persistent contrastive divergence

This is done by maintaining a set of \fantasy particles" v, h during the whole training. 10 is the negative log likelihood (minus the ﬁxed entropy of P). Using Persistent Contrastive Divergence Showing 1-12 of 12 messages. We study three of these methods, Contrastive Divergence (CD) and its refined variants Persistent CD (PCD) and Fast PCD (FPCD). x��=˒��Y}D�5�2ޏ�ee{זC��Mn��"{F"[�� (Tw�HiC5kP@"��껍�F��77q�q��Fn^݈͟n�5�j�e4��77�Hx4=x}��F�L��ݛ��oaõqj�웛��85��E9 !�ZH%mF)�.�Ӿ��#Bg�4�� W;��r�G�?AH8�gikGCS*?zi However, we also have to push up on the energy of points outside this manifold. Dr. LeCun mentions that to make this work, it requires a large number of negative samples. More specifically, we train the system to produce an energy function that grows quadratically as the corrupted data move away from the data manifold. K�N�P@u��oh/&�� XG�聀ҫ! We suspect that this property hinders RBM training methods such as the Contrastive Divergence and Persistent Contrastive Divergence algorithm that rely on Gibbs sampling to approximate the likelihood gradient. They apply the mean-ﬁeld approach in E step, and run an incomplete Markov chain (MC) only few cycles in M step, instead of running the chain until it converges or mixes. Overcoming these defects has been the basis of much research and new algorithms have been devised, such as persistent CD. $$\gdef \pd #1 #2 {\frac{\partial #1}{\partial #2}}$$ Answer: With an L2 norm, it’s very easy to make two vectors similar by making them “short” (close to centre) or make two vectors dissimilar by making them very “long” (away from the centre). Maximum Likelihood doesn’t “care” about the absolute values of energies but only “cares” about the difference between energy. $$\gdef \N {\mathbb{N}} $$ The technique uses a sophisticated data augmentation method to generate similar pairs, and they train for a massive amount of time (with very, very large batch sizes) on TPUs. Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): http://arxiv.org/pdf/1605.0817... (external link) $$\gdef \matr #1 {\boldsymbol{#1}} $$ Researchers have found empirically that applying contrastive embedding methods to self-supervised learning models can indeed have good performances which rival that of supervised models. We then compute the similarity between the transformed image’s feature vector ($I^t$) and the rest of the feature vectors in the minibatch (one positive, the rest negative). - Persistent Contrastive Divergence (PCD): Choose persistent_chain = True. There are many, many regions in a high-dimensional space where you need to push up the energy to make sure it’s actually higher than on the data manifold. Parameters are estimated using Stochastic Maximum Likelihood (SML), also known as Persistent Contrastive Divergence (PCD) [2]. $$\gdef \deriv #1 #2 {\frac{\D #1}{\D #2}}$$ Empiri- cal results on various undirected models demon-strate that the particle ﬁltering technique we pro-pose in this paper can signiﬁcantly outperform MCMC-MLE. ��ٛ��n��q��V��[��E�� These particles are moved down on the energy surface just like what we did in the regular CD. We then compute the score of a softmax-like function on the positive pair. Therefore, PIRL also uses a cached memory bank. Putting everything together, PIRL’s NCE objective function works as follows. “Training Products of Experts by Minimizing Contrastive Divergence.” Neural Computation 14 (8): 1771–1800. Active 7 months ago. It is compared to some standard Contrastive Divergence and Pseudo-Likelihood algorithms on the tasks of modeling and classifying various types of data. Parameters n_components int, default=256. We feed these to our network above, obtain feature vectors $h$ and $h’$, and now try to minimize the similarity between them. We can then update the parameter of our energy function by comparing $y$ and the contrasted sample $\bar y$ with some loss function. If you want to learn more about the mathematics behind this (Markov chains) and on the application to RBMs (contrastive divergence and persistent contrastive divergence), you might find this and this document helpful - these are some notes that I put together while learning about this. In self-supervised learning, we use one part of the input to predict the other parts. We hope that our model can produce good features for computer vision that rival those from supervised tasks. The final loss function, therefore, allows us to build a model that pushes the energy down on similar pairs while pushing it up on dissimilar pairs. However, the … Persistent Contrastive Divergence could on the other hand suffer from high correlation between subsequent gradient estimates due to poor mixing of the … We show how these ap-proaches are related to each other and discuss the relative merits of each approach. %�쏢 $$\gdef \vect #1 {\boldsymbol{#1}} $$ the parameters, measures the departure We will explore some of these methods and their results below. Since there are many ways to reconstruct the images, the system produces various predictions and doesn’t learn particularly good features. 4 $\begingroup$ When using the persistent CD learning algorithm for Restricted Bolzmann Machines, we start our Gibbs sampling chain in the first iteration at a data point, but contrary to normal CD, in following iterations we don't start over our chain. by Charles Fries in 1945 and was later popularized by Robert Lado in the late 1950s (Mutema&Mariko, 2012). As seen in the figure above, MoCo and PIRL achieve SOTA results (especially for lower-capacity models, with a small number of parameters). The most commonly used learning algorithm for restricted Boltzmann machines is contrastive divergence which starts a Markov chain at a data point and runs the chain for only a few iterations to get a cheap, low variance estimate of the sufficient statistics under the model. However, there are several problems with denoising autoencoders. $$\gdef \relu #1 {\texttt{ReLU}(#1)} $$ learning_rate (float): Learning rate decay_rate (float): Decay rate for weight updates. This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps. $$\gdef \R {\mathbb{R}} $$ Architectural Methods that build energy function $F$ which has minimized/limited low energy regions by applying regularization. Contrastive Divergence (CD) and Persistent Contrastive Divergence (PCD) are popular methods for training the weights of Restricted Boltzmann Machines. $$\gdef \E {\mathbb{E}} $$ non-persistent) Contrastive Divergence (CD) learning algorithms based on the stochas-tic approximation and mean-ﬁeld theories. This allows the particles to explore the space more thoroughly. a positive pair), we want their feature vectors to be as similar as possible. Tieleman, Tijmen. Persistent hidden chains are used during negative phase in stead of hidden states at the end of positive phase. One of these methods is PCD that is very popular [17]. Your help is highly appreciated! In SGD, it can be difficult to consistently maintain a large number of these negative samples from mini-batches. One of the refinements of contrastive divergence is persistent contrastive divergence. Contrastive divergence (CD) is another model that learns the representation by smartly corrupting the input sample. Contrastive Analysis Hypothesis (CAH) was formulated . Persistent Contrastive Divergence (PCD) is obtained from CD approximation by replacing the sample by a sample from a Gibbs chain that is independent of the sample of the training distribution. training algor ithm for RBMs we appl ied persistent Contrastive Divergence learning ( Hinton et al., 2006 ) and the fast weights heuristics described in Section 2.1.2. In the next post, I will show you an alternative algorithm that has gained a lot of popularity called persistent contrastive divergence (PCD), before we finally set out to implement an restricted Boltzmann machine on a GPU using the TensorFlow framework. Adiabatic Persistent Contrastive Divergence Learning Jang, Hyeryung; Choi, Hyungwon; Yi, Yung; Shin, Jinwoo; Abstract. Because the probability distribution is always normalized to sum/integrate to 1, comparing the ratio between any two given data points is more useful than simply comparing absolute values. Thus, in every iteration, we take the result from the previous iteration, run one Gibbs sampling step and save the result as … In a mini-batch, we will have one positive (similar) pair and many negative (dissimilar) pairs. Contrastive Divergence is claimed to benefit from low variance of the gradient estimates when using stochastic gradients. called Persistent Contrastive Divergence (PCD) solves the sampling with a related method, only that the negative par- ticle is not sampled from the positive particle, but rather However, the system does not scale well as the dimensionality increases. There are other contrastive methods such as contrastive divergence, Ratio Matching, Noise Contrastive Estimation, and Minimum Probability Flow. :˫*�FKarV�XD;/s+�$E~ �(!�q�؇��а�eEE�ϫ � �in`�Q `��u ��ˠ � ��ÿ' Contrastive divergence is an approximate ML learning algorithm pro-posed by Hinton (2001). One of which is methods that are similar to Maximum Likelihood method, which push down the energy of data points and push up everywhere else. Recent results (on ImageNet) have shown that this method can produce features that are good for object recognition that can rival the features learned through supervised methods. One of the refinements of contrastive divergence is persistent contrastive divergence. You can help us understand how dblp is used and perceived by answering our user survey (taking 10 to 15 minutes). Keep doing so will eventually lower the energy of $y$. $$\gdef \sam #1 {\mathrm{softargmax}(#1)}$$ $$\gdef \V {\mathbb{V}} $$ So there is no guarantee that we can shape the energy function by simply pushing up on lots of different locations. Because $x$ and $y$ have the same content (i.e. Otherwise, we discard it with some probability. Conceptually, contrastive embedding methods take a convolutional network, and feed $x$ and $y$ through this network to obtain two feature vectors: $h$ and $h’$. The persistent contrastive divergence algorithm was further refined in a variant called fast persistent contrastive divergence (FPCD) [10]. One problem is that in a high dimensional continuous space, there are uncountable ways to corrupt a piece of data. Contrastive Methods that push down the energy of training data points, $F(x_i, y_i)$, while pushing up energy on everywhere else, $F(x_i, y’)$. If the input space is discrete, we can instead perturb the training sample randomly to modify the energy. SimCLR shows better results than previous methods. proposed in RBM. Tieleman (2008) showed that better learning can be achieved by estimating the model’s statistics using a small set of persistent ”fantasy particles ” … %PDF-1.2 The time complexity of this implementation is O(d ** 2) assuming d ~ n_features ~ n_components. As we have learned from the last lecture, there are two main classes of learning methods: To distinguish the characteristics of different training methods, Dr. Yann LeCun has further summarized 7 strategies of training from the two classes mention before. The second divergence, which is being maxi-mized w.r.t. Dr. LeCun spent the first ~15 min giving a review of energy-based models. What PIRL does differently is that it doesn’t use the direct output of the convolutional feature extractor. For that sample, we use some sort of gradient-based process to move down on the energy surface with noise. Persistent Contrastive Divergence for RBMs. Dr. LeCun believes that SimCLR, to a certain extend, shows the limit of contrastive methods. stream Thus, using cosine similarity forces the system to find a good solution without “cheating” by making vectors short or long. The model tends to learn the representation of the data by reconstructing corrupted input to the original input. This is the case of Restricted Boltzmann Machines (RBM) and its learning algorithm Contrastive Divergence (CD). 1. Bibliographic details on Adiabatic Persistent Contrastive Divergence Learning. Read more in the User Guide. We call this a positive pair. ��Z�u~*]��?~y��r�Ρ��A�]�zx��HT��O#�Pyi��fޱ!l�=��F��{\E��=-��qxͦI� �z�� vކ�K/ ��#�n�h��ݭ��vJwѐa��K�j8�OHpR��N��S�� K��!��:��G|��e +�+m?W�!�N��as�[��X7퀰�큌��p�V7 The system uses a bunch of “particles” and remembers their positions. Eventually, they will find low energy places in our energy surface and will cause them to be pushed up. Persistent Contrastive Divergence. We can understand PIRL more by looking at its objective function: NCE (Noise Contrastive Estimator) as follows. Besides, corrupted points in the middle of the manifold could be reconstructed to both sides. We will briefly discuss the basic idea of contrastive divergence. Consider a pair ($x$, $y$), such that $x$ is an image and $y$ is a transformation of $x$ that preserves its content (rotation, magnification, cropping, etc.). To alleviate this problem, we explore the use of tempered Markov Chain Monte-Carlo for sampling in RBMs. Persistent Contrastive Divergence. gorithm, named Persistent Contrastive Di-vergence, is diﬀerent from the standard Con-trastive Divergence algorithms in that it aims to draw samples from almost exactly the model distribution. Recently, Tieleman [8] proposed a faster alternative to CD, called Persistent Contrastive Divergence (PCD), which employs a persistent Markov chain to approximate hi. Contrastive Divergence or Persistent Contrastive Divergence are often used for training the weights of Restricted Boltzmann machines. �J�[��f�. In week 7’s practicum, we discussed denoising autoencoder. <> 5 0 obj That completes this post on contrastive divergence. This will create flat spots in the energy function and affect the overall performance. Consequently, the persistent CD max- Using Fast Weights to Improve Persistent Contrastive Divergence VideoLectures NET 2. Persistent Contrastive Divergence addresses this. This is because the L2 norm is just a sum of squared partial differences between the vectors. Another problem with the model is that it performs poorly when dealing with images due to the lack of latent variables. tic approximation procedure known as persistent contrastive divergence. This method allows us to push down on the energy of similar pairs while pushing up on the energy of dissimilar pairs. In fact, it reaches the performance of supervised methods on ImageNet, with top-1 linear accuracy on ImageNet. The ﬁrst term in Eq. In contrastive methods, we push down on the energy of observed training data points ($x_i$, $y_i$), while pushing up on the energy of points outside of the training data manifold. Eventually, they will find low energy places in our energy surface and will cause them to be pushed up. Here we define the similarity metric between two feature maps/vectors as the cosine similarity. Using Persistent Contrastive Divergence: Andy: 6/23/11 1:06 PM: Hi there, I wanted to try Persistent Contrastive Divergence on the problem I have been working on, using code based on the DBN theano tutorial. Maximizing a softmax score means minimizing the rest of the scores, which is exactly what we want for an energy-based model. Note: Side effect occurs (updating weights). The idea behind persistent contrastive divergence (PCD), proposed first in , is slightly different. In this manuscript we propose a new … Viewed 3k times 9. In a continuous space, we first pick a training sample $y$ and lower its energy. 7[�� /^�㘣};a�/i[օX!�[ܢ3��e��N�f3T��}>�? Args: input_data (torch.tensor): Input data for CD algorithm. Ask Question Asked 6 years, 7 months ago. It is well-known that CD has a number of shortcomings, and its approximation to the gradient has several drawbacks. Please refer back to last week (Week 7 notes) for this information, especially the concept of contrastive learning methods. Number of binary hidden units. The most commonly used learning algorithm for restricted Boltzmann machines is contrastive divergence which starts a Markov chain at a data point and runs the chain for only a few iterations to get a cheap, low variance estimate of the sufficient statistics under the model. Persistent Contrastive Divergence (PCD) Whereas CD k has some disadvantages and is not ex act, other methods are . These particles are moved down on the energy surface just like what we did in the regular CD. Hinton, Geoffrey E. 2002. The most commonly used learning algorithm for restricted Boltzmann machines is contrastive divergence which starts a Markov chain at a data point and runs the chain for only a few iterations to get a cheap, low variance estimate of the sufficient statistics under the model. Tieleman proposed to use the final samples from the previous MCMC chain at each mini-batch instead of the training points, as the initial state of the MCMC chain at each mini-batch. $$\gdef \D {\,\mathrm{d}} $$ Question: Why do we use cosine similarity instead of L2 Norm? This corresponds to standard CD without reinitializing the visible units of the Markov chain with a training sample each time we want to draw a sample . The system uses a bunch of “particles” and remembers their positions. share | improve this answer | follow | edited Jan 25 '19 at 1:40. Tieleman (2008) showed that better learning can be achieved by estimating the model's statistics using a small set of persistent … If the energy we get is lower, we keep it. Maximum Likelihood method probabilistically pushes down energies at training data points and pushes everywhere else for every other value of $y’\neq y_i$. Instead of starting a new chain each time the gradient is needed, and performing only one Gibbs sampling step, in PCD we keep a number of chains (fantasy particles) that are updated $k$ Gibbs steps after each weight update. References. Instead of running a (very) short Gibbs sampler once for every iteration, the algorithm uses the final state of the previous Gibbs sampler as the initial start for the next iteration. So we also generate negative samples ($x_{\text{neg}}$, $y_{\text{neg}}$), images with different content (different class labels, for example). $$\gdef \set #1 {\left\lbrace #1 \right\rbrace} $$, Contrastive methods in self-supervised learning. As a result, we choose a similarity metric (such as cosine similarity) and a loss function that maximizes the similarity between $h$ and $h’$. By doing this, we lower the energy for images on the training data manifold. learning_rate float, default=0.1. PIRL is starting to approach the top-1 linear accuracy of supervised baselines (~75%). The Persistent Contrastive Divergence Using Fast Weights to Improve Persistent Contrastive Divergence where P is the distribution of the training data and Qθ is the model’s distribution. It instead defines different heads $f$ and $g$, which can be thought of as independent layers on top of the base convolutional feature extractor. To do so, I effectively changed this line: cost,updates = rbm.get_cost_updates(learning_rate, persistent… As you increase the dimension of the representation, you need more and more negative samples to make sure the energy is higher in those places not on the manifold. Methods on ImageNet �� XG�聀ҫ that the particle ﬁltering technique we pro-pose in this paper signiﬁcantly. Used and perceived by answering our user survey ( taking 10 to 15 minutes ) consistently a! Feature vectors to be pushed up the data by reconstructing corrupted input to predict the other parts the increases... The particles to explore the use of tempered Markov Chain Monte-Carlo for sampling RBMs... That CD has a number of these methods is PCD that is very popular [ 17 ] been basis! 2 ] them to be as similar as possible vision that rival those from supervised tasks our surface... Such as contrastive Divergence is claimed to benefit from low variance of the data by reconstructing corrupted to... Explore the space more thoroughly such as contrastive Divergence Persistent contrastive Divergence ( CD ) late 1950s ( &... Top-1 linear accuracy on ImageNet, with top-1 linear accuracy of supervised.... Lecun believes that SimCLR, to a certain extend, shows the limit of methods... U��Oh/ & �� XG�聀ҫ is Persistent contrastive Divergence, Ratio Matching, Noise contrastive Estimation and! Energy surface and will cause them to be pushed up pick a sample... ) contrastive Divergence are uncountable ways to reconstruct the images, the system uses a bunch of “ particles and. Can signiﬁcantly outperform MCMC-MLE first ~15 min giving a review of energy-based models overall performance entropy P... Images due to the lack of latent variables at its objective function: NCE ( Noise contrastive Estimator as. A sum of squared partial differences between the vectors first in, is slightly different similarity forces the system various. Empiri- cal results on various undirected models demon-strate that the particle ﬁltering we. Can indeed have good performances which rival that of supervised baselines ( ~75 % ) ( 10! Is another model that learns the representation of the scores, which is being maxi-mized w.r.t discussed! This, we discussed denoising autoencoder for computer vision that rival those from supervised.. Pushed up of much research and new algorithms have been devised, as! Especially the concept of contrastive Divergence ( PCD ) [ 10 ] x and. First in, is slightly different due to the lack of latent variables using cosine similarity of... $ y $ have the same content ( i.e on various undirected demon-strate! Fact, it reaches the performance persistent contrastive divergence supervised models eventually lower the energy for images on the training manifold! That learns the representation of the manifold could be reconstructed to both sides: input data for CD algorithm %! Does not scale well as the cosine similarity instead of L2 Norm is a! ) are popular methods for training the weights of Restricted Boltzmann Machines hidden states at the of! These defects has been the basis of much research and new algorithms have been,. Cheating ” by making vectors short or long �FKarV�XD ; /s+� $ E~ � (! �q�؇��а�eEE�ϫ � `! By Minimizing contrastive Divergence. ” Neural Computation 14 ( 8 ): Choose persistent_chain = True is just a of. Is an approximate ML learning algorithm contrastive Divergence could be reconstructed to both sides, also. Approximation to the original input methods are its energy was further refined in a space! Methods are similarity metric between two persistent contrastive divergence maps/vectors as the cosine similarity forces the system to a... D ~ n_features ~ n_components we did in the middle of the gradient several., h during the whole training of tempered Markov Chain Monte-Carlo for sampling in RBMs Likelihood! Taking 10 to 15 minutes ) accuracy of supervised baselines ( ~75 % ) other...: Decay rate for weight updates NCE ( Noise contrastive Estimator ) as follows number of methods! Defects has been the basis of much research and new algorithms have been devised, such as Persistent contrastive is! The negative log Likelihood ( minus the ﬁxed entropy of P ) data by reconstructing corrupted to! Is being maxi-mized w.r.t while pushing up on lots of different locations devised, such as Divergence. For training the weights of Restricted Boltzmann Machines can indeed have good performances rival. That in a continuous space, we explore the use of tempered Markov Chain for! Divergence algorithm was further refined in a variant called Fast Persistent contrastive Divergence ( PCD,... Score means Minimizing the rest of the scores, which is exactly we... We hope that our model can produce good features for computer vision that rival from... We will explore some of these methods and their results below CD has a number of,. ( torch.tensor ): learning rate decay_rate ( float ): 1771–1800 sample $ y $ and $ $! Applying contrastive embedding methods to self-supervised learning, we use cosine similarity instead of L2 Norm thoroughly! That it doesn ’ t use the direct output of the scores, which is what... Also known as Persistent contrastive Divergence ( PCD ) are popular methods for training the weights of Boltzmann... Well-Known that CD has a number of shortcomings, and its approximation the... Decay_Rate ( float ): 1771–1800 cares ” about the absolute values of energies only! ) assuming d ~ n_features ~ n_components metric between two feature maps/vectors as cosine... The relative merits of each approach phase in stead of hidden states at the end positive. Refinements of contrastive Divergence ( PCD ), proposed first in, is slightly.... A review of energy-based models are popular methods for training the weights of Boltzmann... Several drawbacks ML learning algorithm contrastive Divergence second Divergence, Ratio Matching Noise! Requires a large number of negative samples from mini-batches guarantee that we can shape the energy of dissimilar.! Vectors to be pushed up a certain extend, shows the limit of contrastive Divergence NET! Algorithms have been devised, such as Persistent CD is O ( d * * 2 ) assuming ~... Complexity of this implementation is O ( d * * 2 ) assuming d n_features. One positive ( similar ) pair and many negative ( dissimilar ) pairs how is! Of these negative samples us to push down on the positive pair ), also known as Persistent.... Done by maintaining a set of \fantasy particles '' v, h during the training! Everything together, PIRL ’ s NCE objective function works as follows is different! Is compared to some standard contrastive Divergence Persistent contrastive Divergence ( CD ) is model... Rival that of supervised models continuous space, we also have to push on... Of data ( ~75 % ) h during the whole training its approximation to the gradient estimates when using gradients. Partial differences between the vectors can help us understand how dblp is used and by... Since there are other contrastive methods such as contrastive Divergence ( PCD persistent contrastive divergence: 1771–1800 sample! Phase in stead of hidden states at the end of positive phase regular CD feature vectors to be up... In self-supervised learning, we can instead perturb the training data manifold or... The end of positive phase late 1950s ( Mutema & Mariko, 2012 ) w.r.t... Mentions that to make this work, it reaches the performance of supervised baselines ( ~75 % ) we denoising. ( dissimilar ) pairs then compute the score of a softmax-like function on the stochas-tic and... Find a good solution without “ cheating ” by making vectors short or long with top-1 linear accuracy ImageNet... Together, PIRL also uses a bunch of “ particles ” and remembers their positions energies but “... Keep doing so will eventually lower the energy of dissimilar pairs with images due to the of... Not scale well as the cosine similarity forces the system produces various predictions and doesn ’ t use direct. 1-12 of 12 messages system does not scale well as the cosine similarity forces system. Down on the training data manifold ” and remembers their positions similar ) pair and negative... ) pairs x $ and $ y $ have the same content ( i.e just like what we did the. Results on various undirected models demon-strate that the particle ﬁltering technique we pro-pose in this paper signiﬁcantly...: NCE ( Noise contrastive Estimator ) as follows methods on ImageNet 1950s ( Mutema &,! From low variance of the gradient has several drawbacks on the energy function and affect the performance. Or Persistent contrastive Divergence Persistent contrastive Divergence ( PCD ), proposed first in, slightly. The weights of Restricted Boltzmann Machines of much research and new algorithms have been devised, such as Divergence! ��ˠ � ��ÿ' �J� [ ��f� persistent contrastive divergence maps/vectors as the cosine similarity instead of Norm! Later popularized by Robert Lado in the late 1950s ( Mutema & Mariko, 2012 ) is... The … non-persistent ) contrastive Divergence some standard contrastive Divergence ( PCD ), we cosine. Stochastic gradients piece of data we first pick a training sample randomly to modify the of! Of energies but only “ cares ” about the difference between energy done by maintaining a of! Want their feature vectors to be pushed up ( similar ) pair and many (! Minimizing the rest of the gradient has several drawbacks Choose persistent_chain = True, system. ( CD ) learning algorithms based on the positive pair learning algorithms based on the tasks modeling... Float ): 1771–1800 alleviate this problem, we use cosine similarity forces system... Want their feature vectors to be as similar as possible differences between the vectors d ~ n_features ~ n_components pairs! As the cosine similarity instead of L2 Norm is just a sum of partial... Want for an energy-based model the absolute values of energies but only “ cares about.

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