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: Computes self influence scores for the examples in `inputs_dataset`, which is
  either a single batch or a Pytorch `DataLoader` that yields batches. Therefore,
  the computed self influence scores are *not* for the examples in training
  dataset `train_dataset` (unlike when computing self influence scores using the
  `influence` method). Note that if `inputs_dataset` is a single batch, this
  will call `model` on that single batch, and if `inputs_dataset` yields
  batches, this will call `model` on each batch that is yielded. Therefore,
  please ensure that for both cases, the batch(es) that `model` is called
  with are not too large, so that there will not be an out-of-memory error.
  
  Implementation-wise, the self-influence score for an example is simply the
  squared norm of the example's "embedding" vector. Therefore, the implementation
  leverages `compute_intermediate_quantities`.
  
  Args:
      inputs_dataset (tuple or DataLoader): Either a single tuple of any, or a
              `DataLoader`, where each batch yielded is a tuple of any. In
              either case, the tuple represents a single batch, 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`.
              Default: None
      show_progress (bool, optional): Computation of self influence scores can
              take a long time if `inputs_dataset` represents many examples. If
              `show_progress`is true, the progress of this computation will be
              displayed. In particular, the number of batches for which
              self influence scores have been computed 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
docstr_tok: ["Computes","self","influence","scores","for","the","examples","in","`","inputs_dataset","`",",","which","is","either","a","single","batch","or","a","Pytorch","`","DataLoader","`","that","yields","batches",".","Therefore",",","the","computed","self","influence","scores","are","*","not","*","for","the","examples","in","training","dataset","`","train_dataset","`","(","unlike","when","computing","self","influence","scores","using","the","`","influence","`","method",")",".","Note","that","if","`","inputs_dataset","`","is","a","single","batch",",","this","will","call","`","model","`","on","that","single","batch",",","and","if","`","inputs_dataset","`","yields","batches",",","this","will","call","`","model","`","on","each","batch","that","is","yielded",".","Therefore",",","please","ensure","that","for","both","cases",",","the","batch","(","es",")","that","`","model","`","is","called","with","are","not","too","large",",","so","that","there","will","not","be","an","out-of-memory","error",".","Implementation-wise",",","the","self-influence","score","for","an","example","is","simply","the","squared","norm","of","the","example","'s","``","embedding","''","vector",".","Therefore",",","the","implementation","leverages","`","compute_intermediate_quantities","`",".","Args",":","inputs_dataset","(","tuple","or","DataLoader",")",":","Either","a","single","tuple","of","any",",","or","a","`","DataLoader","`",",","where","each","batch","yielded","is","a","tuple","of","any",".","In","either","case",",","the","tuple","represents","a","single","batch",",","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","`",".","Default",":","None","show_progress","(","bool",",","optional",")",":","Computation","of","self","influence","scores","can","take","a","long","time","if","`","inputs_dataset","`","represents","many","examples",".","If","`","show_progress","`","is","true",",","the","progress","of","this","computation","will","be","displayed",".","In","particular",",","the","number","of","batches","for","which","self","influence","scores","have","been","computed","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"]
code: def self_influence(
      self,
      inputs_dataset: Optional[
          Union[Tuple[Any, ...], DataLoader]
      ] = None,
      show_progress: bool = False,
  ) -> Tensor:
      """
      Computes self influence scores for the examples in `inputs_dataset`, which is
      either a single batch or a Pytorch `DataLoader` that yields batches. Therefore,
      the computed self influence scores are *not* for the examples in training
      dataset `train_dataset` (unlike when computing self influence scores using the
      `influence` method). Note that if `inputs_dataset` is a single batch, this
      will call `model` on that single batch, and if `inputs_dataset` yields
      batches, this will call `model` on each batch that is yielded. Therefore,
      please ensure that for both cases, the batch(es) that `model` is called
      with are not too large, so that there will not be an out-of-memory error.
  
      Implementation-wise, the self-influence score for an example is simply the
      squared norm of the example's "embedding" vector. Therefore, the implementation
      leverages `compute_intermediate_quantities`.
  
      Args:
          inputs_dataset (tuple or DataLoader): Either a single tuple of any, or a
                  `DataLoader`, where each batch yielded is a tuple of any. In
                  either case, the tuple represents a single batch, 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`.
                  Default: None
          show_progress (bool, optional): Computation of self influence scores can
                  take a long time if `inputs_dataset` represents many examples. If
                  `show_progress`is true, the progress of this computation will be
                  displayed. In particular, the number of batches for which
                  self influence scores have been computed 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
      """
      return _self_influence_helper_intermediate_quantities_influence_function(
          self, inputs_dataset, show_progress
      )
  
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 7 for calling the ArnoldiInfluenceFunction obj's underlying member method code with example usage: obj.self_influence(inputs_dataset, show_progress) and returns: _self_influence_helper_intermediate_quantities_influence_function