arXiv subjects

Michael Hardy

Publications and source records attributed to Michael Hardy.

13 recordsLinked to original sources

arXiv2026

Evaluation Cards: An Interpretive Layer for AI Evaluation Reporting

AI evaluation results are produced at scale but reported inconsistently across leaderboards, model cards, benchmark papers, and company blogs. The cost is interpretive: readers cannot reliably compare results across sources, identify what a report omits, or trace an aggregate claim to its underlying evidence. Recent efforts address isolated components but leave three gaps: they cover only narrow slices of the evaluation lifecycle and do not compose into a single interpretable record; they specify static representations that do not differentiate the questions different stakeholders bring to the same evidence; and they remain proposals on paper, lacking the extraction infrastructure required for adoption at scale. We present \EvalCards{}, an operational reporting layer that composes benchmark metadata, evaluation run data, and model metadata into a unified record. We (1) derive a reporting schema from a structured review of 52 papers and 10 stakeholder interviews, (2) implement four interpretive signals (reproducibility, documentation completeness, provenance and risk, and score comparability), rendered through reader modes calibrated to research and non-research audiences, and (3) deploy a monitoring tool that applies \EvalCards{} across 5,816 models, 635 benchmarks, and 101,843 results, surfacing systematic gaps in current reporting practice.

cs.AI↗

arXiv2026

AI Cartography: Mapping the Latent Landscape of AI Benchmark Ecosystems

While aggregate leaderboard scores drive AI development, they contain substantial measurement noise whose sources and magnitudes remain unquantified, making it unclear when rankings reflect genuine capability differences versus evaluation artifacts. We introduce a framework for measuring the latent landscape in AI benchmark ecosystems. Applying Confirmatory Factor Analysis (CFA) and Generalizability Theory to 4,000+ models from the Open LLM Leaderboard, we decompose sources of ranking variance and establish: (1) structures assumed in current reporting practice underestimate the strength of relationships between benchmarks; (2) evidence of local dependence among leaderboard items, undermining uses of benchmarks as measurement instruments under current scoring systems; (3) contributor metadata explains more rank-relevant variance ($\approx9\%$) than architecture or deployment categories in this context; (4) a manifest-score "scaling law" slope has low reliability ($R_{\beta}=0.53$); by contrast, the latent general-factor size slope is highly stable across ecosystem controls ($R_g=0.97$). We are able to provide unique insights into benchmark dynamics, such as which benchmarks are a function of LLM size and which can be oppositely impacted by post-training practices. We provide actionable diagnostics to determine how benchmark rankings can be trusted and how benchmark design can be improved.

cs.AI↗

arXiv2026

Efficient Detection of Bad Benchmark Items with Novel Scalability Coefficients

The validity of assessments, from large-scale AI benchmarks to human classrooms, depends on the quality of individual items, yet modern evaluation instruments often contain thousands of items with minimal psychometric vetting. We introduce a new family of nonparametric scalability coefficients based on interitem isotonic regression for efficiently detecting globally bad items (e.g., miskeyed, ambiguously worded, or construct-misaligned). The central contribution is the signed isotonic $R^2$, which measures the maximal proportion of variance in one item explainable by a monotone function of another while preserving the direction of association via Kendall's $\tau$. Aggregating these pairwise coefficients yields item-level scores that sharply separate problematic items from acceptable ones without assuming linearity or committing to a parametric item response model. We show that the signed isotonic $R^2$ is extremal among monotone predictors (it extracts the strongest possible monotone signal between any two items) and show that this optimality property translates directly into practical screening power. Across three AI benchmark datasets (HS Math, GSM8K, MMLU) and two human assessment datasets, the signed isotonic $R^2$ consistently achieves top-tier AUC for ranking bad items above good ones, outperforming or matching a comprehensive battery of classical test theory, item response theory, and dimensionality-based diagnostics. Crucially, the method remains robust under the small-n/large-p conditions typical of AI evaluation, requires only bivariate monotone fits computable in seconds, and handles mixed item types (binary, ordinal, continuous) without modification. It is a lightweight, model-agnostic filter that can materially reduce the reviewer effort needed to find flawed items in modern large-scale evaluation regimes.

stat.AP↗

arXiv2026

Refactor Analysis: Predictive Evaluations of Factor Models and Dimensionality

Unidimensional factor models justify some of the most consequential summaries in science -- single scores, single ranks, and single leaderboards -- yet unidimensionality is usually assessed indirectly by fitting and evaluating models on images of the data (e.g., correlation matrices) rather than on the response matrix itself. We introduce Refactor analysis, a data-first evaluation paradigm that converts a one-factor solution into a rank-1 prediction of the original matrix by estimating both respondent- and item-side structure from dual association images. We further introduce Verifactor analysis, which evaluates the same construction under bi-cross-validated (BCV) row-column partitions for improved generalization. In simulations where the data-generating mechanism is truly rank-1 and correlational, Refactor metrics align with classical unidimensionality indices, validating the approach. However, across 200 public dichotomous datasets, traditional fit and unidimensionality measures, though highly intercorrelated, are weakly related to data recoverability, especially out of sample. This gap exposes a methodological vulnerability: excellent image-based fit can coexist with poor data-level explanatory power. Finally, treating the association measure itself as a testable hypothesis, we compare $\phi$, tetrachoric, and quadrant correlation, $q^\prime$, an important reintroduction. Quadrant correlation emerges as a simple, interpretable, and remarkably robust alternative, yielding consistently stronger reconstruction and more stable behavior under sample-size variation than commonly used correlations. Together, Refactor and Verifactor shift unidimensionality assessment from "does a one-factor model fit the correlation matrix?" to the question that matters for measurement and benchmarking: does a one-factor dependence structure recover and generalize the observed responses?

stat.ME↗

arXiv2026

Autoscoring Anticlimax: A Meta-analytic Understanding of AI's Short-answer Shortcomings and Wording Weaknesses

Automated short-answer scoring lags other LLM applications. We meta-analyze 890 culminating results across a systematic review of LLM short-answer scoring studies, modeling the traditional effect size of Quadratic Weighted Kappa (QWK) with mixed effects metaregression. We quantitatively illustrate that that the level of difficulty for human experts to perform the task of scoring written work of children has no observed statistical effect on LLM performance. Particularly, we show that some scoring tasks measured as the easiest by human scorers were the hardest for LLMs. Whether by poor implementation by thoughtful researchers or patterns traceable to autoregressive training, on average decoder-only architectures underperform encoders by 0.37--a substantial difference in agreement with humans. Additionally, we measure the contributions of various aspects of LLM technology on successful scoring such as tokenizer vocabulary size, which exhibits diminishing returns--potentially due to undertrained tokens. Findings argue for systems design which better anticipates known statistical shortcomings of autoregressive models. Finally, we provide additional experiments to illustrate wording and tokenization sensitivity and bias elicitation in high-stakes education contexts, where LLMs demonstrate racial discrimination. Code and data for this study are available.

cs.CL↗

arXiv2026

Knowledge without Wisdom: Measuring Misalignment between LLMs and Intended Impact

LLMs increasingly excel on AI benchmarks, but doing so does not guarantee validity for downstream tasks. This study contrasts LLM alignment on benchmarks, downstream tasks, and, importantly the intended impact of those tasks. We evaluate the performance of leading LLMs (i.e., generative pre-trained base models) on difficult-to-verify tasks of the teaching and learning of schoolchildren. Across all LLMs, inter-model behaviors on disparate tasks correlate higher than they do with expert human behaviors on target tasks. These biases shared across LLMs are poorly aligned with downstream measures of teaching quality and often negatively aligned with the intended impact of student learning outcomes. Further, we find multi-model ensembles, both unanimous model voting and expert-weighting by benchmark performance, further exacerbate misalignment with learning. We measure that selection of LLM and/or prompting strategy only reliably accounts for $15\%$ of all measured misalignment error and that variation in misalignment error is shared across LLMs, suggesting that common pretraining accounts for much of the misalignment in these tasks. We demonstrate methods for robustly measuring alignment of complex tasks and provide unique insights into practical applications of LLMs in high-noise contexts.

cs.LG↗

arXiv2025

Fantastic Bugs and Where to Find Them in AI Benchmarks

Benchmarks are pivotal in driving AI progress, and invalid benchmark questions frequently undermine their reliability. Manually identifying and correcting errors among thousands of benchmark questions is not only infeasible but also a critical bottleneck for reliable evaluation. In this work, we introduce a framework for systematic benchmark revision that leverages statistical analysis of response patterns to flag potentially invalid questions for further expert review. Our approach builds on a core assumption commonly used in AI evaluations that the mean score sufficiently summarizes model performance. This implies a unidimensional latent construct underlying the measurement experiment, yielding expected ranges for various statistics for each item. When empirically estimated values for these statistics fall outside the expected range for an item, the item is more likely to be problematic. Across nine widely used benchmarks, our method guides expert review to identify problematic questions with up to 84\% precision. In addition, we introduce an LLM-judge first pass to review questions, further reducing human effort. Together, these components provide an efficient and scalable framework for systematic benchmark revision.

cs.AI↗

arXiv2025

Measuring Teaching with LLMs

Objective and scalable measurement of teaching quality is a persistent challenge in education. While Large Language Models (LLMs) offer potential, general-purpose models have struggled to reliably apply complex, authentic classroom observation instruments. This paper uses custom LLMs built on sentence-level embeddings, an architecture better suited for the long-form, interpretive nature of classroom transcripts than conventional subword tokenization. We systematically evaluate five different sentence embeddings under a data-efficient training regime designed to prevent overfitting. Our results demonstrate that these specialized models can achieve human-level and even super-human performance with expert human ratings above 0.65 and surpassing the average human-human rater correlation. Further, through analysis of annotation context windows, we find that more advanced models-those better aligned with human judgments-attribute a larger share of score variation to lesson-level features rather than isolated utterances, challenging the sufficiency of single-turn annotation paradigms. Finally, to assess external validity, we find that aggregate model scores align with teacher value-added measures, indicating they are capturing features relevant to student learning. However, this trend does not hold at the individual item level, suggesting that while the models learn useful signals, they have not yet achieved full generalization. This work establishes a viable and powerful new methodology for AI-driven instructional measurement, offering a path toward providing scalable, reliable, and valid feedback for educator development.

cs.CL↗

arXiv2024

"All that Glitters": Approaches to Evaluations with Unreliable Model and Human Annotations

"Gold" and "ground truth" human-mediated labels have error. The effects of this error can escape commonly reported metrics of label quality or obscure questions of accuracy, bias, fairness, and usefulness during model evaluation. This study demonstrates methods for answering such questions even in the context of very low reliabilities from expert humans. We analyze human labels, GPT model ratings, and transformer encoder model annotations describing the quality of classroom teaching, an important, expensive, and currently only human task. We answer the question of whether such a task can be automated using two Large Language Model (LLM) architecture families--encoders and GPT decoders, using novel approaches to evaluating label quality across six dimensions: Concordance, Confidence, Validity, Bias, Fairness, and Helpfulness. First, we demonstrate that using standard metrics in the presence of poor labels can mask both label and model quality: the encoder family of models achieve state-of-the-art, even "super-human", results across all classroom annotation tasks. But not all these positive results remain after using more rigorous evaluation measures which reveal spurious correlations and nonrandom racial biases across models and humans. This study then expands these methods to estimate how model use would change to human label quality if models were used in a human-in-the-loop context, finding that the variance captured in GPT model labels would worsen reliabilities for humans influenced by these models. We identify areas where some LLMs, within the generalizability of the current data, could improve the quality of expensive human ratings of classroom instruction.

cs.CL↗

arXiv2019

The Rearrangement Number

How many permutations of the natural numbers are needed so that every conditionally convergent series of real numbers can be rearranged to no longer converge to the same sum? We define the \emph{rearrangement number}, a new cardinal characteristic of the continuum, as the answer to this question. We compare the rearrangement number with several natural variants, for example one obtained by requiring the rearranged series to still converge but to a new, finite limit. We also compare the rearrangement number with several well-studied cardinal characteristics of the continuum. We present some new forcing constructions designed to add permutations that rearrange series from the ground model in particular ways, thereby obtaining consistency results going beyond those that follow from comparisons with familiar cardinal characteristics. Finally, we deal briefly with some variants concerning rearrangements by a special sort of permutation and with rearranging some divergent series to become (conditionally) convergent.

math.LO↗

arXiv2006

Combinatorics of Partial Derivatives

The natural forms of the Leibniz rule for the $k$th derivative of a product and of Faà di Bruno's formula for the $k$th derivative of a composition involve the differential operator $\partial^k/\partial x_1 ... \partial x_k$ rather than $d^k/dx^k$, with no assumptions about whether the variables $x_1,...,x_k$ are all distinct, or all identical, or partitioned into several distinguishable classes of indistinguishable variables. Coefficients appearing in forms of these identities in which some variables are indistinguishable are just multiplicities of indistinguishable terms (in particular, if all variables are distinct then all coefficients are 1). The computation of the multiplicities in this generalization of Faà di Bruno's formula is a combinatorial enumeration problem that, although completely elementary, seems to have been neglected. We apply the results to cumulants of probability distributions.

math.CO↗

arXiv2002

An Illuminating Counterexample

We give a visually appealing counterexample to the proposition that unbiased estimators are better than biased estimators.

math.ST↗

arXiv2002

Scaled Boolean Algebras

Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but rather as degrees of belief in uncertain propositions. This paper separates the study of these objects from that not-entirely-mathematical problem that motivated them. That motivating problem is explicated in the first section, and the application of scaled Boolean algebras to it is explained in the last section. The intermediate sections deal only with the mathematics. It is hoped that this isolation of the mathematics from the motivating problem makes the mathematics clearer.

math.PR↗