code: def _draw_kernel_feature_paths_fallback(
      num_inputs: int,
      mean_module: Optional[Module],
      covar_module: Kernel,
      sample_shape: Size,
      num_features: int = 1024,
      map_generator: TKernelFeatureMapGenerator = gen_kernel_features,
      input_transform: Optional[TInputTransform] = None,
      output_transform: Optional[TOutputTransform] = None,
      weight_generator: Optional[Callable[[Size], Tensor]] = None,
  ) -> GeneralizedLinearPath:
      # Generate a kernel feature map
      feature_map = map_generator(
          kernel=covar_module,
          num_inputs=num_inputs,
          num_outputs=num_features,
      )
  
      # Sample random weights with which to combine kernel features
      if weight_generator is None:
          weight = draw_sobol_normal_samples(
              n=sample_shape.numel() * covar_module.batch_shape.numel(),
              d=feature_map.num_outputs,
              device=covar_module.device,
              dtype=covar_module.dtype,
          ).reshape(
              sample_shape
              + covar_module.batch_shape
              + (feature_map.num_outputs,)
          )
      else:
          weight = weight_generator(
              sample_shape
              + covar_module.batch_shape
              + (feature_map.num_outputs,)
          ).to(device=covar_module.device, dtype=covar_module.dtype)
  
      # Return the sample paths
      return GeneralizedLinearPath(
          feature_map=feature_map,
          weight=weight,
          bias_module=mean_module,
          input_transform=input_transform,
          output_transform=output_transform,
      )
  
imports: from __future__ import annotations
  from typing import Any, Callable, List, Optional
  from botorch.models.approximate_gp import ApproximateGPyTorchModel
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.sampling.pathwise.features import gen_kernel_features
  from botorch.sampling.pathwise.features.generators import TKernelFeatureMapGenerator
  from botorch.sampling.pathwise.paths import GeneralizedLinearPath, PathList, SamplePath
  from botorch.sampling.pathwise.utils import get_input_transform, get_output_transform, get_train_inputs, TInputTransform, TOutputTransform
  from botorch.utils.dispatcher import Dispatcher
  from botorch.utils.sampling import draw_sobol_normal_samples
  from gpytorch.kernels import Kernel
  from gpytorch.models import ApproximateGP, ExactGP, GP
  from gpytorch.variational import _VariationalStrategy
  from torch import Size, Tensor
  from torch.nn import Module
label_desc: Use image node_id 2 for calling a global function with example usage: _draw_kernel_feature_paths_fallback(num_inputs, mean_module, covar_module, sample_shape, num_features, map_generator, input_transform, output_transform, weight_generator) and returns: GeneralizedLinearPath