{Resnet, VICReg, 2 term of Regularizations, Collapse}
Paper: https://openreview.net/pdf?id=xm6YD62D1Ub
Official Code: https://github.com/facebookresearch/vicreg
Colab: https://colab.research.google.com/drive/1Bi-nbAbwFpEUOxfM1qXfOOeigE7Ur2F_?usp=sharing
Pytorch-version: https://github.com/untitled-ai
Recent self-supervised methods for image representation learning maximize the agreement between embedding vectors produced by encoders fed with different views of the same image.
The main challenge is to prevent a collapse in which the encoders produce constant or non-informative vectors.
Explicitly avoids the collapse problem with two regularizations terms applied to both embeddings separately:
A term that maintains the variance of each embedding dimension above a threshold.
A term that decorrelates each pair of variables.
Not require techniques such as:
weight sharing between the branches
batch normalization
feature-wise normalization
output quantization
stop gradient
memory banks
Achieves results on par with the state of the art on several downstream tasks.
Variance regularization term stabilizes the training of other methods and leads to performance improvements.
One of the most interesting feature of VICReg is the fact that the two branches are not required to share the same parameters, architecture, or input modality. This opens the door to the use of non-contrastive self-supervised joint-embedding for multi-modal signals, such as video and audio.
Furthermore, we show that incorporating variance preservation into other self-supervised joint-embedding methods yields better training stability and performance improvement on downstream tasks.
More generally, we show that VICReg is an explicit and effective, yet simple method for preventing collapse in self-supervised joint-embedding learning.
Two networks (share the same weights) are trained to produce similar embeddings for different views of the same image.
Siamese network architecture Bromley et al. (1994)
The main challenge is to prevent a collapse in which the two branches ignore the inputs and produce identical and constant output vectors.
Bromley et al. (1994);
Chopra et al. (2005);
He et al. (2020);
Hjelm et al. (2019);
Chen et al. (2020a)
Problem:
methods tend to be costly, require large batch sizes or memory banks, and use a loss that explicitly pushes the embeddings of dissimilar images away from each other.
require a mining procedure to search for offending dissimilar samples from a memory bank He et al. (2020) or from the current batch Chen et al. (2020a).
Caron et al. (2020; 2018) force the embeddings of different samples to belong to different clusters on the unit sphere.
Collapse is prevented by ensuring that the assignment of samples to clusters is as uniform as possible.
A similarity term encourages the cluster assignment score vectors from the two branches to be similar.
Methods:
BYOL Grill et al. (2020)
SimSiam Chen & He (2020).
They exploit several tricks:
batch-wise or feature-wise normalization
a "momentum encoder" in which the parameter vector of one branch is a low-pass-filtered version of the parameter vector of the other branch Grill et al. (2020); Richemond et al. (2020),
a stop-gradient operation in one of the branches Chen & He (2020).
The dynamics of learning in these methods, and how they avoid collapse, is not fully understood, although theoretical and empirical studies point to the crucial importance of batch-wise or feature-wise normalization Richemond et al. (2020); Tian et al. (2021).
Methods:
Zbontar et al. (2021): The Barlow Twins method drives the normalized cross-correlation matrix of the two embeddings towards the identity.
Ermolov et al. (2021): The Whitening-MSE method whitens and spreads out the embedding vectors on the unit sphere.
Prevent informational collapse by decorrelating every pair of variables of the embedding vectors.
This indirectly maximizes the information content of the embedding vectors.
Contrastive Learning:
The output embeddings for a sample and its distorted version are brought close to each other, while other samples and their distortions are pushed away.
Applied to Siamese architectures in which the two branches have identical architectures and share weights
Misra & Maaten (2020);
He et al. (2020);
Bromley et al. (1994);
Hjelm et al. (2019);
Chen et al. (2020a;c);
Hadsell et al. (2006);
Ye et al. (2019);
Wu et al. (2018);
van den Oord et al. (2018);
Chen et al. (2020b).
Many authors use the InfoNCE loss in which the repulsive force is larger for contrastive samples that are closer to the reference.
van den Oord et al. (2018)
These methods yield good performance,
Require large amounts of contrastive pairs in order to work well.
These contrastive pairs can be sampled from a memory bank as in MoCo He et al. (2020), or given by the current batch of data as in SimCLR Chen et al. (2020a), with a significant memory footprint.
This downside of contrastive methods motivates a search for alternatives.
Clustering Methods:
Instead of viewing each sample as its own class, clustering-based methods group them into clusters based on some similarity measure
Caron et al. (2020; 2018);
Bautista et al. (2016);
Yang et al. (2016);
Xie et al. (2016);
Huang et al. (2019);
Zhuang et al. (2019);
Caron et al. (2019);
Asano et al. (2020);
Yan et al. (2020).
DeepCluster Caron et al. (2018) uses k-means assignments of representations from previous iterations as pseudo-labels for the new representations, which requires an expensive clustering phase done asynchronously, and makes the method hard to scale up.
SwAV Caron et al. (2020) mitigates this issue by learning the clusters online while maintaining a balanced partition of the assignments through the Sinkhorn-Knopp transform Cuturi (2013).
These clustering approaches can be viewed as contrastive learning at the level of clusters which still requires a lot of negative comparisons to work well.
Distillation Methods:
Recent proposals such as BYOL, SimSiam, OBoW and variants Grill et al. (2020); Chen & He (2020); Gidaris et al. (2021); Richemond et al. (2020); Gidaris et al. (2020) have shown that collapse can be avoided by using architectural tricks inspired by knowledge distillation Hinton et al. (2015). These methods train a student network to predict the representations of a teacher network, for which the weights are a running average of the student network’s weights Grill et al. (2020), or are shared with the student network, but no gradient is back-propagated through the teacher Chen & He (2020). These methods are effective, but there is no clear understanding of why and how they avoid collapse. Alternatively, the images can be represented as bags of word over a dictionary of visual features, which effectively prevents collapse. In OBoW Gidaris et al. (2020) and Gidaris et al. (2021) the dictionary is obtained by off-line or on-line clustering. By contrast, our method explicitly prevents collapse in the two branches independently, which removes the requirement for shared weights and identical architecture, opening the door to the application of joint-embedding SSL to multi-modal signals.
Information Maximization Methods:
A principle to prevent collapse is to maximize the information content of the embeddings. Two such methods were recently proposed: W-MSE Ermolov et al. (2021) and Barlow Twins Zbontar et al. (2021). In W-MSE, an extra module transforms the embeddings into the eigenspace of their covariance matrix (whitening or Karhunen-Loève transform), and forces the vectors thereby obtained to be uniformly distributed on the unit sphere. In Barlow Twins, a loss term attempts to make the normalized cross-correlation matrix of the embedding vectors from the two branches to be close to the identity. Both methods attempt to produce embedding variables that are decorrelated from each other, thus preventing an informational collapse in which the variables carry redundant information. Because all variables are normalized over a batch, there is no incentive for them to shrink nor expand. This seems to sufficient to prevent collapse. Our method borrows the decorrelation mechanism of Barlow Twins. But it includes an explicit variance-preservation term for each variable of the two embeddings and thus does not require any normalization.
VICReg (Variance-Invariance-Covariance Regularization)
A self-supervised method for training joint embedding architectures based on the principle of preserving the information content of the embeddings.
The basic idea is to use a loss function with three terms:
Invariance: the mean square distance between the embedding vectors.
Variance: a hinge loss to maintain the standard deviation (over a batch) of each variable of the embedding above a given threshold. This term forces the embedding vectors of samples within a batch to be different.
paper main contribution
explicitly prevents a collapse due to a shrinkage of the embedding vectors towards zero.
Covariance: a term that attracts the covariances (over a batch) between every pair of (centered) embedding variables towards zero. This term decorrelates the variables of each embedding and prevents an informational collapse in which the variables would vary together or be highly correlated.
borrowed from the Barlow Twins method and prevents informational collapse due to redundancy between the embedding variables Zbontar et al. (2021).
==> Variance and Covariance: preserving the information content of each embedding at a certain level and preventing informational collapse independently for the two branches.
VICReg:
does not require that the weights of the two branches be shared, not that the architectures be identical, nor that the inputs be of the same nature;
does not require a memory bank, nor contrastive samples, nor a large batch size;
does not require batch-wise nor feature-wise normalization;
does not require vector quantization nor a predictor module.
Other methods require:
asymmetric stop gradient operations, as in SimSiam Chen & He (2020)
weight sharing between the two branches as in classical Siamese nets,
weight sharing through exponential moving average dampening with stop gradient in one branch, as in BYOL and MoCo He et al. (2020); Grill et al. (2020); Chen et al. (2020c)
large batches of contrastive samples, as in SimCLR Chen et al. (2020a),
batch-wise and/or feature-wise normalization Caron et al. (2020); Grill et al. (2020); Chen & He (2020); Zbontar et al. (2021); Ermolov et al. (2021).
1. VICReg: Detailed Description
VICReg follows recent trends in self-supervised learning Caron et al. (2020); Grill et al. (2020); Chen & He (2020); Zbontar et al. (2021); Chen et al. (2020a) and is based on a joint embedding architecture. Contrary to many previous approaches, our architecture may be completely symmetric or completely asymmetric with no shared structure or parameters between the two branches. In most of our experiments, we use a Siamese net architecture in which the two branches are identical and share weights. Each branch consists of an encoder fθ that outputs the representations (used for downstream tasks), followed by an expander hφ that maps the representations into an embedding space where the loss function will be computed. The role of the expander is twofold: (1) eliminate the information by which the two representations differ, (2) expand the dimension in a non-linear fashion so that decorrelating the embedding variables will reduce the dependencies (not just the correlations) between the variables of the representation vector. The loss function uses a term s that learns invariance to data transformations and is regularized with a variance term v that prevents norm collapse and a covariance term c that prevents informational collapse by decorrelating the different dimensions of the vectors. After pretraining, the expander is discarded and the representations of the encoder are used for downstream tasks.
1.1 Method:
:
1.2 Implementation Details:
Implementation details for pretraining with VICReg on the 1000-classes ImagetNet dataset without labels are as follows. Coefficients λ and µ are 25 and ν is 1 in Eq. (6), and is 0.0001 in Eq. (1). We give more details on how we choose the coefficients of the loss function in Appendix D.4. The encoder network fθ is a standard ResNet-50 backbone He et al. (2016) with 2048 output units. The expander hφ is composed of two fully-connected layers with batch normalization (BN) Ioffe & Szegedy (2015) and ReLU, and a third linear layer. The sizes of all 3 layers were set to 8192. As with Barlow Twins, performance improves when the size of the expander layers is larger than the dimension of the representation. The impact of the expander dimension on performance is studied in Appendix D. The training protocol follows those of BYOL and Barlow Twins: LARS optimizer You et al. (2017); Goyal et al. (2017) run for 1000 epochs with a weight decay of 10−6 and a learning rate lr = batch_size/256 × base_lr, where batch_size is set to 2048 by default and base_lr is a base learning rate set to 0.2. The learning rate follows a cosine decay schedule Loshchilov & Hutter (2017), starting from 0 with 10 warmup epochs and with final value of 0.002.
2.1 Evaluation on ImageNet:
Following the ImageNet Deng et al. (2009) linear evaluation protocol, we train a linear classifier on top of the frozen representations of the ResNet-50 backbone pretrained with VICReg. We also evaluate the performance of the backbone when fine-tuned with a linear classifier on a subset of ImageNet’s training set using 1% or 10% of the labels, using the split of Chen et al. (2020a). We give implementation details about the optimization procedure for these tasks in Appendix C. We have applied the training procedure described in section 4 with three different random initialization. The numbers reported in Table 1 for VICReg are the mean scores, and we have observed that the difference between worse and best run is lower than 0.1% accuracy for linear classification, which shows that VICReg is a very stable algorithm. Lack of time has prevented us from doing the same for the semi-supervised classification experiments, and the experiments of section 5.2 and 6, but we expect similar conclusion to hold. We compare in Table 1 our results on both tasks against other methods on the validation set of ImageNet. The performance of VICReg is on par with the state of the art without using the negative pairs of SimCLR, the clusters of SwAV, the bag-of-words representations of OBoW, or any asymmetric networks architectural tricks such as the momentum encoder of BYOL and the stop-gradient operation of SimSiam. The performance is comparable to that of Barlow Twins, which shows that VICReg’s more explicit way of constraining the variance and comparing views has the same power than maximizing cross-correlations between pairs of twin dimensions. The main advantage of VICReg is the modularity of its objective function and the applicability to multi-modal setups.
1.2 Transfer to other Downstream tasks:
Following the setup from Misra & Maaten (2020), we train a linear classifier on top of the frozen representations learnt by our pretrained ResNet-50 backbone on a variety of different datasets: the Places205 Zhou et al. (2014) scene classification dataset, the VOC07 Everingham et al. (2010) multi-label image classification dataset and the iNaturalist2018 Horn et al. (2018) fine-grained image classification dataset. We then evaluate the quality of the representations by transferring to other vision tasks including VOC07+12 Everingham et al. (2010) object detection using Faster R-CNN Ren et al. (2015) with a R50-C4 backbone, and COCO Lin et al. (2014) instance segmentation using Mask-R-CNN He et al. (2017) with a R50-FPN backbone. We report the performance in Table 2, VICReg performs on par with most concurrent methods, and better than Barlow Twins, across all classification tasks, but is slightly behind the top-3 on detection tasks.
1.3 Multi-modal pretraining on MS-COCO:
One fundamental difference of VICReg compared to Barlow Twins is the way the branches are regularized. In VICReg, both branches are regularized independently, as the covariance term is applied on each branch separately, which works better in the scenarios where the branches are completely different, have different types of architecture and process different types of data. Indeed, the statistics of the output of the two branches can be very different, and the amount of regularization required for each may vary a lot. In Barlow Twins, the regularization is applied on the cross-correlation matrix, which favors the scenarios where the branches produce outputs with similar statistics. We demonstrate the capabilities of VICReg in a multi-modal experiment where we pretrain on pairs of images and corresponding captions on the MS-COCO dataset. We regularize each branch with a different coefficient, which is not possible with Barlow Twins, and we show that VICReg outperforms Barlow Twins on image and text retrieval downstream tasks. Table 3 reports the performance of VICReg against the contrastive loss proposed by VSE++ Faghri et al. (2018), and against Barlow Twins, in the identical setting proposed in Faghri et al. (2018). VICReg outperforms the two by a significant margin.
