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Register a new userImplicit Regularization of Stochastic Gradient Descent in Natural Language Processing: Observations and Implications
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Deren Lei
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some theoretical studies have analyzed the implicit regularization effect of stochastic gradient descent (SGD) on simple machine learning models with certain assumptions. However, how it behaves practically in state-of-the-art models and real-world datasets is still unknown. To bridge this gap, we study the role of SGD implicit regularization in deep learning systems. We show pure SGD tends to converge to minimas that have better generalization performances in multiple natural language processing (NLP) tasks. This phenomenon coexists with dropout, an explicit regularizer. In addition, neural networks finite learning capability does not impact the intrinsic nature of SGDs implicit regularization effect. Specifically, under limited training samples or with certain corrupted labels, the implicit regularization effect remains strong. We further analyze the stability by varying the weight initialization range. We corroborate these experimental findings with a decision boundary visualization using a 3-layer neural network for interpretation. Altogether, our work enables a deepened understanding on how implicit regularization affects the deep learning model and sheds light on the future study of the over-parameterized models generalization ability.
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Transformers are ubiquitous in Natural Language Processing (NLP) tasks, but they are difficult to be deployed on hardware due to the intensive computation. To enable low-latency inference on resource-constrained hardware platforms, we propose to design Hardware-Aware Transformers (HAT) with neural architecture search. We first construct a large design space with $textit{arbitrary encoder-decoder attention}$ and $textit{heterogeneous layers}$. Then we train a $textit{SuperTransformer}$ that covers all candidates in the design space, and efficiently produces many $textit{SubTransformers}$ with weight sharing. Finally, we perform an evolutionary search with a hardware latency constraint to find a specialized $textit{SubTransformer}$ dedicated to run fast on the target hardware. Extensive experiments on four machine translation tasks demonstrate that HAT can discover efficient models for different hardware (CPU, GPU, IoT device). When running WMT14 translation task on Raspberry Pi-4, HAT can achieve $textbf{3}times$ speedup, $textbf{3.7}times$ smaller size over baseline Transformer; $textbf{2.7}times$ speedup, $textbf{3.6}times$ smaller size over Evolved Transformer with $textbf{12,041}times$ less search cost and no performance loss. HAT code is https://github.com/mit-han-lab/hardware-aware-transformers.git
We study the implicit regularization of mini-batch stochastic gradient descent, when applied to the fundamental problem of least squares regression. We leverage a continuous-time stochastic differential equation having the same moments as stochastic gradient descent, which we call stochastic gradient flow. We give a bound on the excess risk of stochastic gradient flow at time $t$, over ridge regression with tuning parameter $lambda = 1/t$. The bound may be computed from explicit constants (e.g., the mini-batch size, step size, number of iterations), revealing precisely how these quantities drive the excess risk. Numerical examples show the bound can be small, indicating a tight relationship between the two estimators. We give a similar result relating the coefficients of stochastic gradient flow and ridge. These results hold under no conditions on the data matrix $X$, and across the entire optimization path (not just at convergence).
Neural networks models for NLP are typically implemented without the explicit encoding of language rules and yet they are able to break one performance record after another. This has generated a lot of research interest in interpreting the representations learned by these networks. We propose here a novel interpretation approach that relies on the only processing system we have that does understand language: the human brain. We use brain imaging recordings of subjects reading complex natural text to interpret word and sequence embeddings from 4 recent NLP models - ELMo, USE, BERT and Transformer-XL. We study how their representations differ across layer depth, context length, and attention type. Our results reveal differences in the context-related representations across these models. Further, in the transformer models, we find an interaction between layer depth and context length, and between layer depth and attention type. We finally hypothesize that altering BERT to better align with brain recordings would enable it to also better understand language. Probing the altered BERT using syntactic NLP tasks reveals that the model with increased brain-alignment outperforms the original model. Cognitive neuroscientists have already begun using NLP networks to study the brain, and this work closes the loop to allow the interaction between NLP and cognitive neuroscience to be a true cross-pollination.
A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.
We study discrete-time mirror descent applied to the unregularized empirical risk in matrix sensing. In both the general case of rectangular matrices and the particular case of positive semidefinite matrices, a simple potential-based analysis in terms of the Bregman divergence allows us to establish convergence of mirror descent -- with different choices of the mirror maps -- to a matrix that, among all global minimizers of the empirical risk, minimizes a quantity explicitly related to the nuclear norm, the Frobenius norm, and the von Neumann entropy. In both cases, this characterization implies that mirror descent, a first-order algorithm minimizing the unregularized empirical risk, recovers low-rank matrices under the same set of assumptions that are sufficient to guarantee recovery for nuclear-norm minimization. When the sensing matrices are symmetric and commute, we show that gradient descent with full-rank factorized parametrization is a first-order approximation to mirror descent, in which case we obtain an explicit characterization of the implicit bias of gradient flow as a by-product.
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