class_docstr: This is a computationally-efficient implementation that computes the type of
  "infinitesimal" influence scored defined in the paper "Understanding Black-box
  Predictions via Influence Functions" by Koh et al
  (https://arxiv.org/pdf/1703.04730.pdf). This implementation does *not* follow
  the approach in that paper, however. Instead, it follows an implementation that is
  several orders of magnitudes faster, described in the paper "Scaling Up Influence
  Functions" by Schioppa et al (https://arxiv.org/pdf/2112.03052.pdf).
  
  This implementation computes a low-rank approximation of the inverse Hessian, i.e.
  a tall and skinny (with width k) matrix :math`R` such that
  :math`H^{-1} \approx RR'`, where k is small. In particular, let :math`V` be the
  matrix of width k whose columns contain the top-k eigenvectors of :math`H`, and let
  :math`S` be the k by k matrix whose diagonals contain the corresponding eigenvalues.
  This implementation lets :math`R=VS^{-0.5}`. Thus, the core computational step is
  computing the top-k eigenvalues / eigenvectors.
  
  This approximation is useful for several reasons:
  - It avoids numerical issues associated with inverting small eigenvalues
  - Since the influence score is given by
    :math`\nabla_\theta L(x)' H^{-1} \nabla_\theta L(z)`, which is approximated by
    :math`(\nabla_\theta L(x)' R) (\nabla_\theta L(z)' R)`, we can compute an
    "influence embedding" for a given example :math`x`, :math`\nabla_\theta L(x)' R`,
    such that the influence score of one example on another is approximately the
    dot-product of their respective embeddings.
  - Even for large models, we can store `R` in memory, provided k is small. This
    means influence embeddings (and thus influence scores) can be efficiently
    computed by doing a backwards pass to compute :math`\nabla_\theta L(x)` and then
    multiplying by :math`R'`. This is orders of magnitude faster than the previous
    LISSA approach of Koh et al, which to compute the influence score involving a
    given example, need to compute Hessian-vector products involving on the order
    of 10^4 examples.
  
  The key novelty of the approach by Schioppa et al is that it uses the Arnoldi
  iteration to find the top-k eigenvalues / eigenvectors of the Hessian without
  explicitly forming the Hessian. In more detail, the approach first runs the
  Arnoldi iteration, which only requires the ability to compute Hessian-vector
  products, to find a Krylov subspace of moderate dimension, i.e. 200. It then finds
  the top-k eigevalues / eigenvectors of the restriction of the Hessian to the
  subspace, where k is small, i.e. 50. Finally, it expresses the eigenvectors in
  the original basis. This approach for finding the top-k eigenvalues / eigenvectors
  is justified by the property of the Arnoldi iteration, that the Krylov subspace
  it returns tends to contain the top eigenvectors.
  
  This implementation require some computation time `__init__`, where it
  runs the Arnoldi iteration to calculate `R`. This computation is linear in
  `arnoldi_dim` as well as the size of `hessian_dataset`. After that initial
  overhead, calculation of influence scores is quick, only requiring a backwards pass
  and multiplication, per example.
  
  Unlike `NaiveInfluenceFunction`, this implementation does not flatten any
  parameters, as the 2D Hessian is never formed, and Pytorch's Hessian-vector
  implementation (`torch.autograd.functional.hvp`) allows the input and output
  vector to be a tuple of tensors. Avoiding flattening / unflattening parameters
  brings scalability gains.
docstr: Args:
  
      inputs (tuple): `inputs` is the test batch and is a tuple of
              any, where the last element is assumed to be the labels for the
              batch. That is, `model(*batch[0:-1])` produces the output for
              `model`, and `batch[-1]` are the labels, if any. This is the same
              assumption made for each batch yielded by training dataset
              `train_dataset` - please see its documentation in `__init__` for
              more details on the assumed structure of a batch.
      k (int, optional): The number of proponents or opponents to return per test
              example.
              Default: 5
      proponents (bool, optional): Whether seeking proponents (`proponents=True`)
              or opponents (`proponents=False`)
              Default: True
      show_progress (bool, optional): To compute the proponents (or opponents)
              for the batch of examples, we perform computation for each batch in
              training dataset `train_dataset`, If `show_progress` is
              true, the progress of this computation will be displayed. In
              particular, the number of batches for which the computation has
              been performed will be displayed. It will try to use tqdm if
              available for advanced features (e.g. time estimation). Otherwise,
              it will fallback to a simple output of progress.
              Default: False
  
  Returns:
      (indices, influence_scores) (namedtuple): `indices` is a torch.long Tensor
              that contains the indices of the proponents (or opponents) for each
              test example. Its dimension is `(inputs_batch_size, k)`, where
              `inputs_batch_size` is the number of examples in `inputs`. For
              example, if `proponents==True`, `indices[i][j]` is the index of the
              example in training dataset `train_dataset` with the
              k-th highest influence score for the j-th example in `inputs`.
              `indices` is a `torch.long` tensor so that it can directly be used
              to index other tensors. Each row of `influence_scores` contains the
              influence scores for a different test example, in sorted order. In
              particular, `influence_scores[i][j]` is the influence score of
              example `indices[i][j]` in training dataset `train_dataset`
              on example `i` in the test dataset represented by `inputs`.
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code: def _get_k_most_influential(
      self,
      inputs: Union[Tuple[Any, ...], DataLoader],
      k: int = 5,
      proponents: bool = True,
      show_progress: bool = False,
  ) -> KMostInfluentialResults:
      r"""
      Args:
  
          inputs (tuple): `inputs` is the test batch and is a tuple of
                  any, where the last element is assumed to be the labels for the
                  batch. That is, `model(*batch[0:-1])` produces the output for
                  `model`, and `batch[-1]` are the labels, if any. This is the same
                  assumption made for each batch yielded by training dataset
                  `train_dataset` - please see its documentation in `__init__` for
                  more details on the assumed structure of a batch.
          k (int, optional): The number of proponents or opponents to return per test
                  example.
                  Default: 5
          proponents (bool, optional): Whether seeking proponents (`proponents=True`)
                  or opponents (`proponents=False`)
                  Default: True
          show_progress (bool, optional): To compute the proponents (or opponents)
                  for the batch of examples, we perform computation for each batch in
                  training dataset `train_dataset`, If `show_progress` is
                  true, the progress of this computation will be displayed. In
                  particular, the number of batches for which the computation has
                  been performed will be displayed. It will try to use tqdm if
                  available for advanced features (e.g. time estimation). Otherwise,
                  it will fallback to a simple output of progress.
                  Default: False
  
      Returns:
          (indices, influence_scores) (namedtuple): `indices` is a torch.long Tensor
                  that contains the indices of the proponents (or opponents) for each
                  test example. Its dimension is `(inputs_batch_size, k)`, where
                  `inputs_batch_size` is the number of examples in `inputs`. For
                  example, if `proponents==True`, `indices[i][j]` is the index of the
                  example in training dataset `train_dataset` with the
                  k-th highest influence score for the j-th example in `inputs`.
                  `indices` is a `torch.long` tensor so that it can directly be used
                  to index other tensors. Each row of `influence_scores` contains the
                  influence scores for a different test example, in sorted order. In
                  particular, `influence_scores[i][j]` is the influence score of
                  example `indices[i][j]` in training dataset `train_dataset`
                  on example `i` in the test dataset represented by `inputs`.
      """
      desc = (
          None
          if not show_progress
          else (
              (
                  f"Using {self.get_name()} to perform computation for "
                  f'getting {"proponents" if proponents else "opponents"}. '
                  "Processing training batches"
              )
          )
      )
      return KMostInfluentialResults(
          *_get_k_most_influential_helper(
              self.train_dataloader,
              functools.partial(
                  _influence_batch_intermediate_quantities_influence_function,
                  self,
              ),
              inputs,
              k,
              proponents,
              show_progress,
              desc,
          )
      )
  
imports: import functools
  from typing import Any, Callable, List, Optional, Tuple, Union
  import torch
  from captum._utils.gradient import _extract_parameters_from_layers
  from captum.influence._utils.common import _compute_batch_loss_influence_function_base, _compute_jacobian_sample_wise_grads_per_batch, _dataset_fn, _format_inputs_dataset, _functional_call, _get_k_most_influential_helper, _influence_batch_intermediate_quantities_influence_function, _influence_helper_intermediate_quantities_influence_function, _influence_route_to_helpers, _load_flexible_state_dict, _parameter_add, _parameter_dot, _parameter_linear_combination, _parameter_multiply, _parameter_to, _params_to_names, _progress_bar_constructor, _self_influence_helper_intermediate_quantities_influence_function, _top_eigen, KMostInfluentialResults
  from captum.log import log_usage
  from torch import Tensor
  from torch.nn import Module
  from torch.utils.data import DataLoader, Dataset
  from tqdm import tqdm
  from .influence_function import _get_dataset_embeddings_intermediate_quantities_influence_function, InfluenceFunctionBase, IntermediateQuantitiesInfluenceFunction
label_desc: Use image node_id 5 for calling the ArnoldiInfluenceFunction obj's underlying member method code with example usage: obj._get_k_most_influential(inputs, k, proponents, show_progress) and returns: KMostInfluentialResults