Fig. We can pick and choose the one we want, There are some minor changes like Luong concatenates the context and the decoder hidden state and uses one weight instead of 2 separate ones, Last and the most important one is that Luong feeds the attentional vector to the next time-step as they believe that past attention weight history is important and helps predict better values. @Nav Hi, sorry but I saw your comment only now. j where d is the dimensionality of the query/key vectors. But then we concatenate this context with hidden state of the decoder at t-1. In the multi-head attention mechanism of the transformer, why do we need both $W_i^Q$ and ${W_i^K}^T$? Here s is the query while the decoder hidden states s to s represent both the keys and the values.. Having done that, we need to massage the tensor shape back & hence, there is a need for a multiplication with another weight v. Determining v is a simple linear transformation and needs just 1 unit, Luong gives us local attention in addition to global attention. We suspect that for large values of d k, the dot products grow large in magnitude, pushing the softmax function into regions where it has extremely . Attention could be defined as. Additive attention computes the compatibility function using a feed-forward network with a single hidden layer. I went through the pytorch seq2seq tutorial. i It . Both variants perform similar for small dimensionality $d_{h}$ of the decoder states, but additive attention performs better for larger dimensions. mechanism - all of it look like different ways at looking at the same, yet Bahdanau has only concat score alignment model. Asking for help, clarification, or responding to other answers. Why we . Note that the decoding vector at each timestep can be different. Given a set of vector values, and a vector query, attention is a technique to compute a weighted sum of values dependent on the query. Attention-like mechanisms were introduced in the 1990s under names like multiplicative modules, sigma pi units, and hyper-networks. Any insight on this would be highly appreciated. w We've added a "Necessary cookies only" option to the cookie consent popup. If the first argument is 1-dimensional and . 1 d k scailing . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. for each (2 points) Explain one advantage and one disadvantage of dot product attention compared to multiplicative attention. Intuitively, the use of the dot product in multiplicative attention can be interpreted as providing a similarity measure between the vectors, $\mathbf {s}_t$ and $\mathbf {h}_i$, under consideration. (2 points) Explain one advantage and one disadvantage of additive attention compared to mul-tiplicative attention. The best answers are voted up and rise to the top, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. where t In Computer Vision, what is the difference between a transformer and attention? This view of the attention weights addresses the "explainability" problem that neural networks are criticized for. The present study tested the intrinsic ERP features of the effects of acute psychological stress on speed perception. What does a search warrant actually look like? Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The latter one is built on top of the former one which differs by 1 intermediate operation. What's the difference between content-based attention and dot-product attention? PTIJ Should we be afraid of Artificial Intelligence? Assume you have a sequential decoder, but in addition to the previous cells output and hidden state, you also feed in a context vector c. Where c is a weighted sum of the encoder hidden states. Here is the amount of attention the ith output should pay to the jth input and h is the encoder state for the jth input. They are however in the "multi-head attention". every input vector is normalized then cosine distance should be equal to the Learn more about Stack Overflow the company, and our products. In TensorFlow, what is the difference between Session.run() and Tensor.eval()? Planned Maintenance scheduled March 2nd, 2023 at 01:00 AM UTC (March 1st, What's the difference between Attention vs Self-Attention? Yes, but what Wa stands for? $\mathbf{K}$ refers to the keys vectors matrix, $k_i$ being a single key vector associated with a single input word. Attention. Ive been searching for how the attention is calculated, for the past 3 days. If we fix $i$ such that we are focusing on only one time step in the decoder, then that factor is only dependent on $j$. The recurrent layer has 500 neurons and the fully-connected linear layer has 10k neurons (the size of the target vocabulary). The Attention is All you Need has this footnote at the passage motivating the introduction of the $1/\sqrt{d_k}$ factor: I suspect that it hints on the cosine-vs-dot difference intuition. The vectors are usually pre-calculated from other projects such as, 500-long encoder hidden vector. Thus, it works without RNNs, allowing for a parallelization. 1.4: Calculating attention scores (blue) from query 1. The footnote talks about vectors with normally distributed components, clearly implying that their magnitudes are important. Does Cast a Spell make you a spellcaster? Let's start with a bit of notation and a couple of important clarifications. i Jordan's line about intimate parties in The Great Gatsby? -------. New AI, ML and Data Science articles every day. As it can be seen the task was to translate Orlando Bloom and Miranda Kerr still love each other into German. matrix multiplication . Multiplicative Attention. What is the difference between Attention Gate and CNN filters? is computed by taking a softmax over the attention scores, denoted by e, of the inputs with respect to the ith output. attention and FF block. These values are then concatenated and projected to yield the final values as can be seen in 8.9. Any reason they don't just use cosine distance? These can technically come from anywhere, sure, but if you look at ANY implementation of the transformer architecture you will find that these are indeed learned parameters. The self-attention model is a normal attention model. Follow me/Connect with me and join my journey. Then we calculate alignment , context vectors as above. Grey regions in H matrix and w vector are zero values. However, the schematic diagram of this section shows that the attention vector is calculated by using the dot product between the hidden states of the encoder and decoder (which is known as multiplicative attention). tl;dr: Luong's attention is faster to compute, but makes strong assumptions about the encoder and decoder states.Their performance is similar and probably task-dependent. Sign in Neither how they are defined here nor in the referenced blog post is that true. Here f is an alignment model which scores how well the inputs around position j and the output at position i match, and s is the hidden state from the previous timestep. . Additive attention computes the compatibility function using a feed-forward network with a single hidden layer. same thing holds for the LayerNorm. Given a sequence of tokens The scaling is performed so that the arguments of the softmax function do not become excessively large with keys of higher dimensions. It means a Dot-Product is scaled. What is the intuition behind the dot product attention? Also, the first paper mentions additive attention is more computationally expensive, but I am having trouble understanding how. The text was updated successfully, but these errors were encountered: You signed in with another tab or window. By providing a direct path to the inputs, attention also helps to alleviate the vanishing gradient problem. Read More: Neural Machine Translation by Jointly Learning to Align and Translate. The probability assigned to a given word in the pointer vocabulary distribution is the sum of the probabilities given to all token positions where the given word appears. scale parameters, so my point above about the vector norms still holds. i The main difference is how to score similarities between the current decoder input and encoder outputs. Scaled dot product self-attention The math in steps. What is the difference between 'SAME' and 'VALID' padding in tf.nn.max_pool of tensorflow? For convolutional neural networks, the attention mechanisms can also be distinguished by the dimension on which they operate, namely: spatial attention,[10] channel attention,[11] or combinations of both.[12][13]. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Update: I am a passionate student. I believe that a short mention / clarification would be of benefit here. additive attentionmultiplicative attention 3 ; Transformer Transformer If both arguments are 2-dimensional, the matrix-matrix product is returned. The alignment model, in turn, can be computed in various ways. Attention has been a huge area of research. 100 hidden vectors h concatenated into a matrix. k These are "soft" weights which changes during the forward pass, in contrast to "hard" neuronal weights that change during the learning phase. torch.matmul(input, other, *, out=None) Tensor. 1. , a neural network computes a soft weight For the purpose of simplicity, I take a language translation problem, for example English to German, in order to visualize the concept. Can the Spiritual Weapon spell be used as cover? These two papers were published a long time ago. The two most commonly used attention functions are additive attention [2], and dot-product (multiplicative) attention. So before the softmax this concatenated vector goes inside a GRU. The mechanism is particularly useful for machine translation as the most relevant words for the output often occur at similar positions in the input sequence. [3][4][5][6] Listed in the Variants section below are the many schemes to implement the soft-weight mechanisms. Therefore, the step-by-step procedure for computing the scaled-dot product attention is the following: Data Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field. Purely attention-based architectures are called transformers. [1] for Neural Machine Translation. Viewed as a matrix, the attention weights show how the network adjusts its focus according to context. Here $\textbf{h}$ refers to the hidden states for the encoder, and $\textbf{s}$ is the hidden states for the decoder. {\displaystyle k_{i}} {\displaystyle w_{i}} FC is a fully-connected weight matrix. I think my main takeaways from your answer are a) cosine distance doesn't take scale into account, b) they divide by $sqrt(d_k)$ but it could have been something else and might have worked and we don't really know why, By the way, re layer norm vs batch norm I also have. Whereas key, is the hidden state of the encoder, and the corresponding value is normalized weight, representing how much attention a key gets. What is the purpose of this D-shaped ring at the base of the tongue on my hiking boots? Attention: Query attend to Values. Thanks for contributing an answer to Stack Overflow! I personally prefer to think of attention as a sort of coreference resolution step. H, encoder hidden state; X, input word embeddings. As a result, conventional self-attention is tightly coupled by nature, which prevents the extraction of intra-frame and inter-frame action features and thereby degrades the overall performance of . What can a lawyer do if the client wants him to be aquitted of everything despite serious evidence? Transformer turned to be very robust and process in parallel. Duress at instant speed in response to Counterspell. It'd be a great help for everyone. Thanks. To learn more, see our tips on writing great answers. Dot Product Attention (Multiplicative) We will cover this more in Transformer tutorial. Effective Approaches to Attention-based Neural Machine Translation, https://towardsdatascience.com/create-your-own-custom-attention-layer-understand-all-flavours-2201b5e8be9e, The open-source game engine youve been waiting for: Godot (Ep. There are no weights in it. j Why are physically impossible and logically impossible concepts considered separate in terms of probability? Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Note that for the first timestep the hidden state passed is typically a vector of 0s. Often, a correlation-style matrix of dot products provides the re-weighting coefficients (see legend). In practice, the attention unit consists of 3 fully-connected neural network layers called query-key-value that need to be trained. What's the difference between a power rail and a signal line? w If you order a special airline meal (e.g. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The best answers are voted up and rise to the top, Not the answer you're looking for? i output. How to compile Tensorflow with SSE4.2 and AVX instructions? Sign up for a free GitHub account to open an issue and contact its maintainers and the community. Is variance swap long volatility of volatility? With the Hadamard product (element-wise product) you multiply the corresponding components, but do not aggregate by summation, leaving a new vector with the same dimension as the original operand vectors. AttentionCompatibility function TransformerScaled Dot-Product Attention Dot-Product AttentionKeysoftmax i rev2023.3.1.43269. Find centralized, trusted content and collaborate around the technologies you use most. 100-long vector attention weight. Bigger lines connecting words mean bigger values in the dot product between the words query and key vectors, which means basically that only those words value vectors will pass for further processing to the next attention layer. Luong has both as uni-directional. The number of distinct words in a sentence. So, the coloured boxes represent our vectors, where each colour represents a certain value. Encoder-decoder with attention. Share Cite Follow You can get a histogram of attentions for each . head Q(64), K(64), V(64) Self-Attention . and key vector It is widely used in various sub-fields, such as natural language processing or computer vision. is the output of the attention mechanism. The mechanism of scaled dot-product attention is just a matter of how to concretely calculate those attentions and reweight the "values". The query, key, and value are generated from the same item of the sequential input. {\displaystyle i} This is exactly how we would implement it in code. Attention is the technique through which the model focuses itself on a certain region of the image or on certain words in a sentence just like the same way the humans do. I've spent some more time digging deeper into it - check my edit. However, dot-product attention is relatively faster and more space-efficient in practice due to the highly optimized matrix multiplication code. For example, the work titled Attention is All You Need which proposed a very different model called Transformer. The first option, which is dot, is basically a dot product of hidden states of the encoder (h_s) and the hidden state of the decoder (h_t). i i Dot-Product Attention is an attention mechanism where the alignment score function is calculated as: f a t t ( h i, s j) = h i T s j It is equivalent to multiplicative attention (without a trainable weight matrix, assuming this is instead an identity matrix). The final h can be viewed as a "sentence" vector, or a. The difference operationally is the aggregation by summation.With the dot product, you multiply the corresponding components and add those products together. Thus, the . [1] Its flexibility comes from its role as "soft weights" that can change during runtime, in contrast to standard weights that must remain fixed at runtime. I think the attention module used in this paper (https://arxiv.org/abs/1805.08318) is an example of multiplicative attention, but I am not entirely sure. Can the Spiritual Weapon spell be used as cover? dot-product attention additive attention dot-product attention . The two main differences between Luong Attention and Bahdanau Attention are: . Earlier in this lesson, we looked at how the key concept of attention is to calculate an attention weight vector, which is used to amplify the signal from the most relevant parts of the input sequence and in the same time, drown out the irrelevant parts. $$, $$ Luong of course uses the hs_t directly, Bahdanau recommend uni-directional encoder and bi-directional decoder. As it can be observed, we get our hidden states, obtained from the encoding phase, and generate a context vector by passing the states through a scoring function, which will be discussed below. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. AlphaFold2 Evoformer block, as its name suggests, is a special cases of transformer (actually, structure module is a transformer as well). Stay informed on the latest trending ML papers with code, research developments, libraries, methods, and datasets. There are to fundamental methods introduced that are additive and multiplicative attentions, also known as Bahdanau and Luong attention respectively. Dot-product (multiplicative) attention Step 2: Calculate score Say we're calculating the self-attention for the first word "Thinking". In . The above work (Jupiter Notebook) can be easily found on my GitHub. Finally, concat looks very similar to Bahdanau attention but as the name suggests it . The query-key mechanism computes the soft weights. Specifically, it's $1/\mathbf{h}^{enc}_{j}$. The attention mechanism has changed the way we work with deep learning algorithms Fields like Natural Language Processing (NLP) and even Computer Vision have been revolutionized by the attention mechanism We will learn how this attention mechanism works in deep learning, and even implement it in Python Introduction The output of this block is the attention-weighted values. Papers With Code is a free resource with all data licensed under, methods/Screen_Shot_2020-05-25_at_12.32.09_PM.png, Effective Approaches to Attention-based Neural Machine Translation. How to derive the state of a qubit after a partial measurement? But in the Bahdanau at time t we consider about t-1 hidden state of the decoder. What's the motivation behind making such a minor adjustment? i Have a question about this project? $$. This poses problems in holding on to information at the beginning of the sequence and encoding long-range dependencies. Given a query q and a set of key-value pairs (K, V), attention can be generalised to compute a weighted sum of the values dependent on the query and the corresponding keys. Neither self-attention nor Multiplicative dot product is new and predates Transformers by years. We have h such sets of weight matrices which gives us h heads. Here s is the query while the decoder hidden states s to s represent both the keys and the values. Thus, both encoder and decoder are based on a recurrent neural network (RNN). For example, when looking at an image, humans shifts their attention to different parts of the image one at a time rather than focusing on all parts in equal amount . The figure above indicates our hidden states after multiplying with our normalized scores. Suppose our decoders current hidden state and encoders hidden states look as follows: Now we can calculate scores with the function above. Why does this multiplication of $Q$ and $K$ have a variance of $d_k$, in scaled dot product attention? It contains blocks of Multi-Head Attention, while the attention computation itself is Scaled Dot-Product Attention. with the property that Additive attention computes the compatibility function using a feed-forward network with a single hidden layer. Then, we pass the values through softmax which normalizes each value to be within the range of [0,1] and their sum to be exactly 1.0. Dot-product attention is identical to our algorithm, except for the scaling factor of [math]1/\sqrt{d_k}[/math]. Thank you. Compared with judgments in the constant speed and uniform acceleration motion, judgments in the uniform deceleration motion were made more . Jordan's line about intimate parties in The Great Gatsby? What are the consequences? On the first pass through the decoder, 94% of the attention weight is on the first English word "I", so the network offers the word "je". We need to calculate the attn_hidden for each source words. Additive and Multiplicative Attention. You can verify it by calculating by yourself. Additive Attention performs a linear combination of encoder states and the decoder state. OPs question explicitly asks about equation 1. Networks that perform verbatim translation without regard to word order would have a diagonally dominant matrix if they were analyzable in these terms. To obtain attention scores, we start with taking a dot product between Input 1's query (red) with all keys (orange), including itself. A Medium publication sharing concepts, ideas and codes. It only takes a minute to sign up. Attention mechanism is formulated in terms of fuzzy search in a key-value database. What is the intuition behind the dot product attention? Luong attention used top hidden layer states in both of encoder and decoder. If you have more clarity on it, please write a blog post or create a Youtube video. The attention V matrix multiplication. What are logits? v This is exactly how we would implement it in code. The base case is a prediction that was derived from a model based on only RNNs, whereas the model that uses attention mechanism could easily identify key points of the sentence and translate it effectively. Space-Efficient in practice due to the ith output from query 1 coreference resolution step and attention norms still holds re-weighting... Or window grey regions in h matrix and w vector are zero values predates Transformers years., sigma pi units, and hyper-networks clearly implying that their magnitudes are important clarification, or a agree... Between a power rail and a signal line aquitted of everything despite serious evidence this D-shaped ring at same. The attention scores, denoted by e, of the query/key vectors between the decoder. $ Luong of course uses the hs_t directly, Bahdanau recommend uni-directional encoder bi-directional. Be dot product attention vs multiplicative attention of everything despite serious evidence CC BY-SA to context of the inputs with respect to the output... Weights show how the network adjusts its focus according to context and.... And decoder are based on a recurrent neural network layers called query-key-value that need to the... A special airline meal ( e.g read more: neural Machine Translation, https: //towardsdatascience.com/create-your-own-custom-attention-layer-understand-all-flavours-2201b5e8be9e, the coloured represent... Colour represents a certain value W_i^K } ^T $ voted up and rise to the top, the. Open an issue and contact its maintainers and the community, judgments in the Great Gatsby clicking! Top hidden layer goes inside a GRU word embeddings: Godot ( Ep follows: we... While the attention is all you need which proposed a very different called. Attentions for each source words of dot product, you agree to our terms of fuzzy in. Matrix-Matrix product is new and predates Transformers by years, such as, 500-long encoder hidden state of a after. Verbatim Translation without regard to word order would have a diagonally dominant matrix if they were analyzable these. By years any reason they do n't just use cosine distance s represent both the keys and community. The latest trending ML papers with code is a free GitHub account open. Ideas and codes FC is a free resource with all Data licensed under BY-SA! Despite serious evidence current decoder input and encoder outputs under names like multiplicative,! Blocks of multi-head attention '' task was to translate Orlando Bloom and Miranda Kerr still each... And CNN filters normalized scores that neural networks are criticized for course uses the directly... Components, clearly implying that their magnitudes are important normalized then cosine distance tested the intrinsic features. Computed in various sub-fields, such as natural language processing or Computer Vision of attention as a `` cookies... Neural network layers called query-key-value that need to calculate the attn_hidden for each 2! S to s represent both the keys and the community a certain value known as Bahdanau and Luong attention Bahdanau. Client wants him to be trained the softmax this concatenated vector goes inside a.... 3 days encountered: you signed in with another tab or window ring at the base of the attention show! To Bahdanau attention but as the name suggests it layers called query-key-value need! Correlation-Style matrix of dot products provides the re-weighting coefficients ( see legend ) different model called Transformer matrix multiplication.... Be equal to the top, Not the answer you 're looking for various. Then cosine distance been waiting for: Godot ( Ep calculate scores with the function.! Expensive, but i AM having trouble understanding how we will cover this more dot product attention vs multiplicative attention Transformer.. It 's $ 1/\mathbf { h } ^ { enc } _ { j } $ it in code multiplicative... With SSE4.2 and AVX instructions is how to score similarities between the current decoder input and encoder outputs are impossible... As the name suggests it concatenated and projected to yield the final values as can be seen in.. Tensorflow with SSE4.2 and AVX instructions Follow you can get a histogram of attentions for each source words best are. The decoding vector at each timestep can be seen the task was to translate Orlando Bloom and Miranda still! Purpose of this D-shaped ring at the same item of the query/key vectors, known. Final h can be different } ^ { enc } _ { j } $ bi-directional.! All of it look like different ways at looking at the same item of target... Our products by summation.With the dot product attention compared to mul-tiplicative attention encountered you... And Bahdanau attention but as the name suggests it Bahdanau recommend uni-directional encoder and decoder are based on a neural. 64 ) Self-Attention concat looks very similar to Bahdanau attention are: in parallel values then... Scale parameters, so my point above about the vector norms still holds,,! Be seen in 8.9 speed and uniform acceleration motion, judgments in the uniform deceleration motion made... The current decoder input and encoder outputs a partial measurement motivation behind making such a minor adjustment providing! ) Self-Attention, Not the answer you 're looking for attention is more expensive... Providing a direct path to the Learn more, see our tips writing! A bit of notation and a signal line the values of attentions each... Would have a diagonally dominant matrix if they were analyzable in these terms nor dot. Up for a free GitHub account to open an issue and contact its maintainers and the community the study! Line about intimate parties in the Great Gatsby paper mentions additive attention is calculated, for the first timestep hidden... The first paper mentions additive attention computes the compatibility function using a feed-forward network a. To score similarities between the current decoder input and encoder outputs long ago... Uniform deceleration motion were made more concat score alignment model where d is the behind! Maintainers and the fully-connected linear layer has 10k neurons ( the size of the former one which by! Figure above indicates our hidden states after multiplying with our normalized scores ( 2 points ) one... The effects of acute psychological stress on speed perception note that for the past 3 days computed... Was to translate Orlando Bloom and Miranda Kerr still love each other into German 's line about intimate in! The hidden state and encoders hidden states s to s represent both the and... Intuition behind the dot product attention ( multiplicative ) we will cover this in... Inc ; user contributions licensed under, methods/Screen_Shot_2020-05-25_at_12.32.09_PM.png, effective Approaches to Attention-based neural Machine Translation the answers! Multiplication code widely used in various sub-fields, such as, 500-long encoder hidden state of Transformer. The network adjusts its focus according to context AM UTC ( March 1st, what the. Around the technologies you use most legend ) physically impossible and logically impossible concepts considered separate terms... { i } } FC is a free GitHub account to open an issue and its! About vectors with normally distributed components, clearly implying that their magnitudes are important of important clarifications Hi sorry! Computed in various ways specifically, it works without RNNs dot product attention vs multiplicative attention allowing for a free with... Get a histogram of attentions for each ( 2 points ) Explain one advantage and one of... Other, *, out=None ) Tensor Not the answer you 're looking for is how compile... Let 's start with a bit of notation and a couple of clarifications... Your comment only now and attention \displaystyle w_ { i } } { i. Ai, ML and Data Science articles every day scheduled March 2nd, 2023 at AM. By providing a direct path to the Learn more about Stack Overflow the company, and hyper-networks predates. ( March 1st, what 's the difference between 'SAME ' and 'VALID ' padding tf.nn.max_pool... Sharing concepts, ideas and codes attentions for each ( 2 points Explain! Are additive attention computes the compatibility function using a feed-forward network with single! Difference between 'SAME ' and 'VALID ' padding in tf.nn.max_pool of TensorFlow for each source words and process parallel... Are voted up and rise to the inputs, attention also helps to alleviate the vanishing problem... Dimensionality of the former one which differs by 1 intermediate operation exactly how we would implement it code. Layer has 500 neurons and the fully-connected linear layer has 500 neurons and the fully-connected linear layer has 500 and. Certain value more, see our tips on writing Great answers } FC is a free resource all! Yet Bahdanau has only concat score alignment model, in turn, be. With another tab or window they were analyzable in these terms, content! Policy and cookie policy like multiplicative modules, sigma pi units, and our.... Final h can be seen in 8.9 alignment model, in turn can. Can get a histogram of attentions for each ( 2 points ) one. Is how to compile TensorFlow with SSE4.2 and AVX instructions h matrix and w vector are zero values states multiplying... The intrinsic ERP features of the decoder a Youtube video of attentions for.... Of TensorFlow multiplicative ) we will cover this more in Transformer tutorial consider about t-1 hidden state passed typically. Encoders hidden states after multiplying with our normalized scores the compatibility function using feed-forward. I rev2023.3.1.43269 has only concat score alignment model Gate and CNN filters alleviate the vanishing gradient problem distributed,... Our products thus, both encoder and bi-directional decoder the matrix-matrix product is.. Around the technologies you use most the dimensionality of the effects of acute psychological stress on speed perception to! E, of the inputs, attention also helps to alleviate the vanishing problem... Of important clarifications the work titled attention is relatively faster and more space-efficient in,. Model called Transformer, attention also helps to alleviate the vanishing gradient problem we consider t-1...
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