def nngp_fn(x1: np.ndarray,
x2: Optional[np.ndarray],
params: PyTree,
keys: Union[PRNGKey,
Tuple[PRNGKey, PRNGKey],
np.ndarray] = None,
**apply_fn_kwargs) -> np.ndarray:
"""Computes a single sample of the empirical NNGP.
Args:
x1:
first batch of inputs.
x2:
second batch of inputs. `x2=None` means `x2=x1`. `f(x2)` must have a
matching shape with `f(x1)` on `trace_axes` and `diagonal_axes`.
params:
A `PyTree` of parameters about which we would like to compute the
neural tangent kernel.
keys: `None` or a PRNG key or a tuple of PRNG keys or a (2, 2) array of
dtype `uint32`. If `key=None`, then the function `f` is deterministic
and requires no PRNG key; else if `keys` is a single PRNG key, then `x1`
and `x2` must be the same and share the same PRNG key; else `x1` and
`x2` use two different PRNG keys.
**apply_fn_kwargs:
keyword arguments passed to `apply_fn`.
Returns:
A single sample of the empirical NNGP. The shape of the kernel is "almost"
`zip(f(x1).shape, f(x2).shape)` except for:
1) `trace_axes` are absent as they are contracted over.
2) `diagonal_axes` are present only once.
All other axes are present twice.
"""
key1, key2 = _read_keys(keys)
def output(x, rng):
out = f(params, x, rng=rng, **apply_fn_kwargs)
masked_output = utils.get_masked_array(out)
return masked_output.masked_value
out1 = output(x1, key1)
if x2 is None:
out2 = out1
else:
out2 = output(x2, key2)
dot = utils.dot_general(out1, out2, trace_axes, diagonal_axes)
return dot / utils.size_at(out1, trace_axes)
def nngp_fn(x1: np.ndarray,
x2: Optional[np.ndarray],
params: PyTree,
**apply_fn_kwargs) -> np.ndarray:
"""Computes a single sample of the empirical NNGP.
Args:
x1:
first batch of inputs.
x2:
second batch of inputs. `x2=None` means `x2=x1`. `f(x2)` must have a
matching shape with `f(x1)` on `trace_axes` and `diagonal_axes`.
params:
A `PyTree` of parameters about which we would like to compute the
neural tangent kernel.
**apply_fn_kwargs:
keyword arguments passed to `apply_fn`. `apply_fn_kwargs` will be split
into `apply_fn_kwargs1` and `apply_fn_kwargs2` by the `_split_kwargs`
function which will be passed to `apply_fn`. In particular, the rng key
in `apply_fn_kwargs`, will be split into two different (if `x1!=x2`) or
same (if `x1==x2`) rng keys. See the `_read_key` function for more
details.
Returns:
A single sample of the empirical NNGP. The shape of the kernel is "almost"
`zip(f(x1).shape, f(x2).shape)` except for:
1) `trace_axes` are absent as they are contracted over.
2) `diagonal_axes` are present only once.
All other axes are present twice.
"""
def output(x, **kwargs):
out = f(params, x, **kwargs)
masked_output = utils.get_masked_array(out)
return masked_output.masked_value
apply_fn_kwargs1, apply_fn_kwargs2 = _split_kwargs(apply_fn_kwargs, x1, x2)
out1 = output(x1, **apply_fn_kwargs1)
if x2 is None:
out2 = out1
else:
out2 = output(x2, **apply_fn_kwargs2)
dot = utils.dot_general(out1, out2, trace_axes, diagonal_axes)
return dot / utils.size_at(out1, trace_axes)
def contract(x, y):
param_axes = list(range(x.ndim))[ndim:]
contract_axes = _trace_axes + param_axes
return utils.dot_general(x, y, contract_axes,
_diagonal_axes) / size
def contract(out1, out2):
dot = utils.dot_general(out1, out2, trace_axes, diagonal_axes)
return dot / utils.size_at(out1, trace_axes)
