<p>There are a lot of ways to answer this question. The answer depends on your interpretation of phrases and sentences.</p>

<p>These distributional models such as <code>word2vec</code> which provide vector representation for each word can only show how a word usually is used in a window-base context in relation with other words. Based on this interpretation of context-word relations, you can take average vector of all words in a sentence as vector representation of the sentence. For example, in this sentence:</p>

<blockquote>
  <p>vegetarians eat vegetables .</p>
</blockquote>

<p><img src="https://chart.googleapis.com/chart?cht=tx&amp;chl=v_s%20%3D%20v(%60%60vegetarians%22)%20%2B%20v(%60%60eat%22)%20%2B%20v(%60%60vegrables%22)" alt="V_s"></p>

<p>We can take the normalised vector as vector representation:</p>

<p><img src="https://chart.googleapis.com/chart?cht=tx&amp;chl=v(%60%60vegetarians%5C%20eat%5C%20vegrables%22)%20%3D%20%5Cfrac%7Bv_s%7D%7B%7C%7Cv_s%7C%7C%7D" alt="V(sentence)"></p>

<p>The problem is in compositional nature of sentences. If you take the average word vectors as above, these two sentences have the same vector representation:</p>

<blockquote>
  <p>vegetables eat vegetarians .</p>
</blockquote>

<p>There are a lot of researches in distributional fashion to learn tree structures through corpus processing. For example: <a href="http://www.socher.org/index.php/Main/ParsingWithCompositionalVectorGrammars">Parsing With Compositional Vector Grammars</a>. This <a href="https://www.youtube.com/watch?v=NJozqoejJnA">video</a> also explain this method.</p>

<p>Again I want to emphasise on interpretation. These sentence vectors probably have their own meanings in your application. For instance, in sentiment analysis in <a href="http://nlp.stanford.edu/sentiment/">this project in Stanford</a>, the meaning that they are seeking is the positive/negative sentiment of a sentence. Even if you find a perfect vector representation for a sentence, there are philosophical debates that these are not actual meanings of sentences if you cannot judge the truth condition (David Lewis "General Semantics" 1970). That's why there are lines of works focusing on computer vision (<a href="http://arxiv.org/pdf/1501.02598.pdf">this paper</a> or <a href="http://nlp.stanford.edu/~socherr/SocherKarpathyLeManningNg_TACL2013.pdf">this paper</a>). My point is that it can completely depend on your application and interpretation of vectors.</p>
How can a sentence or a document be converted to a vector?
<p>We have models for converting words to vectors (for example the word2vec model). Do similar models exist which convert sentences/documents into vectors, using perhaps the vectors learnt for the individual words?</p>