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# Quantifying Reviewer Trust

#### Identifying Reviewers as Trustworthy Through kNN

Notice anything backwards, missing, misleading, or wrong?

#### Authors

Data Scientist

##### Jason Cohen

Production managers, sensory experts, and quality control professionals use the Gastrograph system to find and detect flaws or batch variations in their products. Though all of our clients are serious about the flavor profile and consistency of their products, and review with a critical palate, not all reviews are of equal trust and weight. Any single Gastrograph review is not solely dependent on the product; the reviewer’s experience, preferences, environment, and health all play a role in their response to flavor.

Trust is important for our clients, because they are interested in how much trust they can place in a product review ($$r$$). For example if they were to ask us for a report on a product $$X$$ then we would provide them with the Objective Flavor Profile and the Perceived Quality, both of which are computed from among the trusted reviews (I will explain how I determine which reviews are trustworthy). So in short our clients can get a concrete flavor analysis on $$X$$ computed with trust based weights derived from the reviews.

I will outline how we compute trust by carrying out an analysis on the reviews for product $$X$$. We'll take some detours to explain the differences between a model based strictly on the amount of reviews someone has completed versus a model that is consistent with the amount of reviews completed but additionally based on the character of the flavor profiles.

Product $$X$$ has a set of 4 distinct quality control experts who have produced 700 $$r$$s for $$X$$. Where $$r \in Review~Space := {[0,5]}^{24}\times(Review~Number)$$, $$\ Review~Number = (0,\infty)$$. $$Review~Number~(RN)$$ is the number of reviews that the reviewer or $$r$$ has completed. $$RN$$ is an absolute count, so it counts from the first $$r$$ a reviewer has submitted for $$X$$. Being that our reviewers are quality control professionals we can safely assume that our "distribution" in $$Review~Space$$ is a good profiling of $$X$$. Therefore any $$r$$, regardless of reviewer, that “breaks” away from our distribution can be considered a poor review.

I am using k-Nearest Neighbors (kNN) to uncover the distribution of our data for $$X$$ to ultimately to quantify trustworthiness amongst our reviews. In order to apply kNN first one must have classified data or labeled data. Therefore I classified a subset, $$Validation~Set$$, of our data into three non-overlapping groups. Each group represents a level of experience for our reviews. The three groups can be seen as most $$(\mu)$$, average $$(\alpha)$$, and least $$(\lambda)$$ experienced. The strict classification by $$RN$$ is a reflection of a naive classification of reviews into experience groups. Therefore kNN will serve as an improvement to a naive understanding of experience.

I applied kNN with 10-fold cross validation on the classified $$r$$ but I exclude $$RN$$. I excluded $$RN$$ so that structure of the group depends on the flavor alone. However thanks to the preliminary classification of reviews by $$RN$$ the classification rules will be $$\bf{consistent}$$ with $$RN$$. In short the distribution kNN will compute will be indirectly depending on $$Review~Number.$$ Below I have the plots of the two competing models for trustworthiness when applied to unlabeled reviews of $$X$$, as well as the results of classifying the $$Test~Set$$ by the validation set.

One can see that kNN has been successful because of the results on $$Test~Set$$. In our results we can see there are $$r$$s whose $$RN$$ are low but are still considered trustworthy reviews, and therefore are members of subset $$\mu$$. In other words we can trust such a review based on the reviewer’s ability to perceive flavor, not only the amount of reviews he/she has completed. I ultimately want to classify $$r$$s as the second method illustrates because reviewers have unique flavor tolerances and learning curves. In my model it’s completely possible that reviewers $$A$$ and $$B$$ may have the same amount of reviews completed but may not have the same amount of “experience”, which is not an uncommon real world scenario. This model accounts for a reviewer’s previous tasting experience. The previous flexibility and descriptive power is impossible in a model that is strictly based on $$RN$$.

Now I will outline how I will quantify trust per $$review$$ for $$X$$: Since kNN works well on our test set, I applied kNN to all our data for $$X$$. Then I determined the medoid for all $$r \in \mu$$ , and then I ran a similarity analysis that compared every data point from our data set to $$m := medoid~of~\mu$$. The medoid of $$\mu$$, $$(m)$$, is the data point in $$\mu$$ such that:

$\sum \limits _{j~=~\mu} d(m, r_j) \leq \sum \limits _{j~=~\mu} d(r_i,r_j)$

Where $$r_{i}$$ is the ith member of $$\mu$$ and we are using the Manhattan metric to compute distance. In other words the average and the medoid only differ in that the medoid has to be a data point and the average does not, and frequently isn’t a point in our set. I picked the medoid exactly because it belongs to our data set, so that our "best” reviewer has a score of 100.

The results from the similarity analysis will be used to compute the Trust function whose results will be ranged from 0 to 100.

Below are the results of the trust computation per reviewer.

Naively one believes that trust in a quality control specialist should grow in time or stay constant. The model produces a desirable upward trend.

In conclusion, my approach to the problem exploits the power of kNN so that the structure of our data can dictate which $$r$$s are the most trustworthy $$r$$s. If you are curious as to how the similarity analysis is carried out and the definition of the Trust function, then submit an application to join our team.

Future work to produce a more accurate model of Trust would require incorporating $$RN$$. So far I have considered two similar approaches: i) apply a transformation to $$RN$$ and include $$RN$$ in my $$Review~Space$$ ii) to determine a metric, for $$Review~Space \times RN$$, that would “properly weight” $$RN$$. The transformation would $$RN$$ to a scale from 0 to 5, the same scale flavor is measured on. Then I would add $$RN$$ as another axis in $$Review~Space$$ and I would prep my data and compute trust values in exactly the same way I have outlined earlier. I practice I would need to test out various transformations and see if it improves our models by plotting $$Trust~vs~RN$$. There has been work done in metric learning that I will apply to our data.

As far as metrics go the Manhattan metric is biased towards the $$RN$$ because $$RN$$ has no upper bound and in our example ranges from 0 to 300. So my aim is to determine a metric which produce more accurate classifications, well work has been done towards that end. A metric is learned from our data such that it maximizes distance between points that should not be classified together and minimizes distance between points that should be classified in one group.


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NLP has achieved great progress in the past decade through the use of neural models and large labeled datasets. The dependence on abundant data prevents NLP models from being applied to low-resource settings or novel tasks where significant time, money, or expertise is required to label massive amounts of textual data. Recently, data augmentation methods have been explored as a means of improving data efficiency in NLP. To date, there has been no systematic empirical overview of data augmentation for NLP in the limited labeled data setting, making it difficult to understand which methods work in which settings. In this paper, we provide an empirical survey of recent progress on data augmentation for NLP in the limited labeled data setting, summarizing the landscape of methods (including token-level augmentations, sentence-level augmentations, adversarial augmentations, and hidden-space augmentations) and carrying out experiments on 11 datasets covering topics/news classification, inference tasks, paraphrasing tasks, and single-sentence tasks. Based on the results, we draw several conclusions to help practitioners choose appropriate augmentations in different settings and discuss the current challenges and future directions for limited data learning in NLP.

Deep learning methods have achieved strong performance on a wide range of supervised learning tasks (Sutskever et al., 2014; Deng et al., 2013; Minaee et al., 2021). Traditionally, these results were attained through the use of large, well-labeled datasets. This make them challenging to apply in settings where collecting a large amount of high-quality labeled data for training is expensive. Moreover, given the fast-changing nature of real-world applications, it is infeasible to relabel every example whenever new data comes in. This highlights a need for learning algorithms that can be trained with a limited amount of labeled data.

There has been a substantial amount of research towards learning with limited labeled data for various tasks in the NLP community. One common approach for mitigating the need for labeled data is data augmentation. Data augmentation (Feng et al., 2021) generates new data by modifying existing data points through transformations that are designed based on prior knowledge about the problem’s structure (Yang, 2015; Wei and Zou, 2019). This augmented data can be generated from labeled data, and then directly used in supervised learning (Wei and Zou, 2019), or in semi-supervised learning for unlabeled data through consistency regularization (Xie et al., 2020) (“consistency training”). While various approaches have been proposed to tackle learning with limited labeled data—including unsupervised pre-training (Peters et al., 2018; Devlin et al., 2019; Raffel et al., 2020), multi-task learning (Glorot et al., 2011; Liu et al., 2017; Augenstein et al., 2018), semi-supervised learning (Zhu, 2005; Chapelle et al., 2009; Miyato et al., 2017; Xie et al., 2020), and few-shot learning (Deng et al., 2019)—in this work, we focus on and compare different data augmentation methods and their application to supervised and semi-supervised learning.

In this empirical survey, we comprehensively review and perform experiments on recent data augmentation techniques developed for various NLP tasks. Our contributions are three-fold: (1) summarize and categorize recent methods in textual data augmentation; (2) compare different data augmentation methods through experiments with limited labeled data in supervised and semi-supervised settings on 11 NLP tasks, and (3) discuss current challenges and future directions of data augmentation, as well as learning with limited data in NLP more broadly.

Our experimental results allow us to conclude that:

• Token-level augmentations and specifically word replacement and random swapping consistently improve performance the most for supervised learning while sentence-level augmentation and specifically roundtrip translation improve performance the most for semi-supervised learning.

• Token-level augmentations improve performance more for simpler classification tasks and surprisingly hurt performance for harder tasks where the baseline performance is pretty low.

• Token-level augmentations and sentence- level augmentations are generally more reliable compared to hidden-level augmentations in both supervised and semi-supervised settings.

• The best augmentation method depends on the dataset and setting (either supervised or semi-supervised).

##### Related Surveys.

Recently, several surveys also explore the data augmentation techniques for NLP (Hedderich et al., 2020; Feng et al., 2021; Sahin, 2022). Hedderich et al. (2020) provide a broad overview of techniques for NLP in low resource scenarios and briefly cover data augmentation as one of several techniques. In contrast, we focus on data augmentation and provide a more comprehensive review on recent data augmentation methods in this work. Sahin (2022) focuses on syntax, token, and character level augmentations for part-of-speech tagging, dependency parsing, and semantic role labeling. While Feng et al. (2021) also survey task-specific data augmentation approaches for NLP, our work summarizes recent data augmentation methods in a more fine-grained categorization. We also focus on their application to learning from limited data by providing an empirical study of over different augmentation methods on various benchmark datasets in both supervised and semi-supervised settings, doing an empirical comparison of different types of augmentation methods on over 11 datasets covering various tasks. In doing so, we hope to shed light on data augmentation selections for future research.

Data augmentation increases both the amount (the number of data points) and the diversity (the variety of data) of a given dataset (Cubuk et al., 2019). Limited labeled data often leads to overfitting on the training set and data augmentation works to alleviate this issue by manipulating data either automatically or manually to create additional augmented data. Such techniques have been widely explored in the computer vision field, with methods like geometric/color space transformations (Simard et al., 2003; Krizhevsky et al., 2012; Taylor and Nitschke, 2018), mixup (Zhang et al., 2018), and random erasing (Zhong et al., 2020; DeVries and Taylor, 2017). Although the discrete nature of textual data and its complex syntactic and semantic structures make finding label-preserving transformation more difficult, there nevertheless exists a wide range of methods for augmenting text data that in practice preserve labels. In the following subsections, we describe four broad classes of data augmentation methods.

### 2.1 Token-Level Augmentation

Token-level augmentations manipulate words and phrases in a sentence to generate augmented text while ideally retaining the semantic meaning and labels of the original text.

##### Designed Replacement.

Intuitively, the semantic meaning of a sentence remains unchanged if some of its tokens are replaced with other tokens that have the same meaning. A simple approach is to fetch synonyms as words for substitutions (Kolomiyets et al., 2011; Yang, 2015; Zhang et al., 2015a; Wei and Zou, 2019; Miao et al., 2020). The synonyms are discovered based on pre-defined dictionaries such as WordNet (Kolomiyets et al., 2011), or similarities in word embedding space (Yang, 2015). However, improvements from this technique are usually minimal (Kolomiyets et al., 2011), and in some cases, performance may even degrade (Zhang et al., 2015a). A major drawback stems from the lack of contextual information when fetching synonyms—especially for words with multiple meanings and few synonyms. To resolve this, language models (LMs) have been used to replace the sampled words given their context (Kolomiyets et al., 2011; Fadaee et al., 2017; Kobayashi, 2018; Kumar et al., 2020). Other work preserves the labels of the text by conditioning on the label when generating the LMs’ predictions (Kobayashi, 2018; Wu et al., 2019a). In addition, different sampling strategies for word replacement have been explored. For example, instead of sampling one specific word from candidates by LMs, Gao et al. (2019) propose to compute a weighted average over embeddings of possible words predicted by LMs as the replaced input since the averaged representations could augment text with richer information.

##### Random Insertion, Replacement, Deletion, and Swapping.

While well-designed local modifications can preserve the syntax and semantic meaning of a sentence (Niu and Bansal, 2018), random local modifications such as deleting certain tokens (Iyyer et al., 2015; Wei and Zou, 2019; Miao et al., 2020), inserting random tokens (Wei and Zou, 2019; Miao et al., 2020), replacing non-important tokens with random tokens (Xie et al., 2017, 2020; Niu and Bansal, 2018), or randomly swapping tokens in one sentence (Artetxe et al., 2018; Lample et al., 2018; Wei and Zou, 2019; Miao et al., 2020) can preserve the meaning in practice. Different kinds of operations can be further combined (Wei and Zou, 2019), where each example is randomly augmented with one of insertion, deletion, and swapping. These noise-injection methods can efficiently be applied to training, and show improvements when they augment simple models trained on small training sets. However, the improvements might be unstable due to the possibility that random perturbations change the meanings of sentences (Niu and Bansal, 2018). Also, finetuning large pre-trained models on specific tasks might attenuate improvements due to preexisting generalization abilities of the model (Shleifer, 2019).

##### Compositional Augmentation.

To increase the compositional generalization abilities of models, recent efforts have also focused on compositional augmentations (Jia and Liang, 2016; Andreas, 2020) where different fragments from different sentences are re-combined to create augmented examples. Compared with random swapping, compositional augmentation often requires more carefully designed rules such as lexical overlap (Andreas, 2020), neural-symbolic stack machines (Chen et al., 2020e), and neural program synthesis (Nye et al., 2020). With the potential to greatly improve the generalization abilities to out-of-distribution data, compositional augmentation has been utilized in sequence labeling (Guo et al., 2020), semantic parsing (Andreas, 2020; Nye et al., 2020; Furrer et al., 2020), language modeling (Andreas, 2020; Shaw et al., 2021), and text generation (Feng et al., 2020).

### 2.2 Sentence-Level Augmentation

Instead of modifying tokens, sentence-level augmentation modifies the entire sentence at once.

##### Paraphrasing.

Paraphrasing has been widely adopted as a data augmentation technique in various NLP tasks (Yu et al., 2018; Xie et al., 2020; Kumar et al., 2019; He et al., 2020; Chen et al., 2020b,2020c; Cai et al., 2020), as it generally provides more diverse augmented text with different word choices and sentence structures while preserving the meaning of the original text. The most popular is round-trip translation (Sennrich et al., 2015; Edunov et al., 2018), a pipeline which first translates sentences into certain intermediate languages and then translates them back to generate paraphrases. Translating through intermediate languages with different vocabulary and linguistic structures can generate useful paraphrases. To ensure the diversity of augmented data, sampling and noisy beam search can also be adopted during the decoding stage (Edunov et al., 2018). Other work focuses on directly training end-to-end models to generate paraphrases (Prakash et al., 2016), and further augments the decoding phase with syntactic information (Iyyer et al., 2018; Chen et al., 2019), latent variables (Gupta et al., 2017), and sub-modular objectives (Kumar et al., 2019).

##### Conditional Generation.

Conditional generation methods generate additional text from a language model, conditioned on the label. After training the model to generate the original text given the label, the model can generate new text (Anaby-Tavor et al., 2020; Zhang and Bansal, 2019; Kumar et al., 2020; Yang et al., 2020). An extra filtering process is often used to ensure high-quality augmented data. For example, in text classification, Anaby-Tavor et al. (2020) first fine-tune GPT-2 (Radford et al., 2019) with the original examples prepended with their labels, and then generate augmented examples by feeding the fine-tuned model certain labels. Only confident examples as judged by a baseline classifier trained on the original data are kept. Similarly, new answers are generated on the basis of given questions in question answering and are filtered by customized metrics like question answering probability (Zhang and Bansal, 2019) and n-gram diversity (Yang et al., 2020). Given the recent success of pre-trained language models, Ye et al. (2022) and Wang et al. (2021) generate data from zero-shot models. Generative models used in this setting have been based on conditional VAE (Bowman et al., 2016; Hu et al., 2017; Guu et al., 2017; Malandrakis et al., 2019), GAN Iyyer et al., 2018; (Xu et al., 2018), or pre-trained language models like GPT-2 (Anaby-Tavor et al., 2020; Kumar et al., 2020). Overall, these conditional generation methods can create novel and diverse data that might be unseen in the original dataset, but require significant training effort.

Adversarial methods create augmented examples by adding adversarial perturbations to the original data, which dramatically influences the model’s predictions and confidence without changing human judgments. These adversarial examples (Morris et al., 2020; Zeng et al., 2020) could be leveraged in adversarial training (Goodfellow et al., 2015) to increase neural models’ robustness, and can also be utilized as data augmentation to increase the models’ generalization ability (Miyato et al., 2017; Cheng et al., 2019).1

##### White-Box Methods.

These rely on model architecture and parameters being accessible and create adversarial examples directly using a model’s gradients. Unlike image pixel values that are continuous, textual tokens are discrete and cannot be directly modified based on gradients. To this end, adversarial perturbations are added directly to token embeddings or sentence hidden representations (Miyato et al., 2017; Zhu et al., 2020; Jiang et al., 2019; Chen et al., 2020d) which creates “virtual adversarial examples”. Other approaches vectorize modification operations as the difference of one-hot vectors (Ebrahimi et al., 2018a, b), or find real word neighbors in a model’s hidden representations via its gradients (Cheng et al., 2019).

### 2.4 Hidden-Space Augmentation

This line of work generates augmented data by manipulating the hidden representations through perturbations such as adding noise or performing interpolations with other data points. Hidden-space perturbations augment existing data by adding perturbations to the hidden representations of tokens (Miyato et al., 2017; Zhu et al., 2020; Jiang et al., 2019; Chen et al., 2020d; Shen et al., 2020; Chen et al., 2021) or sentences (Hsu et al., 2017, 2018; Wu et al., 2019b; Malandrakis et al., 2019).

##### Interpolation-Based Methods.

Interpolation-based methods create new examples and labels by linear combinations of existing data-label pairs. Given two data-label pairs, virtual data-label pairs are created through linear interpolations of the pair of data points. Such interpolation-based methods can generate infinite augmented data in the “virtual vicinity” of the original data space, thus improving the generalization performance of models. Interpolation-based methods were first explored in computer vision (Zhang et al., 2018), and have more recently been generalized to the text domain (Miao et al., 2020; Chen et al., 2020c; Cheng et al., 2020b; Chen et al., 2020a) by performing interpolation between original data and token-level augmented data in the output space (Miao et al., 2020), between original data and adversarial data in embedding space (Cheng et al., 2020b), or between different training examples in general hidden space (Chen et al., 2020c). Different strategies to select samples to mix have also been explored (Chen et al., 2020a; Guo et al., 2020; Zhang et al., 2020a) such as k-nearest-neighbors (Chen et al., 2020a) or sentence composition (Guo et al., 2020).

We summarize the preceding overview of recent widely used data augmentation methods in Table 1, characterizing them with respect to augmentation levels, the diversity of generated data, and their applicable tasks.

Table 1:

Overview of different data augmentation techniques in NLP. Diversity refers to the difference of augmented data from existing data and the amount of different augmented data could be generated.

Synonym replacement Token Low Text classification Kolomiyets et al. (2011), Zhang et al. (2015a),
Yang (2015), Miao et al. (2020),
Wei and Zou (2019
Sequence labeling
Word replacement via LM Token Medium Text classification Kolomiyets et al. (2011), Gao et al. (2019
Sequence labeling Kobayashi (2018), Wu et al. (2019a
Machine translation Fadaee et al. (2017
Random insertion, deletion, swapping Token Low Text classification Iyyer et al. (2015), Xie et al. (2017)
Artetxe et al. (2018), Lample et al. (2018)
Xie et al. (2020), Wei and Zou (2019
Sequence labeling
Machine translation
Dialogue generation
Compositional augmentation Token High Semantic Parsing Jia and Liang (2016), Andreas (2020)
Nye et al. (2020), Feng et al. (2020)
Furrer et al. (2020), Guo et al. (2020
Sequence labeling
Language modeling
Text generation
Paraphrasing Sentence High Text classification Yu et al. (2018), Xie et al. (2020)
Chen et al. (2019), He et al. (2020)
Chen et al. (2020c), Cai et al. (2020
Machine translation
Dialogue generation
Text summarization
Conditional generation Sentence High Text classification Anaby-Tavor et al. (2020), Kumar et al. (2020
Question answering Zhang and Bansal (2019), Yang et al. (2020
White-box attack Token or Sentence Medium Text classification Miyato et al. (2017), Ebrahimi et al. (2018b
Sequence labeling Ebrahimi et al. (2018a), Cheng et al. (2019),
Machine translation Chen et al. (2020d
Black-box attack Token or Sentence Medium Text classification Jia and Liang (2017)
Belinkov and Bisk (2017), Zhao et al. (2017)
Ribeiro et al. (2018), McCoy et al. (2019)
Min et al. (2020), Tan et al. (2020
Sequence labeling
Machine translation
Textual entailment
Dialogue generation
Text Summarization
Hidden-space perturbation Token or Sentence High Text classification Hsu et al. (2017), Hsu et al. (2018
Sequence labeling Wu et al. (2019b), Chen et al. (2021
Speech recognition Malandrakis et al. (2019), Shen et al. (2020
Interpolation Token High Text classification Miao et al. (2020), Chen et al. (2020c
Sequence labeling Cheng et al. (2020b), Chen et al. (2020a
Machine translation Guo et al. (2020
Synonym replacement Token Low Text classification Kolomiyets et al. (2011), Zhang et al. (2015a),
Yang (2015), Miao et al. (2020),
Wei and Zou (2019
Sequence labeling
Word replacement via LM Token Medium Text classification Kolomiyets et al. (2011), Gao et al. (2019
Sequence labeling Kobayashi (2018), Wu et al. (2019a
Machine translation Fadaee et al. (2017
Random insertion, deletion, swapping Token Low Text classification Iyyer et al. (2015), Xie et al. (2017)
Artetxe et al. (2018), Lample et al. (2018)
Xie et al. (2020), Wei and Zou (2019
Sequence labeling
Machine translation
Dialogue generation
Compositional augmentation Token High Semantic Parsing Jia and Liang (2016), Andreas (2020)
Nye et al. (2020), Feng et al. (2020)
Furrer et al. (2020), Guo et al. (2020
Sequence labeling
Language modeling
Text generation
Paraphrasing Sentence High Text classification Yu et al. (2018), Xie et al. (2020)
Chen et al. (2019), He et al. (2020)
Chen et al. (2020c), Cai et al. (2020
Machine translation
Dialogue generation
Text summarization
Conditional generation Sentence High Text classification Anaby-Tavor et al. (2020), Kumar et al. (2020
Question answering Zhang and Bansal (2019), Yang et al. (2020
White-box attack Token or Sentence Medium Text classification Miyato et al. (2017), Ebrahimi et al. (2018b
Sequence labeling Ebrahimi et al. (2018a), Cheng et al. (2019),
Machine translation Chen et al. (2020d
Black-box attack Token or Sentence Medium Text classification Jia and Liang (2017)
Belinkov and Bisk (2017), Zhao et al. (2017)
Ribeiro et al. (2018), McCoy et al. (2019)
Min et al. (2020), Tan et al. (2020
Sequence labeling
Machine translation
Textual entailment
Dialogue generation
Text Summarization
Hidden-space perturbation Token or Sentence High Text classification Hsu et al. (2017), Hsu et al. (2018
Sequence labeling Wu et al. (2019b), Chen et al. (2021
Speech recognition Malandrakis et al. (2019), Shen et al. (2020
Interpolation Token High Text classification Miao et al. (2020), Chen et al. (2020c
Sequence labeling Cheng et al. (2020b), Chen et al. (2020a
Machine translation Guo et al. (2020

While data augmentation (DA) can be applied in the supervised setting to produce better results when only a small labeled training dataset is available, data augmentation is also commonly used in semi-supervised learning (SSL). SSL is an alternative approach for learning from limited data that provides a framework for taking advantage of unlabeled data. Specifically, SSL assumes that our training set comprises labeled examples in addition to unlabeled examples drawn from the same distribution. Currently, one of the most common methods for performing SSL with deep neural networks is “consistency regularization” (Bachman et al., 2014; Tarvainen and Valpola, 2017). Consistency regularization-based SSL (or “consistency training” for short) regularizes a model by enforcing that its output doesn’t change significantly when the input is perturbed. In practice, the input is perturbed by applying data augmentation, and consistency is enforced through a loss term that measures the difference between the model’s predictions on a clean input and a corresponding perturbed version of the same input.

Formally, let fθ be a model with parameters θ, $fθ^$ be a fixed copy of the model where no gradients are allowed to flow, xl be a labeled datapoint with label y, xu be an unlabeled datapoint, and α(x) be a data augmentation method. Then, a typical loss function for consistency training is
$CE(fθ(xl),y)+λuCE(fθ^(xu),fθ(α(xu)))$
where CE is the cross entropy loss and λu is a tunable hyperparameter that determines the weight of the consistency regularization term. In practice, various other measures have been used to minimize the difference between $fθ^(xu)$ and fθ(α(xu)), such as the KL divergence (Miyato et al., 2018; Xie et al., 2020) and the mean-squared error (Tarvainen and Valpola, 2017; Laine and Aila, 2017; Berthelot et al., 2019). Because gradients are not allowed to flow through the model when it was fed the clean unlabeled input xu, this objective can be viewed as using the clean unlabeled datapoint to generate a synthetic target distribution for the augmented unlabeled datapoint.

Xie et al. (2020) showed that consistency training can be effectively applied to semi-supervised learning for NLP. To achieve stronger results, they introduce several other tricks including confidence thresholding, training signal annealing, and entropy minimization. Confidence thresholding applies the unsupervised loss only when the model assigns a class probability above a pre-defined threshold. Training signal annealing prevents the model from overfitting on easy examples by applying the supervised loss only when the model is less confident about predictions. Entropy minimization trains the model to output low-entropy (highly-confident) predictions when fed unlabeled data. We refer the reader to Xie et al. (2020) for more details on these tricks.

### 4.1 Datasets and Experiment Setup

To provide a quantitative comparison of the DA methods we have surveyed, we experiment with 10 of the most commonly used and model-agnostic augmentation techniques from different levels in Table 1, including: (i) Token-level augmentation: Synonym Replacement (SR) (Kolomiyets et al., 2011; Yang, 2015), Word Replacement based on Language Model (LM) (Kumar et al., 2020), Random Insertion (RI) (Wei and Zou, 2019; Miao et al., 2020), Random Deletion (RD) (Wei and Zou, 2019), Random Swapping (RS) (Wei and Zou, 2019), and Word Replacement (WR) based on TF-IDF in Vocabulary Set (Xie et al., 2020); (ii) Sentence-level augmentation: Roundtrip Translation (RT) (Xie et al., 2020; Chen et al., 2020c), Generation from Few-shot Models (GF) (Ye et al., 2022; Wang et al., 2021); and (iii) Hidden-space augmentation: Adversarial training (ADV) (Goodfellow et al., 2015), Cutoff (Shen et al., 2020), and Mixup in the embedding space (Zhang et al., 2018). Most aforementioned techniques are not label-dependent (except mixup and Generation from Few-shot), thus can be applied directly to unlabeled data. For generation from few-shot models, we use in-context learning with a few examples and a given label to generate the input, following Wang et al. (2021). Since we use BERT-base as our main model, we use a similar size model for in-context learning and choose GPT2.

We test them on different types of benchmark datasets including: (i) news classification tasks including AG News (Zhang et al., 2015b) and 20 Newsgroup (Joachims, 1997); (ii) topic classification tasks including Yahoo Answers (Chang et al., 2008) and PubMed news classification (Zhang et al., 2015b); (iii) inference tasks including MNLI, QNLI, and RTE (Wang et al., 2018); (iv) similarity and paraphrase tasks including QQP and MRPC (Wang et al., 2018); and (v) single-sentence tasks including SST-2 and CoLA (Wang et al., 2018).

For all datasets, we experiment with 10 labeled data points per class2 in a supervised setup, and an additional 5000 unlabeled data points per class in the semi-supervised setup. We use B E R Tbase (Devlin et al., 2019) as the base language model and use the same hyperparameters across all datasets/methods. We utilize accuracy as the evaluation metric for all datasets except for CoLA (which uses Matthews correlation) and PubMed (which uses accuracy and Macro-F1 score). Because the performance can be heavily dependent on the specific datapoints chosen (Sohn et al., 2020), for each dataset, we sample labeled data from the original dataset with 3 different seeds to form different training sets, and report the average result. For every setup, we fine-tune the model with the same seed as the dataset seed (in contrast to many works which report the max across different seeds).

We train our models on NVIDIA 2080ti and NVIDIA V-100 GPUs. Supervised experiments take 20 minutes, and semi-supervised experiments take two hours. The BERT-base model has 100M parameters. We use the same hyperparameter across all datasets, and so only use the validation set to find the best model checkpoint. We use a learning rate of 2e−5, batch size of 16, ratio of unlabeled to labeled data of 3, and dropout ratio of 0.1 for different augmentation methods.

### 4.2 Results with 10 Labeled Examples Per Class

The results are shown in Table 2. We observe that in supervised settings, token-level augmentations work the best. Specifically, word replacement works well, getting the highest or second highest score every time. On the other hand, Generating from Few-shot models performs very poorly. This is not surprising since the model used for in-context learning is GPT2, which is not that good at in-context learning and the inputs necessary for news/topic classification is much more complicated. In the semi-supervised settings, sentence level augmentations (round-trip translation) work the best, getting the highest or second highest score every time. This makes sense since for many classification tasks, multiple words indicate the label, and so dropping several words will not affect the label.

Table 2:

Topic Classification and News Classification results with 10 examples. We report the average results across 3 different random seeds with the 95% confidence interval and bold the best results. For PubMed, we report the accuracy and F1 score.

MethodsTypesNews ClassificationTopic Classification
Supervised None – 78.8(8.9) 65.2(4.8) 56.6(9.4) 63.7(6.1)/49.3(3.9)

SR Token 79.4(5.9) 66.1(2.5) 56.0(10.1) 62.4(5.7)/48.3(3.9)
LM 76.8(5.1) 60.0(14.4) 56.2(8.4) 60.9(3.0)/47.4(2.5)
RI 79.5(4.9) 66.6(0.6) 57.3(12.0) 63.7(4.2)/49.4(2.1)
RD 79.6(5.0) 66.8(3.0) 58.0(8.3) 63.4(5.0)/49.3(1.5)
RS 79.5(5.3) 64.8(10.8) 57.1(10.3) 63.8(7.4)/49.5(3.3)
WR 79.7(2.0) 67.5(4.2) 59.3(8.9) 64.9(4.9)/49.4(2.5)

RT Sentence 80.1(4.3) 65.1(7.9) 57.1(9.6) 60.2(5.1)/46.3(6.4)
GF Sentence 25.3(0.7) 5.2(0.1) 27.4(3.5) 33.0(0.0)/9.9(0.0)

ADV Hidden 78.2(5.3) 65.5(1.6) 53.8(4.89) 37.4(2.6)/19.9(10.6)
Cutoff 79.3(5.0) 66.6(1.4) 57.3(9.3) 60.5(8.3)/46.6(9.4)
Mixup 80.0(6.52) 65.9(3.1) 57.8(4.19) 51.4(19.3)/39.8(3.2)

Semi Supervised SR Token 69.6(29.3) 65.7(1.8) 51.4(9.4) 59.3(5.9)/43.1(11.9)
LM 68.5(13.7) 68.3(2.1) 53.2(6.3) 61.5(6.6)/46.4(4.4)
RI 65.8(5.5) 66.7(1.1) 50.5(3.2) 61.4(11.3)/44.4(17.4)
RD 73.2(14.0) 66.1(3.3) 51.5(7.5) 59.3(7.1)/46.0(3.8)
RS 71.6(16.6) 65.0(2.0) 51.1(7.1) 64.2(12.1)/46.7(11.5)
WR 74.1(12.3) 69.3(2.5) 55.6(5.9) 60.4(7.5)/43.7(14.2)

RT Sentence 82.1(8.2) 68.8(2.4) 59.8(3.9) 64.3(1.2)/49.8(1.9)
ADV Hidden 82.3(2.33) 66.8(5.9) 55.9(3.89) 62.2(10.8)/46.2(9.8)
Cutoff 79.9(5.5) 67.9(0.8) 60.1(1.0) 62.7(9.0)/48.1(3.2)
MethodsTypesNews ClassificationTopic Classification
Supervised None – 78.8(8.9) 65.2(4.8) 56.6(9.4) 63.7(6.1)/49.3(3.9)

SR Token 79.4(5.9) 66.1(2.5) 56.0(10.1) 62.4(5.7)/48.3(3.9)
LM 76.8(5.1) 60.0(14.4) 56.2(8.4) 60.9(3.0)/47.4(2.5)
RI 79.5(4.9) 66.6(0.6) 57.3(12.0) 63.7(4.2)/49.4(2.1)
RD 79.6(5.0) 66.8(3.0) 58.0(8.3) 63.4(5.0)/49.3(1.5)
RS 79.5(5.3) 64.8(10.8) 57.1(10.3) 63.8(7.4)/49.5(3.3)
WR 79.7(2.0) 67.5(4.2) 59.3(8.9) 64.9(4.9)/49.4(2.5)

RT Sentence 80.1(4.3) 65.1(7.9) 57.1(9.6) 60.2(5.1)/46.3(6.4)
GF Sentence 25.3(0.7) 5.2(0.1) 27.4(3.5) 33.0(0.0)/9.9(0.0)

ADV Hidden 78.2(5.3) 65.5(1.6) 53.8(4.89) 37.4(2.6)/19.9(10.6)
Cutoff 79.3(5.0) 66.6(1.4) 57.3(9.3) 60.5(8.3)/46.6(9.4)
Mixup 80.0(6.52) 65.9(3.1) 57.8(4.19) 51.4(19.3)/39.8(3.2)

Semi Supervised SR Token 69.6(29.3) 65.7(1.8) 51.4(9.4) 59.3(5.9)/43.1(11.9)
LM 68.5(13.7) 68.3(2.1) 53.2(6.3) 61.5(6.6)/46.4(4.4)
RI 65.8(5.5) 66.7(1.1) 50.5(3.2) 61.4(11.3)/44.4(17.4)
RD 73.2(14.0) 66.1(3.3) 51.5(7.5) 59.3(7.1)/46.0(3.8)
RS 71.6(16.6) 65.0(2.0) 51.1(7.1) 64.2(12.1)/46.7(11.5)
WR 74.1(12.3) 69.3(2.5) 55.6(5.9) 60.4(7.5)/43.7(14.2)

RT Sentence 82.1(8.2) 68.8(2.4) 59.8(3.9) 64.3(1.2)/49.8(1.9)
ADV Hidden 82.3(2.33) 66.8(5.9) 55.9(3.89) 62.2(10.8)/46.2(9.8)
Cutoff 79.9(5.5) 67.9(0.8) 60.1(1.0) 62.7(9.0)/48.1(3.2)

As shown in Table 3, we observe that token-level augmentations work the best overall (e.g., random insertion, random deletion, and word replacement) for both supervised and semi-supervised settings. This is a bit surprising since the inference tasks usually heavily depend on several words, and changing these words can easily change the label for inferene tasks.

Table 3:

GLUE results with 10 labeled examples per class. We report the average results across 3 different random seeds with the 95% confidence interval and bold the best results.

MethodsTypesInferenceParaphraseSingle Sentence
MNLIQNLIRTEQQPMRPCSST-2CoLA
Supervised None – 35.2(0.7) 51.8(7.0) 49.8(3.1) 63.9(9.1) 61.8(21.2) 60.5(13.1) 12.9(6.32)

SR Token 35.1(2.3) 51.4(7.2) 51.5(3.4) 61.3(9.7) 59.7(26.3) 62.1(17.4) 7.2(11.6)
LM 35.3(0.8) 51.0(8.0) 49.0(1.4) 62.4(11) 61.0(24.3) 62.8(9.8) 6.8(15.8)
RI 34.9(2.6) 51.5(8.4) 51.5(1.4) 60.6(10.9) 60.6(25.0) 63.3(12.2) 7.8(7.42)
RD 35.5(2.1) 51.1(8.4) 50.9(2.4) 62.4(11.3) 61.2(22.0) 59.7(18.4) 7.1(16.6)
RS 35.1(1.1) 51.5(7.0) 50.9(5.0) 62.6(6.7) 63.2(22.5) 61.2(10.8) 5.2(17.0)
WR 34.5(2.6) 52.0(3.8) 50.0(0.9) 60.6(10.2) 61.0(25.3) 61.8(12.5) 7.0(10.6)

RT Sentence 35.3(0.5) 51.1(9.6) 50.8(4.4) 60.5(17.8) 61.8(23.7) 62.0(1.99) 8.37(8.35)
GF Sentence 33.8(1.7) 50.5(2.3) 47.6(3.2) 59.4(6.6) 56.6(1.7) 53.5(4.1) 3.89 (7.2)

ADV Hidden 33.3(4.7) 49.7(1.8) 48.3(12.1) 57.5(24.7) 61.5(21.5) 53.3(13.07) 1.37(4.66)
Cutoff 35.1(2.3) 51.4(8.3) 52.2(3.6) 62.6(8.8) 61.0(21.2) 63.5(8.45) 12.4(9.58)
Mixup 32.6(3.5) 49.9(1.4) 49.8(9.2) 63.0(0.3) 62.1(19.8) 62.3(12.3) 4.03(8.68)

Semi-Supervised SR Token 35.6(1.0) 52.1(4.5) 52.9(5.4) 53.5(10.7) 68.1(4.0) 61.8(37.9) 6.65(5.69)
LM 35.0(3.3) 52.5(4.2) 50.2(6.5) 47.9(34.1) 68.4(3.8) 57.3(14.2) 6.38(6.3)
RI 35.8(1.7) 52.1(4.1) 50.7(1.4) 59.6(5.1) 64.9(8.9) 58.3(14.8) 6.55(0.91)
RD 35.2(0.5) 52.1(5.2) 52.6(4.9) 56.1(16.0) 62.4(30.6) 55.7(16.4) 4.33(10.9)
RS 34.6(2.5) 52.1(6.2) 51.5(3.7) 49.8(7.9) 63.2(22.5) 55.2(15.3) 7.77(11.77)
WR 34.8(2.5) 52.1(4.1) 50.9(1.8) 51.8(16.0) 63.1(23.5) 54.8(13.8) 5.43(17.8)

RT Sentence 35.3(2.7) 52.7(4.8) 51.6(4.1) 63.9(7.5) 62.2(12.5) 61.9(20.8) 11.6(14.5)

ADV Hidden 36.2(8.9) 50.6(1.9) 50.9(6.8) 59.1(14.7) 63.9(9.1) 53.1(5.0) 7.64(25.1)
Cutoff 35.3(2.8) 52.5(4.3) 51.7(6.5) 62.9(9.9) 68.6(4.4) 54.3(9.8) 4.11(11.8)
MethodsTypesInferenceParaphraseSingle Sentence
MNLIQNLIRTEQQPMRPCSST-2CoLA
Supervised None – 35.2(0.7) 51.8(7.0) 49.8(3.1) 63.9(9.1) 61.8(21.2) 60.5(13.1) 12.9(6.32)

SR Token 35.1(2.3) 51.4(7.2) 51.5(3.4) 61.3(9.7) 59.7(26.3) 62.1(17.4) 7.2(11.6)
LM 35.3(0.8) 51.0(8.0) 49.0(1.4) 62.4(11) 61.0(24.3) 62.8(9.8) 6.8(15.8)
RI 34.9(2.6) 51.5(8.4) 51.5(1.4) 60.6(10.9) 60.6(25.0) 63.3(12.2) 7.8(7.42)
RD 35.5(2.1) 51.1(8.4) 50.9(2.4) 62.4(11.3) 61.2(22.0) 59.7(18.4) 7.1(16.6)
RS 35.1(1.1) 51.5(7.0) 50.9(5.0) 62.6(6.7) 63.2(22.5) 61.2(10.8) 5.2(17.0)
WR 34.5(2.6) 52.0(3.8) 50.0(0.9) 60.6(10.2) 61.0(25.3) 61.8(12.5) 7.0(10.6)

RT Sentence 35.3(0.5) 51.1(9.6) 50.8(4.4) 60.5(17.8) 61.8(23.7) 62.0(1.99) 8.37(8.35)
GF Sentence 33.8(1.7) 50.5(2.3) 47.6(3.2) 59.4(6.6) 56.6(1.7) 53.5(4.1) 3.89 (7.2)

ADV Hidden 33.3(4.7) 49.7(1.8) 48.3(12.1) 57.5(24.7) 61.5(21.5) 53.3(13.07) 1.37(4.66)
Cutoff 35.1(2.3) 51.4(8.3) 52.2(3.6) 62.6(8.8) 61.0(21.2) 63.5(8.45) 12.4(9.58)
Mixup 32.6(3.5) 49.9(1.4) 49.8(9.2) 63.0(0.3) 62.1(19.8) 62.3(12.3) 4.03(8.68)

Semi-Supervised SR Token 35.6(1.0) 52.1(4.5) 52.9(5.4) 53.5(10.7) 68.1(4.0) 61.8(37.9) 6.65(5.69)
LM 35.0(3.3) 52.5(4.2) 50.2(6.5) 47.9(34.1) 68.4(3.8) 57.3(14.2) 6.38(6.3)
RI 35.8(1.7) 52.1(4.1) 50.7(1.4) 59.6(5.1) 64.9(8.9) 58.3(14.8) 6.55(0.91)
RD 35.2(0.5) 52.1(5.2) 52.6(4.9) 56.1(16.0) 62.4(30.6) 55.7(16.4) 4.33(10.9)
RS 34.6(2.5) 52.1(6.2) 51.5(3.7) 49.8(7.9) 63.2(22.5) 55.2(15.3) 7.77(11.77)
WR 34.8(2.5) 52.1(4.1) 50.9(1.8) 51.8(16.0) 63.1(23.5) 54.8(13.8) 5.43(17.8)

RT Sentence 35.3(2.7) 52.7(4.8) 51.6(4.1) 63.9(7.5) 62.2(12.5) 61.9(20.8) 11.6(14.5)

ADV Hidden 36.2(8.9) 50.6(1.9) 50.9(6.8) 59.1(14.7) 63.9(9.1) 53.1(5.0) 7.64(25.1)
Cutoff 35.3(2.8) 52.5(4.3) 51.7(6.5) 62.9(9.9) 68.6(4.4) 54.3(9.8) 4.11(11.8)

From Table 3, in the supervised settings, we observe that token-level augmentations (random swapping) achieve the best performances, while hidden space augmentations work well in semi-supervised settings, with cutoff performing the best on average. This makes sense since for paraphrasing tasks, augmenting the text usually consists of paraphrases, and so can easily change whether two texts are paraphrases of each other.

Based on the single-sentence tasks results in Table 3, hidden space augmentations (cutoff) provides the biggest boost in performance in supervised settings, while in semi-supervised settings, sentence level augmentations (roundtrip translation) work best. We note most augmentation methods hurt performance on CoLA, a task for judging grammatical acceptability. This could be caused by the fact that most of the augmentation methods try to preserve meaning and not grammatical correctness.

##### Token Level Methods

Overall, we see that word replacement works the best for news and topic classification tasks and random swapping perform the best among token level methods for inference, paraphrase, and single sentence tasks.

### 4.3 Summary of Findings

Based on the results on 10 labeled examples we conclude that:

• Overall, the best augmentation method depends on the dataset and whether we have unlabeled data or not.

• In general, word replacement and random swapping work the best for supervised learning while roundtrip translation works the best for semi-supervised learning.

• Token-level augmentation methods work better for easier classification tasks and surprisingly hurt performance for harder tasks when the baseline performance is low.

• Token-level and sentence-level augmentations are most robust than hidden-level augmentation in the supervised and semi-supervised settings.

This work mainly focuses on data augmentation and semi-supervised learning (consistency regularization) in NLP; However, there are other orthogonal directions for tackling the problem of learning with limited data. For completeness, we summarize this related work below.

##### Low-Resourced Languages.

Most languages lack large monolingual or parallel corpora, or sufficient manually crafted linguistic resources for building statistical NLP applications (Garrette and Baldridge, 2013). Researchers have therefore developed a variety of methods for improving performance on low-resource languages, including cross-lingual transfer learning, which transfers models from resource-rich to resource-poor languages (Do and Gaspers, 2019; Lee and Lee, 2019; Schuster et al., 2019), few/zero-shot learning (Johnson et al., 2017; Blissett and Ji, 2019; Pham et al., 2019; Abad et al., 2020), which uses only a few examples from the low-resource domain to adapt models trained in another domain, and polyglot learning (Cotterell and Heigold, 2017; Tsvetkov et al., 2016; Mulcaire et al., 2019; Lample and Conneau, 2019), which combines resource-rich and resource-poor learning using an universal language representation.

##### Other Methods for Semi-Supervised Learning.

Semi-supervised learning methods further reduce the dependency on labeled data and enhance the models when there is only limited labeled data available. These methods use large amounts of unlabeled data in the training process, as unlabeled data is usually cheap and easy to obtain compared to labeled data. In this paper, we focus on consistency regularization, while there are also other widely used methods for NLP including self-training (Yarowsky, 1995; Zhang and Zong, 2016; He et al., 2020; Lin et al., 2020), generative methods (Xu et al., 2017; Yang et al., 2017; Kingma et al., 2014; Cheng et al., 2016), and co-training (Blum and Mitchell, 1998; Clark et al., 2018; Cai and Lapata, 2019).

##### Few-shot Learning.

Few-shot learning is a broad technique for dealing with tasks with less labeled data based on prior knowledge. Compared to semi-supervised learning, which utilizes unlabeled data as additional information, few-shot learning leverages various kinds of prior knowledge such as pre-trained models or supervised data from other domains and modalities (Wang et al., 2020). While most work on few-shot focuses on computer vision, few-shot learning has recently seen increasing adoption in NLP (Han et al., 2018; Rios and Kavuluru, 2018; Hu et al., 2018; Herbelot and Baroni, 2017). To better leverage pre-trained models, PET (Schick and Schütze, 2021a, b) converts the text and label in an example into a fluent sentence, and then uses the probability of generating the label text as the class logit, outperforming GPT3 for few shot learning (Brown et al., 2020). How to better model and incorporate prior knowledge to handle few-shot learning for NLP remains an open challenge and has the potential to significantly improve model performance with less labeled data.

In this work, we empirically surveyed data augmentation methods for limited-data learning in NLP and compared them on 11 different NLP tasks. Despite the success, there are still certain challenges that need to be tackled to improve their performance. This section highlights some of these challenges and discusses future research directions.

##### Theoretical Guarantees and Data Distribution Shift.

Current data augmentation methods for text typically assume that they are label-preserving and will not change the data distribution. However, these assumptions are often not true in practice, which can result in noisy labels or a shift in the data distribution and consequently a decrease in performance or generalization (e.g., QQP in Table 3). Thus, providing theoretical guarantees that augmentations are label- and distribution-preserving under certain conditions would ensure the quality of augmented data and further accelerate the progress of this field.

##### Automatic Data Augmentation.

Despite being effective, current data augmentation methods are generally manually designed. Methods for automatically selecting the appropriate types of data augmentation still remain under-investigated. Although certain augmentation techniques have been shown effective for a particular task or dataset, they often do not transfer well to other datasets or tasks (Cubuk et al., 2019), as shown in Table 3. For example, paraphrasing works well for general text classification tasks, but may fail for some subtle scenarios like classifying bias because paraphrasing might change the label in this setting. Automatically learning data augmentation strategies or searching for an optimal augmentation policy for given datasets/tasks/models could enhance the generalizability of data augmentation techniques (Maharana and Bansal, 2020; Hu et al., 2019).

We would like to thank the members of Georgia Tech SALT and UNC-NLP groups for their feedback. This work is supported by grants from Amazon and Salesforce, ONR grant N00014-18-1-2871, DARPA YFA17-D17AP00022.

1

For more detailed discussion on textual adversarial examples, please refer to recent comprehensive surveys (Zhang et al., 2020b; Huq and Pervin, 2020; Goel et al., 2021).

2

We also did experiments with 100 labeled examples per class and found the results consistent.

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## Author notes

Action Editor: Emily Pitler

*

Equal contribution.

This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For a full description of the license, please visit https://creativecommons.org/licenses/by/4.0/legalcode.

format: plain


text:
## anonymous one year ago Clark has 7 and 1 over 2 feet of wire. Part A: How many 3 over 4 foot pieces can Clark cut from the 7 and 1 over 2 feet of wire? Show your work. Part B: Using the information in Part A, interpret the meaning of the quotient in terms of the two fractions given.

1. mathstudent55

Part A: This is a division problem. You need to divide 7 1/2 by 3/4

2. anonymous

@Michele_Laino

3. mathstudent55

First, write 7 1/2 as a fraction. Then divide that fraction by 3/4.

4. anonymous

ok

5. mathstudent55

Do you know how to change a mixed numeral into a fraction?

6. anonymous

kinda

7. Michele_Laino

we can write this: $\Large 7\;\frac{1}{2} = 7 + \frac{1}{2} = ...?$

8. mathstudent55

|dw:1439930748823:dw|

9. anonymous

ok

10. mathstudent55

To write a mixed numeral as a fraction, multiply the number by the denominator and add the numerator. That is the numerator of the fration. The denominator is the same you had.

11. mathstudent55

|dw:1439930905576:dw|

12. mathstudent55

Ok. So far I changed the mixed numeral into a fractions. Now we need to divide a fraction by a fraction. Do you know how to divide a fraction by a fraction?

13. anonymous

nope i was never good at it

14. mathstudent55

No problem. I'll help you with it. Do you know how to multiply a fraction by a fraction?

15. mathstudent55

To multiply fractions together, multiply together the numerators and multiply together the denominators. Then reduce if possible, To divide a fraction by a fraction, change the division into a multiplication by flipping the second fraction. Then multiply the fractions.

16. mathstudent55

|dw:1439931429872:dw|


text:
## sdhawan -2

Hi Guys ,
I have a line which is like this :-
"C:\\Users\\saurabh\\Desktop\\Projects\\Texts\\A Sign of the Times.txt"
how can i jus extract the last part of it which is
A Sign of the Times.

Thanks

## finito 46

Here pseudo code

``````Do streamreader untill null
{
}

## sdhawan -2

this is to reaqd the line.what i want to do is to get a substring froma sting.so if suppose i have string like C:\\Users\\saurabh\\Desktop\\Projects\\Texts\\A Sign of the Times.txt then i just want "A Sign of the Times" part of the string.Thanks for the help

## sdhawan -2

I got it guys .This is what i was suppose to do

``````int coll = names[currentFile].LastIndexOf(@"\");
string sub = names[currentFile].Substring(coll + 1);
int coll2 = sub.LastIndexOf(@".");
string sub2 = sub.Remove(coll2);
item.article = sub2;``````

## finito 46

O sorry I see what happened.


text:
# Plotting equipotentials gone wrong

I'm plotting the equipotential of the potential function: $$\phi(x,y,z):=\frac{1+x^{2}+y^{2}+z^{2}}{[\left(1+x^{2}+y^{2}+z^{2}\right)^{2}-4z^{2}]^{1/2}}$$ Mathematica code:

Φ[x_, y_, z_] := (1 + x^2 + y^2 + z^2)/((1 + x^2 + y^2 + z^2)^2 - 4 z^2)^(1/2)

So I write, for example

ContourPlot3D[Φ[x, y, z] == 1, {x, -100, 100}, {y, -100, 100}, {z, -100, 100}]

But, I get this image:

And, sometimes if I change the plot region, I get absolutely nothing.

My question is, what did I wrong? I think I should obtain smooth 3D curves, but I don't.

-
The problem is that $\Phi(x,y,z)\ge1$ everywhere... –  Rahul Narain Jun 8 '13 at 19:46
I think you should manipulate it mathematically a bit further. –  Spawn1701D Jun 8 '13 at 19:49
Try p[x_, z_] := (x x + z^2)/((x x + z^2)^2 - 4 z^2)^(1/2) a = 5; Plot3D[p[x, z], {x, 1, a}, {z, -a, a}] –  belisarius Jun 8 '13 at 20:10
Or a = 2; ContourPlot3D[{\[CapitalPhi][x, y, z] == 1 + 1/100, \[CapitalPhi][x, y, z] == 1 + 1/10}, {x, -a, a}, {y, -a, a}, {z, -a, a}] –  belisarius Jun 8 '13 at 20:53
As Rahul already pointed out, your contour is never crossed, only touched. ContourPlot3D fails with such things which I already answered here. For a quick solution you should follow belisarius' last comment. –  halirutan Jun 8 '13 at 21:46


text:
# What packages are available to typeset SQL in LaTeX?

I'm looking for a package to typeset SQL statements in LaTeX. So far I have heard of listings and lgrind, are there any other suggestions?

 Added requirement: I'd like the package to be able in intelligently insert page breaks, so that where possible statements do not span multiple pages. Still reading documentation, so it is possible that either of the a/m are able to do this already- Please let me know if this is the case.

Related: question

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Not from me. Both the package you mention are mature, and they both claim to support SQL. I'd try them out before looking farther afield. –  dmckee Apr 21 '09 at 0:46

You want to use the listings package. Is there a specific thing you want to do with it, or are you just asking which package works best in general? I've never encountered any big problems with listings, though getting it to do Exactly What I Want is sometimes tricky (it's LaTeX; to expect anything else would be folly).

Edit (to address your edit): intelligent page breaking might be problematic; it's certainly beyond my abilities. listings might be able to do it with explicit markup (escape to LaTeX and insert a negative page break penalty at appropriate place; likely macro-izable), but I don't think listings can do it automatically, and I doubt LGrind can do it either. You might have better luck searching or asking on a LaTeX-specific list (comp.text.tex on Usenet is a great place to try), but page breaking in TeX has never been as good as line breaking, and so I wouldn't hold out too much hope, unfortunately.

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I use the listings package, but mostly for snippets. I haven't needed to worry about page breaks in general. One of the great things about listings is the high degree of flexibility available. For instance, I don't capitalize my SQL, but I can print my listings with capitalized keywords:

\makeatletter
\newcommand{\lstuppercase}{\uppercase\expandafter{\expandafter\lst@token
\expandafter{\the\lst@token}}}
\newcommand{\lstlowercase}{\lowercase\expandafter{\expandafter\lst@token
\expandafter{\the\lst@token}}}
\makeatother

\lstdefinestyle{Oracle}{basicstyle=\ttfamily,
keywordstyle=\lstuppercase,
emphstyle=\itshape,
showstringspaces=false,
}

And define more keywords as I need them:

\lstdefinelanguage[Oracle]{SQL}[]{SQL}{
morekeywords={ACCESS, MOD, NLS_DATE_FORMAT, NVL, REPLACE, SYSDATE,
TO_CHAR, TO_NUMBER, TRUNC},
}

To make use of these definitions:

\lstset{language=[Oracle]SQL,
style=Oracle,
}

If I were to print out larger pieces of code, I'd either not worry about page breaks or write a preprocessor to divide the code up before passing it to LaTeX.

-


text:
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp011831cn814
DC FieldValueLanguage
dc.contributor.authorTeng, Yun-
dc.date.accessioned2019-09-04T17:50:22Z-
dc.date.available2019-09-04T17:50:22Z-
dc.date.created2019-05-06-
dc.date.issued2019-09-04-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp011831cn814-
dc.description.abstractCornerNet is a new approach to object detection that involves predicting bounding boxes as paired top-left and bottom-right keypoints. Having outperformed all existing one-stage detectors on COCO, CornerNet demonstrates that anchor boxes are not necessary, or even desirable. One major drawback of keypoint-based methods is that the improved accuracy comes at a high processing cost, and in its current state, CornerNet is prohibitively slow in applications requiring real-time detection. We address CornerNet’s inefficiency by using smaller feature maps 1/64 the size of the input image, replacing the residual module of the Hourglass backbone with a depthwise fire module, and re-implementing corner pooling to make better use of GPU parallelism. Our new lightweight CornerNet runs at 30ms on a GTX 1080Ti and achieves 34.4 AP on COCO, outperforming YOLOv3.en_US
dc.format.mimetypeapplication/pdf-
dc.language.isoenen_US
dc.titleFast CornerNet for Real-time Systemsen_US
dc.typePrinceton University Senior Theses-
pu.date.classyear2019en_US
pu.departmentComputer Scienceen_US
pu.pdf.coverpageSeniorThesisCoverPage-
pu.contributor.authorid961192178-
Appears in Collections:Computer Science, 1988-2021

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