get a version of n-dimensional vit with golden gate polar coordinate embeddings into the repo for future use

Use lru_cache to cache unique (ph, pw, device) position grids, avoiding
redundant computation when multiple images share the same patch
dimensions. Cache persists across forward passes.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

README.md

@@ -49,7 +49,7 @@
 
 ## Vision Transformer - Pytorch
 
-Implementation of <a href="https://openreview.net/pdf?id=YicbFdNTTy">Vision Transformer</a>, a simple way to achieve SOTA in vision classification with only a single transformer encoder, in Pytorch. Significance is further explained in <a href="https://www.youtube.com/watch?v=TrdevFK_am4">Yannic Kilcher's</a> video. There's really not much to code here, but may as well lay it out for everyone so we expedite the attention revolution.
+Implementation of <a href="https://openreview.net/pdf?id=YicbFdNTTy">Vision Transformer</a>, a simple way to achieve SOTA in vision classification with only a single transformer encoder, in Pytorch. Significance is further explained in <a href="https://www.youtube.com/watch?v=TrdevFK_am4">Yannic Kilcher's</a> video. There's really not much to code here, but may as well lay it out for everyone so we expedite the [attention](https://www.youtube.com/watch?v=eMlx5fFNoYc) revolution.
 
 For a Pytorch implementation with pretrained models, please see Ross Wightman's repository <a href="https://github.com/rwightman/pytorch-image-models">here</a>.
 
@@ -2213,4 +2213,16 @@ Coming from computer vision and new to transformers? Here are some resources tha
 }
 ```
 
+```bibtex
+@misc{gopalakrishnan2025decouplingwhatwherepolar,
+    title   = {Decoupling the "What" and "Where" With Polar Coordinate Positional Embeddings}, 
+    author  = {Anand Gopalakrishnan and Robert Csordás and Jürgen Schmidhuber and Michael C. Mozer},
+    year    = {2025},
+    eprint  = {2509.10534},
+    archivePrefix = {arXiv},
+    primaryClass = {cs.LG},
+    url     = {https://arxiv.org/abs/2509.10534}, 
+}
+```
+
 *I visualise a time when we will be to robots what dogs are to humans, and I’m rooting for the machines.* — Claude Shannon

pyproject.toml

@@ -4,7 +4,7 @@ build-backend = "setuptools.build_meta"
 
 [project]
 name = "vit-pytorch"
-version = "1.16.3"
+version = "1.17.1"
 description = "Vision Transformer (ViT) - Pytorch"
 readme = { file = "README.md", content-type = "text/markdown" }
 license = { file = "LICENSE" }

vit_pytorch/distill.py

@@ -25,12 +25,12 @@ class DistillMixin:
         x = self.to_patch_embedding(img)
         b, n, _ = x.shape
 
-        cls_tokens = repeat(self.cls_token, '1 n d -> b n d', b = b)
+        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.pos_embedding[:(n + 1)]
 
         if distilling:
-            distill_tokens = repeat(distill_token, '1 n d -> b n d', b = b)
+            distill_tokens = repeat(distill_token, 'n d -> b n d', b = b)
             x = torch.cat((x, distill_tokens), dim = 1)
 
         x = self._attend(x)
@@ -125,7 +125,7 @@ class DistillWrapper(Module):
         self.alpha = alpha
         self.hard = hard
 
-        self.distillation_token = nn.Parameter(torch.randn(1, 1, dim))
+        self.distillation_token = nn.Parameter(torch.randn(1, dim))
 
         self.distill_mlp = nn.Sequential(
             nn.LayerNorm(dim) if mlp_layernorm else nn.Identity(),

vit_pytorch/na_vit.py

@@ -1,6 +1,6 @@
 from __future__ import annotations
 
-from functools import partial
+from functools import partial, lru_cache
 from typing import List
 
 import torch
@@ -27,6 +27,12 @@ def pair(t):
 def divisible_by(numer, denom):
     return (numer % denom) == 0
 
+@lru_cache(maxsize=128)
+def posemb_grid(ph, pw, device):
+    h_idx = torch.arange(ph, device=device).repeat_interleave(pw)
+    w_idx = torch.arange(pw, device=device).repeat(ph)
+    return torch.stack([h_idx, w_idx], dim=-1)
+
 # auto grouping images
 
 def group_images_by_max_seq_len(
@@ -293,12 +299,8 @@ class NaViT(nn.Module):
             # extract patches for all images
             sequences = [rearrange(img, 'c (h p1) (w p2) -> (h w) (c p1 p2)', p1=p, p2=p) for img in images]
 
-            # compute positions using repeat_interleave (faster than meshgrid per image)
-            positions = []
-            for ph, pw in patch_dims:
-                h_idx = arange(ph).repeat_interleave(pw)
-                w_idx = arange(pw).repeat(ph)
-                positions.append(torch.stack([h_idx, w_idx], dim=-1))
+            # compute positions - uses lru_cache to avoid redundant computation across forward passes
+            positions = [posemb_grid(ph, pw, device) for ph, pw in patch_dims]
 
             # handle token dropout
             if has_token_dropout:

vit_pytorch/vit_nd_pope.py

@@ -0,0 +1,352 @@
+from __future__ import annotations
+
+import torch
+import torch.nn.functional as F
+from torch import pi, nn, arange, cat, stack, Tensor
+from torch.nn import Module, ModuleList
+from torch.amp import autocast
+
+from einops import rearrange, repeat, reduce, pack, unpack
+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/
+
+# but using polar version instead
+# Gopalakrishnan et al. https://arxiv.org/abs/2509.10534
+
+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 GoldenGatePoPENd(Module):
+    def __init__(
+        self,
+        dim_pos: int,
+        heads: int,
+        dim_head: int,
+        min_freq: float = 1.0,
+        max_freq: float = 10000.0,
+        p_zero_freqs: float = 0.0, # proportion of frequencies set to 0
+        init_learned_bias_uniform = False
+    ):
+        super().__init__()
+        n_freqs = dim_head
+        n_zero_freqs = round(p_zero_freqs * n_freqs)
+
+        omega = cat((
+            torch.zeros(n_zero_freqs),
+            min_freq * (max_freq / 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)
+
+        self.learned_bias = nn.Parameter(torch.zeros(heads, dim_head))
+
+        if init_learned_bias_uniform:
+            self.learned_bias.uniform_(-2. * pi, 0.)
+
+    @autocast('cuda', enabled = False)
+    def forward(self, pos):
+
+        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')
+
+        bias = self.learned_bias.clamp(-2. * pi, 0.)
+        bias = rearrange(bias, 'h d -> h 1 d')
+
+        return theta, bias
+
+@autocast('cuda', enabled = False)
+def apply_polar_pos_emb(t, freqs):
+    orig_dtype = t.dtype
+
+    t = t.float()
+    t = F.softplus(t)
+
+    out = cat((t * freqs.cos(), t * freqs.sin()), dim = -1)
+
+    return out.type(orig_dtype)
+
+# 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.):
+        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.norm = nn.LayerNorm(dim)
+        self.attend = nn.Softmax(dim = -1)
+        self.dropout = nn.Dropout(dropout)
+        
+        self.to_qk = nn.Linear(dim, inner_dim * 2, bias = False)
+        self.to_v = nn.Linear(dim, inner_dim, 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, polar_pos_emb = None):
+        x = self.norm(x)
+        qkv = (*self.to_qk(x).chunk(2, dim = -1), self.to_v(x))
+
+        q, k, v = map(lambda t: rearrange(t, 'b n (h d) -> b h n d', h = self.heads), qkv)
+
+        if exists(polar_pos_emb):
+            freqs, bias = polar_pos_emb
+            q = apply_polar_pos_emb(q, freqs)
+            k = apply_polar_pos_emb(k, freqs + bias)
+        
+        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., polar_emb = None):
+        super().__init__()
+        self.norm = nn.LayerNorm(dim)
+
+        self.polar_emb = polar_emb
+
+        self.layers = ModuleList([])
+
+        for _ in range(depth):
+            self.layers.append(ModuleList([
+                Attention(dim, heads = heads, dim_head = dim_head, dropout = dropout),
+                FeedForward(dim, mlp_dim, dropout = dropout)
+            ]))
+    
+    def forward(self, x, pos = None):
+
+        # pope embedding
+
+        polar_pos_emb = None
+        if exists(pos) and exists(self.polar_emb):
+            polar_pos_emb = self.polar_emb(pos)
+
+        # transformer layers
+
+        for attn, ff in self.layers:
+            x = attn(x, polar_pos_emb) + 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.,
+        pope_min_freq: float = 1.0,
+        pope_max_freq: float = 10000.0,
+        pope_p_zero_freqs: float = 0.0,
+        pope_init_learned_bias_uniform = False
+    ):
+        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)
+        
+        # golden gate pope
+
+        self.polar_emb = GoldenGatePoPENd(
+            dim_pos = ndim,
+            heads = heads,
+            dim_head = dim_head,
+            min_freq = pope_min_freq,
+            max_freq = pope_max_freq,
+            p_zero_freqs = pope_p_zero_freqs,
+            init_learned_bias_uniform = pope_init_learned_bias_uniform
+        )
+        
+        self.transformer = Transformer(dim, depth, heads, dim_head, mlp_dim, dropout, polar_emb = self.polar_emb)
+        
+        self.to_latent = nn.Identity()
+        self.mlp_head = nn.Linear(dim, num_classes)
+    
+    def muon_parameters(self):
+        params = []
+
+        for m in self.modules():
+            if isinstance(m, Attention):
+                params.extend([
+                    m.to_v.weight,
+                    m.to_out[0].weight
+                ])
+            elif isinstance(m, FeedForward):
+                params.extend([
+                    m.net[1].weight,
+                    m.net[-2].weight
+                ])
+
+        return params
+
+    def forward(
+        self,
+        x,
+        return_embed = False
+    ):
+        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, packed_shape = pack([x], 'b * d')
+
+        x = self.dropout(x)
+        
+        embed = self.transformer(x, pos)
+
+        # return the embed with reconstituted patch shape
+
+        if return_embed:
+            embed, = unpack(embed, packed_shape, 'b * d')
+            return embed
+
+        # pooling to logits
+
+        pooled = reduce(embed, 'b n d -> b d', 'mean')
+
+        pooled = self.to_latent(pooled)
+        return self.mlp_head(pooled)
+
+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(3, 3, 4, 8, 16, 32, 64)
+
+    logits = model(data)
+
+    embed = model(data, return_embed = True) # (2, 2, 4, 4, 8, 8, 512)