# What does tf.nn.embedding_lookup function do?

## Question:

``````tf.nn.embedding_lookup(params, ids, partition_strategy='mod', name=None)
``````

I cannot understand the duty of this function. Is it like a lookup table? Which means to return the parameters corresponding to each id (in ids)?

For instance, in the `skip-gram` model if we use `tf.nn.embedding_lookup(embeddings, train_inputs)`, then for each `train_input` it finds the correspond embedding?

`embedding_lookup` function retrieves rows of the `params` tensor. The behavior is similar to using indexing with arrays in numpy. E.g.

``````matrix = np.random.random([1024, 64])  # 64-dimensional embeddings
ids = np.array([0, 5, 17, 33])
print matrix[ids]  # prints a matrix of shape [4, 64]
``````

`params` argument can be also a list of tensors in which case the `ids` will be distributed among the tensors. For example, given a list of 3 tensors `[2, 64]`, the default behavior is that they will represent `ids`: `[0, 3]`, `[1, 4]`, `[2, 5]`.

`partition_strategy` controls the way how the `ids` are distributed among the list. The partitioning is useful for larger scale problems when the matrix might be too large to keep in one piece.

Yes, this function is hard to understand, until you get the point.

In its simplest form, it is similar to `tf.gather`. It returns the elements of `params` according to the indexes specified by `ids`.

For example (assuming you are inside `tf.InteractiveSession()`)

``````params = tf.constant([10,20,30,40])
ids = tf.constant([0,1,2,3])
print tf.nn.embedding_lookup(params,ids).eval()
``````

would return `[10 20 30 40]`, because the first element (index 0) of params is `10`, the second element of params (index 1) is `20`, etc.

Similarly,

``````params = tf.constant([10,20,30,40])
ids = tf.constant([1,1,3])
print tf.nn.embedding_lookup(params,ids).eval()
``````

would return `[20 20 40]`.

But `embedding_lookup` is more than that. The `params` argument can be a list of tensors, rather than a single tensor.

``````params1 = tf.constant([1,2])
params2 = tf.constant([10,20])
ids = tf.constant([2,0,2,1,2,3])
result = tf.nn.embedding_lookup([params1, params2], ids)
``````

In such a case, the indexes, specified in `ids`, correspond to elements of tensors according to a partition strategy, where the default partition strategy is ‘mod’.

In the ‘mod’ strategy, index 0 corresponds to the first element of the first tensor in the list. Index 1 corresponds to the first element of the second tensor. Index 2 corresponds to the first element of the third tensor, and so on. Simply index `i` corresponds to the first element of the (i+1)th tensor , for all the indexes `0..(n-1)`, assuming params is a list of `n` tensors.

Now, index `n` cannot correspond to tensor n+1, because the list `params` contains only `n` tensors. So index `n` corresponds to the second element of the first tensor. Similarly, index `n+1` corresponds to the second element of the second tensor, etc.

So, in the code

``````params1 = tf.constant([1,2])
params2 = tf.constant([10,20])
ids = tf.constant([2,0,2,1,2,3])
result = tf.nn.embedding_lookup([params1, params2], ids)
``````

index 0 corresponds to the first element of the first tensor: 1

index 1 corresponds to the first element of the second tensor: 10

index 2 corresponds to the second element of the first tensor: 2

index 3 corresponds to the second element of the second tensor: 20

Thus, the result would be:

``````[ 2  1  2 10  2 20]
``````

`params` is
interpreted as a partitioning of a large embedding tensor. It can be a single tensor representing the complete embedding tensor,
or a list of X tensors all of same shape except for the first dimension,
representing sharded embedding tensors.

The function `tf.nn.embedding_lookup` is written considering the fact that embedding (params) will be large. Therefore we need `partition_strategy`.

Another way to look at it is , assume that you flatten out the tensors to one dimensional array, and then you are performing a lookup

(eg) Tensor0=[1,2,3], Tensor1=[4,5,6], Tensor2=[7,8,9]

The flattened out tensor will be as follows
[1,4,7,2,5,8,3,6,9]

Now when you do a lookup of [0,3,4,1,7] it will yeild [1,2,5,4,6]

(i,e) if lookup value is 7 for example , and we have 3 tensors (or a tensor with 3 rows) then,

7 / 3 : (Reminder is 1, Quotient is 2) So 2nd element of Tensor1 will be shown, which is 6

When the params tensor is in high dimensions, the ids only refers to top dimension. Maybe it’s obvious to most of people but I have to run the following code to understand that:

``````embeddings = tf.constant([[[1,1],[2,2],[3,3],[4,4]],[[11,11],[12,12],[13,13],[14,14]],
[[21,21],[22,22],[23,23],[24,24]]])
ids=tf.constant([0,2,1])
embed = tf.nn.embedding_lookup(embeddings, ids, partition_strategy='div')

with tf.Session() as session:
result = session.run(embed)
print (result)
``````

Just trying the ‘div’ strategy and for one tensor, it makes no difference.

Here is the output:

``````[[[ 1  1]
[ 2  2]
[ 3  3]
[ 4  4]]

[[21 21]
[22 22]
[23 23]
[24 24]]

[[11 11]
[12 12]
[13 13]
[14 14]]]
``````

Yes, the purpose of `tf.nn.embedding_lookup()` function is to perform a lookup in the embedding matrix and return the embeddings (or in simple terms the vector representation) of words.

A simple embedding matrix (of shape: `vocabulary_size x embedding_dimension`) would look like below. (i.e. each word will be represented by a vector of numbers; hence the name word2vec)

Embedding Matrix

``````the 0.418 0.24968 -0.41242 0.1217 0.34527 -0.044457 -0.49688 -0.17862
like 0.36808 0.20834 -0.22319 0.046283 0.20098 0.27515 -0.77127 -0.76804
between 0.7503 0.71623 -0.27033 0.20059 -0.17008 0.68568 -0.061672 -0.054638
did 0.042523 -0.21172 0.044739 -0.19248 0.26224 0.0043991 -0.88195 0.55184
just 0.17698 0.065221 0.28548 -0.4243 0.7499 -0.14892 -0.66786 0.11788
national -1.1105 0.94945 -0.17078 0.93037 -0.2477 -0.70633 -0.8649 -0.56118
day 0.11626 0.53897 -0.39514 -0.26027 0.57706 -0.79198 -0.88374 0.30119
country -0.13531 0.15485 -0.07309 0.034013 -0.054457 -0.20541 -0.60086 -0.22407
under 0.13721 -0.295 -0.05916 -0.59235 0.02301 0.21884 -0.34254 -0.70213
such 0.61012 0.33512 -0.53499 0.36139 -0.39866 0.70627 -0.18699 -0.77246
second -0.29809 0.28069 0.087102 0.54455 0.70003 0.44778 -0.72565 0.62309
``````

I split the above embedding matrix and loaded only the words in `vocab` which will be our vocabulary and the corresponding vectors in `emb` array.

``````vocab = ['the','like','between','did','just','national','day','country','under','such','second']

emb = np.array([[0.418, 0.24968, -0.41242, 0.1217, 0.34527, -0.044457, -0.49688, -0.17862],
[0.36808, 0.20834, -0.22319, 0.046283, 0.20098, 0.27515, -0.77127, -0.76804],
[0.7503, 0.71623, -0.27033, 0.20059, -0.17008, 0.68568, -0.061672, -0.054638],
[0.042523, -0.21172, 0.044739, -0.19248, 0.26224, 0.0043991, -0.88195, 0.55184],
[0.17698, 0.065221, 0.28548, -0.4243, 0.7499, -0.14892, -0.66786, 0.11788],
[-1.1105, 0.94945, -0.17078, 0.93037, -0.2477, -0.70633, -0.8649, -0.56118],
[0.11626, 0.53897, -0.39514, -0.26027, 0.57706, -0.79198, -0.88374, 0.30119],
[-0.13531, 0.15485, -0.07309, 0.034013, -0.054457, -0.20541, -0.60086, -0.22407],
[ 0.13721, -0.295, -0.05916, -0.59235, 0.02301, 0.21884, -0.34254, -0.70213],
[ 0.61012, 0.33512, -0.53499, 0.36139, -0.39866, 0.70627, -0.18699, -0.77246 ],
[ -0.29809, 0.28069, 0.087102, 0.54455, 0.70003, 0.44778, -0.72565, 0.62309 ]])

emb.shape
# (11, 8)
``````

Embedding Lookup in TensorFlow

Now we will see how can we perform embedding lookup for some arbitrary input sentence.

``````In [54]: from collections import OrderedDict

# embedding as TF tensor (for now constant; could be tf.Variable() during training)
In [55]: tf_embedding = tf.constant(emb, dtype=tf.float32)

# input for which we need the embedding
In [56]: input_str = "like the country"

# build index based on our `vocabulary`
In [57]: word_to_idx = OrderedDict({w:vocab.index(w) for w in input_str.split() if w in vocab})

# lookup in embedding matrix & return the vectors for the input words
In [58]: tf.nn.embedding_lookup(tf_embedding, list(word_to_idx.values())).eval()
Out[58]:
array([[ 0.36807999,  0.20834   , -0.22318999,  0.046283  ,  0.20097999,
0.27515   , -0.77126998, -0.76804   ],
[ 0.41800001,  0.24968   , -0.41242   ,  0.1217    ,  0.34527001,
-0.044457  , -0.49687999, -0.17862   ],
[-0.13530999,  0.15485001, -0.07309   ,  0.034013  , -0.054457  ,
-0.20541   , -0.60086   , -0.22407   ]], dtype=float32)
``````

Observe how we got the embeddings from our original embedding matrix (with words) using the indices of words in our vocabulary.

Usually, such an embedding lookup is performed by the first layer (called Embedding layer) which then passes these embeddings to RNN/LSTM/GRU layers for further processing.

Side Note: Usually the vocabulary will also have a special `unk` token. So, if a token from our input sentence is not present in our vocabulary, then the index corresponding to `unk` will be looked up in the embedding matrix.

P.S. Note that `embedding_dimension` is a hyperparameter that one has to tune for their application but popular models like Word2Vec and GloVe uses `300` dimension vector for representing each word.

Since I was also intrigued by this function, I’ll give my two cents.

The way I see it in the 2D case is just as a matrix multiplication (it’s easy to generalize to other dimensions).

Consider a vocabulary with N symbols.
Then, you can represent a symbol x as a vector of dimensions Nx1, one-hot-encoded.

But you want a representation of this symbol not as a vector of Nx1, but as one with dimensions Mx1, called y.

So, to transform x into y, you can use and embedding matrix E, with dimensions MxN:

y = E x.

This is essentially what tf.nn.embedding_lookup(params, ids, …) is doing, with the nuance that ids are just one number that represents the position of the 1 in the one-hot-encoded vector x.

Here’s an image depicting the process of embedding lookup.

Concisely, it gets the corresponding rows of a embedding layer, specified by a list of IDs and provide that as a tensor. It is achieved through the following process.

1. Define a placeholder `lookup_ids = tf.placeholder([10])`
2. Define a embedding layer `embeddings = tf.Variable([100,10],...)`
3. Define the tensorflow operation `embed_lookup = tf.embedding_lookup(embeddings, lookup_ids)`
4. Get the results by running `lookup = session.run(embed_lookup, feed_dict={lookup_ids:[95,4,14]})`

The existing explanations are not enough.
The main purpose of this function is to efficiently retrieve the vectors for each word in a given sequence of word indices. Suppose we have the following matrix of embeddings:

``````embds = np.array([[0.2, 0.32,0.9],
[0.8, 0.62,0.19],
[0.0, -0.22,-1.9],
[1.2, 2.32,6.0],
[0.11, 0.10,5.9]])
``````

Let’s say we have the following sequences of word indices:

``````data=[[0,1],
[3,4]]
``````

Now to get the corresponding embedding for each word in our data:

``````tf.nn.embedding_lookup(
embds, data
)
``````

out:

``````array([[[0.2 , 0.32, 0.9 ],
[0.8 , 0.62, 0.19]],

[[1.2 , 2.32, 6.  ],
[0.11, 0.1 , 5.9 ]]])>
``````

Note If embds are not an array or tensor, the output will not be like this (I won’t go into details). For example, if embds were a list, the output would be:

``````array([[0.2 , 0.32],
[0.8 , 0.62]], dtype=float32)>
``````
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