code: def empirical_ntk_fn_tf(
      f: Union[tf.Module, tf.types.experimental.PolymorphicFunction],
      trace_axes: Axes = (-1,),
      diagonal_axes: Axes = (),
      vmap_axes: VMapAxes = None,
      implementation: Union[
          NtkImplementation, int
      ] = DEFAULT_NTK_IMPLEMENTATION,
      _j_rules: bool = _DEFAULT_NTK_J_RULES,
      _s_rules: bool = _DEFAULT_NTK_S_RULES,
      _fwd: Optional[bool] = _DEFAULT_NTK_FWD,
  ) -> Callable[..., PyTree]:
      r"""Returns a function to draw a single sample the NTK of a given network `f`.
  
      This function follows the API of :obj:`neural_tangents.empirical_ntk_fn`, but
      is applicable to Tensorflow :class:`tf.Module`, :class:`tf.keras.Model`, or
      :obj:`tf.function`, via a TF->JAX->TF roundtrip using `tf2jax` and `jax2tf`.
      Docstring below adapted from :obj:`neural_tangents.empirical_ntk_fn`.
  
      .. warning::
        This function is experimental and risks returning wrong results or
        performing slowly. It is intended to demonstrate the usage of
        :obj:`neural_tangents.empirical_ntk_fn` in Tensorflow, but has not been
        extensively tested. Specifically, it appears to have very long
        compile times (but OK runtime), is prone to triggering XLA errors, and does
        not distinguish between trainable and non-trainable parameters of the model.
  
      TODO(romann): support division between trainable and non-trainable variables.
  
      TODO(romann): investigate slow compile times.
  
      Args:
        f:
          :class:`tf.Module` or :obj:`tf.function` whose NTK we are computing. Must
          satisfy the following:
  
            - if a :obj:`tf.function`, must have the signature of `f(params, x)`.
  
            - if a :class:`tf.Module`, must be either a :class:`tf.keras.Model`, or
              be callable.
  
            - input signature (`f.input_shape` for :class:`tf.Module` or
              :class:`tf.keras.Model`, or `f.input_signature` for `tf.function`)
              must be known.
  
        trace_axes:
          output axes to trace the output kernel over, i.e. compute only the trace
          of the covariance along the respective pair of axes (one pair for each
          axis in `trace_axes`). This allows to save space and compute if you are
          only interested in the respective trace, but also improve approximation
          accuracy if you know that covariance along these pairs of axes converges
          to a `constant * identity matrix` in the limit of interest (e.g.
          infinite width or infinite `n_samples`). A common use case is the channel
          / feature / logit axis, since activation slices along such axis are i.i.d.
          and the respective covariance along the respective pair of axes indeed
          converges to a constant-diagonal matrix in the infinite width or infinite
          `n_samples` limit.
          Also related to "contracting dimensions" in XLA terms.
          (https://www.tensorflow.org/xla/operation_semantics#dotgeneral)
  
        diagonal_axes:
          output axes to diagonalize the output kernel over, i.e. compute only the
          diagonal of the covariance along the respective pair of axes (one pair for
          each axis in `diagonal_axes`). This allows to save space and compute, if
          off-diagonal values along these axes are not needed, but also improve
          approximation accuracy if their limiting value is known theoretically,
          e.g. if they vanish in the limit of interest (e.g. infinite
          width or infinite `n_samples`). If you further know that on-diagonal
          values converge to the same constant in your limit of interest, you should
          specify these axes in `trace_axes` instead, to save even more compute and
          gain even more accuracy. A common use case is computing the variance
          (instead of covariance) along certain axes.
          Also related to "batch dimensions" in XLA terms.
          (https://www.tensorflow.org/xla/operation_semantics#dotgeneral)
  
        vmap_axes:
          A triple of `(in_axes, out_axes, kwargs_axes)`
          passed to `vmap` to evaluate the empirical NTK in parallel ove these axes.
          Precisely, providing this argument implies that `f.call(x, **kwargs)`
          equals to a concatenation along `out_axes` of `f` applied to slices of
          `x` and `**kwargs` along `in_axes` and `kwargs_axes`. In other words, it
          certifies that `f` can be evaluated as a `vmap` with `out_axes=out_axes`
          over `x` (along `in_axes`) and those arguments in `**kwargs` that are
          present in `kwargs_axes.keys()` (along `kwargs_axes.values()`).
  
          This allows us to evaluate Jacobians much more
          efficiently. If `vmap_axes` is not a triple, it is interpreted as
          `in_axes = out_axes = vmap_axes, kwargs_axes = {}`. For example a very
          common use case is `vmap_axes=0` for a neural network with leading (`0`)
          batch dimension, both for inputs and outputs, and no interactions between
          different elements of the batch (e.g. no BatchNorm, and, in the case of
          `nt.stax`, also no Dropout). However, if there is interaction between
          batch elements or no concept of a batch axis at all, `vmap_axes` must be
          set to `None`, to avoid wrong (and potentially silent) results.
  
        implementation:
          An :class:`NtkImplementation` value (or an :class:`int` `0`, `1`, `2`, or
          `3`). See the :class:`NtkImplementation` docstring for details.
  
        _j_rules:
          Internal debugging parameter, applicable only when `implementation` is
          :attr:`~neural_tangents.NtkImplementation.STRUCTURED_DERIVATIVES` (`3`)
          or :attr:`~neural_tangents.NtkImplementation.AUTO` (`0`). Set to `True`
          to allow custom Jacobian rules for intermediary primitive `dy/dw`
          computations for MJJMPs (matrix-Jacobian-Jacobian-matrix products). Set
          to `False` to use JVPs or VJPs, via JAX's :obj:`jax.jacfwd` or
          :obj:`jax.jacrev`. Custom Jacobian rules (`True`) are expected to be not
          worse, and sometimes better than automated alternatives, but in case of a
          suboptimal implementation setting it to `False` could improve performance.
  
        _s_rules:
          Internal debugging parameter, applicable only when `implementation` is
          :attr:`~neural_tangents.NtkImplementation.STRUCTURED_DERIVATIVES` (`3`) or
          :attr:`~neural_tangents.NtkImplementation.AUTO` (`0`). Set to `True` to
          allow efficient MJJMp rules for structured `dy/dw` primitive Jacobians.
          In practice should be set to `True`, and setting it to `False` can lead
          to dramatic deterioration of performance.
  
        _fwd:
          Internal debugging parameter, applicable only when `implementation` is
          :attr:`~neural_tangents.NtkImplementation.STRUCTURED_DERIVATIVES` (`3`) or
          :attr:`~neural_tangents.NtkImplementation.AUTO` (`0`). Set to `True` to
          allow :obj:`jax.jvp` in intermediary primitive Jacobian `dy/dw`
          computations, `False` to always use :obj:`jax.vjp`. `None` to decide
          automatically based on input/output sizes. Applicable when
          `_j_rules=False`, or when a primitive does not have a Jacobian rule.
          Should be set to `None` for best performance.
  
      Returns:
        A function `ntk_fn` that computes the empirical ntk.
      """
      warnings.warn("This function is an early proof-of-concept.")
  
      kwargs = dict(
          trace_axes=trace_axes,
          diagonal_axes=diagonal_axes,
          vmap_axes=vmap_axes,
          implementation=implementation,
          _j_rules=_j_rules,
          _s_rules=_s_rules,
          _fwd=_fwd,
      )
      if isinstance(f, tf.Module):
          apply_fn, _ = get_apply_fn_and_params(f)
  
      elif isinstance(f, tf.types.experimental.PolymorphicFunction):
          apply_fn = tf2jax.convert_functional(f, *f.input_signature)
  
      else:
          raise NotImplementedError(
              f"Got `f={f}` of unsupported type {type(f)}, "
              f"please file a bug at "
              f"https://github.com/google/neural-tangents."
          )
  
      ntk_fn = empirical_ntk_fn(apply_fn, **kwargs)
      ntk_fn = jax2tf.convert(ntk_fn)
      ntk_fn = tf.function(ntk_fn, jit_compile=True, autograph=False)
      return ntk_fn
  
file_path: neural-tangents/neural_tangents/experimental/empirical_tf/empirical.py
imports: from typing import Callable, Optional, Union
  import warnings
  from jax.experimental import jax2tf
  from neural_tangents._src.empirical import _DEFAULT_NTK_FWD
  from neural_tangents._src.empirical import _DEFAULT_NTK_J_RULES
  from neural_tangents._src.empirical import _DEFAULT_NTK_S_RULES
  from neural_tangents._src.empirical import DEFAULT_NTK_IMPLEMENTATION
  from neural_tangents._src.empirical import empirical_ntk_fn
  from neural_tangents._src.empirical import NtkImplementation
  from neural_tangents._src.utils.typing import Axes
  from neural_tangents._src.utils.typing import PyTree
  from neural_tangents._src.utils.typing import VMapAxes
  import tensorflow
  import tf2jax
label_desc: Use image node_id 1 for calling a global function with example usage: empirical_ntk_fn_tf(f, trace_axes, diagonal_axes, vmap_axes, implementation, _j_rules, _s_rules, _fwd) and returns: ntk_fn