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Register a new userAverage Approximates First Principal Component? An Empirical Analysis on Representations from Neural Language Models
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Added by
Zihan Wang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Contextualized representations based on neural language models have furthered the state of the art in various NLP tasks. Despite its great success, the nature of such representations remains a mystery. In this paper, we present an empirical property of these representations -- average approximates first principal component. Specifically, experiments show that the average of these representations shares almost the same direction as the first principal component of the matrix whose columns are these representations. We believe this explains why the average representation is always a simple yet strong baseline. Our further examinations show that this property also holds in more challenging scenarios, for example, when the representations are from a model right after its random initialization. Therefore, we conjecture that this property is intrinsic to the distribution of representations and not necessarily related to the input structure. We realize that these representations empirically follow a normal distribution for each dimension, and by assuming this is true, we demonstrate that the empirical property can be in fact derived mathematically.
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Neural networks are among the state-of-the-art techniques for language modeling. Existing neural language models typically map discrete words to distributed, dense vector representations. After information processing of the preceding context words by hidden layers, an output layer estimates the probability of the next word. Such approaches are time- and memory-intensive because of the large numbers of parameters for word embeddings and the output layer. In this paper, we propose to compress neural language models by sparse word representations. In the experiments, the number of parameters in our model increases very slowly with the growth of the vocabulary size, which is almost imperceptible. Moreover, our approach not only reduces the parameter space to a large extent, but also improves the performance in terms of the perplexity measure.
The distributed and continuous representations used by neural networks are at odds with representations employed in linguistics, which are typically symbolic. Vector quantization has been proposed as a way to induce discrete neural representations that are closer in nature to their linguistic counterparts. However, it is not clear which metrics are the best-suited to analyze such discrete representations. We compare the merits of four commonly used metrics in the context of weakly supervised models of spoken language. We compare the results they show when applied to two different models, while systematically studying the effect of the placement and size of the discretization layer. We find that different evaluation regimes can give inconsistent results. While we can attribute them to the properties of the different metrics in most cases, one point of concern remains: the use of minimal pairs of phoneme triples as stimuli disadvantages larger discrete unit inventories, unlike metrics applied to complete utterances. Furthermore, while in general vector quantization induces representations that correlate with units posited in linguistics, the strength of this correlation is only moderate.
Scaling existing applications and solutions to multiple human languages has traditionally proven to be difficult, mainly due to the language-dependent nature of preprocessing and feature engineering techniques employed in traditional approaches. In this work, we empirically investigate the factors affecting language-independent models built with multilingual representations, including task type, language set and data resource. On two most representative NLP tasks -- sentence classification and sequence labeling, we show that language-independent models can be comparable to or even outperforms the models trained using monolingual data, and they are generally more effective on sentence classification. We experiment language-independent models with many different languages and show that they are more suitable for typologically similar languages. We also explore the effects of different data sizes when training and testing language-independent models, and demonstrate that they are not only suitable for high-resource languages, but also very effective in low-resource languages.
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependence on the number of top principal components. We show that it can be used to give a fast iterative method for the popular principal component regression problem, giving the first major runtime improvement over the naive method of combining PCA with regression. To achieve our results, we first observe that ridge regression can be used to obtain a smooth projection onto the top principal components. We then sharpen this approximation to true projection using a low-degree polynomial approximation to the matrix step function. Step function approximation is a topic of long-term interest in scientific computing. We extend prior theory by constructing polynomials with simple iterative structure and rigorously analyzing their behavior under limited precision.
Biomedical knowledge graphs (KGs) hold rich information on entities such as diseases, drugs, and genes. Predicting missing links in these graphs can boost many important applications, such as drug design and repurposing. Recent work has shown that general-domain language models (LMs) can serve as soft KGs, and that they can be fine-tuned for the task of KG completion. In this work, we study scientific LMs for KG completion, exploring whether we can tap into their latent knowledge to enhance biomedical link prediction. We evaluate several domain-specific LMs, fine-tuning them on datasets centered on drugs and diseases that we represent as KGs and enrich with textual entity descriptions. We integrate the LM-based models with KG embedding models, using a router method that learns to assign each input example to either type of model and provides a substantial boost in performance. Finally, we demonstrate the advantage of LM models in the inductive setting with novel scientific entities. Our datasets and code are made publicly available.
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