This paper theoretically investigates the following empirical phenomenon: given a high-complexity network with poor generalization bounds, one can distill it into a network with nearly identical predictions but low complexity and vastly smaller generalization bounds. The main contribution is an analysis showing that the original network inherits this good generalization bound from its distillation, assuming the use of well-behaved data augmentation. This bound is presented both in an abstract and in a concrete form, the latter complemented by a reduction technique to handle modern computation graphs featuring convolutional layers, fully-connected layers, and skip connections, to name a few. To round out the story, a (looser) classical uniform convergence analysis of compression is also presented, as well as a variety of experiments on cifar and mnist demonstrating similar generalization performance between the original network and its distillation.
Amid the pandemic COVID-19, the world is facing unprecedented infodemic with the proliferation of both fake and real information. Considering the problematic consequences that the COVID-19 fake-news have brought, the scientific community has put effort to tackle it. To contribute to this fight against the infodemic, we aim to achieve a robust model for the COVID-19 fake-news detection task proposed at CONSTRAINT 2021 (FakeNews-19) by taking two separate approaches: 1) fine-tuning transformers based language models with robust loss functions and 2) removing harmful training instances through influence calculation. We further evaluate the robustness of our models by evaluating on different COVID-19 misinformation test set (Tweets-19) to understand model generalization ability. With the first approach, we achieve 98.13% for weighted F1 score (W-F1) for the shared task, whereas 38.18% W-F1 on the Tweets-19 highest. On the contrary, by performing influence data cleansing, our model with 99% cleansing percentage can achieve 54.33% W-F1 score on Tweets-19 with a trade-off. By evaluating our models on two COVID-19 fake-news test sets, we suggest the importance of model generalization ability in this task to step forward to tackle the COVID-19 fake-news problem in online social media platforms.
Cross-domain named entity recognition (NER) models are able to cope with the scarcity issue of NER samples in target domains. However, most of the existing NER benchmarks lack domain-specialized entity types or do not focus on a certain domain, leading to a less effective cross-domain evaluation. To address these obstacles, we introduce a cross-domain NER dataset (CrossNER), a fully-labeled collection of NER data spanning over five diverse domains with specialized entity categories for different domains. Additionally, we also provide a domain-related corpus since using it to continue pre-training language models (domain-adaptive pre-training) is effective for the domain adaptation. We then conduct comprehensive experiments to explore the effectiveness of leveraging different levels of the domain corpus and pre-training strategies to do domain-adaptive pre-training for the cross-domain task. Results show that focusing on the fractional corpus containing domain-specialized entities and utilizing a more challenging pre-training strategy in domain-adaptive pre-training are beneficial for the NER domain adaptation, and our proposed method can consistently outperform existing cross-domain NER baselines. Nevertheless, experiments also illustrate the challenge of this cross-domain NER task. We hope that our dataset and baselines will catalyze research in the NER domain adaptation area. The code and data are available at https://github.com/zliucr/CrossNER.
Multi-hop Question Generation (QG) aims to generate answer-related questions by aggregating and reasoning over multiple scattered evidence from different paragraphs. It is a more challenging yet under-explored task compared to conventional single-hop QG, where the questions are generated from the sentence containing the answer or nearby sentences in the same paragraph without complex reasoning. To address the additional challenges in multi-hop QG, we propose Multi-Hop Encoding Fusion Network for Question Generation (MulQG), which does context encoding in multiple hops with Graph Convolutional Network and encoding fusion via an Encoder Reasoning Gate. To the best of our knowledge, we are the first to tackle the challenge of multi-hop reasoning over paragraphs without any sentence-level information. Empirical results on HotpotQA dataset demonstrate the effectiveness of our method, in comparison with baselines on automatic evaluation metrics. Moreover, from the human evaluation, our proposed model is able to generate fluent questions with high completeness and outperforms the strongest baseline by 20.8% in the multi-hop evaluation. The code is publicly available at https://github.com/HLTCHKUST/MulQG}{https://github.com/HLTCHKUST/MulQG .
Recent work across many machine learning disciplines has highlighted that standard descent methods, even without explicit regularization, do not merely minimize the training error, but also exhibit an implicit bias. This bias is typically towards a certain regularized solution, and relies upon the details of the learning process, for instance the use of the cross-entropy loss. In this work, we show that for empirical risk minimization over linear predictors with arbitrary convex, strictly decreasing losses, if the risk does not attain its infimum, then the gradient-descent path and the algorithm-independent regularization path converge to the same direction (whenever either converges to a direction). Using this result, we provide a justification for the widely-used exponentially-tailed losses (such as the exponential loss or the logistic loss): while this convergence to a direction for exponentially-tailed losses is necessarily to the maximum-margin direction, other losses such as polynomially-tailed losses may induce convergence to a direction with a poor margin.
In this paper, we show that although the minimizers of cross-entropy and related classification losses are off at infinity, network weights learned by gradient flow converge in direction, with an immediate corollary that network predictions, training errors, and the margin distribution also converge. This proof holds for deep homogeneous networks -- a broad class of networks allowing for ReLU, max pooling, linear, and convolutional layers -- and we additionally provide empirical support not just close to the theory (e.g., the AlexNet), but also on non-homogeneous networks (e.g., the ResNet). If the network further has locally Lipschitz gradients, we show that these gradients converge in direction, and asymptotically align with the gradient flow path, with consequences on margin maximization. Our analysis complements and is distinct from the well-known neural tangent and mean-field theories, and in particular makes no requirements on network width and initialization, instead merely requiring perfect classification accuracy. The proof proceeds by developing a theory of unbounded nonsmooth Kurdyka-Lojasiewicz inequalities for functions definable in an o-minimal structure, and is also applicable outside deep learning.
This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and the network is nearly equivalent to its linearization. Concretely, the paper has two main contributions: a generic scheme to approximate functions with the NTK by sampling from transport mappings between the initial weights and their desired values, and the construction of transport mappings via Fourier transforms. Regarding the first contribution, the proof scheme provides another perspective on how the NTK regime arises from rescaling: redundancy in the weights due to resampling allows individual weights to be scaled down. Regarding the second contribution, the most notable transport mapping asserts that roughly $1 / \delta^{10d}$ nodes are sufficient to approximate continuous functions, where $\delta$ depends on the continuity properties of the target function. By contrast, nearly the same proof yields a bound of $1 / \delta^{2d}$ for shallow ReLU networks; this gap suggests a tantalizing direction for future work, separating shallow ReLU networks and their linearization.
Recent theoretical work has guaranteed that overparameterized networks trained by gradient descent achieve arbitrarily low training error, and sometimes even low test error. The required width, however, is always polynomial in at least one of the sample size $n$, the (inverse) target error $1/\epsilon$, and the (inverse) failure probability $1/\delta$. This work shows that $\widetilde{O}(1/\epsilon)$ iterations of gradient descent with $\widetilde{\Omega}(1/\epsilon^2)$ training examples on two-layer ReLU networks of any width exceeding $\mathrm{polylog}(n,1/\epsilon,1/\delta)$ suffice to achieve a test misclassification error of $\epsilon$. The analysis further relies upon a margin property of the limiting kernel, which is guaranteed positive, and can distinguish between true labels and random labels.
This paper investigates the approximation power of three types of random neural networks: (a) infinite width networks, with weights following an arbitrary distribution; (b) finite width networks obtained by subsampling the preceding infinite width networks; (c) finite width networks obtained by starting with standard Gaussian initialization, and then adding a vanishingly small correction to the weights. The primary result is a fully quantified bound on the rate of approximation of general general continuous functions: in all three cases, a function $f$ can be approximated with complexity $\|f\|_1 (d/\delta)^{\mathcal{O}(d)}$, where $\delta$ depends on continuity properties of $f$ and the complexity measure depends on the weight magnitudes and/or cardinalities. Along the way, a variety of ancillary results are developed: an exact construction of Gaussian densities with infinite width networks, an elementary stand-alone proof scheme for approximation via convolutions of radial basis functions, subsampling rates for infinite width networks, and depth separation for corrected networks.