A Simple and Efficient Baseline for Data Attribution on Images

We thank the reviewer for the extensive review of our work. We address the questions and comments below -

Visual Similarity

Ignoring how long (and how much storage) it would take to estimate data support using Datamodels and TRAK, we demonstrate in Figure 7 that the training samples with the most influence on the test query are, in most cases, not visually similar. Rankings from Datamodel (300K) and TRAK (100) show images of different classes on varying backgrounds and poses. The TRAK paper states that “in computer vision, visual similarity between two images does not fully capture the influence of one on the other in terms of model behavior.” Our work seeks to evaluate that claim.

Real-World Application

Unfortunately, Datamodels and TRAK cannot estimate data support on ImageNet due to the required storage space and compute time, as we comment on in Section 4.3. Our method is practical in the sense that it is tractable on a large-scale dataset like ImageNet. Evaluating brittleness is considered an application in the Datamodels and TRAK paper.

Prior Work and LDS Scores

We apologize the discussion regarding methods from prior works was unclear. We will rewrite the baseline and evaluation section for clarity in the next version of the paper. We will also move LDS scores to the main section of the paper.

We thank the reviewer for the extensive review of our work. We address the questions and comments below -

Model Dependent Features

We agree that algorithm behavior is dependent on a combination of architecture, optimization, and training data. Our goal was to demonstrate how far we could get by analyzing the training data exclusively. We have re-written relevant phrases in the text to emphasize that visual similarity can be effective while emphasizing there are other factors at play. Our work serves to stake out a baseline based only on the training data, and may help serve to compare against other attribution approaches.

Similarity and Data Attribution

Thank you for your extensive review. We believe there is a misunderstanding of what a data attribution method is. Our method is a data attribution method by definition:

“Consider an ordered training set of examples $S = \{z_1, …, z_n \}$ and a model output function $f(z, \theta)$. A data attribution method $\tau(z, S)$ is a function $\tau: \mathcal{Z} \times \mathcal{Z} \rightarrow R^n$ that for any example $z \in \mathcal{Z}$ and a training set $S$, assigns a real valued score to each input $z_i \in S$ indicating its importance to the model output $f(z; \theta^{*}(S))$.” [2]

By measuring the distance of a training sample to the decision boundary of the ESVM, our method actually does assign real number values to training samples which help classification of the query sample, as we describe in Appendix A.5. While the method only assigns positive scores to training examples of the same class, it is a function $\tau: \mathcal{Z} \times \mathcal{Z} \rightarrow \mathbb{R}^n$. Calling a zero function a data attribution method would be misleading because it is useless. In contrast, our method is competitive for data removal and data mislabel support, which are counterfactual by definition [1,2]. Our approach achieves similar scores to computationally expensive methods for data removal support. We achieve among the best AUCs on mislabel support for CIFAR-10 and are the only method to date that can tractably estimate data support on ImageNet.

We apologize this wasn’t clear in our paper, we’ll revise the introduction and relevant phrases accordingly.

[1] Datamodels [2] TRAK

Negative Influence and LDS

We’d like to note that the scores mentioned, TRAK (5 models) in Appendix E.3 in fact uses an ensemble of 100 models with 5 independent runs and thus still has a very high storage cost. We expand on the storage cost of TRAK below. A high LDS does not imply the method will be effective at other counterfactual estimation tasks like estimating data support. At the very least, our results emphasize that attribution metrics of LDS and data support are orthogonal. We agree, that our baseline may not show significant gains with more compute and we apologize this wasn't clear in the paper. We'll highlight this limitation in the next version.

Space Efficiency

For each training and test data, TRAK uses a projected gradient of dimension (from up to 4096 to 20480) which is significantly higher storage than MoCo embeddings (128 for CIFAR-10). So, even for a single checkpoint the approach typically requires higher memory. We tested the performance of TRAK-100 with 4096 dimensions and noticed the AUC on data removal support deteriorated, and hence for CIFAR-10 we used 20480 as the default dimension. We'll update the draft to reflect the same.

We thank the reviewer for their extensive insights. We provide responses to comments and questions below -

Algorithm Independence

Our proposed attribution approach is indeed algorithm-independent. We think this is interesting, that an algorithm-independent approach can be pushed much further than was claimed. We know this assumption is simplified and doesn’t hold for all applications. The intuition behind our approach is that models broadly learn very similar features from the training samples. This has been shown by several works [1, 2]. We agree this limits the downstream applications for example LDS score estimation, as we’ve shown in our work, and other applications as the reviewer stated. However, we’d again highlight that our simple approach works extremely well for data support metrics, a core debugging application claimed to work well in both Datamodels and TRAK.

[1] Li, Yixuan, et al. "Convergent learning: Do different neural networks learn the same representations?." arXiv preprint arXiv:1511.07543 (2015). [2] Kornblith, Simon, et al. "Similarity of neural network representations revisited." International conference on machine learning. PMLR, 2019.

Focuses on positive influence samples

Indeed, our baseline approach shows better performance on samples with high positive influence. We only tested a simple heuristic to identify -ve and zero influence samples for performance on the LDS score. While we agree our LDS scores are relatively low, we'd again emphasize that our approach is meant to serve as a baseline and shows much better results on data brittleness estimates. Our results highlight that attribution metrics of LDS and data brittleness may be orthogonal, while the latter may be more easily achievable. While attribution approaches have been applied for several tasks, at the core these are meant to estimate counterfactuals. Data removal and data mislabel supports are other forms of counterfactual tasks, as shown in Datamodels and TRAK. We'd also like to clarify that our results in the appendix show an LDS score of 0.08, equivalent to TRAK using 5 models higher than the 0.05 number the reviewer stated.

Duplication Assumption

We thank the reviewer for pointing out this example. Sample independence is indeed a strong assumption. But for estimating data support, a downstream application which other data attribution methods have been used for, our results indicate that relying on visual similarity can perform analogously, and be tractable for large-scale datasets like ImageNet. We agree in future works, it would be interesting to relax this assumption.

Same class as Positive Influences and Extensions to CLIP

Our assumption that same-class samples are positive influences is indeed simple. Our results however show this assumption works well in practice. Even for Datamodels on CIFAR-10 using 300K models, we find that for 500 of the most +ve samples, more than 250 belong to the ground truth class of the test data. Thus, this assumption while simplified, even holds true for datamodels. We only define our baseline approach for classification, yes. In future work, it would be interesting to extend this to multimodal approaches.

Writing is Vague

We thank the reviewer for pointing this out. We will clarify the relevant phrases in the next version of our paper.

We thank the reviewer for analyzing the strengths of our work in using a simple approach to reduce the cost of data attribution. We provide responses to comments and questions below -

Smallest subset identification as a proxy task

We focus on the smallest subset since this subset has the highest cumulative positive influence on the test sample, and has been used as a proxy task for measuring the performance of attribution methods on prior work [1, 2]. While several such subsets can exist, the smallest subset provides a simple intuitive explanation and allows us to compare against other attribution methods by directly comparing support sizes. Note that while our baseline approach focuses on finding the smallest subset, it also provides attribution beyond this subset.

Self-Supervised Features

We hypothesized that visual similarity plays a larger role in data attribution than prior works claimed [1, 2]. Visual similarity b/w samples are better captured using self-supervised models compared to supervised models since the former are trained to be invariant towards different augmentations.

While it isn’t clear why DINO performs significantly worse than other SSL methods, we find it also performs worse in terms of kNN test accuracy on CIFAR-10 (results in the table below). We suspect that the DINO recipe we used may not be suitable for small datasets such as CIFAR-10.

[1] DataModels [2] Trak

Quantitative Comparison

We highlight that our results already show quantitative comparisons against baselines. In Figure 4 for each validation sample, we compute if our estimated support is smaller than other baselines. We will also add results regarding the intersection of these subsets in the next version of our paper.

Subset Class Assumption

Our assumption is supported by the intuition that to misclassify a sample, we should remove training data from its vicinity that shares the same class. This would help in increasing the density near the test sample, toward a different class. While we cannot be sure if samples from other classes also have a positive impact on the validation sample, this approach is meant to serve as a baseline. As the reviewer stated, we find this simplistic assumption works very well and outperforms TRAK on Imagenet.