An Image is Worth More Than 16x16 Patches: Exploring Transformers on Individual Pixels
Authors: Duy Kien Nguyen
Mido Assran
Unnat Jain
Martin R. Oswald
Cees G. M. Snoek
Xinlei Chen
Venue: ICLR 2025 Poster (2025)
Keywords: locality
convolutional networks
transformers
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: we show locality is not a fundamental inductive bias for vision architectures

Abstract: This work does not introduce a new method. Instead, we present an interesting finding that questions the necessity of the inductive bias of locality in modern computer vision architectures. Concretely, we find that vanilla Transformers can operate by directly treating each individual pixel as a token and achieve highly performant results. This is substantially different from the popular design in Vision Transformer, which maintains the inductive bias from ConvNets towards local neighborhoods (e.g., by treating each 16x16 patch as a token). We showcase the effectiveness of pixels-as-tokens across three well-studied computer vision tasks: supervised learning for classification and regression, self-supervised learning via masked autoencoding, and image generation with diffusion models. Although it's computationally less practical to directly operate on individual pixels, we believe the community must be made aware of this surprising piece of knowledge when devising the next generation of neural network architectures for computer vision.

Published as a conference paper at ICLR 2025
AN IMAGE IS WORTH MORE THAN 16x 16 PATCHES: EXPLORING TRANSFORMERS ON INDIVIDUAL PIXELS
Duy-Kien Nguyen²
Mahmoud Assran!
Unnat Jain'
Martin R. Oswald
Cees G. M. Snoek?
Xinlei Chen
FAIR, Meta AI
Universiity of Amsterdam
ABSTRACT
This work does not introduce new method. Instead, we present interesting finding that questions the necessity of the inductive bias of locality in modern computer vision architectures. Concretely, we find that vanilla Transformers can operate by directly treating each individual pixel as a token and achieve highly performant results. This is substantially different from the popular design in Vision Transformer, which maintains the inductive bias from ConvNets towards local neighborhoods (e.g. by treating each 16x 16 patch as a token). We showcase the effectiveness of pixels-as-tokens across three well-studied computer vision tasks: supervised learning for classification and regression, self-supervised learning via masked autoencoding, and image generation with diffusion models. Although it's computationally less practical to directly operate on individual pixels, we believe the community must be made aware of this surprising piece of knowledge when devising the next generation of neural network architectures for computer vision.
INTRODUCTION
For computer vision, the deep learning revolution can be characterized as revolution in inductive biases. Learning previously occurred on top of manually crafted features, such as those described in Lowe (2004); Dalal & Triggs (2005), which encoded preconceived notions about useful patterns and structures for specific tasks. In contrast, biases in modern features are no longer predetermined but instead shaped by direct learning from data using predefined model architectures. This paradigm shift's dominance highlights the potential of reducing feature biases create more versatile and capable systems that excel across a wide range of vision tasks.
Beyond features, model architectures also possess inductive biases. Reducing these biases can potentially facilitate greater unification not only across tasks but also across data modalities. The Transformer architecture (Vaswani al., 2017) serves great example. Initially developed to process natural languages, its effectiveness was subsequently demonstrated for images (Dosovitskiy al., 2021), point clouds (Zhao al., 2021), codes (Chen al., 2021a), and many other types of data. Notably. compared to its predecessor in vision ConvNets (LeCun et al., 1989; He et al., 2016), the Vision Transformer (ViT) (Dosovitskiy et al., 2021) carries much less image-specific inductive bias. Nonetheless, the initial advantage from such biases is quickly offset by more data (and models that have enough capacities to store patterns observed within the data), ultimately becoming restrictions that prevent ConvNets from scaling further (Dosovitskiy et al., 2021).
Of course, ViT is not entirely free of inductive bias. gets rid of the spatial hierarchy in the ConvNet and models multiple scales in plain architecture. However, for other inductive biases, the removal is merely way through: location equivariance still exists in its patch projection layer and all the intermediate blocks; and locality- the notion that neighboring pixels more related than pixels that are farther apart - still exists in its 'patchification' step (that represents an image with 16x 16 2D patches) and position embeddings (when they are manually designed). Therefore. natural question arises: can we completely eliminate either or both of these two major inductive biases? In this work, we aim to answer this important question.
Surprisingly, we find locality can indeed be removed. We arrive at this conclusion by directly treating each individual pixel as a token for the Transformer and using position embeddings learned from
By llocation equivariance', we refer to the adoption of weight-sharing mechanism which ensures that the same weights are applicd regardless of spatial locations.

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Published as a conference paper at ICLR 2025
inductive bias
ConvNet
VIT
our work
spatial hierarchy
X
location equivariance
locality
X
Table I: Major inductive biases for vision. A ConvNet (LeCun et al., 1989; He et al., 2016) has all three: spatial hierarchy, location equivariance, and locality, with neighboring pixels being more related than pixels farther apart. Vision Transformer (ViT) (Dosovitskiy et al., 2021) 1) removes the spatial hierarchy, reduces (but still retains) location equivariance and locality. We investigate the complete removal of locality by simply applying Transformers on individual pixels. It works surprisingly well, challenging the mainstream belief that locality is a necessity for vision architectures.
scratch. In this way, we introduce zero priors about the 2D grid structure of images. Interestingly, instead of training divergence or steep performance degeneration, we can obtain better results in quality from this setup. The fact that this naïve, locality-free Transformer works so well suggests there are more signals Transformers can capture by viewing images sets of individual pixels, rather than 16x 16 patches. This finding challenges the conventional community belief that 'locality is a fundamental inductive bias for vision tasks' (see Tab. 1).
We showcase the effectiveness of Transformer on pixels via three different case studies: (i su- pervised learning for object classification, where CIFAR-100 (Krizhevsky, 2009) is used for our main experiments thanks to its default 32x32 input size, but the observation also generalizes well to ImageNet (Deng et al., 2009), fine-grained classification using Oxford-102-Floove 102-Flowers (Nilsback & Zisserman, 2008) and depth estimation via regression using NYU-v2 (Silberman et al., 2012); (ii) self- supervvee learning on CIFAR- 100 via Masked Autoencoding (MAE) (He al., 2022) for pre- pre-training, and fine-tuning for classification; and (ii) image generation with diffusion models, where we follow the architecture of the Diffusion Transformer (DiT) (Peebles & Xie, 2023), and study its pixel variant on ImageNet using the latent token space provided by VQGAN (Esser et al., 2021). In all three cases, we find Transformers on pixels exhibit reasonable behaviors, and achieves results better in quality than baselines equipped with the locality inductive bias.
As a related investigation, we also examine the importance of two locality designs (position embedding and patchification) within the standard ViT architecture on ImageNet. For position embedding, we have three options: sin-cos (Vaswani et al., 2017), learned, and none - with sin-cos carrying the locality bias whilst the other two do not. To systematically 'corrupt' the locality bias in patchification, we perform a pixel permutation before dividing the input into 256-pixel (akin to a 16x 16 patch in ViT) tokens. The permutation is fixed across images, and consists of multiple steps that each swaps a pixel pair within a distance threshold. Our results suggest that patchification imposes a stronger locality prior, and removing both location equivariance and locality is not yet feasible.
Treating each pixel as a token will lead to a sequence length much longer than commonly used for images. This is especially cumbersome Self-Attention in Transformers demands quadratic compu- tations. Therefore, the contribution of our work is on the finding, not on proposing a new method. In practice, patchification is still a simple and effective idea that trades quality for efficiency, and locality is still highly useful. Nevertheless, we believe our investigation delivers a clean, compelling message that locality is not a necessary inductive bias for vision. We believe this finding will be integrated into the community knowledge when exploring the next generations of vision architectures.
2 INDUCTIVE BIAS OF LOCALITY
Here we discuss about the inductive bias of locality in mainstream vision architectures: ConvNets and ViTs. Locality the notion that neighboring pixels are more related than pixels farther apart.
2.1 LOCALITY IN CONVNETS
In ConvNet, locality is reflected in the receptive fields of the features computed in each layer. Intu- itively, receptive fields cover all the pixels involved in computing a specific feature, and for ConvNets, the fields are local. Specifically, ConvNets consist of several layers, each having convolutional kernels or pooling operations- both of which are local. The field is progressively expanded as the network stacks more layers, but the window is still locally centered the location of the pixel.
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Position
Embedding
Seff. felf-Atention
mamm
mmmm
M'LP
Image
Pixels
Transformer
Tasks
Figure I: Transformer on pixels, or xx 'patches', which we use to investigate the role of locality, Given an image, we simply treat it as set of pixels. Besides, we also use randomly initialized and learnable position embeddings without prior about the 2D image grid, thus removing the remaining locality bias from previous architectures (e.g., VIT (Dosovitskiy et al., 2014)) that operate non- degenerated patches. Transformers are employed on the top, with interlcaved Self-Attention and MLP blocks (only showing pair for clarity). We showcase the effectiveness of this locality-free architecture through three case studies, spanning both discriminative and generative tasks.
2.2 LOCALITY IN VISION TRANSFORMERS
At first glance, Transformers are locality-free. This is because the majority of Transformer operations either global (e.g.. Self-Attention), purely within each individual token (e.g.. MLP). However, a closer look will reveal two designs within VIT (Dosovitskiy et al., 2021) that can still retain the locality inductive bias: patchification and position embedding.
Locality in patchification. In VIT. the tokens fed into the Transformer blocks are patches, not pixels. Each patch consists of 16x 16 pixels, and becomes the basic unit of operation after the first projection layer. This means the amount of computation imposed within the patch is substantially different from the amount across patches: the information outside the 16x 16 neighborhood can only be propagated with Self-Attention, and the information among the 256 pixels are always processed jointly as token. While the receptive field becomes global after the first Aele-Antention block, the bias towards local neighborhoods is already inducted in the patchification step.
Locality in position embedding. Position embeddings can be learned (Dosovitskiy et al., 2021), manually designed and fixed during training. A natural choice for images to 2D sin-cos embedding (Chen et al., b0;1b; He et al., 2022), which extends from the original ID one ( (Vaswani al., 2017). As sin-cos functions are smooth, they tend to introduce locality biases that nearby tokens are more similar in the embedding space. Other designed variants are also possible and have been explored (Dosovitskiy et al., 2021). , but all of them can carry information about the 2D grid structure of images, unlike learned ones which do not make any assumption about the input.
The locality bias has also been exploited when the position embeddings are interpolated (Dehghani et al., 2023; Li et al., 2021). Through bilinear or bicubic interpolation, spatially close embeddings are used to generate a new embedding of the current position, which also leverages locality as a prior.
Compared to ConvNets, ViTs designed with much less pronounced bias toward locality. This paves the way for our investigation to completely remove this bias, described next.
EXPLORING TRANSFORMERS ON INDIVIDUAL PIXELS
To study the impact of removing the locality inductive bias, we closely follow the standard Trans- former encoder (Vaswani et al., 2017) which processes sequence of tokens. Particularly, we apply the architecture directly on an unordered set of pixels from an input image with learnable position embeddings. This removes the remaining inductive bias of locality in the ViT (Dosovitskiy et al., 2021) (see Fig. l). Conceptually, the resulting architecture can viewed as a simplified version of ViT, with degenerated x patches instead of non-degenerated ones (e.g., 16x 16 or 2x2).
While sin-cos functions also cyclic, it's easy to verify that the majority of their periods are longer than the typical sequence lengths encountered by ViTs.
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model
layers (N)
hidden dim (d)
MLP dim
heads
param (M)
T(iny)
12
192
768
12
5.6
S(mall)
12
384
1536
12
21.8
B(ase)
12
768
3072
86.0
L(arge)
24
1024
4096
16
303.5
Table 2: Specifications of size variants explored. We use ViT (Dosovitskiy et al., 2021) or DiT (Peebles & Xie, 2023) with the same size but non-degenerated patches for head-on comparisons.
Formally, we denote the input sequence as X TLL) E Rx where L is the sequence length and d is the hidden dimension. The Transformer maps the input sequence X to sequence of representations = (,I,,..,;,) =t,) E Lxd The architecture is stack of N layers, each of which contains blocks: multi-headed Self-Attention block and MLP block:
- = DelfAttention(nne (Z* (z)))))))))))))))))))))) ===1
z MLP (norm( 2²) 2*
where Zo is the imput sequence X, k [I,...,NT N the layer index, and norm(-) is normalization (e.g.. LayerNorm (Ba et al., 2016)). Both blocks use residual connections (He et al., 2016).
Pixels tokens. Given image / E R of RGB values, denote (H, W) as the size of the original imput. We follow simple philosophy and treat / as an unordered set of pixels (Pi) Pt R2 The first layer simply projects each pixel into dimensional vector via linear projection, f I Rdd resulting in the input We learn a content-agnode with learnable [els token (Devlin al., 2019). The pixel tokens are then fed into the Transformer to produce the set of representations Z.
tokens X (f(p)), ((r) with L H.W. position embedding for each position, and optionally append the sequence
[1 s, f()))(()))))) (.., [(L)) + PE,
where PE E IR 1xd is a set of learnable position embeddings.
Pixel transformer removes the locality inductive bias and is permutation equivariant the pixel level. By treating individual pixels directly as tokens, we assume no spatial relationship in the architecture and let the model learn structures directly from data. This is in contrast to the design of the convolution kernel in ConvNets or the patch-based tokenization in ViT (Dosovitskiy et al., 2021), which enforces an inductive bias based on the proximity of pixels. this regard, the resulting model is more versatile - it can naturally model arbitrarily sized images (no need to be divisible by the stride or patch size). or even generalize irregular regions (Ke al., 2022).
While our focus is on the study of locality, using each pixel as separate token has additional benefits. Similar to treating characters tokens for language, we can greatly reduce the vocabulary size of input tokens to the Transformer. Specifically, given the pixel of RGB channels in the range of [0, 255), the maximum size of vocabulary is 256 (as pixels take integer values); a patch token of size pxp in VIT, however, can lead to vocabulary size of up to 35p3pP'P modeled in a non-parametric manner, this will heavily suffer from vocabu-oocbulaary issues.
Of course, Transformers on pixels are computationally expensive (or even prohibitive). However, given the rapid development of techniques that handle massive sequence lengths for large language models (up million) (Dao al., 2022; Liu et al., 2023), it is entirely possible that soon, can train Transformers on individual pixels directly (e.g., a standard 224x224 crop on ImageNet 'only' contains 50, 176 pixels). In this sense, work is to scientifically verify the effectiveness and potential locality-fres freee architectures at an affordable scale (which we next), and leave the engineering effort of scaling for the future.
EXPERIMENTS
We verify the effectiveness of the locality-free modification with three case studies: supervised learning with VIT (Dosovitskiy et al., 2014), self-supervised learning with MAE (He et al., 2022), and image generation with DiT (Peebles & Xie, 2023). We use four size variants: Tiny (T), Small
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@cc
Acc@5
Acc@1
Acc@5
VIT-T/2
83.6
94.6
ViT-S/2
72.9
90.9
ViT-T/1
85.1
96.4
VIT-S/1
74.1
91.7
ViT-S/2
83.7
VIT-B/2
75.7
92.3
VIT-S/1
86.4
96.6
VIT-B/1
76.1
92.6
ViT-B/2 (Shen et al., 2023)
72.6
VIT-L/2
75.6
92.3
VIT-I/1
76.9
93.0
(a) CIFAR-100 classification
(b) ImageNet classification
Acc@1
Acc@5
RMSE (4)
RAE (4)
VI2-S/2
45.8
68.3
VIT-S/2
0.80
0.78
ViT-S/1
46.3
68.9
VIT-S/1
0.72
0.74
(c)
fine- fine-grained classification
(d) NYU-v2 depth estimation (regression)
Table 3: Results for case study #1: supervised learning. We use ViT (Dosovitskiy et al., 202 I), either with non-degenerated patch size (2x2), or with our locality-free modification that treats each pixel as a token (in bold). We report results on (a) CIFAR-100 (Krizhevsky. 2009): the pixel variant outperforms ViT with 2x2 patches of the same model size. Note that baselines already highty-optimized, e.g- Shen et al. (2023) reports significantly worse results despite larger model size; the observation generalizes well to the larger (b) ImageNet (Deng al., 2009) dataset, fine- grained classification on (c) Oxford-102-Flowv
(Nilsback & Zisserman, 2008), and depth estimation (regression) (d) NYU-v2 (Silberman al., 2012) which further requires spatial understanding. All these suggest Transformers can not just learn, but learn well without any inductive bias of locality.
(S), Base (B) and I Large (L.) with the specifications shown in Tab. 2. Unless otherwise noted, we use Transformers with the same size but non-degenerated patches section is to show locality-frre architectures can still learn strong vision representations.
baselines. Our only goal in this
4.1 CASE STUDY #1: SUPERVISED LEARNING
In this study, we train and evaluate ViTs (Dosovitskiy al., 2021) with or without locality for supervised learning tasks. Our baselines are ViTs with patch sizes 2x2. For more implementation details, please Appendix A.
Datasets. In total we use four datasets, with two for object classification: CIFAR-100 (Krizhevsky, 2009) has 100 classes and 60K images combined, and ImageNet (Deng al., 2009) has 1K classes and 1.28M images for training, 50K for evaluation. CIFAR- 100 is well-suited for exploring the effectiveness locality-free architectures due its intrinsic image size of 32 32. ImageNet has many more images and is more frequently used for modern architecture design. We also validate our finding on: fine-grained classification using the Oxford- 102-Flower dataset (Nilsback Zisserman, 2008) and depth estimation using the NYU-v2 dataset (Silberman et al., 2012).
Evaluation metrics. For the classification datasets, we train our models on the train split and report the top-1 (Acc@) 1) and top-5 (Acc@) accuracy the val split. The root squared error (RMSE) and relative absolute error (RAE) are reported on the val split for depth estimation.
Main results. As shown in Tab. 3, while our baselines for both ViT variants (ViT-T and ViT-S) well-optimized on CIFAR- 100 (e.g.. Shen et al. (2023) reports 72.6% Acc@1 when training from scratch with ViT-B, whilst we achieve 80+% with smaller sized models), our locality-free variant, ViT-T/1, improves over ViT-T/2 by 1.5% of Acc@ 1; and when moving to the bigger model (S), ViT-S/1 leads an improvement of 1.3% in Ace@1 over ViT-T/1, while ViT/2 starts to saturate. These results suggest compared to the patch-based VIT, ViT with our locality-free design is potentially learning new, data-driven patterns directly from individual pixels.
Our observation also transfers to ImageNet though with much lower resolution our results also lower than the state-of- of-t-oof-hhearr (Dosovitskiy et al., 2021; Touvron et al., 2021) (80+%), the pixel-based ViT still outperforms patch-based ViT with all model sizes have experimented, and interestingly synergizes better with larger-sized models like VIT-L. To see what the models have learned, we visualize the attention maps, position embeddings in Appendix B.
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80
12.0
80.3
75.7
50
74.5
29.0
lycelity-ccc
818
70
70
534
locality free
16
16
8
potch (logescale)
patch size (log-scale)
(a) Acc@1 with fixed sequence length.
(b) Acc@) with fixed imput size.
Figure 2: Two trends with ViT. Since our Transformer on pixels can be viewed as ViT with patch size 1 xx 1, the trends w.r.t. patch size is crucial to our finding. In (a), we vary the VīT-B patch size but keep the sequence length fixed (last data point is locality-free) so the input size is also varied. While Acc@] remains constant in the beginning, the input size, or the amount of information quickly becomes the dominating factor that deteriorates accuracy. On the other hand, in (b) we vary the ViT-S patch size while keeping the input size fixed. The trend is opposite reducing the patch size is always helpful and the last point (locality-free) becomes the best. The juxtaposition of these two trends gives more complete picture of the relationship between input size, patch size and sequence length.
At the expense of longer sequence length, our experiments on fine-grained classification and depth estimation further confirm the effectiveness of the locality-frre architecture in boosting accura- cies/reducing errors. Notably, whereas depth estimation demands better capture of spatial relationships. It's impressive that Trans- formers can learn useful patterns purely from data, without assuming inputs are on 2D image grids.
classification requires nuanced understanding in details;
Two trends with VIT. With learned position embeddings, our finding is simply based on a ViT variant with 1 Xx1 'patches'. Then why this is not discovered earlier? To us, the major reason is that there are two different trends with the three variables in concern: sequence length (T.), input size (H x W) and patch size (p). They have deterministic relationship: -= H x W/(p))))) and can be studied on ImageNet either via fixed sequence length or fixed input size:
Fixed sequence length. We show this trend with fixed L in Fig. 2a. The model size is ViT-B. In this plot, the input size varies (from x24x222 to 14x 14) as we vary the patch size (from 16x16 to x I). If we follow this trend, then a locality-free architecture (right most) is the worst. This means sequence length not the only deciding factor - input size, or the amount of information fed into the model is arguably more important factor, especially when it's small. It's only when the size is sufficiently large (e.g.. 112x 112), the additional benefit of further enlarging the size starts to diminish. This also gives an intuitive explanation that when there is no enough input information, advanced architecture or pre-training (e.g., iGPT (Chen et al., 2020a)) would struggle recover this hard gap.
Fixed input size. Our finding is made when following the other trend fixing the input size to 64x64 (thus the amount of information), and varying the patch size on ImageNet in Fig. 2b. The model size is ViT-S. Interestingly, we observe an opposite trend here: it is always helpful to decrease the patch size (or increase the sequence length), aligned with the prior studies that find sequence length is highly important (Beyer et al., 2022; Hu et al., 2022). Note that the trend holds even when the architecture ultimately becomes locality-free (right-most). With the longest sequence length, it achieves the best accuracy.
Together, the two trends in Fig. 2 augment the observations from prior work that mainly focused on sufficiently large input sizes (Beyer et al., 2022; Hu et al., 2022), and give a more complete picture.
4.2 CASE STUDY #2: SHLF-SUPERVISED LEARNING
Next, we study the impact of removing locality with self superviedd pre-training and then fine-tuning for classification. In particular, we stick ViT and choose MAE (He et al., 2022) for pre- are-training. thanks to its efficiency in computation and effectiveness for fine-tuning based evaluation protocols.
Setup. We use CIFAR- 100 (Krizhevsky, 2009) due to its inherent size of 32x32. This allows us to fully explore the use of pixels as tokens the original resolution. After pre-training, we test the classification performance on the same set, reporting top-1 (Ace@ 1) and top-5 (Aco@55 accuracy. For more details, please see Appendix A.

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pre-train Acc@1
A
pre-train
Acc@1
Acc@5
85.1
96.4
86.4
96.6
VIT-T/1
VIT-S/1
86.0
97.1
87.7
97.5
VIT-T/2
85.7
97.0
VIT-S/2
87.4
97.3
Tiny-sized models.
(b) Small-sized models.
Table Results for case study #2: self-supervised learning. We still ViT (Dosovitskiy et al., 2021) as the model architecture, but explore MAE (He et al., 2022) as a pre-training technique for enhanced performance. The observation that locality-free variants (in bold) work well still holds with pre-training and the two model sizes we experimented.
Results. As shown in Tab. 4, the observation that locality- variants of ViT work well still holds with MAE pre-training and the two model sizes we experimented.
4.3 CASE STUDY #3: IMAGE GENERATION
Next, switch image generation with Diffusion Transformer (DiT) (Peebles & Xie, 2023), which has a modulation-based architecture different from the vanilla ViT, and operates on the latent token space from VQGAN (Esser et al., 2021) that shrinks the input size 8x. Dataset-wise, ImageNet for cansiconniiional generation, and each image is center-cropped to 256x256, resulting an input feature map size of 32x32x4 4. More details are found in Appendix A. Our locality-free model, DiT/1, is fed with this feature map, same as its baseline DīT-L/2 with locality.
Evaluation metrics. The generation quality is measured by standard metrics: Fréchet Inception Distance (FID) (Heusel et al., 2017) with 50K samples, sFID (Nash al., 2021), Inception Score (IS) (Salimans et al., 2016), and precision/recall (Kynkäänniemi et al., 2019), using reference batches from the original TensorFlow evaluation suite of Dhariwal & Nichol (2021).
Qualitative results. Sampled generations from DiT-L are shown in Fig. 3. The latent diffusion outputs are mapped back the pixel space using the VQGAN decoder. classifier-free guidance (Ho & Salimans, 2022) scale of 4.0 is used. For DiT/1, all generations are detailed and reasonable compared the DiT/2 models with locality.
Quantitative comparisons. Tab. 5 summarizes our observations. First, our baseline is strong: compared to the reference 10.67 FID (Peebles Xie, 2023) with a larger model (DiT-XL/2) and longer training (~470 epochs), our DiT-L/2 achieves 8.90 without classifier-free guidance. Our main comparison (first two rows) uses a classifier-free guidance of 1.5. DiT-L/I, the locality-free variant, outperforms the baseline all the main metrics (FID, sFID and IS), and is on-par precision/recall. With extended training of 1400 epochs, the gap is bigger: 2.68 FID with DFT-L/1 vs. 2.89 from DiT-L/2 (see Appendix C).
(a) DVT-L/2 generations.
(b) DIT-L/1 generations.
Figure Qualitative results for case study #3: image generation. These 256x256 samples are generated from ImageNet-trained DiT's (Peebles & Xie, 2023). For direct comparisons, we fix random seeds and categories to prompt the model (none of the people classes from ImageNet are used), with the only difference that (a) uses locality-biased DiT-L/2, and (b) uses the locality-free variant (DiT-L/I). Overall, generations from locality-frre models have fine features and detailed and reasonable, similar to locality-base based models.
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model
FID (1)
sFID (L)
(
precision (1)
recall (t)
DiT-L/2
4.16
4,97
210.18
0.88
0.49
DiT-L/1
4.05
4.66
232.95
0.88
0.49
DIT-L/2, no guidance
8.90
4.63
104.43
0.75
0.61
DIT-X1/2 (Pechles & Xie, 2023), no guidance
10.67
Table 5: Results for case study #3: image generation. We use references from the evaluation suite of Dhariwal & Nichol (2021), and report 5 metrics comparing locality-hiased DiT-1/22 and locality- free DiT-L/1. Last row is from Peebles & Xie (2023), compared to which our baseline is significantly stronger (8.90 FID with DiT-L, vs. 10.67 with DiT-XL and longer training). Overall, our finding generalizes well to this new task with a different architecture and different input representations.
Our demonstration on image generation is an important extension of our finding. Compared to the case studies discriminative benchmarks in Sec. 4.1 and Sec. 4.2, the task is more challenging; the model architecture is changed to be conditional; the input space is also changed from raw pixels to latent tokens. The fact that locality-free modification works out-of-the-box suggests the observation can be generalized across different tasks, architectural variants, and operating representations.
5 LOCALITY DESIGNS IN VIT
Finally, we complete the loop of our investigation by revisiting the ViT architecture, and examining the importance of its two locality-related designs: (i) position embedding and (ii) patchification.
Setup. We use VIT-B for ImageNet supervised classification, adopting the exact same hyper- parameters, augmentations, and other training details from the scratch training recipe of He al. (2022). Notably, images grop-and-resizee to 224 and divided into 16x 16 patches.
Position embedding. Similar to the investigation in Chen et al. (2021b). we choose from three candidates: sin-cos (Vaswani et al., 2017), learned, and none. The first option introduces locality into the model, while the other two do not. The results are summarized below:
PE
sin-cos
leamned
none
Acc@1
1
82.7
82.8
81.2
Our conclusion is similar to the one drawn by Chen et al. (2021b) for self-supervised representation evaluation: learnable position embeddings are on-par with fixed sin-cos ones. Interestingly, observe only a minor drop in performance even there no position embedding at all 'none' is only worse by 1.5% compared sin-cos. Note that without position emhedding, the classification model is fully permutation invariant w.r.t. patches, though not w.r.t. pixels.
Next, we use learnable position embeddings and study patchification. To system- atically reduce locality from patchification, our key insight is that neighboring pixels should no longer be tied in the same patch. To this end, we perform a pixel-wise permutation before diving the resulting sequence into separate tokens. Each token contains 256 pixels, same in number pixels in a 16x 16 patch. The permutation is shared, staying same for the images including testing ones.
Patchification.
(a) 2
(b) 8=1
(c) 8=8
(d) 8= inf
Figure 4: Pixel permutation for VIT. We swap pixels within Hamming distance of 6 and do this T times (no distance constraint if 8 inf). Illustrated is an 8x8 image divided into 2x2 patches. Here show permutation with T pixel swaps (denoted by double-heade arrows).
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T. inf
Acc@1
AAAc
X1.9
0
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81.2
80.5
80.5
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80.5
100 (0.4%)
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1K (4.0%)
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79
20K (79. 756)
10K (39.9%)
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-5.3
7-10K
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79.1
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78.3
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77.5
25K. (99.69)
57.6
-25.2
16
inf
% the perceniage among pizel pairs
distance threshold &
Figure 5: Results of pixel permutation for VTT-B on ImageNet. We vary the number of pixel swaps T (left) and additionally varying the maximum distance of pixel swaps d (right). Pixel permutations can drop accuracy by 25.2% (when 25K pairs are swapped), compared to the relatively minor drop (1.6%) when the position embedding is completely removed. And when farther-away pixels are allowed for swapping, more damage is caused. These results suggest pixel permutation imposes a much more significant impact on performance, compared to swapping position embeddings.
The permutation is performed in steps, each step will swap a pixel pair within a distance threshold 6 E [2, inf] (2 means within the x22 neighborhood, inf means any pixel pair can be swapped). We use hamming distance on the 2D image grid. T and control how 'corrputed' an image is larger T or 8 indicates more damage to the local neighborhood and thus more locality bias is taken away. Fig. 4 illlssrates four such permutations.
Fig. 5 illustrates the results we have obtained. In the table (left), we vary T with no distance constraint (i.e.. 8 = inf). As we increase the number of shuffled pixel pairs, the performance degenerates further increase T. And at T = 25,, Acc@ drops to 57.2%, 25.2% decrease from the intact image. Note that in total there are 224 x 224/2 = 25, 088 pixel pairs. T 25K means almost all the pixels have moved away from their original location. Fig. 5 (right) shows the influence of ó given fixed I' (10K or 20K). We can see when farther-ane away pixels are allowed for swapping (with greater 8), performance gets hurt more. The trend is more salient when more pixel pairs are swapped (T 20
slowly in the beginning (up 10K). Then it quickly deteriorates
Overall, pixel permutation imposes a much more significant impact on Acc compared to changing position embeddings, suggesting that patchification is much more crucial for the overall design of ViT', and underscores the value of our work that removes the patchification altogether.
Discussion. As another way remove locality, pixel permutation is highly destructive. On the other hand, we show successful climination of locality is possible by treating individual pixels as tokens. We hypothesize this is because permuting pixels not only damages the locality bias, but also hurts the other inductive bias - location equivariance. Although locality is removed, the Transformer weights are still shared across pixels preserve location equivariance; but with shuffling, this inductive bias is also largely removed. The difference suggests that proper weight-sharing remains important and should not be disregarded, especially after locality is already compromised.
RELATED WORK
Locality for images. To of our knowledge, most modern vision architectures (He et al., 2016; Parmar et al., 2018), including those aimed at simplifications of inductive biases (Dasovitskiy et al., 2021; Tolstikhin et al., 2021), still maintain locality in the design. Manual features before deep learning also locally biased. For example, SIFT (Lowe, 2004) uses a local descriptor to represent each point of interest; HOG (Dalal & Triggs, 2005) locally normalizes the gradient strengths account for changes in illumination and contrast. Interestingly, with these features, bag-of-words models (Csurka al., 2004; Lazebnik et al., 2006) were popular- analogous to the set-of-pixels explored in our work.
Locality beyond images. The inductive bias of locality is widely accepted beyond modeling images. For text, a natural language sequence is often pre-processed with 'tokenizers' (Sennrich et al., 2015; Kudo & Richardson, 2018), which aggregate the dataset statistics for grouping frequently-occurring adjacent characters into sub- words Before Transformers, recurrent neural networks (Mikolov et al., 2010; Hochreiter & Schmidhuber, 1997) were the default architecture for such data, which exploit temporal connectivity to process sequences step-by-step. For even less structured data (e.g. point clouds (Chang al., 2015; Dai et al., 2017)), modern networks (Qi al., 2017; Zhao et al., 2021) will
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resort to various sampling and pooling strategies to increase their sensitivity to the local geometric layout. In graph neural networks (Scarselli et al., 2009), nodes with edges are often viewed as locally connected, and information is propagated through these connections to farther-away nodes. Such designs make them particularly useful for analyzing social networks, molecular structures, etc. Despite its higher computational cost, Transformers with global Self-Attention is increasingly favored for real-world problems due to its powerful pattern-lcariin capabilities.
Other notable efforts. We list four efforts in a rough chronological order, and hope can provide historical context from multiple perspectives for our work:
To remove locality for ConvNets, Brendel & Bethge (2019) replaced all spatial convolutional filters in a ResNet (He et al., 2016) with 1x1 filters. It has values in interpretability, but without inter-pixel communications the resulting network is substantially worse in performance. Our work instead uses Transformers, which are inherently built on set operations, with Self-Altention handling all-to-all communications; understandably, we obtain better results.
Before ViT gained popularity, iGPT (Chen et al., 2020a) was proposed to directly pre-train Transformers on pixels following their success on text (Radford et al., 2018; Devlin al., 2019). In retrospect, iGPT is locality- free model for self-supervised next- (or masked-) pixel prediction. But despite extensive scaling efforts, its performance still falls short compared to simple contrastive pre-training (Chen et al., 2020b) on ImageNet. Later, ViT (Dosovitskiy et al., 2014) re-introduced locality (e.g-, via patchification) into the architecture, achieving impressive results on many benchmarks including ImageNet. This shift cemented 16x 16 patches as the standard for vision tasks. However, it remained unclear whether ViT's performance gains were primarily due to higher resolution or patch-based locality. Through systematic analyses, our work puts a conclusive remark, pointing to resolution as the enabler for ViT, not locality.
Perceiver (Jaegle et al., 2021 is another series of architectures that operate directly on pixels for images. Aimed at being modality-agnostic, Perceiver designs latent Transformers with cross-attention modules tackle the efficiency issue when the input high-dimensional. However, this design is not as widely adopted as plain Transformers, which have consistently demonstrated scalability across multiple domains (Brown et al., 2020; Dosovitskiy et al., 2021). We show Transformers can indeed work directly with pixels, and given the rapid development of Self-Attention implementations to handle massive sequence length (up to a million) (Dao et al., 2022; Liu et al., 2023), efficiency may not be critical bottleneck even counting all the pixels.
Transformer has also been shown to work well for distribution modeling of generalized signals, including pixels in Tulsiani & Gupta (2021).
Our work can also be viewed as extending sequence length scaling to the extreme (individual pixels for images). Longer sequence (or higher resolution) is generally beneficial, evidenced in Chen et al. (2021b); Hu et al. (2022); Peebles & Xie (2023). However, all of them stopped short of reaching the extreme case that completely gets rid of locality.
Besides individual pixels, there has been sustained interest in learning flexible and data-driven patches for vision models via grouping (Zhang & Maire, 2020; Ke et al., 2022: Ma et al., 2023; Deng et al., 2024). While conceptually appealing e.g. can reconcile the long-sequence issue faced with pixels, they are yet show salient practical promise this context. Nonetheless, they are related work and we point to this direction for interested readers.
7 CONCLUSION AND LIMITATIONS
Through multiple case studies, we have demonstrated that Transformers can directly work with individual pixels. This is surprising, as it allows for clean, potentially scalable architecture without locality- - an inductive bias presumably fundamental for vision models. Given the spirit of deep learning that aims to replace manual priors with data-driven, learnable alternatives, we believe our finding is along the right direction and valuable to the community.
However, the practicality and coverage of our current demonstrations remain limited. Given the quadratic computation complexity, treating pixel-basee Transformer is more of an approach for investigation, and less for applications. And even with several tasks, the study is still not comprchen- sive. Nonetheless, we believe this work has sent out a clear, unfiltered message that locality is not fundamental, and patchification is simply a useful heuristic that trades-off efficiency vs. accuracy.
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Case study #2. We follow standard MAE and use a mask ratio of 75% and select tokens randomly. Given the remaining 25% of visible tokens, the model needs to reconstruct masked regions using pixel regression. Since there no known default setting for MAE on CIFAR- 100 (even for ViT), we search for recipes and report results using models of Tiny and Small sizes. The same augmentations as in He et al. (2022) are applied to the images during the pre-training for simplicity. All models are pre-trained using AdamW with 0099, 82 0.95. We follow all of the syper-parameter' in He et al. (2022) for the pre-training of 1600 epochs except for the initial learning rate of 0.004 and learning rate decay of 0.85 (Clark et al., 2020). Thanks to MAE pre- pre-training we can fine-tune our model with a higher learning rate of 0.024. We also set weight decay to 0.02, layer-wise rate decay to 0,65, and closely follow Published as a conference paper at ICLR 2025
A IMPLEMENTATION DETAILS
Below, we list the implementation details for the three case studies conducted in Sec. 4.
Case study #1. For CIFAR-100, due to the lack of optimal settings even for ViT, we search for the recipe and report results using model sizes T(iny) and S(mall). We use the augmentations from the released demo of He et al. (2020), as we found more advanced augmentations (e.g., AutoAug (Cubuk et al., 2018)) not helpful in this case. All models are trained using AdamW (Loshchilov & Hutter, 2019) with 31 00.9, 32-9.55. We use a batch size of 1024, weight decay of 0.3, drop path (Huang al., 2016) of 0.1, and initial learning rate of 0.004 which found to be the best for all the models. We use a linear learning rate warm-up up of 20 epochs and cosine learning rate decay to a minimum of le-6. Our training lasts for 2400 epochs, compensating for the small size of the dataset.
On ImageNet, we closely follow the scratch training recipe from Touvron et al. (2021); He et al. (2022) for ViT. Due our computation budget, images are crop-and-resized to 28x as the low- resolution inputs by default. The training batch size is 4096, initial learning rate is 1.6x 10-3, weight decay is 0.3, drop path is 0.1, and training length is 300 epochs. MixUp (Zhang al., 2018) (0.8), CutMix (Yun et al., 2019) (1.0), RandAug (Cubuk et al., 2020) (9, 0.5), and exponential moving average (0.9999) are used.
For the-ggrined classification, we use the same training recipe as in CIFAR- 100 with 32 inputs. For depth estimation, we resize images to the size of x8x64 (respecting the original image aspect- ratios) and follow the standard training procedure from Oquab et al. (2023).
drop path to 0.3, f2 to 0.999, and fine-tune for 800 epochs. Other the scratch training recipe for supervised learning in case study #1.
Case study #3. We followed the settings for DiT training, with a larger batch size (2048) to make the training faster (the original recipe uses batch size of 256). To make the training stable, we perform linear learning rate warm up (Goyal et al., 2017) for 100 epochs and then keep it constant for total of 400 epochs. We use maximum learning rate of 8c-4, with no weight decay applied. For generation, a sampling step of 250 is used.
B VISUALIZATIONS OF TRANSFORMER ON PIXELS
To check what pixel-based Transformer has learned, we experimented different ways for visualizations. Unless otherwise specified, we use ViT-B and the locality-free variant (i.e., ViT-B/1) trained with supervised learning on ImageNet classification, and compare them side by side.
Mean attention distances. In Fig. 6, we present the mean attention distances for VIT/I and VIT across three categories: late layers (last 4), middle layers (middle 4), and early layers (first 4). Following Dosovitskiy et al. (2021), this metric is computed by aggregating the distances between query token and all the key tokens in the image space, weighted by their corresponding attention weights. It can be interpreted as the size of the 'receptive field' for Transformers. The distance is normalized by the image size, and sorted based on the distance value for different attention heads from left to right.
As shown in Fig. 6a and Fig. 6b, both models exhibit similar patterns in the late layers, with the metric increasing from the 8th to the 11th layer. In the middle layers, while ViT displays a mixed trend among layers (see Fig. 6d), VIT/1 clearly extract patterns from larger areas in the relatively later
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Figure 6: Mean attention distances in late, middle, and early layers between VIT/I and ViT/2. This metric can be interpreted as the receptive field size for Transformers. The distance is normalized by the image size, and sorted based on the distance value for different attention heads from left to right.
layers (see Fig. 6c). Most notably, VIT/I focuses more on local patterns by paying more attention to small groups of pixels in the early layers, illustrated in Fig. 6e and Fig. 6f.
Mean attention offsets. Fig. shows the mean attention offsets between VIT/1 and ViT as introduced in Walmer al. (2023). This metric calculated by determining the center of the attention map generated by query and measuring the spatial distance (or offset) from the query's 's location to this center. Thus, the attention offset refers to the degree of spatial deviation the 'receptive field' the area of the input that the model focuses on from the query's original position. Note that different from ConvNets, Aff-Atttntion is global operation, not a local operation that is always centered on the current pixel (offset always being zero).
Interestingly. Fig. 7e suggests that VIT/1 captures long-range relationships in the first layer. Specif- ically, the attention maps generated ViT/I focus regions far away from the query token although according to the previous metric (mean attention distance), the overall "size" the attention can be small and focused in this layer.
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(a) VIT/I in late layers.
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(c) VIT/I in middle layers.
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(c) ViT/I in early layers.
(f) VIT/2 early layers.
Figure 7: Mean attention offsets in late, middle, and early layers between ViT/1 and ViT/2. This metric measures the deviation of the attention map from the current token location. The offset normalized with the image size, and sorted based on the distance value for different attention heads from left to right.
Figure-ground segmentation in early layers. In Fig. 8, we observe another interesting behavior of VIT/I. Here, we use the central pixel in the image space as the query and visualize its attention maps the early layers. We find that the attention maps in the early layers can already capture the foreground of objects. Figure-grount segmentation (Boykov et al., 2001) can be effectively performed with low-level signals (e.g., RGB values) and therefore approaches with few layers. And this separation prepares the model to potentially capture higher-order relationships in later layers.
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Published as a conference paper at ICLR 2025
W
Figure 8: Figure-ground segmentation in early layers of VIT/1. In each row, we show the original image and the attention maps of two selected early layers (from first fourth). We use the central pixel in the image space as the query and visualize its attention maps. Structures that can capture the foreground of objects have already emerged these layers, which prepares for the later layers to learn higher-order relationships.
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Published as a conference paper at ICLR 2025
epochs
model
FID (J)
sFID (L)
(t)
precision (1)
recall (1)
DiT-L/2
4.16
4.97
210.18
0.88
0.49
400
DIT-L/1
4.05
4.66
232.95
0.88
0.49
DFT-L/2
2.89
4.43
242.13
0.85
0.54
1400
DIT-L/1
2.68
4.34
268.82
0.85
0.55
Table 6: Extended results for image generation. We continue the training from 400 epochs (main paper) to 1400 epochs, and find the gap between DiT/2 and DiT/1 becomes larger, especially on FID.
C EXTENDED RESULTS ON IMAGE GENERATION
In the main paper (Sec. 4.3), both image generation models, DiT-L/2 and DiT-L/I, are trained for 400 epochs. To see the trend for longer training, followed Peebles & Xie (2023) and simply continued training them till 1400 epochs while keeping the learning rate constant.
The results summarized in Tab. 6. Interestingly, longer-training also benefits DiT/I more than DiT. Note that FID shall be compared in a relative sense a 0.2 gap around 2 is bigger than 0.2 around 4.
D TEXTURE vs. SHAPE BIAS ANALYSIS
As final interesting observation, we used an external benchmark which checks if an ImageNet classifier's 's decision is based on texture or shape. ConvNets are heavily biased toward texture (~20 in shape bias). Interestingly,
find VIT/I relies more on shape than ViT (57.2 vs. 56.7), suggesting that even when images are treated as sets of pixels, Transformers can still sift through potentially abundant texture patterns identify and rely on the sparse shape signals for tasks like object recognition.
E ADDITIONAL NOTES FOR TRAINING TRANSFORMER ON PIXELS
While for some cases (e.g., DiT (Peebles & Xie, 2023)), the training recipe can be directly transferred to pixel-based Transformer; for some other cases, we do want to note more potential challenges during training. Below want to especially highlight the effect of reduced learning rates when training a supervised ViT from scratch.
Acc@1
80
40
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Figure Training curves of different learning rates (VIT-T/1, batch size 1024, CIFAR-100), With reduced learning rate from VIT/2, the curve is more stable, and ultimately leads to better accuracy.
We take CIFAR-100 as an example. As shown in Fig. 9, we find for pixel-based Transformer, the training becomes unstable if we maintain the same learning rate vanilla ViTs. It is especially vulnerable toward the end. When the initial learning rate is reduced from 2e to le 1e the training more stable and leads better accuracy. Similar observations are also made on ImageNet.
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shape
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Published as a conference paper at ICLR 2025
dictionary
Acc@1
Acc@5
VIT-B/2
75.7
92.3
76.1
92.6
VTT-B/1
76.6
92.8
Table 7: Compared to the default ViT that uses parametric projection layers, we find a simple dictionary-basee VIT that leverages the reduced vocabulary size to learn non-parametric embeddings for pixel intensity values works better for ImageNet supervised classification.
downsizing
Acc@1
Acc@5
VIT-B/2
75.7
92.3
bicubic
VIT-B/1
76.1
92.6
VIT-B/2
70.5
89.0
single-pixel
VTT-B/1
75.6
92.3
Table 8: Influence of downsizing algorithms to our finding. Here we specifically experimented to downsize the original image by simply copying the value of its corresponding pixel from the original image (" ('single-pixel",. as opposed to 'bicubic interpolation' which leverages nearby pixels/locality. While single-pixel downsizing are generally worse, locality-free models are much more robust to such change for their representations being lonality-agnostic.
F EXPLORING DICTIONARY-BAR
VIT
As discussed in Sec. 3, one advantage for treating individual pixels as tokens ViT is the reduction in vocabulary size. Specifically, the size of the vocabulary (i.e., the unique values the model must handle) becomes much more manageable.
To exploit this fact, we experimented with dictionary-based approach for pixel tokens in VIT (other settings exactly follow default VIT for supervised learning). Specifically, we employed non-parametric, 256-dimensional embedding for each of the 256 possible values pixel can take, and different color channels have different embeddings. For pixel with three (RGB) values, we mapped each value to its corresponding vector, and concatenated the three vectors. An optional linear projection was applied to ensure compatibility with the hidden dimension d of VIT. Note that this approach has even less inductive bias because intensity values: the embedded value of 127 is not necessarily in-between 255 and 0, whereas it must be in-between if modeled directly with a parametric projection.
longer assume the relative order for pixel
Tab. summarizes the results. Interestingly, we find this ViT variant works better than our default ViT-B/1 on ImageNet. The improvement in performance further endorses our finding: 1) reducing inductive bias can be beneficial; and 2) locality- -ree ViTs can unlock the potential of dictionary-basee token representations for gext-generation vision architectures.
G INFLUENCE OF DOWNSIZING ALGORITHMS
By default, we use bicubic interpolation to perform downsizing. But since such algorithms also leverage nearby pixel values to estimate the value of the current pixel, there can be concerns that our pixel-based Transformers still rely on subtle locality biases.
To investigate the influence of downsizing algorithms, we have conducted additional experiments comparing bicubic interpolation with a simpler approach where each pixel in the downsized image directly copies the value of its corresponding pixel from the original image. In this way, it circumvents the locality bias introduced by interpolation. We call this downsizing algorithm 'single-pixel".
The results for ImageNet classification, VIT-B are summarized in Tab. 8. Two observations are made. First, as expected, single-pixel downsizing results in lower performance compared to bicubic interpolation. But second and more interestingly, patch-based VIT-B/2 shows more significant performance drop than the locality-fre ViT-B/I, and the gap becomes larger. This suggests that locality- based models more sensitive to this change in downsizing algorithm. In contrast, locality- free models are more robust, likely due to their ability to learn locality-agnosti representations and do not rely the inductive bias of locality for classification.
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Published as a conference paper at ICLR 2025
type of tokens
Acc@1
Acc@5
patchification (16 16)
82.7
96.3
FH
81.3
95.6
SLIC (iter=2)
78.9
94.3
SLIC (iter=1)
82.4
96.1
Table 9: An exploration of advanced tokenizations. Here, find that the performance improves when moving away from irregular shape and closer to patchification.
H EXPLORATION OF TOKENS VIA ADVANCED GROUPING
Before journey with pixels tokens, SLIC (Achanta et al., 2010) and FH segmentation (Felzenszwalb & Huttenlocher, 2004)) due to its ability quickly produce high-semantic and irregular shape tokens.
interested in tokens via advanced grouping (L.e.,
To compare these advanced tokenizations, we setup an experiment with the scratch training recipe from Touvron al. (2021); He et al. (2022) with patch size being 16 16 and sequence length of 196. For FH segmentation, we use the implementation from scikit. The optimal FH scale (which indirectly controls the resulting sizes of tokens) 30. We also set the maximum number of tokens 225, as the number of tokens can vary across images. Different from FH which relies on graph-based grouping. SLIC is similar to k-means, so an important hyper- parameee is the number of iterations used to optimize the segments.
The results for ImageNet classification are shown in Tab. 9. The patchification (16 16) performs best, even when compared against advanced tokens with additional training (e.g.. FH does not converges as fast, so we used 400 epochs, longer than the default 300 epochs). SLIC (iter=1) performs close to patchification but visual inspection shows that it essentially reverts to patch-based tokens part of the algorithm initialization. Further SLIC iterations, even with one more (iter=2), degrade performance. This suggests that the simple patchification is superior more advanced grouping tokenization.
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Reviews:
[{"review_id": "2GjNh2VMa3", "reviewer": "Reviewer_NZzh", "summary": "The study investigates whether the inductive bias of locality is necessary for modern computer vision models. It explores the effectiveness of using vanilla Transformers to directly treat each individual pixel as a token for various computer vision tasks. The findings show that pixel-based Transformers can perform competitively in supervised and self-supervised learning, as well as image generation, challenging the belief that locality is essential. The research examines how removing locality impacts architectures like Vision Transformers (ViT) and compares results with patch-based models. Although computationally intensive, the study demonstrates that locality-free Transformers can still learn effective visual representations, which may inform future neural network designs.", "questions": "See Weaknesses.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "1. This paper is well-written.\n2. The topic is of great interest to the computer vision community.\n3. The experiments are extensive.", "weaknesses": "In general, I agree to recommend the acceptance of this paper. However, I think it is a borderline paper, due to the following reasons.\n1. The finding is not surprising: removing the locality of visual backbones, and the models still work, at least to some extent. I think this conclusion can be expected by most of the researchers within the community (btw, I appreciate the efforts of authors to make these observations clear).\n2. As also recognized by the authors, the practicality of this conclusion is questionable, given its limited computation efficiency.\n3. The down-sampling algorithm (e.g., bicubic resampling) has already introduced some inductive biases of locality. It can be seen as a convolutional layer with fixed kernels. This effect may be particularly notable when the resolution is relatively small (e.g., 28x28 on ImageNet).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "I1u4LRwqRR", "reviewer": "Reviewer_5fCb", "summary": "This paper presents a study of locality in ViT, through decreasing the patch size down to 1x1. The paper shows that smaller patch will always get better performance and 1x1, which does not encode locality in each patch, gets the best performance. The work contributes to understandings of whether locality / patchification is necessary. The authors conduct experiments on supervised learning, self-supervised learning, and image generation. The results validate the hypotheses and statements.", "questions": "See weakness.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "+ The paper is well-written and has great clarity on motivation and experiment designs.\n+ The authors extensively test the model on various tasks and benchmarks.\n+ It's interesting to see that the patchification design to be explicitly re-checked.", "weaknesses": "- The work focuses on using smaller side of ViTs. I wonder if scaling up, does 1x1 patch still help in performance? Could it be that for ViT/L or ViT/H the patchification does not matter that much among 1x1, 2x2, or 4x4? \n\n- This paper proposes a finding, but it seems no good solution is available for now. The growth of #tokens is quadratic, 512 x 512 will give you 262144, and 1048576 for 1024 x1024. Further more, video will even give more tokens. Flash Attention and other efficient version will still have a tough time taking these many tokens as inputs.\n\n- The authors discuss a series of related works. Another important and emerging line of work that uses grouping operation is missing though. Images as set of points[1] is strongly relevant work that breaks the image into 1x1 pixel representation and uses fixed centers clustering / pooling for representation learning. The slot attention-based backbone [2], although do not use 1x1 patches, made the grouping operator (instead of key-axis attention in ViT) work on ImageNet scale and should also be discussed. Do the authors think grouping can be a more handy way for forming \"flexible and irregular-shaped patches\" automatically, and enjoy the sweet spot of lower computation while having smaller patch sizes?\n\n[1] Image as Set of Points\n\n[2] Perceptual Group Tokenizer: Building Perception with Iterative Grouping", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HlIpnbm8Xs", "reviewer": "Reviewer_PhHu", "summary": "This work poses an intriguing question regarding locality-free modeling of images using Transformers. The new modeling perspective centered on the locality-free concept presents an interesting direction for applying Transformers in computer vision, given their success in machine translation tasks. The study conducts extensive experiments across various scale tasks, revealing consistent and general observations. These findings lead to broader conclusions regarding the effectiveness of locality-free modeling under certain conditions.", "questions": "The concept of locality-free in this work is conditional and needs to be clearly differentiated from random pixel-level training. All discussions regarding locality-free should specify these conditions; otherwise, the statements may be too bold. While the paper identifies a problem, it does not explore potential solutions or the feasibility of addressing them. The authors should address these questions during the rebuttal to improve the rating score.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 2, "strengths": "1. The questions raised are interesting. The locality-free concept is essential for bridging the gap between computer vision and natural language processing when language models are adopted to solve visual recognition tasks.\n2. The observations are compelling and support the general conclusions on the potentials of locality-free modeling under certain conditions. The study performs extensive experiments across various scales, revealing consistent and widespread findings.\n3. The experiments are well designed to demonstrate the potential of locality-free modeling for images.", "weaknesses": "The conditions underlying the observations and conclusions require greater emphasis and detail. While \"locality-free\" suggests that input patches or tokens can be fragmented, it is still essential to preserve the relationships among adjacent input vectors or scalars. Developing a dictionary or tokenizer for image pixels is challenging, which hinders the advancement of locality-free models. The conclusions presented summarize valuable insights, but many of these observations, especially pixel-based modeling, probably have been considered during the design of Vision Transformers (ViTs). The limitations in their efficient training contribute to their performance issues. It is also quite challenging to represent image pixels semantically in a linguistic manner. If the authors could propose an effective training scheme or a pixel dictionary design for locality-free approaches, this work would become even more insightful and beneficial.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "DVq0CCT632", "reviewer": "Reviewer_Atm6", "summary": "The paper studies the role of locality biases in Vision Transformers (ViTs) by examining whether treating individual pixels as tokens (1x1 patches)—rather than conventional 16×16 patches—is sufficient for computer vision tasks (image classification or generation). \n\nThis pixel-based approach yields 2 benefits:\n1. Reduced Vocabulary Size: By treating each pixel as an independent token, the \"vocabulary\" size (i.e., unique values the model must handle) becomes more manageable.\n2. Model Agnosticism to Locality Bias: The pixel-based Transformer performs competitively across various tasks, such as image classification, self-supervised learning, and image generation, suggesting that locality may not be as essential for vision tasks for ViT as previously thought.\n\nThe authors evaluate this approach on tasks like classification (CIFAR-100, ImageNet), self-supervised learning, and image generation through diffusion models. They find that the pixel-based Transformer achieves results comparable to patch-based ViTs, though with higher computational costs due to increased sequence lengths.\n\nWhile the paper is well-written, it falls short in addressing the practical implications of using 1x1 patches beyond merely demonstrating feasibility. (i.e. other than knowing that we can use 1x1 patches, what is the value of using 1x1 in practice?). I am hesitant to recommend this paper for NeurIPS.", "questions": "Rather than questions, I have a few suggestions to improve writing.\n\nL411 Intrestingly, -> Interestingly\n\nL201: in range [0,255],  the vocab size is 256^3 not 255^3. Please revise all the writing to ensure the correct information.\n\nL44-46: The authors should clarify **why** translation equivariance still exists in ViT. Translation equivariance in neural networks, particularly in convolutional neural networks (CNNs), is the property where shifting the input (e.g., an image) results in a corresponding shift in the output features. This means the network recognizes that the content has moved spatially without altering the actual information content, which is useful for tasks like object detection and localization.\n\nIn transformers, translation equivariance is not naturally present. Transformers process input sequences as tokens, where each token attends to all other tokens through self-attention. transformers don’t inherently “understand” spatial shifts in the same way that CNNs do because each token’s positional information is encoded separately, often through positional embeddings.\n\nAll my concerns are written in Weaknesses section.", "limitations": "", "rating": 5, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "* Clear and Detailed Writing: The paper is well-organized, with clear explanations of the rationale behind pixel-based tokenization, the potential benefits, and the authors are upfront about the trade-offs involved. I only suggest a few writing modifications below.\n\n* Thorough Experimental Evaluation: The paper includes a comprehensive set of experiments across multiple tasks—classification, self-supervised learning, and image generation, although adding more baselines will make the evaluation more complete and convincing.", "weaknesses": "* The empirical results in Table 3 for Case Study #1 show only marginal performance improvements when using 1×1 tokens on datasets like ImageNet and Oxford-102-Flower. The evaluation would be more convincing if results were presented for all four size variants (ViT-T/S/B/L) and included a 16×16 baseline for comparison.\n* In Case Study #2, there is a lack of detailed information on the setup and evaluation. It’s unclear what new value or insights this setup offers beyond those in Case Study #1. This section appears to have been completed in a rush.\n* In Table 5, there is no clear advantage in using 1×1 tokens over 2×2 tokens. Results might benefit from additional baselines, such as 4×4 or 8×8 tokens.\n* In Figure 3, qualitative examples for the 1×1 approach are shown without comparable examples from baseline methods. Including baseline results would provide a more effective comparison.\n* While the authors are upfront about the inefficiency of using 1x1 patches, I am unsure about the practical value of using 1x1 patches (though vocab size benefit was mentioned). The overall takeaway for me is: “We can use 1x1 rather than 2x2 and we still get good performance” but the answer why this finding matters is not clearly explained.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)