Why is unsupervised alignment of English embeddings from different algorithms so hard?

This paper presents a challenge to the community: Generative adversarial networks (GANs) can perfectly align independent English word embeddings induced using the same algorithm, based on distributional information alone; but fails to do so, for two different embeddings algorithms. Why is that? We believe understanding why, is key to understand both modern word embedding algorithms and the limitations and instability dynamics of GANs. This paper shows that (a) in all these cases, where alignment fails, there exists a linear transform between the two embeddings (so algorithm biases do not lead to non-linear differences), and (b) similar effects can not easily be obtained by varying hyper-parameters. One plausible suggestion based on our initial experiments is that the differences in the inductive biases of the embedding algorithms lead to an optimization landscape that is riddled with local optima, leading to a very small basin of convergence, but we present this more as a challenge paper than a technical contribution.Comment: Accepted at EMNLP 201

Context Vectors are Reflections of Word Vectors in Half the Dimensions

This paper takes a step towards theoretical analysis of the relationship between word embeddings and context embeddings in models such as word2vec. We start from basic probabilistic assumptions on the nature of word vectors, context vectors, and text generation. These assumptions are well supported either empirically or theoretically by the existing literature. Next, we show that under these assumptions the widely-used word-word PMI matrix is approximately a random symmetric Gaussian ensemble. This, in turn, implies that context vectors are reflections of word vectors in approximately half the dimensions. As a direct application of our result, we suggest a theoretically grounded way of tying weights in the SGNS model

Characterizing the impact of geometric properties of word embeddings on task performance

Analysis of word embedding properties to inform their use in downstream NLP tasks has largely been studied by assessing nearest neighbors. However, geometric properties of the continuous feature space contribute directly to the use of embedding features in downstream models, and are largely unexplored. We consider four properties of word embedding geometry, namely: position relative to the origin, distribution of features in the vector space, global pairwise distances, and local pairwise distances. We define a sequence of transformations to generate new embeddings that expose subsets of these properties to downstream models and evaluate change in task performance to understand the contribution of each property to NLP models. We transform publicly available pretrained embeddings from three popular toolkits (word2vec, GloVe, and FastText) and evaluate on a variety of intrinsic tasks, which model linguistic information in the vector space, and extrinsic tasks, which use vectors as input to machine learning models. We find that intrinsic evaluations are highly sensitive to absolute position, while extrinsic tasks rely primarily on local similarity. Our findings suggest that future embedding models and post-processing techniques should focus primarily on similarity to nearby points in vector space.Comment: Appearing in the Third Workshop on Evaluating Vector Space Representations for NLP (RepEval 2019). 7 pages + reference

Factors Influencing the Surprising Instability of Word Embeddings

Despite the recent popularity of word embedding methods, there is only a small body of work exploring the limitations of these representations. In this paper, we consider one aspect of embedding spaces, namely their stability. We show that even relatively high frequency words (100-200 occurrences) are often unstable. We provide empirical evidence for how various factors contribute to the stability of word embeddings, and we analyze the effects of stability on downstream tasks.Comment: NAACL HLT 201

What the Vec? Towards Probabilistically Grounded Embeddings

Word2Vec (W2V) and GloVe are popular, fast and efficient word embedding algorithms. Their embeddings are widely used and perform well on a variety of natural language processing tasks. Moreover, W2V has recently been adopted in the field of graph embedding, where it underpins several leading algorithms. However, despite their ubiquity and relatively simple model architecture, a theoretical understanding of what the embedding parameters of W2V and GloVe learn and why that is useful in downstream tasks has been lacking. We show that different interactions between PMI vectors reflect semantic word relationships, such as similarity and paraphrasing, that are encoded in low dimensional word embeddings under a suitable projection, theoretically explaining why embeddings of W2V and GloVe work. As a consequence, we also reveal an interesting mathematical interconnection between the considered semantic relationships themselves.Comment: Advances in Neural Information Processing, 201

Unsupervised Features Learning for Sampled Vector Fields

In this paper we introduce a new approach to computing hidden features of sampled vector fields. The basic idea is to convert the vector field data to a graph structure and use tools designed for automatic, unsupervised analysis of graphs. Using a few data sets we show that the collected features of the vector fields are correlated with the dynamics known for analytic models which generates the data. In particular the method may be useful in analysis of data sets where the analytic model is poorly understood or not known