add a vit nd with rotary nd, from Jerry Xiong at UIUC

Author: lucidrains

README.md

@@ -2181,4 +2181,13 @@ Coming from computer vision and new to transformers? Here are some resources tha
 }
 ```
 
+```bibtex
+@misc{xiong2025ndrope,
+    author = {Jerry Xiong},
+    title  = {On n-dimensional rotary positional embeddings},
+    year   = {2025},
+    url    = {https://jerryxio.ng/posts/nd-rope/}
+}
+```
+
 *I visualise a time when we will be to robots what dogs are to humans, and I’m rooting for the machines.* — Claude Shannon

setup.py

@@ -6,7 +6,7 @@
 setup(
   name = 'vit-pytorch',
   packages = find_packages(exclude=['examples']),
-  version = '1.12.0',
+  version = '1.12.1',
   license='MIT',
   description = 'Vision Transformer (ViT) - Pytorch',
   long_description = long_description,

vit_pytorch/vit_nd_rotary.py

@@ -0,0 +1,292 @@
+from __future__ import annotations
+
+import torch
+from torch import nn, arange, cat, stack, Tensor
+from torch.nn import Module, ModuleList
+import torch.nn.functional as F
+
+from einops import rearrange, repeat, reduce
+from einops.layers.torch import Rearrange
+
+# helpers
+
+def exists(val):
+    return val is not None
+
+def l2norm(t):
+    return F.normalize(t, dim = -1, p = 2)
+
+def join(arr, delimiter = ' '):
+    return delimiter.join(arr)
+
+def ensure_tuple(t, length):
+    if isinstance(t, (tuple, list)):
+        assert len(t) == length, f'Expected tuple of length {length}, got {len(t)}'
+        return tuple(t)
+    return (t,) * length
+
+# golden gate rotary - Jerry Xiong, PhD student at UIUC
+# https://jerryxio.ng/posts/nd-rope/
+
+def _phi(m: int) -> float:
+    x = 2.0
+    for _ in range(10):
+        x = (1 + x) ** (1.0 / (m + 1.0))
+    return x
+
+def make_directions(n: int, d: int) -> Tensor:
+    g = _phi(d)
+    alpha = (1.0 / g) ** arange(1, d + 1, dtype = torch.float64)
+    i = arange(1, n + 1, dtype = torch.float64).unsqueeze(1)
+    z = torch.fmod(i * alpha, 1.0)
+    directions = torch.erfinv(2.0 * z - 1.0)
+    directions = l2norm(directions)
+    return directions.float()
+
+class GoldenGateRoPENd(Module):
+    def __init__(
+        self,
+        dim_pos: int,
+        heads: int,
+        dim_head: int,
+        rope_min_freq: float = 1.0,
+        rope_max_freq: float = 10000.0,
+        rope_p_zero_freqs: float = 0.0, # proportion of frequencies set to 0
+    ):
+        super().__init__()
+        n_freqs = dim_head // 2
+        n_zero_freqs = round(rope_p_zero_freqs * n_freqs)
+
+        omega = cat((
+            torch.zeros(n_zero_freqs),
+            rope_min_freq * (rope_max_freq / rope_min_freq) ** torch.linspace(0, 1, n_freqs - n_zero_freqs),
+        ))
+
+        directions = rearrange(
+            make_directions(heads * n_freqs, dim_pos),
+            '(h f) p -> h f p',
+            h = heads
+        )
+
+        omega_expanded = rearrange(omega, 'f -> f 1')
+        self.register_buffer('freqs', directions * omega_expanded)  # shape: (h, f, p)
+
+    def forward(self, input: Tensor, pos: Tensor) -> Tensor:
+        # input shape: (b, h, n, d) where d = head_dim
+        # pos shape: (b, n, p) where p = pos_dim
+        # self.freqs shape: (h, f, p) where f = d // 2
+        
+        x, y = input.float().chunk(2, dim = -1)  # both (b, h, n, f)
+        
+        # Expand dimensions for broadcasting
+        freqs = rearrange(self.freqs, 'h f p -> 1 h 1 f p')
+        positions = rearrange(pos.float(), 'b n p -> b 1 n 1 p')
+        
+        # Compute theta for each (batch, head, seq, freq)
+        theta = reduce(freqs * positions, 'b h n f p -> b h n f', 'sum')
+        
+        cos_theta = torch.cos(theta)
+        sin_theta = torch.sin(theta)
+        
+        # Apply rotation
+        x_out = x * cos_theta - y * sin_theta
+        y_out = x * sin_theta + y * cos_theta
+        
+        output = cat((x_out, y_out), dim=-1)
+        return output.type_as(input)
+
+# classes
+
+class FeedForward(Module):
+    def __init__(self, dim, hidden_dim, dropout = 0.):
+        super().__init__()
+        self.net = nn.Sequential(
+            nn.LayerNorm(dim),
+            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(Module):
+    def __init__(self, dim, heads = 8, dim_head = 64, dropout = 0., rotary_emb = None):
+        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.rotary_emb = rotary_emb
+        
+        self.norm = nn.LayerNorm(dim)
+        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, pos = None):
+        x = self.norm(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)
+        
+        # Apply rotary embeddings if available
+        if exists(self.rotary_emb):
+            assert exists(pos)
+            q = self.rotary_emb(q, pos)
+            k = self.rotary_emb(k, pos)
+        
+        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(Module):
+    def __init__(self, dim, depth, heads, dim_head, mlp_dim, dropout = 0., rotary_emb = None):
+        super().__init__()
+        self.norm = nn.LayerNorm(dim)
+        self.layers = ModuleList([])
+        for _ in range(depth):
+            self.layers.append(ModuleList([
+                Attention(dim, heads = heads, dim_head = dim_head, dropout = dropout, rotary_emb = rotary_emb),
+                FeedForward(dim, mlp_dim, dropout = dropout)
+            ]))
+    
+    def forward(self, x, pos = None):
+        for attn, ff in self.layers:
+            x = attn(x, pos) + x
+            x = ff(x) + x
+        return self.norm(x)
+
+class ViTND(Module):
+    def __init__(
+        self,
+        *,
+        ndim: int,
+        input_shape: int | tuple[int, ...],
+        patch_size: int | tuple[int, ...],
+        num_classes: int,
+        dim: int,
+        depth: int,
+        heads: int,
+        mlp_dim: int,
+        channels: int = 3,
+        dim_head: int = 64,
+        dropout: float = 0.,
+        emb_dropout: float = 0.,
+        rope_min_freq: float = 1.0,
+        rope_max_freq: float = 10000.0,
+        rope_p_zero_freqs: float = 0.0
+    ):
+        super().__init__()
+        
+        assert 1 <= ndim <= 7, 'ndim must be between 1 and 7'
+        
+        self.ndim = ndim
+        
+        input_shape = ensure_tuple(input_shape, ndim)
+        patch_size = ensure_tuple(patch_size, ndim)
+        
+        for i, (inp_dim, patch_dim) in enumerate(zip(input_shape, patch_size)):
+            assert inp_dim % patch_dim == 0, f'Input dimension {i} ({inp_dim}) must be divisible by patch size ({patch_dim})'
+        
+        num_patches_per_dim = [inp_dim // patch_dim for inp_dim, patch_dim in zip(input_shape, patch_size)]
+        num_patches = 1
+        for n in num_patches_per_dim:
+            num_patches *= n
+        
+        patch_dim = channels
+        for p in patch_size:
+            patch_dim *= p
+        
+        dim_names = 'fghijkl'[:ndim]
+        
+        input_dims = [f'({d} p{i})' for i, d in enumerate(dim_names)]
+        patch_dims = [f'p{i}' for i in range(ndim)]
+        
+        input_pattern = f'b c {join(input_dims)}'
+        output_pattern = f'b {join(dim_names)} ({join(patch_dims)} c)'
+        rearrange_str = f'{input_pattern} -> {output_pattern}'
+        
+        rearrange_kwargs = {f'p{i}': p for i, p in enumerate(patch_size)}
+        
+        self.to_patch_embedding = nn.Sequential(
+            Rearrange(rearrange_str, **rearrange_kwargs),
+            nn.Linear(patch_dim, dim),
+            nn.LayerNorm(dim),
+        )
+        
+        self.dropout = nn.Dropout(emb_dropout)
+        
+        # Create rotary embeddings
+        self.rotary_emb = GoldenGateRoPENd(
+            dim_pos = ndim,
+            heads = heads,
+            dim_head = dim_head,
+            rope_min_freq = rope_min_freq,
+            rope_max_freq = rope_max_freq,
+            rope_p_zero_freqs = rope_p_zero_freqs
+        )
+        
+        self.transformer = Transformer(dim, depth, heads, dim_head, mlp_dim, dropout, rotary_emb = self.rotary_emb)
+        
+        self.to_latent = nn.Identity()
+        self.mlp_head = nn.Linear(dim, num_classes)
+    
+    def forward(self, x):
+        x = self.to_patch_embedding(x) # (b, *spatial_dims, patch_dim)
+        
+        batch, *spatial_dims, _, device = *x.shape, x.device
+        
+        # Generate position coordinates
+
+        grids = [arange(d, device = device, dtype = torch.float32) for d in spatial_dims]
+        grid = torch.meshgrid(*grids, indexing = 'ij')
+        pos = stack(grid, dim = -1)  # (*spatial_dims, ndim)
+
+        # flatten spatial dimensions for attention with nd rotary
+        
+        pos = repeat(pos, '... p -> b (...) p', b = batch)
+        x = rearrange(x, 'b ... d -> b (...) d')
+
+        x = self.dropout(x)
+        
+        x = self.transformer(x, pos)
+        
+        x = reduce(x, 'b n d -> b d', 'mean')
+        
+        x = self.to_latent(x)
+        return self.mlp_head(x)
+
+
+if __name__ == '__main__':
+  
+    model = ViTND(
+        ndim = 5,
+        input_shape = (4, 8, 16, 32, 64),
+        patch_size = (2, 2, 4, 4, 8),
+        num_classes = 1000,
+        dim = 512,
+        depth = 6,
+        heads = 8,
+        mlp_dim = 2048,
+        channels = 3,
+        dropout = 0.1,
+        emb_dropout = 0.1
+    )
+
+    data = torch.randn(2, 3, 4, 8, 16, 32, 64)
+    
+    logits = model(data)