Anchor Points: Benchmarking Models with Much Fewer Examples

Our findings mirror Accuracy on the Line and Agreement on the Line at a much more granular scale, i.e., data instances rather than data sets.

“Our findings presented in this work mirror these phenomena at a much more granular scale, i.e., data instances rather than data sets.”

• cites Miller et al., 2021 sourceNot checked — no full text of the source
• cites Baek et al., 2022 sourceSupported

In six popular language classification benchmarks, model confidence in the correct class on many pairs of points is strongly correlated across models.

“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.”

• Also stated in: § 1 Introduction · p. 2 · plain

  “For many pairs of points from a given dataset, the predicted probability of the correct class strongly correlates across models.”

• Also stated in: § 5 Predictive Correlations · p. 5 · boosted

  “This phenomenon is wide-spread: it holds for many pairs of examples across the six GLUE tasks and 87 widely-used language models and prompts.”

Models tend to have correlated performance on groups of questions from the same domain as well as related domains.

“models tend to have correlated performance on groups of questions from the same domain as well as related domains.”

This localization of model behavior starkly contrasts with typical language embedding spaces, where model performance tends to be non-localized.

“This localization of model behavior starkly contrasts with typical language embedding spaces, where model performance tends to be non-localized (Figure 12).”

Positive trends generalize more reliably than negative trends.

“We observe that positive trends generalize more reliably than negative trends.”

Anchor points often transfer both within and across model families.

“While Table 7 shows that anchor points often transfer both within and across model families”

The two models deberta-v3-base and text-davinci-003 are weak in distinct regions of the QQP dataset.

“The two models are weak in distinct regions of the dataset.”

Anchor Points can surpass the upper bound of Nearest Source Neighbor performance.

“The B = |D eval | column is shown only for reference to highlight that Anchor Points can surpass the upper bound of Nearest Source Neighbor performance.”

Optimizing for representativeness naturally leads to discriminability.

“Instead, we optimize for representativeness which we show naturally leads to discriminability.”

Model predictions on pairs of examples are linearly correlated across models.

“Model predictions on pairs of examples are linearly correlated across models.”

• Also stated in: § 5 Predictive Correlations · p. 5 · hedged

  “We see that ϕ n ( x 1 )[ y ] often linearly correlates with the model's prediction on a different instance ϕ n ( x 2 )[ y ] across models, i.e. ϕ n ( x 2 )[ y ] ≈ wϕ n ( x 1 )[ y ] + b , where w and b can be found by fitting a trend line through the correct class confidences of all source models.”

Using source models that span all model families results in the most generalizable trend lines.

“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 still observe these gains when source models are freely-available while all target models are closed-source.

“Moreover, we still observe these gains when source models are freely-available while all target models are closed-source (Table 4).”

APW correlation begins to plateau as the evaluation set size grows to 100 points due to an inherent upper bound.

“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.”

• Also stated in: § A Anchor Points Generalization Analysis · p. 13 · plain

  “For many settings, APW correlation begins to plateau as the evaluation set size grows to 100 points.”

Predictive correlations tend to generalize across diverse models.

“Predictive Correlations Tend to Generalize Across Diverse Models”

• Also stated in: § 5 Predictive Correlations · p. 5 · hedged

  “However, most errors in the table are generally low, suggesting that predictive correlations tend to generalize across diverse models.”

Examples in this region remain poorly captured across random seeds and anchor point set sizes, highlighting a systematic lack of generalization to this minority subset.

“We find that examples in this region remain poorly captured across random seeds and anchor point set sizes, highlighting a systematic lack of generalization to this minority subset.”

High school physics and college physics questions are often not nearest neighbors, despite these datasets having the largest vocabulary overlap (21%) of any pair within the 6 MMLU datasets.

“Notably, Figure 4(b) reveals that high school physics and college physics questions are often not nearest neighbors, despite these datasets having the largest vocabulary overlap (21%) of any pair within the 6 MMLU datasets (Figure 14).”

The prediction matrices are approximately low-rank for all tasks.

“The prediction matrices are approximately low-rank for all tasks (Table 1).”

The Anchor Point Predictor can estimate model performance at the instance-level over the entire dataset.

“The Anchor Point Predictor can estimate model performance at the instance-level over the entire dataset.”

The estimates of a small number of anchor points achieve high average agreement with true model predictions.

“The estimates of a small number of anchor points achieve high average agreement with true model predictions.”

A nearest neighbor of a college chemistry question is equally likely to be about college chemistry or clinical knowledge.

“In contrast, a nearest neighbor of a college chemistry question is equally likely to be about college chemistry or clinical knowledge.”

The same set of anchor points can generalize to models with diverse behaviors.

“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.”

The correlations of randomly selected source models do not necessarily generalize to all target models.

“the correlations of randomly selected source models do not necessarily generalize to all target models (e.g. Figure 13).”

Anchor Points and Nearest Source Neighbor surpass the naive baselines by a large margin.

“Anchor Points and Nearest Source Neighbor surpass the naive baselines by a large margin.”

Observing where Figures 9(a) and 9(b) differ reveals a small subset of points in sparser regions that are poorly captured by the anchor points.

“observing where Figures 9(a) and 9(b) differ reveals a small subset of points in sparser regions that are poorly captured by the anchor points.”

Using B = 100 anchor points surpasses the upper bound of this baseline on 3 of the 6 datasets.

“Note that using B = 100 anchor points surpasses the upper bound of this baseline on 3 of the 6 datasets.”

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.

“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.”

• Also stated in: § 1 Introduction · p. 1 · plain

  “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.”

On average, around 60% of the nearest neighbors of a high school physics question are also from the high school physics domain.

“On average, around 60% of the nearest neighbors of a high school physics question are also from the high school physics domain.”

Nearest Source Neighbor achieves competitive performance at estimating model instance-level predictions.

“Nearest Source Neighbor achieves competitive performance at estimating model instance-level predictions.”

Anchor Point Weighted performance tends to be more reliable across evaluation set sizes and test settings than APP as well as the baselines.

“We observe that Anchor Point Weighted (APW) performance tends to be more reliable across evaluation set sizes and test settings than APP as well as the baselines.”

The predictive correlations of the BERT-family do not generalize well to other model families.

“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).”

For ranking 77 language models on GLUE tasks using small evaluation sets, Anchor Points Weighted achieves the most reliable performance overall at low evaluation set sizes.

“Anchor Points Weighted achieves the most reliable performance overall at low evaluation set sizes.”

• Also stated in: § Algorithm 2 Anchor Points Predictor Predict · p. 24 · plain

  “Anchor Points Weighted achieves the most reliable performance overall at low evaluation set sizes.”

• AssumptionRests on an assumption: Target models follow the same predictive correlations as the source models used to construct the Anchor Point Map.

Both methods are far below random on the Global Facts dataset.

“Notably, both methods are far below random on the Global Facts dataset.”

For ranking language models at 6 GLUE tasks from each model family using 1 to 30 points, AP Weighted and AP Predictor are the most effective at accurately ranking models in this small-data regime.

“AP Weighted and AP Predictor prove to be the most effective at accurately ranking models in this small-data regime.”

• AssumptionRests on an assumption: Target models follow the same predictive correlations as the source models used to construct the Anchor Point Map.

For SST-2, the Anchor Point Weighted Score computed using three anchor points achieves a Kendall Tau correlation of 0.68 with true model performance on the SST-2 validation set (872 points).

“The Anchor Point Weighted Score computed using these three points achieves a Kendall Tau correlation of 0.68 with true model performance on the SST-2 validation set (872 points)”

• AssumptionRests on an assumption: Target models follow the same predictive correlations as the source models used to construct the Anchor Point Map.

For 19 of the 30 settings, the random selection curve eventually reaches the APW curve at some evaluation set size smaller than 100 points.

“For 19 of the 30 settings, the random selection curve eventually reaches the APW curve at some evaluation set size smaller than 100 points.”

Random selection eventually surpasses the APW curve in 5 of these 19 settings.

“However, it is surprising that random selection eventually surpasses the APW curve in 5 of these 19 settings.”

Evaluating a randomly selected pair of models on three randomly selected points would identify the stronger performer with 67% probability.

“(Evaluating the pair on three randomly selected points would identify the stronger performer with 67% probability).”

Anchor Points Predictor outperforms random on only 3 of 6 datasets.

“However, the Anchor Points Predictor outperforms random on only 3 of 6 datasets.”

In the limit where |X acq | = |X eval |, instance-level confidence in the correct class averaged over the entire dataset does not perfectly correlate with accuracy over the entire dataset.

“in the limit where |X acq | = |X eval | , instance-level confidence in the correct class averaged over the entire dataset does not perfectly correlate with accuracy over the entire dataset.”

High Pearson correlations naturally emerge when trend lines have a slope near one and intercept near zero.

“Note that high Pearson correlations naturally emerge when trend lines have a slope near one and intercept near zero.”

The three SST-2 anchor points correspond to easy (0), moderate (1), and difficult (2) examples.

“we see that these points correspond to easy (0), moderate (1), and difficult (2) examples.”

In the pairwise correlation matrix of 87 model-prompt pairs on 50 SST-2 examples, a dark bar at index 13 indicates an example that tends to negatively correlate with all other examples.

“Notably, a dark bar at index 13 indicates an example that tends to negatively correlate with all other examples.”

Among the compared embedding spaces, only the Anchor Points Map results in clean localization of model performance, where a held-out model's performance on each point correlates with its performance on neighboring points.

“Only the Anchor Points Map results in clean localization of model performance where a held-out model's performance on each point correlates with its performance on neighboring points.”

• AssumptionRests on an assumption: Target models follow the same predictive correlations as the source models used to construct the Anchor Point Map.

The APW curve has a tighter upper bound than random selection.

“This is a result of the APW curve having a tighter upper bound than random selection”

This upper bound does not exist for APP.

“This upper bound does not exist for APP.”

Selecting a source model set that is diverse (e.g., comes from multiple families) results in the best generalization.

“As a general rule of thumb, selecting a source model set that is diverse (e.g. comes from multiple families, see Figure 6) results in the best generalization.”

Minimizing evaluation set size poses the risk of excluding minority subsets of the data distribution.

“minimizing evaluation set size poses the risk of excluding minority subsets of the data distribution.”

The selection strategy is agnostic to the target model(s) being evaluated.

“Furthermore, our selection strategy is agnostic to the target model(s) being evaluated.”

Very small benchmark development sets-just several to a few dozen examples-might suffice to capture model behavior over the full breadth of the benchmark.

“Surprisingly, very small-just several to a few dozen examples might suffice.”

The task of selecting a X_acq that is maximally representative of D_eval for all models in S reduces to solving a KMedoids problem that maximizes the correlation between the selected and the remaining points.

“The task of selecting a X acq that is maximally representative of D eval for all models in S reduces to solving a KMedoids problem that maximizes the correlation between the selected and the remaining points:”

The technique minimizes the number of forward-passed examples necessary for reliable model evaluation.

“Our technique instead minimizes the number of forward-passed examples necessary for reliable model evaluation.”

Evaluating a model on both examples of a strongly correlated pair is redundant.

“This suggests that evaluating a model on both examples 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.

“The predictions of existing source models on a given dataset are telling about predictions of a new target model, even across considerable performance gaps.”

Embedding-based approaches to sample-efficient model evaluation tend to fail.

“explaining why embedding-based approaches to sampleefficient model evaluation tend to fail.”

Models with strong knowledge of college chemistry are likely to have strong knowledge of clinical knowledge as well.

“This suggests that models with strong knowledge of college chemistry are likely to have strong knowledge of clinical knowledge as well.”

The semantic similarity of two questions is often a poor proxy for similar model performance on the questions.

“This highlights that the semantic similarity of two questions is often a poor proxy for similar model performance on the questions”

The agreement achieved by Nearest Source Neighbor is upper bounded by the agreement of each target model and its true nearest source model neighbor.

“The agreement achieved by this technique is upper bounded by the agreement of each target model and its true nearest source model neighbor (indicated by the B = | D eval | column in Table 3).”

The resulting evaluation set is transferable to other language models.

“The resulting evaluation set is transferable to other language models.”

The same underlying predictive correlations can engender different model behaviors.

“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.”

Anchor Point Selection is 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 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.”

• AssumptionRests on an assumption: For anchor points and anchor point maps to generalize, the predictive trends of source models must be consistent with those of target models.

Modern benchmarks contain many redundant examples.

“suggests that modern benchmarks contain many redundant examples.”

Anchor Point Maps reveal the extent to which models learn distinct regions of dataset distributions.

“Anchor Point Maps reveal the extent to which models learn distinct regions of dataset distributions.”

The nature of the dataset plays a large role in determining whether Anchor Points outperform Nearest Source Neighbor.

“indicating that the nature of the dataset plays a large role.”

• AssumptionRests on an assumption: Target models follow the same predictive correlations as the source models used to construct the Anchor Point Map.

Spuriously high correlations are not common.

“suggesting that spuriously high correlations are not common.”

Increasing the source model set size would improve the probability of learning generalizable predictive correlations.

“Increasing the source model set size would improve the probability of learning generalizable predictive correlations.”

Different model families may have predictive correlations that do not generalize to other families.

“Notably, it highlights that different model families may have predictive correlations that do not generalize to other families.”

Anchor point sets can be highly representative despite being small.

“Anchor point sets can be highly representative despite being small.”

• AssumptionRests on an assumption: Target models follow the same predictive correlations as the source models used to construct the Anchor Point Map.

The Kendall Tau correlation of 0.68 achieved by the three-point Anchor Point Weighted Score is sufficient to identify the stronger performer of a randomly selected pair of models with 84% probability.

“sufficient to identify the stronger performer of a randomly selected pair of models with 84% probability.”

• AssumptionRests on an assumption: Target models follow the same predictive correlations as the source models used to construct the Anchor Point Map.

This suggests a distinction in how fine-tuned and prompted models fit the task distribution.

“This suggests a distinction in how fine-tuned and prompted models fit the task distribution.”

Semantic similarity in questions can be an effective proxy of model performance similarity when questions emphasize intensive knowledge rather than simple language understanding.

“Interestingly, the improved performance of Pretrained Weighted in MMLU relative to GLUE suggests that semantic similarity in questions can be an effective proxy of model performance similarity when questions emphasize intensive knowledge rather than simple language understanding.”

The estimated predictions from the Anchor Point Map successfully identify regions where Falcon-7b is weak.

“The estimated predictions successfully identify regions where the model is weak (red regions).”

• AssumptionRests on an assumption: Target models follow the same predictive correlations as the source models used to construct the Anchor Point Map.

More complex distributions require larger evaluation sets to be well-represented.

“reflecting that more complex distributions require larger evaluation sets to be well-represented.”

Anchor point methods can reduce the cost of ranking expensive target models with minimal source model costs.

“This highlights that the anchor point methods can reduce the cost of ranking expensive target models with minimal source model costs.”

The observed trend differences highlight the distinct behavior of fine-tuned versus prompted models.

“highlighting the distinct behavior of fine-tuned vs. prompted models.”

The clean localization of model performance by the Anchor Points Map allows fine-grained comparison of how different models perform on the same dataset distribution.

“This allows fine-grained comparison of how different models perform on the same dataset distribution.”

• AssumptionRests on an assumption: Target models follow the same predictive correlations as the source models used to construct the Anchor Point Map.

A randomly-selected evaluation set is sufficiently representative when sufficiently large.

“This is natural: a randomly-selected evaluation set is sufficiently representative when sufficiently large.”

The correlations learned between Global Facts questions using only 7 source models are likely to be weak or spurious.

“The correlations learned between these questions (using only 7 source models) are likely to be weak or spurious.”