text: import torch
  from torch import nn
  
  from einops import rearrange, repeat
  from einops.layers.torch import Rearrange, Reduce
  
  # helpers
  
  def exists(val):
      return val is not None
  
  def default(val ,d):
      return val if exists(val) else d
  
  def pair(t):
      return t if isinstance(t, tuple) else (t, t)
  
  # patch merger class
  
  class PatchMerger(nn.Module):
      def __init__(self, dim, num_tokens_out):
          super().__init__()
          self.scale = dim ** -0.5
          self.norm = nn.LayerNorm(dim)
          self.queries = nn.Parameter(torch.randn(num_tokens_out, dim))
  
      def forward(self, x):
          x = self.norm(x)
          sim = torch.matmul(self.queries, x.transpose(-1, -2)) * self.scale
          attn = sim.softmax(dim = -1)
          return torch.matmul(attn, x)
  
  # 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 Attention(nn.Module):
      def __init__(self, dim, heads = 8, dim_head = 64, dropout = 0.):
          super().__init__()
          inner_dim = dim_head *  heads
          project_out = not (heads == 1 and dim_head == dim)
  
          self.heads = heads
          self.scale = dim_head ** -0.5
  
          self.attend = nn.Softmax(dim = -1)
          self.dropout = nn.Dropout(dropout)
  
          self.to_qkv = nn.Linear(dim, inner_dim * 3, bias = False)
  
          self.to_out = nn.Sequential(
              nn.Linear(inner_dim, dim),
              nn.Dropout(dropout)
          ) if project_out else nn.Identity()
  
      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.scale
  
          attn = self.attend(dots)
          attn = self.dropout(attn)
  
          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., patch_merge_layer = None, patch_merge_num_tokens = 8):
          super().__init__()
          self.layers = nn.ModuleList([])
  
          self.patch_merge_layer_index = default(patch_merge_layer, depth // 2) - 1 # default to mid-way through transformer, as shown in paper
          self.patch_merger = PatchMerger(dim = dim, num_tokens_out = patch_merge_num_tokens)
  
          for _ in range(depth):
              self.layers.append(nn.ModuleList([
                  PreNorm(dim, Attention(dim, heads = heads, dim_head = dim_head, dropout = dropout)),
                  PreNorm(dim, FeedForward(dim, mlp_dim, dropout = dropout))
              ]))
      def forward(self, x):
          for index, (attn, ff) in enumerate(self.layers):
              x = attn(x) + x
              x = ff(x) + x
  
              if index == self.patch_merge_layer_index:
                  x = self.patch_merger(x)
  
          return x
  
  class ViT(nn.Module):
      def __init__(self, *, image_size, patch_size, num_classes, dim, depth, heads, mlp_dim, patch_merge_layer = None, patch_merge_num_tokens = 8, 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
  
          self.to_patch_embedding = nn.Sequential(
              Rearrange('b c (h p1) (w p2) -> b (h w) (p1 p2 c)', p1 = patch_height, p2 = patch_width),
              nn.Linear(patch_dim, dim),
          )
  
          self.pos_embedding = nn.Parameter(torch.randn(1, num_patches + 1, dim))
          self.dropout = nn.Dropout(emb_dropout)
  
          self.transformer = Transformer(dim, depth, heads, dim_head, mlp_dim, dropout, patch_merge_layer, patch_merge_num_tokens)
  
          self.mlp_head = nn.Sequential(
              Reduce('b n d -> b d', 'mean'),
              nn.LayerNorm(dim),
              nn.Linear(dim, num_classes)
          )
  
      def forward(self, img):
          x = self.to_patch_embedding(img)
          b, n, _ = x.shape
  
          x += self.pos_embedding[:, :n]
          x = self.dropout(x)
  
          x = self.transformer(x)
  
          return self.mlp_head(x)
  