MLP-Mixer: An all-MLP Architecture for Vision

1 Introduction . As the history of computer vision demonstrates , the availability of larger datasets coupled with increased computational capacity often leads to a paradigm shift . While Convolutional Neural Networks ( CNNs ) have been the de-facto standard for computer vision , recently Vision Transformers [ 14 ] ( ViT ) , an alternative based on self-attention layers , attained state-of-the-art performance . ViT continues the long-lasting trend of removing hand-crafted visual features and inductive biases from models and relies further on learning from raw data . We propose the MLP-Mixer architecture ( or “ Mixer ” for short ) , a competitive but conceptually and technically simple alternative , that does not use convolutions or self-attention . Instead , Mixer ’ s architecture is based entirely on multi-layer perceptrons ( MLPs ) that are repeatedly applied across either spatial locations or feature channels . Mixer relies only on basic matrix multiplication routines , changes to data layout ( reshapes and transpositions ) , and scalar nonlinearities . Patches Mixer Layer MLP Fully-connected GELU Fully-connected Patches C ha nn el s N x ( Mixer Layer ) Global Average Pooling Per-patch Fully-connected Channels Class L ay er N or m Fully-connected MLP 1 MLP 1 MLP 1 MLP 1 MLP 2 MLP 2 MLP 2 MLP 2 MLP 2 MLP 2 Skip-connections Skip-connections T T L ay er N or mFigure 1 : MLP-Mixer consists of per-patch linear embeddings , Mixer layers , and a classifier head . Mixer layers contain one token-mixing MLP and one channel-mixing MLP , each consisting of two fully-connected layers and a GELU nonlinearity . Other components include : skip-connections , dropout , and layer norm on the channels . they operate on each token independently and take individual rows of the table as inputs . The token-mixing MLPs allow communication between different spatial locations ( tokens ) ; they operate on each channel independently and take individual columns of the table as inputs . These two types of layers are interleaved to enable interaction of both input dimensions . In the extreme case , our architecture can be seen as a very special CNN , which uses 1×1 convolutions for channel mixing , and single-channel depth-wise convolutions of a full receptive field and parameter sharing for token mixing . However , the converse is not true as typical CNNs are not special cases of Mixer . Furthermore , a convolution is more complex than the plain matrix multiplication in MLPs as it requires an additional costly reduction to matrix multiplication and/or specialized implementation . Despite its simplicity , Mixer attains competitive results . When pre-trained on large datasets ( i.e. , ∼100M images ) , it reaches near state-of-the-art performance , previously claimed by CNNs and Transformers , in terms of the accuracy/cost trade-off . This includes 87.94 % top-1 validation accuracy on ILSVRC2012 “ ImageNet ” [ 13 ] . When pre-trained on data of more modest scale ( i.e. , ∼1– 10M images ) , coupled with modern regularization techniques [ 49 , 54 ] , Mixer also achieves strong performance . However , similar to ViT , it falls slightly short of specialized CNN architectures . 2 Mixer Architecture . Modern deep vision architectures consist of layers that mix features ( i ) at a given spatial location , ( ii ) between different spatial locations , or both at once . In CNNs , ( ii ) is implemented with N ×N convolutions ( for N > 1 ) and pooling . Neurons in deeper layers have a larger receptive field [ 1 , 29 ] . At the same time , 1×1 convolutions also perform ( i ) , and larger kernels perform both ( i ) and ( ii ) . In Vision Transformers and other attention-based architectures , self-attention layers allow both ( i ) and ( ii ) and the MLP-blocks perform ( i ) . The idea behind the Mixer architecture is to clearly separate the per-location ( channel-mixing ) operations ( i ) and cross-location ( token-mixing ) operations ( ii ) . Both operations are implemented with MLPs . Figure 1 summarizes the architecture . Mixer takes as input a sequence of S non-overlapping image patches , each one projected to a desired hidden dimension C. This results in a two-dimensional real-valued input table , X ∈ RS×C . If the original input image has resolution ( H , W ) , and each patch has resolution ( P , P ) , then the number of patches is S = HW/P 2 . All patches are linearly projected with the same projection matrix . Mixer consists of multiple layers of identical size , and each layer consists of two MLP blocks . The first one is the token-mixing MLP : it acts on columns of X ( i.e . it is applied to a transposed input table X > ) , maps RS 7→ RS , and is shared across all columns . The second one is the channel-mixing MLP : it acts on rows of X , maps RC 7→ RC , and is shared across all rows . Each MLP block contains two fully-connected layers and a nonlinearity applied independently to each row of its input data tensor . Mixer layers can be written as follows ( omitting layer indices ) : U∗ , i = X∗ , i +W2 σ ( W1 LayerNorm ( X ) ∗ , i ) , for i = 1 . . . C , ( 1 ) Yj , ∗ = Uj , ∗ +W4 σ ( W3 LayerNorm ( U ) j , ∗ ) , for j = 1 . . . S. Here σ is an element-wise nonlinearity ( GELU [ 16 ] ) . DS and DC are tunable hidden widths in the token-mixing and channel-mixing MLPs , respectively . Note that DS is selected independently of the number of input patches . Therefore , the computational complexity of the network is linear in the number of input patches , unlike ViT whose complexity is quadratic . Since DC is independent of the patch size , the overall complexity is linear in the number of pixels in the image , as for a typical CNN . As mentioned above , the same channel-mixing MLP ( token-mixing MLP ) is applied to every row ( column ) of X. Tying the parameters of the channel-mixing MLPs ( within each layer ) is a natural choice—it provides positional invariance , a prominent feature of convolutions . However , tying parameters across channels is much less common . For example , separable convolutions [ 9 , 40 ] , used in some CNNs , apply convolutions to each channel independently of the other channels . However , in separable convolutions , a different convolutional kernel is applied to each channel unlike the token-mixing MLPs in Mixer that share the same kernel ( of full receptive field ) for all of the channels . The parameter tying prevents the architecture from growing too fast when increasing the hidden dimension C or the sequence length S and leads to significant memory savings . Surprisingly , this choice does not affect the empirical performance , see Supplementary A.1 . Each layer in Mixer ( except for the initial patch projection layer ) takes an input of the same size . This “ isotropic ” design is most similar to Transformers , or deep RNNs in other domains , that also use a fixed width . This is unlike most CNNs , which have a pyramidal structure : deeper layers have a lower resolution input , but more channels . Note that while these are the typical designs , other combinations exist , such as isotropic ResNets [ 38 ] and pyramidal ViTs [ 52 ] . Aside from the MLP layers , Mixer uses other standard architectural components : skip-connections [ 15 ] and layer normalization [ 2 ] . Unlike ViTs , Mixer does not use position embeddings because the token-mixing MLPs are sensitive to the order of the input tokens . Finally , Mixer uses a standard classification head with the global average pooling layer followed by a linear classifier . Overall , the architecture can be written compactly in JAX/Flax , the code is given in Supplementary F . 3 Experiments . We evaluate the performance of MLP-Mixer models , pre-trained with medium- to large-scale datasets , on a range of small and mid-sized downstream classification tasks . We are interested in three primary quantities : ( 1 ) Accuracy on the downstream task ; ( 2 ) Total computational cost of pre-training , which is important when training the model from scratch on the upstream dataset ; ( 3 ) Test-time throughput , which is important to the practitioner . Our goal is not to demonstrate state-of-the-art results , but to show that , remarkably , a simple MLP-based model is competitive with today ’ s best convolutional and attention-based models . Downstream tasks We use popular downstream tasks such as ILSVRC2012 “ ImageNet ” ( 1.3M training examples , 1k classes ) with the original validation labels [ 13 ] and cleaned-up ReaL labels [ 5 ] , CIFAR-10/100 ( 50k examples , 10/100 classes ) [ 23 ] , Oxford-IIIT Pets ( 3.7k examples , 36 classes ) [ 33 ] , and Oxford Flowers-102 ( 2k examples , 102 classes ) [ 32 ] . We also use the Visual Task Adaptation Benchmark ( VTAB-1k ) , which consists of 19 diverse datasets , each with 1k training examples [ 58 ] . Pre-training We follow the standard transfer learning setup : pre-training followed by fine-tuning on the downstream tasks . We pre-train our models on two public datasets : ILSVRC2021 ImageNet , and ImageNet-21k , a superset of ILSVRC2012 that contains 21k classes and 14M images [ 13 ] . To assess performance at larger scale , we also train on JFT-300M , a proprietary dataset with 300M examples and 18k classes [ 44 ] . We de-duplicate all pre-training datasets with respect to the test sets of the downstream tasks as done in Dosovitskiy et al . [ 14 ] , Kolesnikov et al . [ 22 ] . We pre-train all models at resolution 224 using Adam with β1 = 0.9 , β2 = 0.999 , linear learning rate warmup of 10k steps and linear decay , batch size 4 096 , weight decay , and gradient clipping at global norm 1 . For JFT-300M , we pre-process images by applying the cropping technique from Szegedy et al . [ 45 ] in addition to random horizontal flipping . For ImageNet and ImageNet-21k , we employ additional data augmentation and regularization techniques . In particular , we use RandAugment [ 12 ] , mixup [ 60 ] , dropout [ 43 ] , and stochastic depth [ 19 ] . This set of techniques was inspired by the timm library [ 54 ] and Touvron et al . [ 48 ] . More details on these hyperparameters are provided in Supplementary B . Fine-tuning We fine-tune using momentum SGD , batch size 512 , gradient clipping at global norm 1 , and a cosine learning rate schedule with a linear warmup . We do not use weight decay when finetuning . Following common practice [ 22 , 48 ] , we also fine-tune at higher resolutions with respect to those used during pre-training . Since we keep the patch resolution fixed , this increases the number of input patches ( say from S to S′ ) and thus requires modifying the shape of Mixer ’ s token-mixing MLP blocks . Formally , the input in Eq . ( 1 ) is left-multiplied by a weight matrix W1 ∈ RDS×S and this operation has to be adjusted when changing the input dimension S. For this , we increase the hidden layer width from DS to DS′ in proportion to the number of patches and initialize the ( now larger ) weight matrix W′2 ∈ RDS′×S ′ with a block-diagonal matrix containing copies of W2 on its diagonal . This particular scheme only allows for S′ = K2S with K ∈ N. See Supplementary C for further details . On the VTAB-1k benchmark we follow the BiT-HyperRule [ 22 ] and fine-tune Mixer models at resolution 224 and 448 on the datasets with small and large input images respectively . Metrics We evaluate the trade-off between the model ’ s computational cost and quality . For the former we compute two metrics : ( 1 ) Total pre-training time on TPU-v3 accelerators , which combines three relevant factors : the theoretical FLOPs for each training setup , the computational efficiency on the relevant training hardware , and the data efficiency . ( 2 ) Throughput in images/sec/core on TPU-v3 . Since models of different sizes may benefit from different batch sizes , we sweep the batch sizes and report the highest throughput for each model . For model quality , we focus on top-1 downstream accuracy after fine-tuning . On two occasions ( Figure 3 , right and Figure 4 ) , where fine-tuning all of the models is too costly , we report the few-shot accuracies obtained by solving the ` 2-regularized linear regression problem between the frozen learned representations of images and the labels . Models We compare various configurations of Mixer , summarized in Table 1 , to the most recent , state-of-the-art , CNNs and attention-based models . In all the figures and tables , the MLP-based Mixer models are marked with pink ( ) , convolution-based models with yellow ( ) , and attention-based models with blue ( ) . The Vision Transformers ( ViTs ) have model scales and patch resolutions similar to Mixer . HaloNets are attention-based models that use a ResNet-like structure with local selfattention layers instead of 3×3 convolutions [ 51 ] . We focus on the particularly efficient “ HaloNet-H4 ( base 128 , Conv-12 ) ” model , which is a hybrid variant of the wider HaloNet-H4 architecture with some of the self-attention layers replaced by convolutions . Note , we mark HaloNets with both attention and convolutions with blue ( ) . Big Transfer ( BiT ) [ 22 ] models are ResNets optimized for transfer learning . NFNets [ 7 ] are normalizer-free ResNets with several optimizations for ImageNet classification . We consider the NFNet-F4+ model variant . We consider MPL [ 35 ] and ALIGN [ 21 ] for EfficientNet architectures . MPL is pre-trained at very large-scale on JFT-300M images , using meta-pseudo labelling from ImageNet instead of the original labels . We compare to the EfficientNetB6-Wide model variant . ALIGN pre-train image encoder and language encoder on noisy web image text pairs in a contrastive way . We compare to their best EfficientNet-L2 image encoder .

Summary: The paper proposes to a new architecture for image classification, based on recently proposed Vision Transformers. Instead of employing self-attention as a global operation on patch embeddings, the authors use fully connected layers, followed by channel mixing done with fully connected layers too. The changes are motivated by improving performance on proprietary hardware (TPU), designed for matrix multiplication. Unlike ViT which has quadratic cost on the number of input patches, the proposed Mixer model has linear cost. However, it loses the ability to handle arbitrary image resolutions. The experimental evaluation shows that the proposed model is comparable performance to state-of-the-art convolutional and Transformer-based models on proprietary and public data.