def get_kernels(get: Get, x_test: Optional[np.ndarray], compute_cov: bool,
**kernel_fn_test_test_kwargs):
get = _get_dependency(get, compute_cov)
k_dd = get_k_train_train(get)
if x_test is None:
k_td = None
nngp_tt = compute_cov or None
else:
args_train, _ = utils.split_kwargs(kernel_fn_train_train_kwargs,
x_train)
args_test, _ = utils.split_kwargs(kernel_fn_test_test_kwargs,
x_test)
def is_array(x):
return tree_all(
tree_map(lambda x: isinstance(x, np.ndarray), x))
kwargs_td = dict(kernel_fn_train_train_kwargs)
kwargs_tt = dict(kernel_fn_train_train_kwargs)
for k in kernel_fn_test_test_kwargs.keys():
v_tt = kernel_fn_test_test_kwargs[k]
v_dd = kernel_fn_train_train_kwargs[k]
if is_array(v_dd) and is_array(v_tt):
if (isinstance(v_dd, tuple) and len(v_dd) == 2
and isinstance(v_tt, tuple) and len(v_tt) == 2):
v_td = (args_test[k], args_train[k])
else:
v_td = v_tt
elif v_dd != v_tt:
raise ValueError(
f'Same keyword argument {k} of `kernel_fn` is set to'
f'different values {v_dd} != {v_tt} when computing '
f'the train-train and test-train/test-test kernels. '
f'If this is your intention, please submit a feature'
f' request at '
f'https://github.com/google/neural-tangents/issues')
else:
v_td = v_tt
kwargs_td[k] = v_td
kwargs_tt[k] = v_tt
k_td = kernel_fn(x_test, x_train, get, **kwargs_td)
if compute_cov:
nngp_tt = kernel_fn(x_test, None, 'nngp', **kwargs_tt)
else:
nngp_tt = None
return k_dd, k_td, nngp_tt
def ntk_fn(x1: NTTree[np.ndarray], x2: Optional[NTTree[np.ndarray]],
params: PyTree, **apply_fn_kwargs) -> np.ndarray:
"""Computes a single sample of the empirical NTK (implicit differentiation).
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 NTK. 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.
"""
kwargs1, kwargs2 = utils.split_kwargs(apply_fn_kwargs, x1, x2)
f1 = _flatten(_get_f_params(f, x1, **kwargs1))
f2 = (f1 if utils.all_none(x2) else _flatten(
_get_f_params(f, x2, **kwargs2)))
def delta_vjp_jvp(delta):
def delta_vjp(delta):
return vjp(f2, params)[1](delta)
return jvp(f1, (params, ), delta_vjp(delta))[1]
# Since we are taking the Jacobian of a linear function (which does not
# depend on its coefficients), it is more efficient to substitute fx_dummy
# for the outputs of the network. fx_dummy has the same shape as the output
# of the network on a single piece of input data.
fx2_struct = eval_shape(f2, params)
@utils.nt_tree_fn()
def dummy_output(fx_struct):
return np.ones(fx_struct.shape, fx_struct.dtype)
fx_dummy = dummy_output(fx2_struct)
ntk = jacobian(delta_vjp_jvp)(fx_dummy)
if utils.is_list_or_tuple(fx_dummy):
fx_treedef = tree_structure(
eval_shape(_get_f_params(f, x1, **kwargs1), params))
ntk = [ntk[i][i] for i in range(len(fx_dummy))]
ntk = tree_unflatten(fx_treedef, ntk)
return _trace_and_diagonal(ntk, trace_axes, diagonal_axes)
def ntk_fn(x1: NTTree[np.ndarray], x2: Optional[NTTree[np.ndarray]],
params: PyTree, **apply_fn_kwargs) -> np.ndarray:
"""Computes a single sample of the empirical NTK (jacobian outer product).
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 NTK. 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.
"""
kwargs1, kwargs2 = utils.split_kwargs(apply_fn_kwargs, x1, x2)
fx1 = eval_shape(f, params, x1, **kwargs1)
x_axis, fx_axis, kw_axes = _canonicalize_axes(vmap_axes, x1, fx1,
**kwargs1)
keys = apply_fn_kwargs.keys()
args1, args2 = (kwargs1[k] for k in keys), (kwargs2[k] for k in keys)
def j_fn(x, *args):
_kwargs = {k: v for k, v in zip(keys, args)}
fx = _get_f_params(f, x, x_axis, fx_axis, kw_axes, **_kwargs)
jx = jacobian(fx)(params)
return jx
if x_axis is not None or kw_axes:
in_axes = [x_axis] + [
kw_axes[k] if k in kw_axes else None for k in keys
]
j_fn = vmap(j_fn, in_axes=in_axes, out_axes=fx_axis)
j1 = j_fn(x1, *args1)
j2 = j_fn(x2, *args2) if not utils.all_none(x2) else j1
ntk = sum_and_contract(fx1, j1, j2)
return ntk
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 utils.nt_tree_fn()(lambda x: x.masked_value)(masked_output)
kwargs1, kwargs2 = utils.split_kwargs(apply_fn_kwargs, x1, x2)
out1 = output(x1, **kwargs1)
if utils.all_none(x2):
out2 = out1
else:
out2 = output(x2, **kwargs2)
@utils.nt_tree_fn()
def contract(out1, out2):
dot = utils.dot_general(out1, out2, trace_axes, diagonal_axes)
return dot / utils.size_at(out1, trace_axes)
return contract(out1, out2)
def ntk_fn(x1: NTTree[np.ndarray], x2: Optional[NTTree[np.ndarray]],
params: PyTree, **apply_fn_kwargs) -> np.ndarray:
"""Computes a single sample of the empirical NTK (jacobian outer product).
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 NTK. 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.
"""
kwargs1, kwargs2 = utils.split_kwargs(apply_fn_kwargs, x1, x2)
f1 = _get_f_params(f, x1, **kwargs1)
jac_fn1 = jacobian(f1)
j1 = jac_fn1(params)
if x2 is None:
j2 = j1
else:
f2 = _get_f_params(f, x2, **kwargs2)
jac_fn2 = jacobian(f2)
j2 = jac_fn2(params)
fx1 = eval_shape(f1, params)
ntk = sum_and_contract(fx1, j1, j2)
return ntk
def ntk_fn(x1: NTTree[np.ndarray], x2: Optional[NTTree[np.ndarray]],
params: PyTree, **apply_fn_kwargs) -> np.ndarray:
"""Computes a single sample of the empirical NTK (implicit differentiation).
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 NTK. 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.
"""
kwargs1, kwargs2 = utils.split_kwargs(apply_fn_kwargs, x1, x2)
fx1 = eval_shape(f, params, x1, **kwargs1)
x_axis, fx_axis, kw_axes = _canonicalize_axes(vmap_axes, x1, fx1,
**kwargs1)
keys = apply_fn_kwargs.keys()
args1 = (kwargs1[k] for k in keys)
args2 = (kwargs1[k]
if k in kw_axes and kwargs2[k] is None else kwargs2[k]
for k in keys)
def get_ntk(x1, x2, *args):
args1, args2 = args[:len(args) // 2], args[len(args) // 2:]
_kwargs1 = {k: v for k, v in zip(keys, args1)}
_kwargs2 = {k: v for k, v in zip(keys, args2)}
f1 = _get_f_params(f, x1, x_axis, fx_axis, kw_axes, **_kwargs1)
f2 = f1 if utils.all_none(x2) else _get_f_params(
f, x2, x_axis, fx_axis, kw_axes, **_kwargs2)
def delta_vjp_jvp(delta):
def delta_vjp(delta):
return vjp(f2, params)[1](delta)
return jvp(f1, (params, ), delta_vjp(delta))[1]
fx1, fx2 = eval_shape(f1, params), eval_shape(f2, params)
eye = _std_basis(fx1)
ntk = vmap(linear_transpose(delta_vjp_jvp, fx2))(eye)
ntk = tree_map(
lambda fx12: _unravel_array_into_pytree(fx1, 0, fx12), ntk)
ntk = _diagonal(ntk, fx1)
return ntk
if x_axis is not None or kw_axes:
x2 = x1 if utils.all_none(x2) else x2
kw_in_axes = [kw_axes[k] if k in kw_axes else None for k in keys]
in_axes1 = [x_axis, None] + kw_in_axes + [None] * len(kw_in_axes)
in_axes2 = [None, x_axis] + [None] * len(kw_in_axes) + kw_in_axes
get_ntk = vmap(vmap(get_ntk, in_axes1, fx_axis), in_axes2,
_add(fx_axis, _ndim(fx1)))
return _trace_and_diagonal(get_ntk(x1, x2, *args1, *args2), trace_axes,
diagonal_axes)
