True)
)[0]
def prepare_centered_oks(
apply_fun: Callable,
params: PyTree,
samples: Array,
model_state: Optional[PyTree],
mode: str,
rescale_shift: bool,
pdf=None,
chunk_size: int = None,
) -> PyTree:
"""
compute ΔOⱼₖ = Oⱼₖ - ⟨Oₖ⟩ = ∂/∂pₖ ln Ψ(σⱼ) - ⟨∂/∂pₖ ln Ψ⟩
divided by √n
In a somewhat intransparent way this also internally splits all parameters to real
in the 'real' and 'complex' modes (for C→R, R&C→R, R&C→C and general C→C) resulting in the respective ΔOⱼₖ
which is only compatible with split-to-real pytree vectors
Args:
apply_fun: The forward pass of the Ansatz
params : a pytree of parameters p
samples : an array of (n in total) batched samples σ
model_state: untrained state parameters of the model
mode: differentiation mode, must be one of 'real', 'complex', 'holomorphic'
rescale_shift: whether scale-invariant regularisation should be used (default: True)
pdf: |ψ(x)|^2 if exact optimization is being used else None
chunk_size: an int specifying the size of the chunks the gradient should be computed in (default: None)
Returns:
if not rescale_shift:
a pytree representing the centered jacobian of ln Ψ evaluated at the samples σ, divided by √n;
None
else:
the same pytree, but the entries for each parameter normalised to unit norm;
pytree containing the norms that were divided out (same shape as params)
"""
# un-batch the samples
samples = samples.reshape((-1, samples.shape[-1]))
# pre-apply the model state
def forward_fn(W, σ):
return apply_fun({"params": W, **model_state}, σ)
if mode == "real":
split_complex_params = True # convert C→R and R&C→R to R→R
centered_jacobian_fun = centered_jacobian_real_holo
jacobian_fun = jacobian_real_holo
elif mode == "complex":
split_complex_params = True # convert C→C and R&C→C to R→C
# centered_jacobian_fun = compose(stack_jacobian, centered_jacobian_cplx)
# avoid converting to complex and then back
# by passing around the oks as a tuple of two pytrees representing the real and imag parts
centered_jacobian_fun = compose(
stack_jacobian_tuple,
partial(centered_jacobian_cplx, _build_fn=lambda *x: x),
)
jacobian_fun = jacobian_cplx
elif mode == "holomorphic":
split_complex_params = False
centered_jacobian_fun = centered_jacobian_real_holo
jacobian_fun = jacobian_real_holo
else:
raise NotImplementedError(
'Differentiation mode should be one of "real", "complex", or "holomorphic", got {}'
.format(mode))
if split_complex_params:
# doesn't do anything if the params are already real
params, reassemble = tree_to_real(params)
def f(W, σ):
return forward_fn(reassemble(W), σ)
else:
f = forward_fn
if pdf is None:
centered_oks = _divide_by_sqrt_n_samp(
centered_jacobian_fun(
f,
params,
samples,
chunk_size=chunk_size,
),
samples,
)
else:
oks = jacobian_fun(f, params, samples)
oks_mean = jax.tree_map(partial(sum, axis=0),
_multiply_by_pdf(oks, pdf))
centered_oks = jax.tree_map(lambda x, y: x - y, oks, oks_mean)
centered_oks = _multiply_by_pdf(centered_oks, jnp.sqrt(pdf))
if rescale_shift:
return _rescale(centered_oks)
else:
return centered_oks, None
partial(_vjp, nondiff_argnums=nondiff_argnums, conjugate=conjugate),
scan_fun=scan_fun,
argnums=argnums,
)(fun, cotangents, *primals)
return _multimap(lambda c, l: _tree_unchunk(l)
if c else l, append_cond, res)
def _gen_append_cond_vjp(primals, nondiff_argnums, chunk_argnums):
diff_argnums = filter(lambda i: i not in nondiff_argnums,
range(len(primals)))
return tuple(map(lambda i: i in chunk_argnums, diff_argnums))
_gen_append_cond_value_vjp = compose(lambda t: (True, ) + t,
_gen_append_cond_vjp)
_vjp_fun_chunked = partial(
__vjp_fun_chunked,
_vjp=compose(lambda yr: yr[1:], _vjp),
_append_cond_fun=_gen_append_cond_vjp,
)
_value_and_vjp_fun_chunked = compose(
lambda yr: (yr[0], yr[1:]),
partial(__vjp_fun_chunked,
_vjp=_vjp,
_append_cond_fun=_gen_append_cond_value_vjp),
)
def vjp_chunked(
Returns:
The Jacobian matrix ∂/∂pₖ ln Ψ(σⱼ) as a PyTree
"""
def _jacobian_cplx(forward_fn, params, samples, _build_fn):
y, vjp_fun = jax.vjp(single_sample(forward_fn), params, samples)
gr, _ = vjp_fun(np.array(1.0, dtype=jnp.result_type(y)))
gi, _ = vjp_fun(np.array(-1.0j, dtype=jnp.result_type(y)))
return _build_fn(gr, gi)
return vmap_chunked(_jacobian_cplx,
in_axes=(None, None, 0, None),
chunk_size=chunk_size)(forward_fn, params, samples,
_build_fn)
centered_jacobian_real_holo = compose(tree_subtract_mean, jacobian_real_holo)
centered_jacobian_cplx = compose(tree_subtract_mean, jacobian_cplx)
def _divide_by_sqrt_n_samp(oks, samples):
"""
divide Oⱼₖ by √n
"""
n_samp = samples.shape[0] * mpi.n_nodes # MPI
return jax.tree_map(lambda x: x / np.sqrt(n_samp, dtype=x.dtype), oks)
def _multiply_by_pdf(oks, pdf):
"""
Computes O'ⱼ̨ₖ = Oⱼₖ pⱼ .
Used to multiply the log-derivatives by the probability density.
