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 = "1.15.6"
+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
@@ -9,7 +9,6 @@ from torch import nn, Tensor
 from torch.nn.utils.rnn import pad_sequence as orig_pad_sequence
 
 from einops import rearrange, repeat
-from einops.layers.torch import Rearrange
 
 # helpers
 
@@ -28,6 +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(
@@ -117,8 +122,7 @@ class Attention(nn.Module):
         self.q_norm = RMSNorm(heads, dim_head)
         self.k_norm = RMSNorm(heads, dim_head)
 
-        self.attend = nn.Softmax(dim = -1)
-        self.dropout = nn.Dropout(dropout)
+        self.dropout_p = dropout
 
         self.to_q = nn.Linear(dim, inner_dim, bias = False)
         self.to_kv = nn.Linear(dim, inner_dim * 2, bias = False)
@@ -145,19 +149,22 @@ class Attention(nn.Module):
         q = self.q_norm(q)
         k = self.k_norm(k)
 
-        dots = torch.matmul(q, k.transpose(-1, -2))
+        # combine masks if both exist
+        if exists(mask) or exists(attn_mask):
+            if exists(mask):
+                mask = rearrange(mask, 'b j -> b 1 1 j')
+            if exists(mask) and exists(attn_mask):
+                attn_mask = mask & attn_mask
+            elif exists(mask):
+                attn_mask = mask
 
-        if exists(mask):
-            mask = rearrange(mask, 'b j -> b 1 1 j')
-            dots = dots.masked_fill(~mask, -torch.finfo(dots.dtype).max)
+        out = F.scaled_dot_product_attention(
+            q, k, v,
+            attn_mask = attn_mask,
+            dropout_p = self.dropout_p if self.training else 0.,
+            scale = 1.  # RMSNorm already includes sqrt(dim) scaling
+        )
 
-        if exists(attn_mask):
-            dots = dots.masked_fill(~attn_mask, -torch.finfo(dots.dtype).max)
-
-        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)
 
@@ -281,42 +288,41 @@ class NaViT(nn.Module):
         for images in batched_images:
             num_images.append(len(images))
 
-            sequences = []
-            positions = []
-            image_ids = torch.empty((0,), device = device, dtype = torch.long)
-
-            for image_id, image in enumerate(images):
-                assert image.ndim ==3 and image.shape[0] == c
+            # compute patch dimensions for all images
+            patch_dims = []
+            for image in images:
+                assert image.ndim == 3 and image.shape[0] == c
                 image_dims = image.shape[-2:]
                 assert all([divisible_by(dim, p) for dim in image_dims]), f'height and width {image_dims} of images must be divisible by patch size {p}'
+                patch_dims.append((image_dims[0] // p, image_dims[1] // p))
 
-                ph, pw = map(lambda dim: dim // p, image_dims)
+            # 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]
 
-                pos = torch.stack(torch.meshgrid((
-                    arange(ph),
-                    arange(pw)
-                ), indexing = 'ij'), 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]
 
-                pos = rearrange(pos, 'h w c -> (h w) c')
-                seq = rearrange(image, 'c (h p1) (w p2) -> (h w) (c p1 p2)', p1 = p, p2 = p)
-
-                seq_len = seq.shape[-2]
-
-                if has_token_dropout:
+            # handle token dropout
+            if has_token_dropout:
+                for i, (seq, pos) in enumerate(zip(sequences, positions)):
+                    image_dims = images[i].shape[-2:]
                     token_dropout = self.calc_token_dropout(*image_dims)
+                    seq_len = seq.shape[0]
                     num_keep = max(1, int(seq_len * (1 - token_dropout)))
-                    keep_indices = torch.randn((seq_len,), device = device).topk(num_keep, dim = -1).indices
+                    keep_indices = torch.randn((seq_len,), device=device).topk(num_keep, dim=-1).indices
+                    sequences[i] = seq[keep_indices]
+                    positions[i] = pos[keep_indices]
 
-                    seq = seq[keep_indices]
-                    pos = pos[keep_indices]
-
-                image_ids = F.pad(image_ids, (0, seq.shape[-2]), value = image_id)
-                sequences.append(seq)
-                positions.append(pos)
+            # build image_ids efficiently using repeat_interleave
+            patch_counts = [seq.shape[0] for seq in sequences]
+            image_ids = torch.repeat_interleave(
+                arange(len(images)),
+                torch.tensor(patch_counts, device=device)
+            )
 
             batched_image_ids.append(image_ids)
-            batched_sequences.append(torch.cat(sequences, dim = 0))
-            batched_positions.append(torch.cat(positions, dim = 0))
+            batched_sequences.append(torch.cat(sequences, dim=0))
+            batched_positions.append(torch.cat(positions, dim=0))
 
         # derive key padding mask
 

vit_pytorch/na_vit_nested_tensor_3d.py

@@ -176,7 +176,7 @@ class NaViT(Module):
 
         self.channels = channels
         self.patch_size = patch_size
-        self.to_patches = Rearrange('c (f pf) (h p1) (w p2) -> f h w (c p1 p2 pf)', p1 = patch_size, p2 = patch_size, pf = frame_patch_size)
+        self.to_patches = Rearrange('c (f pf) (h p1) (w p2) -> f h w (c pf p1 p2)', p1 = patch_size, p2 = patch_size, pf = frame_patch_size)
 
         self.to_patch_embedding = nn.Sequential(
             nn.LayerNorm(patch_dim),

vit_pytorch/simple_flash_attn_vit_3d.py

@@ -146,7 +146,7 @@ class SimpleViT(Module):
         patch_dim = channels * patch_height * patch_width * frame_patch_size
 
         self.to_patch_embedding = nn.Sequential(
-            Rearrange('b c (f pf) (h p1) (w p2) -> b f h w (p1 p2 pf c)', p1 = patch_height, p2 = patch_width, pf = frame_patch_size),
+            Rearrange('b c (f pf) (h p1) (w p2) -> b f h w (pf p1 p2 c)', p1 = patch_height, p2 = patch_width, pf = frame_patch_size),
             nn.LayerNorm(patch_dim),
             nn.Linear(patch_dim, dim),
             nn.LayerNorm(dim),

vit_pytorch/simple_vit_3d.py

@@ -103,7 +103,7 @@ class SimpleViT(nn.Module):
         patch_dim = channels * patch_height * patch_width * frame_patch_size
 
         self.to_patch_embedding = nn.Sequential(
-            Rearrange('b c (f pf) (h p1) (w p2) -> b f h w (p1 p2 pf c)', p1 = patch_height, p2 = patch_width, pf = frame_patch_size),
+            Rearrange('b c (f pf) (h p1) (w p2) -> b f h w (pf p1 p2 c)', p1 = patch_height, p2 = patch_width, pf = frame_patch_size),
             nn.LayerNorm(patch_dim),
             nn.Linear(patch_dim, dim),
             nn.LayerNorm(dim),

vit_pytorch/vaat.py

@@ -421,7 +421,8 @@ class VAAT(Module):
         dim_head,
         dim_action,
         mlp_dim,
-        num_views = None,
+        num_image_views = None,
+        num_audio_views = None,
         num_tasks = None,
         dim_extra_token = None,
         num_register_tokens = 4,
@@ -462,6 +463,8 @@ class VAAT(Module):
 
         ast_dim = ast.dim
 
+        self.ast_accept_spec = ast.accept_spec
+
         assert ast.depth == depth or exists(ast_layer_indices), f'if the VAAT depth is not equal to the AST depth, you must pass in the indices from the AST to be layered to the VAAT in order from bottom to top'
 
         ast_layer_indices = default(ast_layer_indices, tuple(range(depth)))
@@ -480,7 +483,9 @@ class VAAT(Module):
 
         # maybe view embeddings
 
-        self.view_emb = nn.Parameter(torch.randn(num_views, vit_dim) * 1e-2) if exists(num_views) and num_views > 1 else None
+        self.image_view_emb = nn.Parameter(torch.randn(num_image_views, vit_dim) * 1e-2) if exists(num_image_views) and num_image_views > 1 else None
+
+        self.audio_view_emb = nn.Parameter(torch.randn(num_audio_views, ast_dim) * 1e-2) if exists(num_audio_views) and num_audio_views > 1 else None
 
         # handle maybe task conditioning
 
@@ -523,12 +528,12 @@ class VAAT(Module):
 
     def forward(
         self,
-        video_or_image,   # (b v? c t? h w) - batch, views [wrist + third person or more], channels, maybe time, height, width
-        audio_or_spec,    # (b t) | (b f t) - batch, audio len | batch, spec freq, time
+        video_or_image,   # (b v? c t? h w)      - batch, views [wrist + third person or more], channels, maybe time, height, width
+        audio_or_spec,    # (b v? t) | (b v?f t) - batch, audio len | batch, spec freq, time
         *,
-        extra = None,     # (b d)           - batch, dim extra     
+        extra = None,     # (b d)                - batch, dim extra     
         tasks = None,     # (b)
-        actions = None,   # (b k d)         - batch, action chunk length, action dimension
+        actions = None,   # (b k d)              - batch, action chunk length, action dimension
         return_hiddens = False,
         freeze_vit = False,
         freeze_ast = False
@@ -551,11 +556,26 @@ class VAAT(Module):
 
         assert video_or_image.shape[3] == self.time_seq_len
 
+        # audio shapes - adding view if impliciy to be 1
+
+        if audio_or_spec.ndim == 2 and not self.ast_accept_spec:
+            audio_or_spec = rearrange(audio_or_spec, 'b t -> b 1 t')
+
+        elif audio_or_spec.ndim == 3 and self.ast_accept_spec:
+            audio_or_spec = rearrange(audio_or_spec, 'b f t -> b 1 f t')
+
         # to images
 
         images = rearrange(video_or_image, 'b v c t h w -> b v t c h w')
 
-        images, packed_shape = pack([images], '* c h w')
+        images, image_packed_shape = pack([images], '* c h w')
+
+        # to audio
+
+        if self.ast_accept_spec:
+            audio_or_spec, audio_packed_shape = pack([audio_or_spec], '* f t')
+        else:
+            audio_or_spec, audio_packed_shape = pack([audio_or_spec], '* t')
 
         # get representation trajectory from vit
 
@@ -570,9 +590,9 @@ class VAAT(Module):
 
         hiddens = hiddens[self.vit_layer_indices]
 
-        # pack temporarily for embedding
+        # unpack temporarily for embedding
 
-        hiddens, = unpack(hiddens, packed_shape, 'l * n d') # l for layers
+        hiddens, = unpack(hiddens, image_packed_shape, 'l * n d') # l for layers
 
         # maybe add time embeddings
 
@@ -582,11 +602,11 @@ class VAAT(Module):
 
         # maybe view embeddings
 
-        if exists(self.view_emb):
-            assert self.view_emb.shape[0] == hiddens.shape[2]
+        if exists(self.image_view_emb):
+            assert self.image_view_emb.shape[0] == hiddens.shape[2]
 
-            view_emb = rearrange(self.view_emb, 'v d -> v 1 1 d')
-            hiddens = hiddens + view_emb
+            image_view_emb = rearrange(self.image_view_emb, 'v d -> v 1 1 d')
+            hiddens = hiddens + image_view_emb
 
         # get representation trajectory from ast
 
@@ -601,6 +621,18 @@ class VAAT(Module):
 
         audio_hiddens = audio_hiddens[self.ast_layer_indices]
 
+        # unpack audio temporarily for embedding
+
+        audio_hiddens, = unpack(audio_hiddens, audio_packed_shape, 'l * n d') # l for layers
+
+        # maybe audio view embeddings
+
+        if exists(self.audio_view_emb):
+            assert self.audio_view_emb.shape[0] == audio_hiddens.shape[2]
+
+            audio_view_emb = rearrange(self.audio_view_emb, 'v d -> v 1 1 d')
+            audio_hiddens = audio_hiddens + audio_view_emb
+
         # maybe tasks
 
         if exists(tasks):
@@ -612,7 +644,7 @@ class VAAT(Module):
 
         image_context = rearrange(hiddens, 'l b v t n d -> l b (v t n) d')
 
-        audio_context = audio_hiddens # eventually handle views (stereo and beyond)
+        audio_context = rearrange(audio_hiddens, 'l b v n d -> l b (v n) d')
 
         # get main action tokens and maybe append extra
 
@@ -703,7 +735,7 @@ if __name__ == '__main__':
         mlp_dim = 384 * 4
     )
 
-    vat = VAAT(
+    vaat = VAAT(
         vit,
         ast,
         dim = 512,
@@ -714,7 +746,8 @@ if __name__ == '__main__':
         dim_action = 20,
         action_chunk_len = 7,
         time_seq_len = 4,
-        num_views = 2,
+        num_image_views = 2,
+        num_audio_views = 2,
         num_tasks = 4,
         add_self_attn = True,
         dim_extra_token = 33,               # extra token with some variable dimension
@@ -727,18 +760,18 @@ if __name__ == '__main__':
     )
 
     images = torch.randn(2, 2, 3, 4, 256, 256) # (2 views with 4 frames)
-    audio = torch.randn(2, 14_100 * 5)
+    audio = torch.randn(2, 2, 14_100 * 5)
 
     tasks = torch.randint(0, 4, (2,))
     extra = torch.randn(2, 33)                 # extra internal state
 
     actions = torch.randn(2, 7, 20)         # actions for learning
 
-    loss = vat(images, audio, actions = actions, tasks = tasks, extra = extra, freeze_vit = True)
+    loss = vaat(images, audio, actions = actions, tasks = tasks, extra = extra, freeze_vit = True)
     loss.backward()
 
     # after much training
 
-    pred_actions, hiddens = vat(images, audio, tasks = tasks, extra = extra, return_hiddens = True)
+    pred_actions, hiddens = vaat(images, audio, tasks = tasks, extra = extra, return_hiddens = True)
 
     assert pred_actions.shape == (2, 7, 20)

vit_pytorch/vit.py

@@ -1,5 +1,6 @@
 import torch
 from torch import nn
+from torch.nn import Module, ModuleList
 
 from einops import rearrange, repeat
 from einops.layers.torch import Rearrange
@@ -11,7 +12,7 @@ def pair(t):
 
 # classes
 
-class FeedForward(nn.Module):
+class FeedForward(Module):
     def __init__(self, dim, hidden_dim, dropout = 0.):
         super().__init__()
         self.net = nn.Sequential(
@@ -26,7 +27,7 @@ class FeedForward(nn.Module):
     def forward(self, x):
         return self.net(x)
 
-class Attention(nn.Module):
+class Attention(Module):
     def __init__(self, dim, heads = 8, dim_head = 64, dropout = 0.):
         super().__init__()
         inner_dim = dim_head *  heads
@@ -62,13 +63,14 @@ class Attention(nn.Module):
         out = rearrange(out, 'b h n d -> b n (h d)')
         return self.to_out(out)
 
-class Transformer(nn.Module):
+class Transformer(Module):
     def __init__(self, dim, depth, heads, dim_head, mlp_dim, dropout = 0.):
         super().__init__()
         self.norm = nn.LayerNorm(dim)
-        self.layers = nn.ModuleList([])
+        self.layers = ModuleList([])
+
         for _ in range(depth):
-            self.layers.append(nn.ModuleList([
+            self.layers.append(ModuleList([
                 Attention(dim, heads = heads, dim_head = dim_head, dropout = dropout),
                 FeedForward(dim, mlp_dim, dropout = dropout)
             ]))
@@ -80,7 +82,7 @@ class Transformer(nn.Module):
 
         return self.norm(x)
 
-class ViT(nn.Module):
+class ViT(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)
@@ -90,7 +92,9 @@ class ViT(nn.Module):
 
         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)'
+        num_cls_tokens = 1 if pool == 'cls' else 0
 
         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),
@@ -99,8 +103,9 @@ class ViT(nn.Module):
             nn.LayerNorm(dim),
         )
 
-        self.pos_embedding = nn.Parameter(torch.randn(1, num_patches + 1, dim))
-        self.cls_token = nn.Parameter(torch.randn(1, 1, dim))
+        self.cls_token = nn.Parameter(torch.randn(num_cls_tokens, dim))
+        self.pos_embedding = nn.Parameter(torch.randn(num_patches + num_cls_tokens, dim))
+
         self.dropout = nn.Dropout(emb_dropout)
 
         self.transformer = Transformer(dim, depth, heads, dim_head, mlp_dim, dropout)
@@ -111,12 +116,15 @@ class ViT(nn.Module):
         self.mlp_head = nn.Linear(dim, num_classes)
 
     def forward(self, img):
+        batch = img.shape[0]
         x = self.to_patch_embedding(img)
-        b, n, _ = x.shape
 
-        cls_tokens = repeat(self.cls_token, '1 1 d -> b 1 d', b = b)
-        x = torch.cat((cls_tokens, x), dim=1)
-        x += self.pos_embedding[:, :(n + 1)]
+        cls_tokens = repeat(self.cls_token, '... d -> b ... d', b = batch)
+        x = torch.cat((cls_tokens, x), dim = 1)
+
+        seq = x.shape[1]
+
+        x = x + self.pos_embedding[:seq]
         x = self.dropout(x)
 
         x = self.transformer(x)

vit_pytorch/vit_3d.py

@@ -89,7 +89,7 @@ class ViT(nn.Module):
         assert pool in {'cls', 'mean'}, 'pool type must be either cls (cls token) or mean (mean pooling)'
 
         self.to_patch_embedding = nn.Sequential(
-            Rearrange('b c (f pf) (h p1) (w p2) -> b (f h w) (p1 p2 pf c)', p1 = patch_height, p2 = patch_width, pf = frame_patch_size),
+            Rearrange('b c (f pf) (h p1) (w p2) -> b (f h w) (pf p1 p2 c)', p1 = patch_height, p2 = patch_width, pf = frame_patch_size),
             nn.LayerNorm(patch_dim),
             nn.Linear(patch_dim, dim),
             nn.LayerNorm(dim),

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)

vit_pytorch/vivit.py

@@ -141,7 +141,7 @@ class ViT(nn.Module):
         self.global_average_pool = pool == 'mean'
 
         self.to_patch_embedding = nn.Sequential(
-            Rearrange('b c (f pf) (h p1) (w p2) -> b f (h w) (p1 p2 pf c)', p1 = patch_height, p2 = patch_width, pf = frame_patch_size),
+            Rearrange('b c (f pf) (h p1) (w p2) -> b f (h w) (pf p1 p2 c)', p1 = patch_height, p2 = patch_width, pf = frame_patch_size),
             nn.LayerNorm(patch_dim),
             nn.Linear(patch_dim, dim),
             nn.LayerNorm(dim)