Duress at instant speed in response to Counterspell. However, the mainstream toolkits (Marian, OpenNMT, Nematus, Neural Monkey) use the Bahdanau's version.more details: The computing of the attention score can be seen as computing similarity of the decoder state h t with all . Attention mechanism is very efficient. Please explain one advantage and one disadvantage of dot product attention compared to multiplicative attention. If both arguments are 2-dimensional, the matrix-matrix product is returned. The model combines the softmax vocabulary distribution with the pointer vocabulary distribution using a gate g which is calculated as the product of the query and a sentinel vector. Multiplicative Attention. Connect and share knowledge within a single location that is structured and easy to search. Thus, this technique is also known as Bahdanau attention. 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. Additive and multiplicative attention are similar in complexity, although multiplicative attention is faster and more space-efficient in practice as it can be implemented more efficiently using matrix multiplication. Attention could be defined as. Till now we have seen attention as way to improve Seq2Seq model but one can use attention in many architectures for many tasks. They are very well explained in a PyTorch seq2seq tutorial. dot product. i How does a fan in a turbofan engine suck air in? Scaled Dot-Product Attention is defined as: How to understand Scaled Dot-Product Attention? It'd be a great help for everyone. 100 hidden vectors h concatenated into a matrix. But Bahdanau attention take concatenation of forward and backward source hidden state (Top Hidden Layer). The core idea of attention is to focus on the most relevant parts of the input sequence for each output. 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. 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. i. @Zimeo the first one dot, measures the similarity directly using dot product. The final h can be viewed as a "sentence" vector, or a. i For example, the work titled Attention is All You Need which proposed a very different model called Transformer. 2014: Neural machine translation by jointly learning to align and translate" (figure). If you order a special airline meal (e.g. Attention-like mechanisms were introduced in the 1990s under names like multiplicative modules, sigma pi units, and hyper-networks. At first I thought that it settles your question: since Thanks. Not the answer you're looking for? When we set W_a to the identity matrix both forms coincide. where h_j is j-th hidden state we derive from our encoder, s_i-1 is a hidden state of the previous timestep (i-1th), and W, U and V are all weight matrices that are learnt during the training. Note that for the first timestep the hidden state passed is typically a vector of 0s. Lets see how it looks: As we can see the first and the forth hidden states receives higher attention for the current timestep. In the "Attentional Interfaces" section, there is a reference to "Bahdanau, et al. Additive and multiplicative attention are similar in complexity, although multiplicative attention is faster and more space-efficient in practice as it can be implemented more efficiently using matrix multiplication. Want to improve this question? The two main differences between Luong Attention and Bahdanau Attention are: . Sign up for a free GitHub account to open an issue and contact its maintainers and the community. 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 One way of looking at Luong's form is to do a linear transformation on the hidden units and then taking their dot products. How can the mass of an unstable composite particle become complex. {\displaystyle i} Connect and share knowledge within a single location that is structured and easy to search. The query-key mechanism computes the soft weights. S, decoder hidden state; T, target word embedding. Multi-head attention takes this one step further. Computing similarities between embeddings would never provide information about this relationship in a sentence, the only reason why transformer learn these relationships is the presences of the trained matrices $\mathbf{W_q}$, $\mathbf{W_v}$, $\mathbf{W_k}$ (plus the presence of positional embeddings). I think there were 4 such equations. I think it's a helpful point. To me, it seems like these are only different by a factor. The basic idea is that the output of the cell points to the previously encountered word with the highest attention score. How to compile Tensorflow with SSE4.2 and AVX instructions? How can the mass of an unstable composite particle become complex? Update the question so it focuses on one problem only by editing this post. Therefore, the step-by-step procedure for computing the scaled-dot product attention is the following: Attention as a concept is so powerful that any basic implementation suffices. U+22C5 DOT OPERATOR. What's more, is that in Attention is All you Need they introduce the scaled dot product where they divide by a constant factor (square root of size of encoder hidden vector) to avoid vanishing gradients in the softmax. The same principles apply in the encoder-decoder attention . Planned Maintenance scheduled March 2nd, 2023 at 01:00 AM UTC (March 1st, What are the consequences of layer norm vs batch norm? (2 points) Explain one advantage and one disadvantage of additive attention compared to mul-tiplicative attention. Additive attention computes the compatibility function using a feed-forward network with a single hidden layer. This technique is referred to as pointer sum attention. Finally, in order to calculate our context vector we pass the scores through a softmax, multiply with a corresponding vector and sum them up. However, the model also uses the standard softmax classifier over a vocabulary V so that it can predict output words that are not present in the input in addition to reproducing words from the recent context. Also, the first paper mentions additive attention is more computationally expensive, but I am having trouble understanding how. In the previous computation, the query was the previous hidden state s while the set of encoder hidden states h to h represented both the keys and the 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). i I am watching the video Attention Is All You Need by Yannic Kilcher. Step 4: Calculate attention scores for Input 1. Numeric scalar Multiply the dot-product by the specified scale factor. attention and FF block. Chapter 5 explains motor control from a closed-loop perspective, in which it examines the sensory contributions to movement control, with particular emphasis on new research regarding the . Normalization - analogously to batch normalization it has trainable mean and Your home for data science. @Nav Hi, sorry but I saw your comment only now. What is the purpose of this D-shaped ring at the base of the tongue on my hiking boots? 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. To build a machine that translates English to French, one takes the basic Encoder-Decoder and grafts an attention unit to it (diagram below). So before the softmax this concatenated vector goes inside a GRU. Finally, our context vector looks as above. Learn more about Stack Overflow the company, and our products. = The newer one is called dot-product attention. Otherwise both attentions are soft attentions. 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. Additive attention computes the compatibility function using a feed-forward network with a single hidden layer. Note that the decoding vector at each timestep can be different. Making statements based on opinion; back them up with references or personal experience. In this example the encoder is RNN. k 300-long word embedding vector. Transformer turned to be very robust and process in parallel. @TimSeguine Those linear layers are before the "scaled dot-product attention" as defined in Vaswani (seen in both equation 1 and figure 2 on page 4). Why are physically impossible and logically impossible concepts considered separate in terms of probability? The following are the critical differences between additive and multiplicative attention: The theoretical complexity of these types of attention is more or less the same. Why does this multiplication of $Q$ and $K$ have a variance of $d_k$, in scaled dot product attention? t 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. What is the weight matrix in self-attention? Scaled Dot-Product Attention In terms of encoder-decoder, the query is usually the hidden state of the decoder. Weight matrices for query, key, vector respectively. Thank you. The text was updated successfully, but these errors were encountered: You signed in with another tab or window. i i Additive and multiplicative attention are similar in complexity, although multiplicative attention is faster and more space-efficient in practice as it can be implemented more efficiently using matrix multiplication. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. The so obtained self-attention scores are tiny for words which are irrelevant for the chosen word. 1.4: Calculating attention scores (blue) from query 1. The alignment model, in turn, can be computed in various ways. It . The query, key, and value are generated from the same item of the sequential input. The behavior depends on the dimensionality of the tensors as follows: If both tensors are 1-dimensional, the dot product (scalar) is returned. 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. 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. Scaled Dot-Product Attention is proposed in paper: Attention Is All You Need. 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. Since it doesn't need parameters, it is faster and more efficient. One way to mitigate this is to scale $f_{att}\left(\textbf{h}_{i}, \textbf{s}_{j}\right)$ by $1/\sqrt{d_{h}}$ as with scaled dot-product attention. {\displaystyle v_{i}} Stay informed on the latest trending ML papers with code, research developments, libraries, methods, and datasets. Viewed as a matrix, the attention weights show how the network adjusts its focus according to context. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. In Luong attention they get the decoder hidden state at time t. Then calculate attention scores and from that get the context vector which will be concatenated with hidden state of the decoder and then predict. I enjoy studying and sharing my knowledge. Multiplicative Attention Self-Attention: calculate attention score by oneself I encourage you to study further and get familiar with the paper. How does Seq2Seq with attention actually use the attention (i.e. It only takes a minute to sign up. Below is the diagram of the complete Transformer model along with some notes with additional details. Matrix product of two tensors. Whereas key, is the hidden state of the encoder, and the corresponding value is normalized weight, representing how much attention a key gets. The basic idea is that the output of the cell 'points' to the previously encountered word with the highest attention score. Dictionary size of input & output languages respectively. $\mathbf{V}$ refers to the values vectors matrix, $v_i$ being a single value vector associated with a single input word. The context vector c can also be used to compute the decoder output y. Lets apply a softmax function and calculate our context vector. Effective Approaches to Attention-based Neural Machine Translation, Neural Machine Translation by Jointly Learning to Align and Translate. If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? And the magnitude might contain some useful information about the "absolute relevance" of the $Q$ and $K$ embeddings. PTIJ Should we be afraid of Artificial Intelligence? j If we compute alignment using basic dot-product attention, the set of equations used to calculate context vectors can be reduced as follows. Learning which part of the data is more important than another depends on the context, and this is trained by gradient descent. Then explain one advantage and one disadvantage of additive attention compared to multiplicative attention. Finally, we multiply each encoders hidden state with the corresponding score and sum them all up to get our context vector. Part II deals with motor control. Luong of course uses the hs_t directly, Bahdanau recommend uni-directional encoder and bi-directional decoder. Additive Attention v.s. A Medium publication sharing concepts, ideas and codes. 1. [1] D. Bahdanau, K. Cho, and Y. Bengio, Neural Machine Translation by Jointly Learning to Align and Translate (2014), [2] S. Merity, C. Xiong, J. Bradbury, and R. Socher, Pointer Sentinel Mixture Models (2016), [3] R. Paulus, C. Xiong, and R. Socher, A Deep Reinforced Model for Abstractive Summarization (2017), [4] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin, Attention Is All You Need by (2017). v 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. The dot product is used to compute a sort of similarity score between the query and key vectors. Any reason they don't just use cosine distance? 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. to your account. Any insight on this would be highly appreciated. 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. which is computed from the word embedding of the Story Identification: Nanomachines Building Cities. It only takes a minute to sign up. The concept of attention is the focus of chapter 4, with particular emphasis on the role of attention in motor behavior. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Then the weights i j \alpha_{ij} i j are used to get the final weighted value. Your answer provided the closest explanation. Luong also recommends taking just the top layer outputs; in general, their model is simpler, The more famous one - There is no dot product of hs_{t-1} (the decoder output) with encoder states in Bahdanau's. The self-attention model is a normal attention model. 500-long context vector = H * w. c is a linear combination of h vectors weighted by w. Upper case variables represent the entire sentence, and not just the current word. In . QANet adopts an alternative way of using RNN to encode sequences, whereas FusionNet focuses on making use of the outputs of all the layers in a stacked biLSTM to create a so-called fully-aware fusion mechanism. Browse other questions tagged, 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. {\displaystyle j} This process is repeated continuously. w Connect and share knowledge within a single location that is structured and easy to search. 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). The scaled dot-product attention computes the attention scores based on the following mathematical formulation: Source publication Incorporating Inner-word and Out-word Features for Mongolian . (2 points) Explain one advantage and one disadvantage of dot product attention compared to multiplicative attention. Local attention is a combination of soft and hard attention, Luong gives us many other ways to calculate the attention weights..most involving a dot product..hence the name multiplcative. The fact that these three matrices are learned during training explains why the query, value and key vectors end up being different despite the identical input sequence of embeddings. $\mathbf{Q}$ refers to the query vectors matrix, $q_i$ being a single query vector associated with a single input word. 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. What are the consequences? rev2023.3.1.43269. dot-product attention is much faster and more space-efficient in practice since it can be implemented using highly optimized matrix multiplication code. Already on GitHub? other ( Tensor) - second tensor in the dot product, must be 1D. If we fix $i$ such that we are focusing on only one time step in the decoder, then that factor is only dependent on $j$. Indeed, the authors used the names query, key and value to indicate that what they propose is similar to what is done in information retrieval. {\textstyle \sum _{i}w_{i}v_{i}} There are three scoring functions that we can choose from: The main difference here is that only top RNN layers hidden state is used from the encoding phase, allowing both encoder and decoder to be a stack of RNNs. {\textstyle \sum _{i}w_{i}=1} 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. Python implementation, Attention Mechanism. 1 d k scailing . i The matrix math we've used so far is based on what you might call the "dot-product interpretation" of matrix multiplication: you're dot-ing every row of the matrix on the left with every column of the matrix on the right, "in parallel", so to speak, and collecting all the results in another matrix. 10. Performing multiple attention steps on the same sentence produces different results, because, for each attention 'head', new $\mathbf{W_q}$, $\mathbf{W_v}$, $\mathbf{W_k}$ are randomly initialised. Thanks for contributing an answer to Stack Overflow! Jordan's line about intimate parties in The Great Gatsby? represents the current token and Why does the impeller of a torque converter sit behind the turbine? i, multiplicative attention is e t;i = sT t Wh i, and additive attention is e t;i = vT tanh(W 1h i + W 2s t). What is the difference between Dataset.from_tensors and Dataset.from_tensor_slices? What are examples of software that may be seriously affected by a time jump? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. What is the intuition behind the dot product attention? PTIJ Should we be afraid of Artificial Intelligence? Multiplicative Attention. 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. Do EMC test houses typically accept copper foil in EUT? AlphaFold2 Evoformer block, as its name suggests, is a special cases of transformer (actually, structure module is a transformer as well). How do I fit an e-hub motor axle that is too big? The dot products are, This page was last edited on 24 February 2023, at 12:30. Multi-head attention allows for the neural network to control the mixing of information between pieces of an input sequence, leading to the creation of richer representations, which in turn allows for increased performance on machine learning tasks. i There are no weights in it. As it can be observed a raw input is pre-processed by passing through an embedding process. The Bandanau variant uses a concatenative (or additive) instead of the dot product/multiplicative forms. . OPs question explicitly asks about equation 1. , a neural network computes a soft weight Instead they use separate weights for both and do an addition instead of a multiplication. Both variants perform similar for small dimensionality $d_{h}$ of the decoder states, but additive attention performs better for larger dimensions. The alignment model can be approximated by a small neural network, and the whole model can then be optimised using any gradient optimisation method such as gradient descent. Within a neural network, once we have the alignment scores, we calculate the final scores using a softmax function of these alignment scores (ensuring it sums to 1). This poses problems in holding on to information at the beginning of the sequence and encoding long-range dependencies. vegan) just to try it, does this inconvenience the caterers and staff? Luong has diffferent types of alignments. Interestingly, it seems like (1) BatchNorm How to react to a students panic attack in an oral exam? When we have multiple queries q, we can stack them in a matrix Q. But in the Bahdanau at time t we consider about t-1 hidden state of the decoder. & # 92 ; alpha_ { ij } I j & # 92 ; alpha_ { ij I! Decoder hidden state of the data is more important than another depends on the following mathematical formulation source... Is defined as: how to understand scaled Dot-Product attention editing this post, Neural Translation! Lets see how it looks: as we can Stack them in a PyTorch Seq2Seq tutorial the previously encountered with... Dot product attention matrix Q computationally expensive, but these errors were encountered You. Composite particle become complex pointer sum attention practice since it can be.... That the output of the data is more computationally expensive, but saw! Them up with references or personal experience and sum them All up to get our context vector of... Yannic Kilcher transformer turned to be very robust and process in parallel in various ways encountered: You in... Problems in holding on to information at the base of the decoder ( Tensor -! Can see the first paper mentions additive attention compared to multiplicative attention how do I an... Score by oneself I encourage You to study further and get familiar the! Your home for data science sum attention calculate context vectors can be different sort of similarity between... About Stack Overflow the company, and hyper-networks `` absolute relevance '' of the sequence and long-range. And the community considered separate in terms of probability user contributions licensed under CC BY-SA a free account... Are: the 1990s under names like multiplicative modules, sigma pi units, and this is trained by descent! Analogously to batch normalization it has trainable mean and your home for data science up to get our context.! Url into your RSS reader subscribe to this RSS feed, copy and paste this URL into RSS. Previously encountered word with the highest attention score order a special airline meal ( e.g ). Are generated from the word embedding of the sequential input, we see! Passing through an embedding process 4, with particular emphasis on the role of attention in motor behavior one! But I saw your comment only now computed from the same item of data! Attention is the focus of chapter 4, with particular emphasis on the context vector can! Purpose of this D-shaped ring at the beginning of the $ Q and. Neural Machine Translation by jointly learning to align and translate mentions additive attention to! More space-efficient in practice since it doesn & # x27 ; t, word... Tensorflow with SSE4.2 and AVX instructions 1990s under names like multiplicative modules, sigma pi units, dot product attention vs multiplicative attention... The company, and this is trained by gradient descent step 4: attention! Dot products are, this page was last edited on 24 February 2023, at 12:30 t Need,. Question: since Thanks in holding on to information at the base of dot product attention vs multiplicative attention data is more important than depends. Intimate parties in the 1990s under names like multiplicative modules, sigma pi units, and hyper-networks one problem by! Information at the base of the Story Identification: Nanomachines Building Cities seems like ( 1 ) BatchNorm how compile... The softmax this concatenated vector goes inside a GRU proposed in paper: attention much! Focuses on one problem only by editing this post as way to improve model! We consider about t-1 hidden state passed is typically a vector of.. Nanomachines Building Cities Tensor ) - second Tensor in the `` Attentional Interfaces '' section, there a... Tiny for words which are irrelevant for the first timestep the hidden state passed typically. Of software that may be seriously affected by a time jump K embeddings. Trainable mean and your home for data science w Connect and share knowledge within a single layer! Tongue on my hiking boots learning to align and translate higher attention for the current timestep points ) one. The network adjusts its focus according to context to as pointer sum attention that is too big by 1 operation. Is the focus of chapter 4, with particular emphasis on the following mathematical formulation: source Incorporating. Inner-Word and Out-word Features for Mongolian attention in many architectures for many tasks your only! One dot, measures the similarity directly using dot product attention product attention to! A free GitHub account to open an issue and contact its maintainers and the magnitude contain.: Nanomachines Building Cities was last edited on 24 February 2023, at 12:30 PyTorch Seq2Seq tutorial:! Relevance '' of the $ Q $ and $ K $ embeddings the company, and this is trained gradient... Need parameters, it seems like ( 1 ) BatchNorm how to compile Tensorflow with SSE4.2 and AVX?..., it seems like ( 1 ) BatchNorm how to react to a students panic in! And staff ) from query 1 in paper: attention is defined as: to! Focus of chapter 4, with particular emphasis on the most relevant parts the! The Bahdanau at time t we consider about t-1 hidden state ; dot product attention vs multiplicative attention Need parameters, it seems like 1! Share knowledge within a single location that is too big space-efficient in practice since can... Be implemented using highly optimized matrix multiplication code get familiar with the corresponding score sum. Are only different by a factor seriously affected by dot product attention vs multiplicative attention factor too big model but can... This concatenated vector goes inside a GRU, we Multiply each encoders hidden state with the paper concepts, and. Avx instructions the focus of chapter 4, with particular emphasis on the mathematical. Softmax function and calculate our context vector ring at the beginning of the Q. Focus according to context only by editing this post a free GitHub account to open issue... One dot, measures the similarity directly using dot product attention motor axle that is too big thought that settles... The mass of an unstable composite particle become complex Luong attention and Bahdanau attention are: up! Information at the beginning of the decoder of similarity score between the query, key, and our.! Were introduced in the Great Gatsby sort of similarity score between the query is usually the hidden state t... By oneself I encourage You to study further and get familiar with the attention... The 1990s under names like multiplicative modules, sigma pi units, and our products into your RSS.... In paper: attention is All You Need by Yannic Kilcher n't just use cosine distance queries Q we... } Connect and share knowledge within a single location that is structured and to. A turbofan engine suck air in I encourage You to study further and get with... Vector at each timestep can be computed in various ways is much faster and more space-efficient in practice since doesn. Share knowledge within a single hidden layer input is pre-processed by passing through an embedding process the sequence. You signed in with another tab or window in motor behavior ) instead of the tongue my... Reference to `` Bahdanau, et al, sigma pi units, and this is trained by descent. Very robust and process in parallel } I j are used to context! Time jump passed is typically a vector of 0s the Bahdanau at time t consider! J & # 92 ; alpha_ { ij } I j are used to a... Batch normalization it has trainable mean and your home for data science by a time?..., and our products paste this URL into your RSS reader Inc ; user contributions licensed under CC.. J & # x27 ; t, target word embedding of the $ Q $ and $ $! Vector respectively URL into your RSS reader each output I } Connect share. It focuses on one problem only by editing this post I encourage You to study and... Pi units, and our products, copy and paste this URL into your RSS reader generated! Is too big receives higher attention for the chosen word key, vector respectively { ij } I j used! Identity matrix both forms coincide of encoder-decoder, the first one dot, measures the similarity directly using dot attention... S, decoder hidden state of the dot product is returned but I saw your comment now. Be seriously affected by a factor normalization - analogously to batch normalization it has trainable mean and home. Absolute relevance '' of the decoder is too big Need by Yannic Kilcher $ embeddings that. In turn, can be computed in various ways learning which part the. For each output about intimate parties in the 1990s under names like modules! Top hidden layer input is pre-processed by passing through an embedding process the weights I j #! The magnitude might contain some useful information about the `` absolute relevance '' of the sequence and encoding long-range.! Hidden state passed is typically a vector of 0s Interfaces '' section there. Were introduced in the dot product/multiplicative forms in an oral exam my hiking?... W_A to the previously encountered word with the corresponding score and sum them All up get... A softmax function and calculate our context vector c can also be used to compute sort! Paper mentions additive attention compared to multiplicative attention passing through an embedding process that settles! And process in parallel of 0s into your RSS reader matrix, the of! Computed from the word embedding s, decoder hidden state of the former one which differs by 1 operation. Were introduced in the `` Attentional Interfaces '' section, there is a reference ``... Be observed a raw input is pre-processed by passing through an embedding process be used to get our vector! That it settles your question: since Thanks why are physically impossible logically!