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Understanding Dataset Difficulty with $\mathcal{V}$-Usable Information

Kawin Ethayarajh, Yejin Choi, Swabha Swayamdipta

arXiv:2110.08420v3cs.CLcs.AIcs.LG

TL;DR

The paper addresses the limited insight provided by model–human performance comparisons into instance difficulty and useful input attributes. It frames dataset difficulty through V-usable information, introduces PVI for pointwise difficulty, and uses input transformations to interpret datasets. The framework identifies annotation artefacts and relates lower PVI to lower annotator agreement and prediction accuracy.

  • Problem

    Standard performance comparisons provide little understanding of individual-instance difficulty or which input attributes a model finds useful.

  • Method

    The paper estimates dataset difficulty using V-usable information, introduces PVI for instances and slices, and compares transformed inputs to interpret attributes.

  • Results

    The framework finds limited impact from word ordering in SNLI, mislabeled difficult instances in SNLI and CoLA, and concentrated label information in 50 potentially offensive words.

  • Takeaways & Limitations

    V-information offers an efficient means of interpreting NLP datasets and discovering systemic and token-level annotation artefacts.

  • Takeaways & Limitations

    The estimates assume training and evaluation data are identically distributed, and empirical and true V-information differences may be non-negligible for small datasets.

Abstract

from arXiv · show

Estimating the difficulty of a dataset typically involves comparing state-of-the-art models to humans; the bigger the performance gap, the harder the dataset is said to be. However, this comparison provides little understanding of how difficult each instance in a given distribution is, or what attributes make the dataset difficult for a given model. To address these questions, we frame dataset difficulty -- w.r.t. a model $\mathcal{V}$ -- as the lack of $\mathcal{V}$-$\textit{usable information}$ (Xu et al., 2019), where a lower value indicates a more difficult dataset for $\mathcal{V}$. We further introduce $\textit{pointwise $\mathcal{V}$-information}$ (PVI) for measuring the difficulty of individual instances w.r.t. a given distribution. While standard evaluation metrics typically only compare different models for the same dataset, $\mathcal{V}$-$\textit{usable information}$ and PVI also permit the converse: for a given model $\mathcal{V}$, we can compare different datasets, as well as different instances/slices of the same dataset. Furthermore, our framework allows for the interpretability of different input attributes via transformations of the input, which we use to discover annotation artefacts in widely-used NLP benchmarks.

1. Introduction

The paper reframes dataset difficulty for a model as the lack of model-usable information, enabling instance-level analysis and comparisons across datasets, slices, and input attributes. Applying this framework reveals annotation artefacts and difficult mislabeled instances in NLP benchmarks.

  • Standard model–human performance gaps reveal little about individual-instance difficulty or which input attributes a model uses.
  • V-usable information makes a dataset easier for model V when more information about labels can be extracted by V.
  • PVI estimates individual and slice difficulty, correlating with annotator agreement, prediction correctness, and judgments across models, seeds, and training time.
  • Input transformations compare usable information before and after isolating attributes, exposing why datasets are easy or difficult for a model.
  • Word ordering has limited impact on SNLI difficulty, while some of the hardest SNLI and CoLA instances are mislabeled.
  • Just 50 potentially offensive words contain most of the BERT-usable label information in a hate-speech dataset.

2. V-Usable Information

V-usable information measures how much label-relevant information a model family can extract, framing lower values as greater dataset difficulty. The framework supports comparisons across models, datasets, input attributes, and individual instances while revealing sensitivity to over-fitting.

  • Core concept: V-usable information measures dataset difficulty relative to a model family: higher I_V(X →Y) means the dataset is easier for that family.It generalizes Shannon information by restricting extraction to functions in V.
  • Definitions: Predictive V-information subtracts conditional V-entropy from label V-entropy, comparing optimal predictive log-likelihood with and without the input.Cross-entropy training estimates conditional V-entropy on an identically distributed held-out set.
  • Assumptions: Finite-sample estimates can differ from true V-information, with tighter PAC error bounds expected for less complex model families and larger datasets.The estimation framework also assumes training and evaluation data are identically distributed, and empirical error may be non-negligible for small datasets.
  • Comparisons: The framework compares different datasets for the same model, different models on the same dataset, and different input variables through their V-information estimates.These comparisons include datasets with the same task and transformations or subsets of input attributes.
  • Experiments: BART-base extracts the most V-information on SNLI, followed by BERT-base, DistilBERT-base, and GPT2-small; accuracy follows the same trend.The model with the most SNLI test-set V-information is also the most accurate.
  • Experiments: At epoch 10, V-information is lowest for all models while SNLI test accuracy has declined only slightly, indicating greater sensitivity to over-fitting.Models become less certain about correct labels before they begin predicting them incorrectly, increasing conditional V-entropy.

3. Measuring Pointwise Difficulty

Pointwise V-information (PVI) measures individual-instance difficulty relative to a predictive family and distribution. Higher PVI indicates easier instances, enabling comparisons across instances, slices, and model settings, while PVI also supports error and annotation analysis.

  • PVI measures the usable information in an individual instance relative to a predictive family and distribution.It extends aggregate V-information to pointwise difficulty.
  • PVI compares the log-probability assigned to the gold label by models trained with and without the input.For BERT, these models are obtained by finetuning with the input and with a null input, respectively.
  • Higher PVI indicates an easier instance for the model, whereas negative PVI means the model is better off predicting the majority class without using the input.PVI can be negative even though aggregate V-information cannot.
  • Average PVI enables comparisons among data slices or subsets, although it is not the V-information of the slice itself.The model is optimized over the entire training distribution, making average PVI useful for relative comparisons within that distribution.
  • PVI in Practice: PVI differences between correctly and incorrectly predicted held-out instances were 3.03, 2.87, and 2.45 bits for SNLI, MultiNLI, and CoLA, respectively.All differences for BERT-base were statistically significant at p < 0.001.
  • PVI in Practice: PVI estimates are highly correlated across models on SNLI (r > 0.80) but less correlated on CoLA (0.40 < r < 0.65), where lower usable information makes estimates noisier.Across four SNLI BERT-base seeds, correlations exceeded 0.85; the PVI threshold for incorrect predictions was approximately 0.5 across datasets.
  • PVI in Practice: The lowest-PVI CoLA instances include examples the authors assess as mislabelled, showing how PVI can support annotation-error discovery.All ten hardest listed instances were predicted incorrectly by BERT-base.

4. Uncovering Dataset Artefacts

The paper uses input transformations and PVI-based slicing to identify which attributes carry model-usable label information and where annotation artefacts concentrate. Across SNLI, CoLA, and DWMW17, these analyses expose lexical and structural shortcuts associated with dataset difficulty.

  • 4.1. Input Transformations: Input transformations isolate attributes by applying τ_i(X) and measuring the resulting V-usable information about labels.Shuffling tokens isolates word-order effects, while premise-only, hypothesis-only, overlap, and related transformations probe distinct input attributes.
  • 4.1. Input Transformations: Token identity provides most of SNLI’s usable information, while the premise alone is useless and the hypothesis remains useful without it.The hypothesis-only signal suggests instance-specific annotation artefacts, consistent with models exploiting spurious correlations.
  • 4.1. Input Transformations: 0.490 bits of BERT-usable information remain in DWMW17 after retaining only 50 potentially offensive words, compared with 0.724 bits in the full text.The selected words comprise common racial and homophobic slurs, indicating that lexical bias can dominate prediction.
  • 4.1. Input Transformations: Premise-hypothesis overlap contains substantially more BERT-usable information for entailment than for contradiction or neutral classes.Class-conditional mean PVI can reveal when an attribute is disproportionately useful for one label class, although it differs from aggregate V-information.
  • 4.2. Slicing Datasets: Entailment instances with no hypothesis-premise overlap have the lowest mean PVI, whereas contradiction instances with no overlap have the highest.This contrast reflects how entailment and contradiction examples were constructed through relatively trivial premise modifications.
  • 4.3. Token-level Artefacts: Leave-one-out omission identifies auxiliary verbs and prepositions as indicators of ungrammaticality in CoLA, while racial and homophobic slurs top hate-speech indicators in DWMW17.The method reuses one model and evaluates conditional-entropy changes on class-specific slices rather than fine-tuning a model for every token.

5. Related Work

Prior work estimates instance or dataset difficulty using model-agnostic information measures, heuristics, training behavior, probabilistic models, or interpretability methods. This paper positions V-usable information as a model-relative framework for comparing datasets and interpreting their attributes.

  • Information-theoretic measures: DIME estimates a model-agnostic lower bound on the lowest possible 0-1 error, but does not explain why datasets are easier for particular models.The paper distinguishes this from V-information’s model-relative dataset difficulty estimates.
  • Instance-difficulty methods: Word identity, input length, training loss, confidence, prediction variance, and related heuristics capture aspects of difficulty but offer limited model-specific interpretability.These approaches do not readily support interpreting datasets through predictive information about labels.
  • Training dynamics: Cartography provides complementary training-dynamics views, whereas V-information supplies an aggregate formalism for comparing dataset difficulty with respect to a model.Cross-dataset comparisons can be difficult when data maps are constructed from different datasets.
  • Probabilistic difficulty models: IRT learns instance difficulty through probabilistic performance models but does not formally relate difficulty to the evaluated model.Instance-selection estimates for active learning may also change as the model changes.
  • Interpretability: Interpretability and artefact-discovery methods provide related attribute-level analyses, while this work presents V-usable information as an NLP dataset-difficulty framework.The paper states that, to its knowledge, it is the first to use V-usable information for estimating NLP dataset difficulty.

6. Future Work

The framework points to future work on distribution shifts, open-ended generation, and modalities beyond NLP. These directions aim to broaden how V-information characterizes dataset difficulty.

  • Future work should examine how changes to the data distribution alter the difficulty of individual examples.
  • Extending V-information to open-ended text generation may require truncating the output space, such as with fixed-width beam search.
  • V-information can be applied beyond NLP because the framework is not inherently limited to text datasets.One proposed example uses image filters for colors and objects, then measures the resulting change in usable information.

7. Conclusion

The paper presents V-information as an information-theoretic framework for interpreting NLP dataset difficulty at both dataset and instance levels. It also uses input manipulation to uncover annotation artefacts.

  • The paper extends predictive V-information to estimate difficulty at the dataset level and introduces PVI for individual instances.
  • Instances with lower PVI have lower annotator agreement and are less likely to be predicted correctly.
  • Manipulating inputs before calculating V-information measures reveals systemic and token-level annotation artefacts.
  • The studies indicate that V-information provides an efficient means of interpreting NLP datasets.

A. Training Data

The appendix examines training-data sufficiency and compares V-information estimates across datasets and models. The reported analyses assess whether estimates stabilize and whether previously observed trends persist.

  • Figure 6 evaluates whether the SNLI test-set V-information estimate plateaus as BERT-base receives increasing fractions of training data.The figure uses random samples with replacement and reports averages and standard deviations across four samples per fraction.
  • Figure 7 compares accuracy and V-information estimates on the SNLI train and test sets across various models.
  • Figure 8 compares accuracy and V-information estimates on CoLA’s in-domain train and held-out sets across several models, including RoBERTa-large.The passage states that previously observed trends persist despite the increase in model scale.

C. Qualitative Analysis

The qualitative analysis identifies the hardest SNLI test instances according to BERT-base and notes that some may be mislabeled. The listed examples include all three natural language inference classes.

  • Table 4 lists the 10 hardest SNLI test instances according to BERT-base using the lowest PVI values.The table denotes entailment, neutral, and contradiction with E, N, and C.
  • All three SNLI classes are represented among the hardest instances, with entailment slightly over-represented.
  • Some hard examples appear mislabeled, including an instance labeled entailment whose correct label is contradiction.

D. Consistency of PVI estimates

PVI estimates are generally stable across models, epochs, and random seeds, and align with human judgments of instance difficulty. Attribute-specific transformations also expose dataset artefacts and explain differences between individual examples.

  • PVI estimates agree across models on SNLI, while correlations are lower on CoLA because it provides less usable information.
  • Human annotator agreement increases with average PVI, indicating concurrence between human-perceived and PVI-based difficulty.
  • PVI estimates remain stable during finetuning, with cross-epoch correlations above 0.80 during the first five epochs.
  • PVI estimates across BERT training seeds have high correlation, suggesting that model-perceived difficulty is not due to chance.
  • Attribute-specific transformations compare why SNLI instances differ in difficulty and reveal token-level annotation artefacts, including possible bias in DWMW17.Different attributes cannot be compared for the same instance because their models maximize likelihood over all data.

H. Relation to Dataset Cartography

PVI complements dataset cartography by connecting instance difficulty to training dynamics while also providing an aggregate dataset-level measure. Across data-map regions, easy-to-learn instances have the most usable information and hard-to-learn instances the least.

  • PVI tracks closely with the confidence axis of SNLI’s DistilBERT data map, while offering an aggregate dataset-level difficulty estimate unavailable from training-dynamics metrics.
  • PVI and data maps provide orthogonal perspectives: PVI measures usable information, whereas data maps capture instance behavior as training proceeds.
  • Data-map regions: Easy-to-learn instances have the highest average PVI and the greatest amount of DistilBERT-usable information.
  • Data-map regions: Hard-to-learn instances have the lowest average PVI and often correspond to mislabeled examples.
  • Data-map regions: Ambiguous instances have lower average PVI than easy-to-learn instances, indicating that they contain usable but comparatively smaller amounts of information.

I. Creating Datasets

The paper uses V-information to identify and filter confounded preference data, turning raw online votes into larger datasets with more usable information. Correcting for visibility bias yields preference data comparable in usable information to HH-RLHF.

  • Raw Reddit and Stack Exchange preference tuples contain approximately zero usable information for GPT-3, even with a capacious model family.
  • Filtering for cases where the higher-scoring comment was written later produces approximately 0.50 bits of GPT-3-usable information, matching HH-RLHF.The filter addresses the confound that earlier comments have more time to accumulate votes.
  • V-information identifies dataset-construction filters that can improve the usability of collective human-preference data.
  • The resulting Stanford Human Preferences datasets contain 385K Reddit preferences in SHP and 4.8M Reddit and Stack Exchange preferences in SHP-2.
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