Anchor Points: Benchmarking Models with Much Fewer Examples (2024)

Abstract: Modern language models often exhibit powerful but brittle behavior, leading to the development of larger and more diverse benchmarks to reliably assess their behavior. Here, we suggest that model performance can be benchmarked and elucidated with much smaller evaluation sets. We first show that in six popular language classification benchmarks, model confidence in the correct class on many pairs of points is strongly correlated across models. We build upon this phenomenon to propose Anchor Point Selection, a technique to select small subsets of datasets that capture model behavior across the entire dataset. Anchor points reliably rank models: across 87 diverse language model-prompt pairs, evaluating models using 1-30 anchor points outperforms uniform sampling and other baselines at accurately ranking models. Moreover, just a dozen anchor points can be used to estimate model per-class predictions on all other points in a dataset with low error, sufficient for gauging where the model is likely to fail. Lastly, we present Anchor Point Maps for visualizing these insights and facilitating comparisons of the performance of different models on various regions within the dataset distribution.

## introduction language models have unlocked incredible generalization through scaling up parameters and pretraining data. yet these same systems prove to be brittle, spurring the development of larger, more diverse, and more shrewd benchmarks to reliably assess their behavior @xcite @xcite . modern benchmarks typically have on the order of 10 5 validation examples, with 10 3 -10 4 per task. such numbers ensure that validation performance strongly correlates with test performance and that all in-domain regions are captured. but these sizes are often unwieldy for rapid experimentation and do not easily afford interpretability. to we then evaluate a held-out model, falcon-7b, on 30 anchor points (green triangles). the model's predictions on only these 30 points are used to estimate the falcon-7b predictions on the remaining 842 points with a mean absolute error of 0.09, achieving 92% agreement with the model's true predictions. the anchor points identify regions where the model is weak (red regions). we show the same anchor point map colored by the true falcon-7b predictions in figure 9 , demonstrating that the model is indeed weak in these areas. in this work, we investigate the problem of benchmarking model performance and revealing model weaknesses on large datasets with as few evaluation examples as possible, an objective we call micro-benchmarking. we propose anchor figure 2 : anchor points are micro-benchmarks, tiny representative subsets of large benchmarks. correlative structure in the predictions of source models on the large benchmark can be used to extract these points. each anchor point has a weight corresponding to the fraction of the benchmark it represents. evaluating models on the anchor points produces a score that rank correlates with performance on the entire benchmark. anchor point maps visualize a given model's likely instancelevel performance on all points in the benchmark using only its performance on the anchor points. point selection, a technique that finds small evaluation sets that are maximally representative of model behavior over the entirety of a large dataset. we find that anchor points are effective development sets: across 87 diverse language models and prompts, using 1-30 anchor points shows superior performance at ranking model performance over random and embedding-based selection baselines. moreover, evaluating just a dozen anchor points can be used to predict the model's instance-level predictions on all other points in the dataset with high agreement on average, sufficient to estimate where models are likely to fail. our approach builds upon a simple insight: for many pairs of points from a given dataset, the predicted probability of the correct class strongly correlates across models. thus, evaluating every model on the entirety of a dataset is redundant. the predictions of existing source models on a given dataset are telling about predictions of a new target model, even across considerable performance gaps. this mirrors phenomena like accuracy on the line @xcite and agreement on the line @xcite , but at a much more granular scale. anchor points can be selected by identifying dataset medoids in a space where distance is a positive, monotonically decreasing function of cross-model correlations between points. we further propose to visualize this space using multidimensional scaling and u-map @xcite , which we call anchor point maps. anchor point maps show what region each anchor point captures and highlight that different models and prompts may struggle on different dataset regions, allowing fine-grained comparisons. emphatically, we do not aim to replace large benchmarks, but rather provide cheaper signal about model performance on these benchmarks to help accelerate the development of models and prompts. we also strive to be blunt about the limitations of our technique. anchor point generalization relies on the predictive correlations of source models being consistent with that of target models. this is not always the case, leading to poor generalization to specific target models depending on the choice of source models. we share simple rules of thumb to promote this source-target consistency, but lack rigorous theory to guide source model selection. we lay foundations for further research into model predictive correlations and efficient, interpretable model evaluation. ## predictive correlations to motivate our approach, we first show that language models make predictions with consistent structure. for many pairs of points from a given dataset, the predicted probability of the correct class strongly correlates across models. experimental set-up we obtain a diverse set of language models from huggingface and the openai api: 27 bert-family models, 11 non-instruction-tuned gpt-family models, 5 instruction-tuned gpt-family models, and 5 gpt-3/3.5 variants (all listed in tables 9 10 ). we denote these model sets as the bert-family, gptfamily, instructgpt-family, and openai-family respectively. for six datasets from the glue benchmark @xcite , we finetune each bert-family model on the training split d train and obtain its predicted probability of the correct class on each instance in the validation split d eval . for the other model families we zero-shot prompt for the same datasets using three multiple-choice prompts per dataset (appendix d). we obtain the predicted probability of each class by performing softmax over the log probabilities of candidate answer sequences. thus, we obtain a prediction matrix p for each model family and dataset with size n subjects × |d eval | matrix where n @xmath0, 30 for p gp t , 15 for p igp t , 15 for p oai , and 87 for their union p all . model predictions on pairs of examples are linearly correlated across models. the prediction matrices are approximately low-rank for all tasks ( predictive correlations tend to generalize across diverse models figure 6 in appendix a shows how well the strong trends from each family transfer to other families. errors are lowest in the bottom row, suggesting that using source models that span all model families result in the most generalizable trend lines. we also observe that the predictive correlations of the bert-family do not generalize well to other model families, which we explore further in figure 8(b ). however, most errors in the table are generally low, suggesting that predictive correlations tend to generalize across diverse models. ## sample-efficient model evaluation we now evaluate the anchor point techniques and compare against baselines for 1) selecting representative evaluation subsets to rank models foot_1 and 2) estimating model instance-level performance on held-out points in d eval . ## sample-efficient model analysis we now highlight how anchor point maps provide fine-grained analysis of model generalization both within and across datasets. this is achieved in a sample-efficient manner using the anchor point predictor. anchor point maps visualize where models generalize anchor point maps reveal the extent to which models learn distinct regions of dataset distributions. model performance on each sample correlates with performance in the sample's neighborhood, allowing the anchor point predictor to estimate where models will fail without evaluating the entire dataset. figure 1 shows the sst-2 validation set mapped by the predictions of 60 source models and then colored by estimated falcon-7b predictions using thirty anchor points. these estimated predictions are quite faithful to the model's true predictions (achieving 0.09 mae and 92% agreement), revealing regions where the model is weak. this localization of model behavior starkly contrasts with typical language embedding spaces, where model performance tends to be non-localized (figure 12 ). however, like embedding spaces, related examples naturally cluster together. anchor points predict diverse model behavior figure 5 in the appendix shows four anchor point maps of 1000 qqp points, comparing the true and estimated predictions of deberta-v3-base and text-davinci-003 using 30 anchor points. the two models are weak in distinct regions of the dataset. despite deberta-v3-base achieving stronger performance overall, it fails in a region of the negative class cluster where text-davinci-003 is mostly correct. this is perhaps related to "no-free lunch" theorems in statistical learning theory: different models have biases that will lend them to perform the best on different inputs @xcite , which is obscured by single-number evaluation metrics. the fact that the same set of anchor points can generalize to models with diverse behaviors highlights that the same underlying predictive correlations can engender these different behaviors. we explore anchor point generalization further in appendix a. ## limitations anchor points show diminishing returns we discuss in appendix a that apw correlation begins to plateau as the evaluation set size grows to 100 points due to an inherent upper bound. we also discuss that for large evaluation sets, anchor points the map is computed using the predictions of 13 source models. we color each point according to the dataset to which it belongs. we observe that all datasets overlap, but points tend to cluster with other points from the same dataset or a related dataset. anchor points do not always generalize in order for anchor points and anchor point maps to generalize, the predictive trends of source models must be consistent with that of target models. while anchor points can be further optimized in its current form, anchor point maps require computing correlations between all pairs of points in the dataset. this is computationally expensive for huge datasets. multi-dimensional scaling with missing values or correlation matrix completion could dramatically decrease these costs. ## conclusion and future work we present anchor point selection, a technique that finds maximally-representative subsets from large datasets which can be used to efficiently rank models and estimate model behavior over the entire dataset. we also present anchor point maps, a tool to visualize how well models generalize across various subsets of datasets. important future work includes developing better theory underlying when models share predictive correlations and designing intelligent source model selection strategies to ensure anchor point generalization to desired sets of target models. the fact that diverse language models make highly correlated predictions on many pairs of examples suggests that modern benchmarks contain many redundant examples. an interesting future direction would be to use predictive correlations to guide benchmark development by selecting fewer redundant examples, which would ideally lead to more diverse and difficult benchmarks. the potential to extend anchor point maps and anchor point selection to tasks beyond language classification is exciting. perhaps other continuous performance metrics are strongly correlated between examples, such as bleu scores or the rewards given by a reward model. exploiting such phenomena could allow a dramatic reduction in the number of examples that modern language models must be evaluated on, leading to reduced costs for model development.