text: # https://github.com/lucidrains/vit-pytorch/blob/main/vit_pytorch/vit_for_small_dataset.py
  
  from math import sqrt
  import torch
  import torch.nn.functional as F
  from torch import nn
  
  from einops import rearrange, repeat
  from einops.layers.torch import Rearrange
  
  # helpers
  
  def pair(t):
      return t if isinstance(t, tuple) else (t, t)
  
  # classes
  
  class PreNorm(nn.Module):
      def __init__(self, dim, fn):
          super().__init__()
          self.norm = nn.LayerNorm(dim)
          self.fn = fn
      def forward(self, x, **kwargs):
          return self.fn(self.norm(x), **kwargs)
  
  class FeedForward(nn.Module):
      def __init__(self, dim, hidden_dim, dropout = 0.):
          super().__init__()
          self.net = nn.Sequential(
              nn.Linear(dim, hidden_dim),
              nn.GELU(),
              nn.Dropout(dropout),
              nn.Linear(hidden_dim, dim),
              nn.Dropout(dropout)
          )
      def forward(self, x):
          return self.net(x)
  
  class LSA(nn.Module):
      def __init__(self, dim, heads = 8, dim_head = 64, dropout = 0.):
          super().__init__()
          inner_dim = dim_head *  heads
          self.heads = heads
          self.temperature = nn.Parameter(torch.log(torch.tensor(dim_head ** -0.5)))
  
          self.attend = nn.Softmax(dim = -1)
          self.to_qkv = nn.Linear(dim, inner_dim * 3, bias = False)
  
          self.to_out = nn.Sequential(
              nn.Linear(inner_dim, dim),
              nn.Dropout(dropout)
          )
  
      def forward(self, x):
          qkv = self.to_qkv(x).chunk(3, dim = -1)
          q, k, v = map(lambda t: rearrange(t, 'b n (h d) -> b h n d', h = self.heads), qkv)
  
          dots = torch.matmul(q, k.transpose(-1, -2)) * self.temperature.exp()
  
          mask = torch.eye(dots.shape[-1], device = dots.device, dtype = torch.bool)
          mask_value = -torch.finfo(dots.dtype).max
          dots = dots.masked_fill(mask, mask_value)
  
          attn = self.attend(dots)
  
          out = torch.matmul(attn, v)
          out = rearrange(out, 'b h n d -> b n (h d)')
          return self.to_out(out)
  
  class Transformer(nn.Module):
      def __init__(self, dim, depth, heads, dim_head, mlp_dim, dropout = 0.):
          super().__init__()
          self.layers = nn.ModuleList([])
          for _ in range(depth):
              self.layers.append(nn.ModuleList([
                  PreNorm(dim, LSA(dim, heads = heads, dim_head = dim_head, dropout = dropout)),
                  PreNorm(dim, FeedForward(dim, mlp_dim, dropout = dropout))
              ]))
      def forward(self, x):
          for attn, ff in self.layers:
              x = attn(x) + x
              x = ff(x) + x
          return x
  
  class SPT(nn.Module):
      def __init__(self, *, dim, patch_size, channels = 3):
          super().__init__()
          patch_dim = patch_size * patch_size * 5 * channels
  
          self.to_patch_tokens = nn.Sequential(
              Rearrange('b c (h p1) (w p2) -> b (h w) (p1 p2 c)', p1 = patch_size, p2 = patch_size),
              nn.LayerNorm(patch_dim),
              nn.Linear(patch_dim, dim)
          )
  
      def forward(self, x):
          shifts = ((1, -1, 0, 0), (-1, 1, 0, 0), (0, 0, 1, -1), (0, 0, -1, 1))
          shifted_x = list(map(lambda shift: F.pad(x, shift), shifts))
          x_with_shifts = torch.cat((x, *shifted_x), dim = 1)
          return self.to_patch_tokens(x_with_shifts)
  
  class ViT(nn.Module):
      def __init__(self, *, image_size, patch_size, num_classes, dim, depth, heads, mlp_dim, pool = 'cls', channels = 3, dim_head = 64, dropout = 0., emb_dropout = 0.):
          super().__init__()
          image_height, image_width = pair(image_size)
          patch_height, patch_width = pair(patch_size)
  
          assert image_height % patch_height == 0 and image_width % patch_width == 0, 'Image dimensions must be divisible by the patch size.'
  
          num_patches = (image_height // patch_height) * (image_width // patch_width)
          patch_dim = channels * patch_height * patch_width
          assert pool in {'cls', 'mean'}, 'pool type must be either cls (cls token) or mean (mean pooling)'
  
          self.to_patch_embedding = SPT(dim = dim, patch_size = patch_size, channels = channels)
  
          self.pos_embedding = nn.Parameter(torch.randn(1, num_patches + 1, dim))
          self.cls_token = nn.Parameter(torch.randn(1, 1, dim))
          self.dropout = nn.Dropout(emb_dropout)
  
          self.transformer = Transformer(dim, depth, heads, dim_head, mlp_dim, dropout)
  
          self.pool = pool
          self.to_latent = nn.Identity()
  
          self.mlp_head = nn.Sequential(
              nn.LayerNorm(dim),
              nn.Linear(dim, num_classes)
          )
  
      def forward(self, img):
          x = self.to_patch_embedding(img)
          b, n, _ = x.shape
  
          cls_tokens = repeat(self.cls_token, '() n d -> b n d', b = b)
          x = torch.cat((cls_tokens, x), dim=1)
          x += self.pos_embedding[:, :(n + 1)]
          x = self.dropout(x)
  
          x = self.transformer(x)
  
          x = x.mean(dim = 1) if self.pool == 'mean' else x[:, 0]
  
          x = self.to_latent(x)
          return self.mlp_head(x)
  