How aligned are different alignment metrics?

Authors: jannis  ahlert
thomas  klein
felix  wichmann
robert  geirhos
Venue: ICLR_cc_2024_Workshop_Re-Align
Published: 2024-02-09 11:07:48

Abstract: In recent years, various methods and benchmarks have been proposed to empirically evaluate the alignment of artificial neural networks to human neural and behavioral data. But how aligned are different alignment metrics?
To answer this question, we here analyze visual data from Brain-Score (Schrimpf et al., 2018), including metrics from the model-vs-human toolbox (Geirhos et al., 2021), together with human feature alignment (Linsley et al., 2018; Fel et al., 2022) and human similarity judgements (Muttenthaler et al., 2022).
We find that pairwise correlations between neural scores and behavioral scores are quite low and sometimes even negative. For instance, the average correlation between those 80 models on Brain-Score that were fully evaluated on all 69 alignment metrics we considered is only 0.198. Assuming that all of the employed metrics are sound, this implies that alignment with human perception may best be thought of as a multidimensional concept, with different methods measuring fundamentally different aspects. Our results underline the importance of integrative benchmarking, but also raise questions about how to correctly combine and aggregate individual metrics. Aggregating by taking the arithmetic average, as done in Brain-Score, leads to the overall performance currently being dominated by behavior (95.25% explained variance) while the neural predictivity plays a less important role (only 33.33% explained variance). As a first step towards making sure that different alignment metrics all contribute fairly towards an integrative benchmark score, we therefore conclude by comparing three different aggregation options.

Main paper: 
 introduction: 
 A central question in the field of representational alignment is whether two given perceptual systems apply the same transformation to their inputs, thereby extracting equivalent representations from data. These systems could be artificial deep neural networks (DNNs) and biological systems like primate brains, or arbitrary other image-computable models. For a number of reasons, the perceptual alignment of artificial to biological systems has seen growing interest in recent years. Wellaligned DNNs could serve as models of biological visual processing and ultimately be an important step towards building neural prosthetics. Furthermore, measuring discrepancies between machine and biological perception can help to identify shortcomings in DNNs and improve machine perception (Wichmann & Geirhos, 2023) . For example, aligning DNNs with the human visual system promises to increase their robustness and generalization abilities (Dapello et al., 2022; Sucholutsky & Griffiths, 2023) .Since the question of representational alignment between brains and machines cannot be answered theoretically, various empirical methods have been proposed to measure the representational alignment of different systems. These efforts include the comprehensive Brain-Score benchmark (Schrimpf et al., 2018; 2020) , which integrates 51 different metrics to capture the alignment of different models to biological systems. In addition to neural data extracted from primates, other metrics also capture behavioral similarity, such as error pattern analysis (Rajalingham et al., 2018; Geirhos et al., 2020; 2021) and shape bias (Geirhos et al., 2018; Baker et al., 2018; Hermann et al., 2020) . Other commonly used datasets in the literature include behavioral similarity judgements (e.g., Hebart et al., 2023; Muttenthaler et al., 2022) .In light of this wealth of different metrics and datasets, all of which intend to quantify how "humanlike" (or brain-like, or primate-like) machine learning models are, a fundamental question arises:How aligned are different alignment metrics? For instance, if two metrics are highly correlated, it may be sufficient to evaluate models on one of them instead of both. On the other hand, if two metrics lead to highly dissimilar results, they measure different aspects and would lead to very different conclusions and model rankings-assuming the metrics are sound. In contrast, if inconsistencies between different metrics were for instance caused by methodological errors that do not reflect different aspects of brain-likeness, those cases could equally be surfaced by analyzing the agreement of metrics as we do in this study. In order to determine how aligned different alignment metrics are, we therefore analyze a broad set of up to 241 models evaluated on 50 different metrics, depending on data availability. 
methods: 
 Nomenclature. In the following, we will refer to any function that maps a model to a scalar score measuring some form of alignment as a metric or measure. Any set of metrics that together estimate alignment is referred to as a benchmark. The point of this distinction is that for a benchmark, some method of integrating its constituent metrics is necessary, like taking their average.Data sources. A central hub for collecting and integrating similarity measurements between DNNs and biological neural data is the Brain-Score benchmark (Schrimpf et al., 2018; 2020) . We use data from Brain-Score as the foundation of our analyses, but also integrate data from three other sources: Muttenthaler et al. ( 2022), Fel et al. (2022) and Geirhos et al. (2021) .The Brain-Score benchmark (Schrimpf et al., 2018) provides comparative data for two domains, vision and language. Throughout this paper, we focus exclusively on vision and thus on the visual Brain-Score. Brain-Score evaluation results can be thought of as a table, where the columns are different metrics and the rows are models evaluated on these metrics. The columns are semantically grouped into three sets: Neural, behavioral and engineering benchmarks. The neural benchmark can be further subdivided into groups that measure a model's similarity to different brain areas: V1, V2, V4 and IT. The behavioral benchmark consists of image classification metrics like error consistency, either for humans or monkey subjects. The engineering benchmark, which does not enter the final scoring, captures technical properties of models like ImageNet top-1 accuracy.We are particularly interested in the agreement between neural and behavioral measures of similarity between humans and machines, so we use data from Geirhos et al. (2021) , who record human classification performance on (corrupted) ImageNet images and calculate multiple types of behavioral similarity: error consistency (Do humans and machines make mistakes on the same images?) and shape bias (When presented with shape-texture cue conflicts, do models prefer shape, like humans?). Muttenthaler et al. (2022) systematically analyze which design choices affect the human-machine alignment for various DNNs, finding that neither architecture nor model scale are relevant, but that the training data and objective function are driving factors of alignment. They quantify humanmachine alignment as a network's ability to predict human behavior on triplet tasks (Hebart et al., 2020) , for which human subjects are presented with three natural images and classify one of them as the odd-one-out. Hence, we call this metric odd-one-out similarity. Fel et al. (2022) define humanmachine alignment as the similarity between model attention maps and attention maps obtained from human crowd-workers. Linsley et al. (2018) collected about 500k of these human attention maps, which quantify which regions of an image humans attend. We refer to this metric as attention map similarity. See Appendix A.2 for a detailed breakdown of models used in our analyses.Pairwise comparisons. To perform pairwise comparisons between two benchmarks, we calculate correlations between their respective scores for the same set of models. We calculate Spearman's rank correlation, which we believe to be appropriate since we are interested in the ranking of models (rather than measuring linear relationships as Pearson's correlation does). We apply very conservative Bonferroni-corrections to the thresholds of significance to account for multiple comparisons. Specifically, we divide the threshold of α = 0.05 by the number of metric-pairs, resulting in α = 0.0009 for Figure 1 and α = 0.001 for Figure 5 .Integrating metrics: arithmetic mean, z-transformed mean, mean rank. Given a set of metrics, what is the best way of aggregating them to a single, unified score? While a one-size-fits-all solution is unlikely to exist, we observe that aggregation choices can influence conclusions and thus warrant attention. Brain-Score uses a simple arithmetic average; in Section 4 we explore alternatives. A typical technique for dealing with different scales involves z-transforming values before aggregating them, which enforces that all individual metrics have zero mean and unit standard deviation. Alternatively, a ranking of models at some level of the Brain-Score hierarchy could be achieved by first ranking all metrics individually, and then calculating the average rank for every model. 
how aligned are different metrics?: 
 Correlations between Brain-Score benchmarks. To investigate the internal consistency of metrics on Brain-Score, we calculate Spearman's rank correlation coefficient for every pair of metrics, taking only those 95 models into account for which all scores are available. Removing duplicates and one model with an ImageNet accuracy below 1.9% leaves 88 models. We find that behavioral measures correlate strongly, especially those that all use the same dataset (Geirhos et al., 2021) . For many neural metric groups such as V4 and IT, as well as sub-groups within the V1 region relating to texture and receptive field size, internal consistency is higher than consistency with other metrics. We relegate detailed results to the Appendix, see Figure 4 .Moving beyond Brain-Score. Next, we investigate how the two new metrics that are not yet included in the Brain-Score project, odd-one-out similarity and attention map similarity, correlate with metrics on Brain-Score in Figure 1 . We again calculate pairwise Spearman's rank correlations between metrics for the set of models for which scores are available on all metrics. The odd-one-out similarity metric by Muttenthaler et al. ( 2022), which is of behavioral nature, is more correlated with metrics of V1 than with other behavioral metrics or later neural areas such as IT. The attention map similarity by Fel et al. (2022) is not significantly correlated with any other metric. Correlations that are significant after Bonferroni-correction are bold. We include only those 42 models that were evaluated on all metrics. Note that (a) variance of correlation coefficients is quite high and (b) similar metrics tend to agree, with the exception of the odd-one-out similarities. See also Figure 5 for the 80 Brain-Score models that have all scores on the Brain-Score metrics of this heatmap. 
alternatives to the arithmetic average: how do aggregation choices influence alignment results?: 
 The overall score that a model achieves on Brain-Score is calculated as the arithmetic mean of its neural and behavioral scores. In order for this to work well, the two values should at least have roughly the same magnitude, and ideally live in a common metric space. In Figure 2 , we scatter behavioral against neural scores, demonstrating the differences in their variance. Note also Linsley et al. (2023) , who find that models which perform better on ImageNet (which is a behavioral metric) tend to have worse IT-alignment (a neural metric). It is evident that the best behavioral scores of about 0.6 are quite a bit higher than the best neural scores of 0.5. Because of different scaling of the metrics, models with mediocre neural scores can still rank highly in the benchmark by virtue of their good behavioral scores. Assuming that we have obtained a matrix of model scores on different, possibly uncorrelated metrics with different distributions, we should ask ourselves how to best integrate these scores into a final model-score, or at least into an overall ranking of models. We now consider three different possible ranking schemes. The first strategy, which is the default in Brain-Score, is to integrate metrics via their arithmetic mean, which is sensitive to scaling issues and high-variance metrics. As an alternative, we consider z-transforming the score for every metric before averaging. We demonstrate how this scheme would change scores in Figure 2b . A drawback of this approach is that such scores are no longer stable over time, but depend on the scores of other models evaluated on that metric. Alternatively, if one does not care much about absolute model scores but only about their relative order, a possible integration scheme is obtaining the rank order for every metric, to then average over these ranks for the final score. Such a scheme would drop quantitative information about differences, but avoids inconsistency issues like the examples with high overall rank despite extremely low-rank performance on some metrics. In practice, applying these ranking schemes to Brain-Score does indeed lead to changes in model ordering (see Figure 3 ). Each row corresponds to a ranking scheme, and each model is represented as one point. A model's position on the x-axis corresponds to its score: Good models are further on the right, worse models further on the left, with scores normalized to span the range [0-1]. To visualize the impact of the ranking scheme, we colorcode models by their position in the default ranking, with higher scores colored brighter. Arguably, the differences in the resulting rank orderings are not "dramatic". However, if further studies were to e.g. correlate brain-likeness against other quantities, the effects of such changes could be quite large. We believe the issue of how to aggregate metrics deserves more scrutiny in the future. 3) Mean Rank is the result of averaging the ranks implied by the metrics (ranks are inverted for consistency, so higher is still better). All scores are normalized to the interval [0 -1] using Min-Max Normalization and colored according to a model's position under the original integration scheme. Rank-order changes greater than 10 positions (relative to the rank implied by the arithmetic mean) are highlighted in red. Spearman's rank correlations between the original ranking and the new ones are 0.47 (mean rank) and 0.92 (z-transformed mean). 
discussion: 
 Recent years have seen a wealth of datasets, benchmarks and metrics to measure the alignment between brains and machines. This is a promising research avenue, but in light of an ever-expanding set of measures, this raises the question of how aligned different alignment metrics truly are. We have contributed an analysis of the relationships between different alignment measures. The resulting correlations clearly indicate that different metrics capture different aspects of perceptual alignment, sometimes leading to contradictory results. For instance, models that score as highly human-like on one metric may be among the worst models according to a different metric. Consequently, alignment with human perception may best be thought of as a multidimensional concept, and as a community we may need to spend more time thinking about how to properly integrate different metrics. As a first step in this direction, we have investigated how different aggregation choices influence alignment results. Going beyond simple aggregation methods, in which metrics are treated equally and independently, one could also consider aspects like the semantic structure of metrics: Should we discount a model's high IT-score if it performs poorly on V1 and V2, indicating that it arrives at the right solution via the wrong path? Ultimately, it could be valuable for the community to derive a set of axiomatic requirements that an ideal integration scheme should fulfill, and categorize existing aggregation choices according to how well they conform to those. Overall, it seems clear that while there is a need for unified and comprehensive benchmarks, it may be important to consider alignment as an inherently multidimensional concept.A.1 LIMITATIONS Our analyses are limited by several technical issues. First, most of the pairwise correlations calculated in Figure 1 are not statistically significant, because so few models were present in all datasets. There also is some uncertainty about whether model weights were matched perfectly.At the time of writing, Brain-Score consists of 241 models. However, not all of those models were evaluated on all metrics: Only 88 different models were evaluated on all metrics that contribute to the final score (i.e. all neural and behavioral metrics). Completing this evaluation would be valuable to allow broader analyses, as would adding exact pointers to model checkpoints where this is feasible.For the analysis in Figure 1 , we determine a subset of the models on Brain-Score for which weights are publicly available and evaluate them on the metrics of Fel et al. (2022) and Muttenthaler et al. (2022) . This restriction limits the scope of our analysis and we hope to increase this sample in the future. Thus, the models currently evaluated on all considered metrics are: To calculate the correlations presented in Figure 1 , we included all models that were evaluated both on Brain-Score and the metrics proposed by Muttenthaler et al. ( 2022) and Fel et al. (2022) . However, this set of models is relatively small (42 models total), so the correlations reported between the different Brain-Score metrics are not necessarily representative. We demonstrate how Figure 1 would have looked like if all Brain-Score models had been included in Figure 5 . Figure 5 : Pairwise Spearman's rank correlations of Brain-Score metrics, from V1 to IT and behavioral measures. In contrast to Figure 1 , we include all Brain-Score models that had a value available for each metric, not only the subset that was also evaluated on the metrics by Muttenthaler et al. ( 2022) and Fel et al. (2022) . This amounts to a total of 80 models. The average correlation on this heatmap is 0.17, while the average correlation of the smaller set of models in 1 is 0.21, exemplifying the need for further thorough evaluations.The neural score that a model obtains on Brain-Score is defined as the average over four metrics measuring alignment to different brain regions (V1, V2, V4, IT). This averaging strategy will work well if those scores are highly correlated and similarly distributed. We therefore investigate the distributions of neural scores in Figure 6 , revealing similar distributions after removal of models with incomplete evaluations. Evidently, the distribution of scores for areas V1, V4 and IT are very similar, but the scores for area V2 are much lower, either hinting at lack of progress towards predicting V2 or at unfair calibration of this metric.While we find that behavior already accounts for a disproportionate amount of the overall score variance on the current Brain-Score leaderboard, we next investigate which role missing values play in determining the aggregate scores Figure 7 . Coloring each model by the number of non-zero scores available across metrics reveals a striking pattern: Most models fall into one of a few homogeneous groups, having 50, 33, 30 or 5 non-zero metrics respectively. Presumably, not all authors re-triggered scoring when new chunks of metrics were added to Brain-Score. The plot reveals that behavioral scores account for even larger portions of variance when only comparing models that have the same number of non-zero metrics with each other. https://www.brain-score.org/model/vision/1885https://www.brain-score.org/model/vision/646 
 
 Appendix:  



Reviews: review: title: title: Important work on the alignment of different human-machine alignment metrics.
main_review: main_review: Overall I found the study to be very well-motivated, tackling an important issue (heterogeneity between metrics measuring human-machine alignment), and the work has clearly documented that the rank orders of models across metrics is not consistent.

I had only a few minor issues/questions/comments to note:
1) the choice of spearman correlation makes sense for rank ordering models, but it seems to me that getting the magnitudes aligned is equally important. If one metric shows very high alignment for the best models (say .8) and the other very low alignment for the best models (say .2), even if they have the same rank orders of models, I would say these metrics aren't in agreement. You might consider Lin's Concordance, a measure of agreement that's sensitive to both the covariance and absolute agreement between measures (and varies between -1 and 1).

2) It seems import to compute and report noise-corrected scores. Take for instance the correlation between v4 and IT (.3), and v4 versus i2n consistency (.51). Is the v4 metric in greater alignment with the i2n consistency metric than with the IT metric? Numerically yes, but the difference could be due entirely to differences in measurement error / reliability. For instance, if both brain-metrics had a noise ceiling of .3, then the maximum observable correlation between them would be .3. If the i2n consistency metric is more reliability measured (behavioral data can be more reliable if aggregating over many subjects, so reliability .85 isn’t implausible), then it would have a maximum observable correlation of about .51. In other words, it’s possible v4 agrees with IT and i2n consistency equally well and that the apparent difference in those agreement strengths is due to differences in measurement noise.

\[r_{true} = \frac{r_{observed}}{\sqrt{reliability\_a \times reliability\_b}}\]

So the noise ceiling can be estimated as sqrt(reliability_a x reliability_b)

It would be helpful to see, side-by-side with the current heat maps, the heat-maps with noise-adjusted correlations (r_observed / noise_ceiling).

3) The text doesn’t make it very clear that the model attention maps were used to predict brain activations (I’m assuming that’s the case).

4) It would be helpful if the authors could offer suggestions on how these metric-alignment/misalignment scores can be understood beyond the main point (degree of alignment is low). For example, it seems that model agreement increased for many of the metrics for the analysis in Figure 2 versus Figure 1. What are we to make of those increases in agreement for the attention-map based analyses relative to the feature-based ones?

5) Unfortunately the study seems to be under powered, as noted in the Figure captions many of the reported correlations (even high ones) are not statistically significant. What statistical procedure was used? Some visual indication of which correlation scores are significant and which are not would be helpful.
strength_weakness: strength_weakness: Although more work needs to be done to nail this down, the work that was reported seems like a solid first step.
title: title: A thought-provoking topic, shy of solid conclusions, but with high community interest.
main_review: main_review: The authors tackle a very interesting question, how aligned are multiple different metrics by looking at a large set of models on Brain Score’s 51 metrics. Metrics are universally acknowledged as imperfect and while it’s known that different metrics are sensitive to different features of the data (and transformations of said data) it’s entirely understandable that metrics do not align along the same dimensions and can give conflicting results for the same models. The authors suggest that by studying aggregation techniques, a fairer representation might give more insight into common aggregation metrics in place today. The authors are also open to the idea that some metrics might be flawed and do not automatically deserve a place in a hypothesised perfect ranking aggregation. 

The last paragraph of Section 2 is a bit unclear to me. I’m not sure what ‘hierarchy’ is being referred to and this means the logic of applying the mean to all such models doesn’t make much sense to me. However, I assume this point will be clarified later in the paper (it wasn’t). I can see results were described as “not significant” without reference to alpha level, exactly what is being included in the Bonferroni correction etc. I can’t tell if the threshold was 0.01 and the tests reported 0.03, which would have passed a 0.05 threshold. It’s not even possible to get a vague sense of if this is even a limited data issue because we’re not told by how much the the predictions are away from being significant (without getting into the Fisher / Neyman-Pearson debate on p-values here). 

Some more general thoughts:

Why should either “neural” or “behavioural” be weighted equally (playing Devil’s Advocate)? Should we not care about one over the other? These feel like questions we should ask ourselves in the community and I like the fact this paper brings up the issue for consideration. However, are the proposed methods (z-scoring / ranking) the best ones? Without a clear definition for what we want as a community out of leader boards like Brain-Score, we’re just changing one ranking for another without being sure it’s inherently better because we don’t have external guidance to qualitatively say that we should care equally (or not) about average scores on neural or behavioural tasks. 

My take on the paper is that it brings up an important issue that I believe is worthy of consideration and could promote good discussion within the community when speaking of metrics generally. My reservations are that it principally points out a problem with the Brain-Score platform (specifically: arithmetic mean of (i) neural and (ii) behavioural scores). This is a limited domain that doesn’t necessarily apply across the field generally and is up to the creators to decide how they would like to rank / score candidate models. Beyond that, the proposed changes of z-transforming the scores / ranking introduce issues which the authors clearly and openly outline in the paper itself. This leaves the question still open as to whether such a shift in the final ranking is necessarily "better" or "more desirable". I can envisage scenarios where rank ordering is undesirable and the absolute values (i.e. not-ranked) scores are better metrics to work with. There’s still the case where we treat neural metrics as separate to behavioural ones and do away with unified metrics for the reasons claimed in the paper.

Having said that, I certainly feel thankful to the authors for bringing this issue to the surface and forcing me to think through what I would expect in alignment metrics and highlighting the potential for misinterpretation of models that perform highly on Brain-Score, since such models could have uneven performance across multiple domains. I also wasn’t aware of such a high correlation between the “behavioural” metrics and wonder now what they’re all measuring at a more fundamental level. Will this lead to statements like, “Our model scores well on X% of the metrics on Brain-Score?" where X is an inflated percentage, and hide the fact there is a large confound measuring broadly the same effect in the data? It would have been great if this were a long paper that went a bit more into the micro (and less macro) details to explore some of these questions.

I think the paper could be greatly enhanced even with a few modifications. Particularly, I'd like to hear some arguments about the downstream effects of what the effect would be of making the suggested changes in many scenarios that we might run into, in the community. For example, if someone needed to pick a model for a concrete downstream scenario, and they load up Brain-Score benchmark and have a look, what aspects about what they care about would be the most affected by each of your proposed metric changes? I also think you might want to look at page 5 of the Brain-Score paper on bioarxiv, which mentions an effect of taking the arithmetic mean across multiple metrics and why ranking might not be the best metric. In Figure 6, the same issue is sort of hinted at, but I originally thought it was a criticism of how Brain-Score had implemented things, but upon further checking, this is something discussed in the original paper with some (small) rationale. 

Why was this not submitted as a long paper? The main bulk of your results are all in the appendix and reorganisation could have brought these into the main paper where you could have had better organisational capacity to arrange things in a better format. Right now there is a "Further Results" appendix section that flows as a whole section's worth of text and figures. I think Figure 7 is your paper's main "message" but it's been bundled in the appendix while I think it deserves more prominence in the main paper. It's also not clear why you have decided to mark ranking changes (in red) that have moved more than 10 slots, without quantification of why this number makes sense. What does this tell us? This isn't comparable if there were 10% as many models, so maybe shifted position out of the total number of models might make a bit more sense here.

Clarity:

Very well-written and pleasant to read. Useful definitions provided (the "nomenclature" section) and only one or two very small places where I tripped up and wasn't sure of the intended meaning. Overall, very clear. Appendix section feels a little less refined, and also not sure why it's there as there was scope for a longer paper submission that could have had those figures and texts in there to still be under that page limit where things are better organised by sections and supporting text for the figures.

Correctness:

This is a little harder to evaluate specifically, because an issue was pointed out and the proposed 'fixes' are not really aligned with any external criteria and no clear judgement on a recommendation was given in the end. It had more of a thought-provoking essence to it than analysing a correct conclusion. Some missing statistical information in the paper, which I have never seen omitted before. However, this is in terms of showing lack of significance and is less serious than claiming significance without revealing that information. 

Novelty:

I certainly was made aware of some issues I hadn't fully considered and for me I see novelty. However, I can imagine others who are very familiar with Brain-Score who might not see as much novelty in it. The methods proposed (z-transform, ranking) are not necessarily new or interesting of themselves, but the application to how we rank candidate models of brain / behaviour is formulated in light of one of our sole large-scale benchmarks, so overall I would say yes, this work does exhibit relevant novelty. 

Interest to the community: 

Driven mainly by my response to "Novelty" and being a member of the community, I can say I'd be interested to see this work if I wasn't currently reviewing it. How broadly the community will find it interesting is not a point I can answer, but I think it will promote discussion and is definitely targeted at the community of people looking at representational alignment.
strength_weakness: strength_weakness: It's clear this piece of work was aimed at exactly this community and contained interesting things to say. That means I couldn't possibly be unsure whether this work fits the community (it does) and I think there is enough merit to the work to have it above the acceptance threshold (particularly in light of reviewer guidelines urging to interpret evaluation sections widely & generously).

Comments: title: Thank you for your review!
Thank you for your review!
comment: Thank you for writing such a thorough and constructive review! We especially appreciated your feedback on reporting correlations and significance strengths and have updated the respective plots to better reflect which results are significant. We have also evaluated more models on these metrics, so that more values have become significant. Regarding our methodology and statistical details, that were indeed missing before: We obtain the list of model scores for each metric and then, for every pair of metrics, calculate the pairwise Spearman’s correlation coefficient between their two lists. We apply a very conservative Bonferroni-correction to these pairwise correlations, dividing the significance level by the number of pairs. We have updated the figures to represent which specific correlations were significant. 

_“Why should either neural or behavioral scores be weighted equally?”_ This is a great question, and we hope that our paper can spark an open debate about how different types of alignment scores should be weighted when integrating them, or whether we should integrate scores in the first place.

_“The last paragraph of Section 2 is a bit unclear to me. I’m not sure what ‘hierarchy’ is being referred to.”_  We apologize for the confusion - we were referring to the hierarchy of scores in Brain-Score, where scores are grouped hierarchically (e.g. the neural-score consists of the V1, V2, V4 and IT scores, each of which in turn aggregates other scores). We have updated the manuscript to improve clarity.

_“...points out a problem with the Brain-Score platform”_ This is technically correct, since we really draw most of our data from Brain-Score, because it is by far the biggest and most popular benchmark of DNN-brain-alignment. But we also include two data sources that are not (yet) present on Brain-Score, and we believe that the points we raise about integrative benchmarking generalize beyond Brain-Score.

_“...arguments about the downstream effect of making the suggested changes”_ Thank you for this great point. The downstream effects of different ranking algorithms would be the changed ordering of models, which could result in different selections of models for other experiments. Also, correlations of “brain-likeness” against other quantities would be massively different. We have added this concrete example to the manuscript.

_“I can envisage scenarios where rank ordering is undesirable and the absolute values are better”_ This is a fair point - depending on the concrete research question, the scores themselves are sufficient. Rank-ordering models only becomes relevant in the context of benchmarking, as done on Brain-Score.

_“Why was this not submitted as a long paper?”_ In retrospect, that might have been a good idea - we are very happy to hear that you found this work interesting enough to warrant a longer treatment.
Thank you for your highly constructive review. We especially appreciate your insightful comments on the statistics, such as incorporating Lin’s Concordance and reporting noise-corrected scores.

_“The current study is underpowered”_ We were indeed limited by the number of models that were evaluated on both Brain-Score and the respective new metrics at the time of submission. In the meantime, we have evaluated more models on those metrics ourselves, and have learned that a large set of models will be added to Brain-Score soon (unfortunately not in time for the workshop). We will further update our manuscript once more data is available, but the added models have already allowed us to obtain significant results (see new figure 1).

_“You might consider Lin's Concordance”_ Thank you for this interesting proposal. We have looked into Lin’s Concordance and might re-do some of our plots in future iterations of the manuscript, but for now will stick with Spearman’s rank correlation, as it’s more commonly known and more intuitively clear, and because it is robust against different noise ceilings (see next question).

_“It seems important to compute and report noise-corrected scores.”_ You are absolutely correct that noise ceilings should be taken into account when comparing metrics. The Brain-Score platform is aware of this need and reports corrected scores for most of its metrics, and the Attention-Map similarity is also corrected for this. Some other metrics, e.g. behavioral Brain-Score scores and zero-shot similarity by Muttenthaler et al. are not corrected, but since we calculate Spearman’s Rank Correlation, our heatmaps should be inherently robust against this issue.

_“The text doesn’t make it very clear that the model attention maps were used to predict brain activations (I’m assuming that’s the case).”_ We apologize for the confusion. The model attention maps from Fel et al were not used to predict brain activations. Instead, they were compared to human attention maps (collected from crowd workers) to judge similarity between humans and DNNs. We have updated the manuscript to better explain this method. 

_“What statistical procedure was used? Some visual indication of which correlation scores are significant and which are not would be helpful.”_ Thank you for this very sensible suggestion. We have updated our figures to reflect which correlation scores are significant and clarified the wording regarding our methodology. In a nutshell: We obtain the list of model scores for each metric and then, for every pair of metrics, calculate the pairwise Spearman’s correlation coefficient between their two lists. We apply a very conservative Bonferroni-correction to these pairwise correlations, dividing the significance level by the number of pairs.

_“It would be helpful if the authors could offer suggestions on how these metric-alignment/misalignment scores can be understood … What are we to make of those increases in agreement for the attention-map based analyses relative to the feature-based ones?”_ Thank you for this question. In former figures 1 and 2, we were considering two metrics that are not yet included in Brain-Score, but also evaluate alignment between DNNs and brains in some way. The differences between figures 1 and 2 appear because different subsets of the models on Brain-Score were used to calculate the alignment between Brain-Score and the data by Muttenthaler et al and Fel et al. We have since been able to evaluate more of the Brain-Score models on the other two metrics, so that we can now plot this comparison in a joined figure (see new figure 1).
We would like to thank all reviewers for taking the time to review our paper so thoroughly and providing such constructive and helpful feedback. We are delighted to read that reviewers found the study to be “well motivated, tackling an important issue” (tGuJ) and consider our research question “very interesting” (yfAF).
We have updated our manuscript to incorporate as many of the suggested improvements as possible, especially with regards to how we report significance. The camera-ready version of the paper includes more models evaluated on the different benchmarks to increase the statistical power of our analyses. We also evaluated enough models on the two new metrics to be able to merge former figures 1 and 2 into a common heatmap.
Additionally, we updated former figure 3 to only include those models that were actually evaluated on all benchmarks, which both seems fairer and happens to illustrate our point better.