docstr: tests that the result of calling the public method
  "compute_intermediate_quantities" with TracInCPFastRandProj
  with/without projection_dim gives embedding of correct size.
  
  if projection_dim None, size should be dim of
  input to final layer * num classes * num checkpoints.
  otherwise it should be "at most" projection_dim * num checkpoints.
  See inline comments for "at most" caveat
docstr_tok: ["tests","that","the","result","of","calling","the","public","method","''","compute_intermediate_quantities","''","with","TracInCPFastRandProj","with\/without","projection_dim","gives","embedding","of","correct","size",".","if","projection_dim","None",",","size","should","be","dim","of","input","to","final","layer","*","num","classes","*","num","checkpoints",".","otherwise","it","should","be","``","at","most","''","projection_dim","*","num","checkpoints",".","See","inline","comments","for","``","at","most","''","caveat"]
code: def test_tracin_intermediate_quantities_projection_consistency(
      self,
      reduction: str,
      tracin_constructor: Callable,
      projection_dim: int,
      unpack_inputs: bool,
  ) -> None:
      """
  
      tests that the result of calling the public method
      "compute_intermediate_quantities" with TracInCPFastRandProj
      with/without projection_dim gives embedding of correct size.
  
      if projection_dim None, size should be dim of
      input to final layer * num classes * num checkpoints.
      otherwise it should be "at most" projection_dim * num checkpoints.
      See inline comments for "at most" caveat
      """
      with tempfile.TemporaryDirectory() as tmpdir:
          (
              net,
              train_dataset,
          ) = get_random_model_and_data(
              tmpdir,
              unpack_inputs,
              return_test_data=False,
          )
  
          # create a single batch
          batch_size = 1
          single_batch = next(
              iter(DataLoader(train_dataset, batch_size=batch_size))
          )
  
          # NOW add projection_dim as a parameter passed in
          kwargs = {"projection_dim": projection_dim}
  
          # create tracin instance
          criterion = nn.MSELoss(reduction=reduction)
          tracin = tracin_constructor(
              net,
              train_dataset,
              tmpdir,
              batch_size,
              criterion,
              **kwargs,
          )
  
          # compute intermediate quantities using `compute_intermediate_quantities`
          # when passing in a single batch
          single_batch_intermediate_quantities = (
              tracin.compute_intermediate_quantities(single_batch)
          )
  
          """
              net has
              in_features = 5,
              hidden_nodes (layer_input_dim) = 4,
              out_features (jacobian_dim) = 3
              and 5 checkpoints
  
              projection only happens
              (A) if project_dim < layer_input_dim * jacobian_dim  ( 4 * 3 = 12 here )
  
              also if jacobian_dim < int(sqrt(projection dim)),
              then jacobian_dim is not projected down
              similarly if layer_input_dim < int(sqrt(projection dim)),
              then it is not projected down
  
              in other words,
              jacobian_dim_post = min(jacobian_dim, int(sqrt(projection dim)))
              layer_input_dim_post = min(layer_input_dim, int(sqrt(projection dim)))
  
              and if not None and projection_dim < layer_input_dim * jacobian_dim
              (B) final_projection_dim =
                  jacobian_dim_post * layer_input_dim_post * num_checkpoints
  
  
              if project dim = None we expect final dimension size of
              layer_input * jacobian_dim * num checkpoints = 4 * 3 * 5  = 60 dimension
  
              otherwise using (B) if
              project dim = 2  we expect 1 * 1 * 5 = 5
              project dim = 4  we expect 2 * 2 * 5 = 20
              project dim = 9  we expect 3 * 3 * 5 = 45
              project dim = 10 we expect 3 * 3 * 5 = 45
              project dim = 12 we expect 4 * 3 * 5 = 60 ( don't project since not (A))
              """
  
          # print(single_batch_intermediate_quantities.shape)
          expected_dim = {None: 60, 2: 5, 4: 20, 9: 45, 10: 45, 12: 60}
          self.assertEqual(
              expected_dim[projection_dim],
              single_batch_intermediate_quantities.shape[1],
          )
  
file_path: captum/tests/influence/_core/test_tracin_intermediate_quantities.py
imports: import tempfile
  from typing import Callable
  import torch
  import torch.nn
  from captum.influence._core.arnoldi_influence_function import ArnoldiInfluenceFunction
  from captum.influence._core.influence_function import NaiveInfluenceFunction
  from captum.influence._core.tracincp import TracInCP
  from captum.influence._core.tracincp_fast_rand_proj import TracInCPFast, TracInCPFastRandProj
  from parameterized import parameterized
  from tests.helpers.basic import assertTensorAlmostEqual, BaseTest
  from tests.influence._utils.common import _format_batch_into_tuple, build_test_name_func, DataInfluenceConstructor, get_random_model_and_data
  from torch.utils.data import DataLoader
label_desc: Use image node_id 4 for calling the TestTracInIntermediateQuantities obj's underlying member method code with example usage: obj.test_tracin_intermediate_quantities_projection_consistency(reduction, tracin_constructor, projection_dim, unpack_inputs) without return types