<p>The word2vec model uses a network architecture to represent the input word(s) and most likely associated output word(s).</p>

<p>Assuming there is one hidden layer (as in the example linked in the question), the two matrices introduced represent the weights and biases that allow the network to compute its internal representation of the function mapping the input vector (e.g. “cat” in the linked example) to the output vector (e.g. “climbed”).</p>

<p>The weights of the network are a sub-symbolic representation of the mapping between the input and the output – any single weight doesn’t necessarily represent anything meaningful on its own. It’s the connection weights between all units (i.e. the interactions of all the weights) in the network that gives rise to the network’s representation of the function mapping. This is why neural networks are often referred to as “black box” models – it can be very difficult to interpret why they make particular decisions and how they learn. As such, it's very difficult to say what the vector [0.3,0.01,0.04] represents exactly.</p>

<p>Network weights are traditionally initialised to random values for two main reasons:</p>

<ol>
<li>It prevents a bias being introduced to the model before training begins</li>
<li>It allows the network to start from different points in the search space after initialisation (helping reduce the impact of local minima)</li>
</ol>

<p>A network’s ability to learn can be very sensitive to the way its weights are initialised. There are more advanced ways of initialising weights today e.g. <a href="http://arxiv.org/pdf/1206.5533v2.pdf" rel="nofollow">this paper (see section: Weights initialization scaling coefficient)</a>.</p>

<p>The way in which weights are initialised and the dimension of the hidden layer are often referred to as hyper-parameters and are typically chosen according to heuristics and prior knowledge of the problem space.</p>
Where do dimensions in Word2Vec come from?
<p>I am using word2vec model for training a neural network and building a neural embedding for finding the similar words on the vector space. But my question is about dimensions in the word and context embeddings (matrices), which we initialise them by random numbers(vectors) at the beginning of the training, like this <a href="https://iksinc.wordpress.com/2015/04/13/words-as-vectors/" rel="nofollow">https://iksinc.wordpress.com/2015/04/13/words-as-vectors/</a></p>

<p>Lets say we want to display {book,paper,notebook,novel} words on a graph, first of all we should build a matrix with this dimensions 4x2 or 4x3 or 4x4 etc, I know the first dimension of the matrix its the size of our vocabulary |v|. But the second dimension of the matrix (number of vector's dimensions), for example this is a vector for word “book"  [0.3,0.01,0.04], what are these numbers? do they have any meaning? for example the 0.3 number related to the relation between word “book" and “paper” in the vocabulary, the 0.01 is the relation between book and notebook, etc.
Just like TF-IDF, or Co-Occurence matrices that each dimension (column) Y has a meaning - its a word or document related to the word in row X.</p>