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Title: Empirical observations on the instability of aligning word vector spaces with GANs

Paper content:
Unsupervised bilingual dictionary induction (UBDI) is useful for unsupervised machine translation and for cross-lingual transfer of models into low-resource languages.
One approach to UBDI is to align word vector spaces in different languages using Generative adversarial networks (GANs) with linear generators, achieving state-of-the-art performance for several language pairs.
For some pairs, however, GAN-based induction is unstable or completely fails to align the vector spaces.
We focus on cases where linear transformations provably exist, but the performance of GAN-based UBDI depends heavily on the model initialization.
We show that the instability depends on the shape and density of the vector sets, but not on noise; it is the result of local optima, but neither over-parameterization nor changing the batch size or the learning rate consistently reduces instability.
Nevertheless, we can stabilize GAN-based UBDI through best-of-N model selection, based on an unsupervised stopping criterion.
A word vector space -also sometimes referred to as a word embedding -associates similar words in a vocabulary with similar vectors.
Learning a projection of one word vector space into another, such that similar words -across the two word embeddings -are associated with similar vectors, is useful in many contexts, with the most prominent example being the alignment of vocabularies of different languages.
This is a key step in machine translation of low-resource languages ).
An embedding of English words may associate thoughtful, considerate, and gracious with similar vectors, for example, but for English-Icelandic translation, it would be useful to have access to a cross-lingual word embedding space in which hugulsamur (lit.: 'thoughtful') was also associated with a similar vector.
Such joint embeddings of words across languages can also be used to extract bilingual dictionaries.Projections between word vector spaces have typically been learned from dictionary seeds.
In seminal papers such as BID22 and BID11 , these seeds would comprise thousands of words, but BID31 showed that we can learn reliable projections from as little as 50 words.
and BID15 subsequently showed that the seed can be replaced with just words that are identical across languages; and BID1 showed that numerals can also do the job, in some cases; both proposals removing the need for an actual dictionary.
Even more recently, a handful of papers have proposed an entirely unsupervised approach to projecting word vector spaces onto each other, based on Generative Adversarial Networks (GANs) BID12 .
We present the core idea behind such approaches in §3, but briefly put, GANs are used to learn a linear transformation to minimize the divergence between a target distribution (say the Icelandic embeddings) and a source distribution (the English embeddings projected into the Icelandic space).The
possibility of unsupervised bilingual dictionary induction (UBDI) has seemingly removed the data bottleneck in machine translation, evoking the idea that we can now learn to translate without human supervision ). Yet
, it remains an open question whether the initial, positive results extrapolate to real-world scenarios of learning translations between low-resource language pairs. recently
presented results suggesting that UBDI is challenged by some language pairs exhibiting very different morphosyntactic properties, as well as when the monolingual corpora are very different. In this
paper, we identify easy, hard, and impossible instances of GAN-based UBDI, and apply a simple test for discriminating between them. The hard
cases exhibit instability, i.e. their success depends heavily on initialization. We set up
a series of experiments to investigate these hard cases.Our contributions We introduce a distinction between easy, hard, and impossible alignment problems over pairs of word vector spaces and show that a simple linearity test can be used to tell these cases apart. We show that
the impossible cases are caused not necessarily by linguistic differences, but rather by properties of the corpora and the embedding algorithms. We also show
that in the hard cases, the likelihood of being trapped in local minima depends heavily on the shape and density of the vector sets, but not on noise. Changes in the
number of parameters, batch size, and learning rate do not alleviate the instability. Yet, using an
unsupervised model selection method over N different initializations to select the best generators, leads to a 6.74% average error reduction over standard MUSE.Structure of the paper §2 presents MUSE BID6 , an approach to GAN-based UBDI. Here we also
discuss theoretical results from the GAN literature, relevant to our case, and show a relation to a common point set registration method. In §3, we use
a test based on Procrustes Analysis to discriminate between easy, hard, and impossible cases, discussing its relation with tests of isomorphism and isospectrality. We then focus
on the hard cases, where linear transformations provably exist, but GANs exhibit considerable instability. Through a series
of experiments, we analyze what affects the instability of GAN-based UBDI. §4 presents our
unsupervised best-of-N model selection method for stabilizing GAN-based UBDI.
Some pairs of word vector spaces are not alignable based on distributional information alone.
For other pairs, GANs can be used to induce such an alignment, but the degree of instability is very susceptible to the shape and density of the word vector spaces, albeit not to noise.
Instability is caused by local optima, but not remedied by standard techniques such as over-parameterization, increasing the batch size or decreasing the learning rate.
We propose an unsupervised model selection criterion that enables stable learning, leading to a~7% error reduction over MUSE, and present further observations about the alignability of word vector distributions.

assistant: text: An empirical investigation of GAN-based alignment of word vector spaces, focusing on cases, where linear transformations provably exist, but training is unstable.