In word2vec, for analogies do we use "in" or "out" vectors? In word2vec each word is associated with two vectors (one for in and one for out) so that it predicts conditional probability:
$$P(word_{out}|word_{in}) = \frac{\exp(v_{in} \cdot \tilde{v}_{out})}{\sum_k \exp(v_{in} \cdot \tilde{v}_{k})}$$
But which one of the vectors ($v_{in}$ or $\tilde{v}_{out}$) is used for analogies (e.g. the famous man - king = woman - queen)?
See:

from Christopher Moody, word2vec, LDA, and introducing a new hybrid algorithm: lda2vec slides.
EDIT:
The question is on word2vec, not on the slides.
 A: Garten et al. (1) compared word vectors obtained by adding input word vectors with output word vectors, vs. word vectors obtained by concatenating input word vectors with output word vectors. In their experiments, concatenating yield significantly better results:


(1) Garten, J., Sagae, K., Ustun, V., & Dehghani, M. (2015, June). Combining Distributed Vector Representations for Words. In Proceedings of NAACL-HLT (pp. 95-101).
A: From what I see it's typically left vectors.
Most of techniques base on decomposition of a symmetric matrix (either PPMI as for Skip-Gram Negative-Sampling or co-occurrence probability as for GloVe and Skip-Gram Noise Contrastive Estimation). Yet, due to non-uniform sampling of the context vectors (some sublinear) and numerical algorithms, the left and right vectors are different.
See e.g. here:



*

*Semantics with Dense Vectors (Chapter 16) from Speech and Language Processing (3rd ed. draft) by Dan Jurafsky and James H. Martin.

A: To my understanding, irrespective of what architecture is used (skip-gram/CBOW), word vectors are read from same word-vector matrix.
As suggested in second footnote of the paper, $v_{in}$ and $\tilde{v}_{out}$ of same word (say $dog$) should be different, and they are assumed to be coming from different vocabularies during the derivation of the loss function.
Practically, probability of  word appearing in its own context is very low, and most implementations don't save two vector representations of same word for saving memory and efficiency.
