  Characterizing samples that are difficult to learn from is crucial to
developing highly performant ML models. This has led to numerous Hardness
Characterization Methods (HCMs) that aim to identify "hard" samples. However,
there is a lack of consensus regarding the definition and evaluation of
"hardness". Unfortunately, current HCMs have only been evaluated on specific
types of hardness and often only qualitatively or with respect to downstream
performance, overlooking the fundamental quantitative identification task. We
address this gap by presenting a fine-grained taxonomy of hardness types.
Additionally, we propose the Hardness Characterization Analysis Toolkit
(H-CAT), which supports comprehensive and quantitative benchmarking of HCMs
across the hardness taxonomy and can easily be extended to new HCMs, hardness
types, and datasets. We use H-CAT to evaluate 13 different HCMs across 8
hardness types. This comprehensive evaluation encompassing over 14K setups
uncovers strengths and weaknesses of different HCMs, leading to practical tips
to guide HCM selection and future development. Our findings highlight the need
for more comprehensive HCM evaluation, while we hope our hardness taxonomy and
toolkit will advance the principled evaluation and uptake of data-centric AI
methods.
