Quantifying Task-relevant Similarities in Representations Using Decision Variable Correlations
Authors: Yu Eric Qian
Wilson S. Geisler
Xue-Xin Wei
Venue: NeurIPS 2025 poster ()
Keywords: representational similarity
neural networks
neural coding
decision variable
computational neuroscience
Primary area: neuroscience_and_cognitive_science
TL;DR: Using a novel similarity measure, we find that current visual deep networks are diverging from the brain.

Abstract: Previous studies have compared neural activities in the visual cortex to representations in deep neural networks trained on image classification. Interestingly, while some suggest that their representations are highly similar, others argued the opposite. Here, we propose a new approach to characterize the similarity of the decision strategies of two observers (models or brains) using decision variable correlation (DVC). DVC quantifies the image-by-image correlation between the decoded decisions based on the internal neural representations in a classification task. Thus, it can capture task-relevant information rather than general representational alignment. We evaluate DVC using monkey V4/IT recordings and network models trained on image classification tasks.
We find that model–model similarity is comparable to monkey-monkey similarity, whereas model–monkey similarity is consistently lower. Strikingly, DVC decreases with increasing network performance on ImageNet-1k. Adversarial training does not improve model–monkey similarity in task-relevant dimensions assessed using DVC, although it markedly increases the model–model similarity.
Similarly, pre-training on larger datasets does not improve model–monkey similarity. These results suggest a divergence between the task-relevant representations in monkey V4/IT and those learned by models trained on image classification tasks.

Quantifying task-relevant representational similarity using decision variable correlation
Yu (Eric) Qian
Wilson Geisler Department of Psychology
Department of Neuroscience The University of Texas Austin ericqian@utexas.c
The University of Texas at Austin
geisler@utexas.. edu
Xue-Xin Wei Department of Neuroscience The University of Texas at Austin weixxêutexas,
edu edu
Abstract
Previous studies have compared neural activities in the visual cortex to repre- sentations in deep neural networks trained on image classification. Interestingly, while some suggest that their representations are highly similar, others argued the opposite. Here, we propose a new approach to characterize the similarity of the decision strategies of two observers (models brains) using decision variable correlation (DVC). DVC quantifies the srage-by-image correlation between the decoded decisions based the internal neural representations classification task. Thus, it can capture task-relevant information rather than general representa- tional alignment. We evaluate DVC using monkey V4/IT recordings and network models trained on image classification tasks. We find that model-model similarity is comparable monkey-monker similarity, whereas model-monkey similarity is consistently lower. Strikingly, DVC decreases with increasing network perfor- mance on ImageNet-Ik. Adversarial training does not improve model-monker similarity in task-relevant dimensions assessed using DVC, although it markedly increases the model-model similarity. Similarly, pre-training on larger datasets does not improve model model-monkey similarity. These results suggest a divergence between the task-relevant representations in monkey V4/IT and those learned by models trained image classification tasks.
Introduction
Deep learning [1 has substantially impacted how neuroscientists construct brain models. For vision neuroscience. deep neural networks offer candidate models for studying the primate ventral pathway and, more recently, dorsal pathway 66 7 g Early work reported that the representations in convolutional neural networks (CNNs) trained on image categorization tasks can explain substantial fraction of variance in high-level visual areas, surpassing classic models for these areas [3]. Follow-up research has tested many variants of deep networks on their alignment with the brain using both neural data [9] 10 [1] and behavior data [12 13 14). One appealing hypothesis is that deep networks that exhibit higher accuracy and robustness vision tasks, or trained on larger datasets would better explain visual processing in the brain.
3 3 5)
One important question is how compare deep network models and the brain. One class of methods seeks to quantify the similarity of internal representations between models and brains. This includes methods such representational similarity analysis (RSA) [5] linear regression (5 16, and
generalized shape metrics [17 [8]. More recently, another class of methods that put more emphasis
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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on quantifying the behavioral similarity has been proposed, including Cohen's Kappa 13 and 12n behavioral predictivity [22 I9. The goal of these methods is to provide an -m-aage comparison of the decision strategies used by neural networks and the brain. One challenge has been how to properly disentangle the model accuracy, decision biases and decision consistency from behavior 220 [3]. Intriguingly, studies seem to find contradictory trends in model-brain
alignment. While some studies suggest that deep learning systems converge to learning a common representation (2] 22), others suggest that the similarity will not grow indefinitely or has capped 223
24 The reason for this remains unclear.
Here, we propose a principled approach that combines the merits of model comparisons at the representation and behavior levels. Our method is based on decision variable correlation (DVC) developed to measure the behavioral similarity based on choice data [20] in signal detection theory, and we have generalized it to analyze the consistency of high-dimensional neural representations. While prior work developed techniques to estimate DVCs from behavioral data [20), we instead infer DVCs from neural representations. Thus, our proposed DVC metric should be interpreted as
measure of the representational similarity. Our approach specifically quantifies the trial-by-trial consistency of two neural representations for solving a classífication task, ignoring features that are irrelevant for the task. In doing so, our approach enables one to infer the consistency of the decision strategy of two observers from their internal representations based on the assumption of optimal linear readouts.
Applying our method to compare neural representations for solving image recognition tasks from monkey brains and deep network models led to several interesting findings. In particular, we found that model-model and monkey-monks similarities are comparable, whereas model-monkey similarity is consistently lower and decreases with increasing ImageNet- 1k accuracy. Somewhat surprisingly, this gap is not remedied by adversarial training or training on larger datasets.
Background and relevant work
Community efforts have pushed towards better methods to compare brains and models and for brain- model alignment. Different factors have been hypothesized to be relevant for alignment, including model architecture, robustness, and training data, as summarized below.
Model architecture and scale One hypothesis has been that as models improve in task performance or architectural complexity, their internal representations become more brain-like. The Brain-Scores [9] of the image classification models were reported to be positively correlated to ImageNet- k accuracy, although the trend plateaus at higher accuracy. On the other hand, studies using RSA reported that neither model scale nor architecture significantly improved alignment to human behavioral similarity judgments [9). Another study using RSA reported negative correlation between alignment to human neural activity and model complexity
(25). Studies using Cohen's Kappa reported that human-model behavioral consistency at the image level remains low despite improved performance
on out-of-distribution datasets with scaling B [4]
Robustness The primate visual system is robust against external and internal noise, prompting the question of whether robustness to adversarial perturbations or corruptions is related to brain-model alignment (26] Recent work proposed that adversarial robustness might promote the learning of representations better aligned with human perception (27] By enforcing alignment with monkey IT representations, models exhibited both enhanced adversarial robustness and increased behavioral alignment with human subjects (26). Another study found that model metamers artificial stimuli that elicit the same response as natural stimuli, generated by robust models- are more recognizable to humans, but are not themselves predictive of recognizability 28). However, studies using Cohen's 's Kappa report that robust models still diverge from humans in their eиror patterns [4]. Additionally, there has also been evidence suggesting that even though adversarial training increased model robustness, these robust networks may not use human-like features unless explicitly aligned 29 30
Rich and multimodal training data Using Cohen's 's Kappa, [4] reports that models trained on larger and more diverse datasets become more human-like in their behaviors. On the other hand, a recent large-scale study using variation of RSA reported that upgrading from ImageNet- 1k to ImageNet2 k does not significantly improve alignment to human brain, but object-oriented ImageNet datasets lead to much better alignment than datasets containing only places or faces (11. Similarly, an calogically-motivatee dataset seems to improve model-brain alignment [II. Joint language models such CLIP have also been shown to better predict human brain activity [4 10; 32).

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Similarity measures Classic methods such as linear predictivity measure how well neural responses can be predicted from network representation []. Representational similarity analysis (RSA) [T5] is a popular approach that quantifies the similarity in the geometrical structure of two representations. and is blind to the specific features used to solve a task [33]. Other shape metrics such as centered kernel alignment (CKA) and canonical correlation analysis (CCA) also do not specifically address the similarity in task-relevant features. Measures of behavioral similarity such as error consistency are task-focused [13). yet they may be overcalibrated on accuracies of the observers and are therefore sensitive to the choice of decoders [3: 14 as we will show later. Recent studies highlighted the challenges in the interpretation of results based on these methods [1) e.g., different methods for quantifying the brain- model similarity could lead to different conclusions (34:55) As the field continues to develop methods for analyzing and interpreting model- model-brain alignments [36 37]. it would be desirable to have principled, task-relevant, accuracy-agnoisti measures to better illustrate the possible divergence between brains and models.
3 DVC: Quantifying the trial-by-trine consistency of two representations
We develop a new method to evaluate the consistency of two neural representations. This method based on a principled generalization of signal detection theory. It enables one to estimate how correlated the decision strategies of two observers are for a classification task. The method is robust to the observers' biases and is not confounded by the behavioral accuracy. It operates at the level of neural representations, and enables one to analyze the internal representation to infer the consistency of the two representations for solving the classification tasks. Thus, the method can quantify task- relevant representational similarity. Compared to methods purely based on behavior [20 13 it takes advantage of the richness of the internal representations of neural networks and brains. Meanwhile, in contrast to methods for analyzing the similarity of two neural representations (such as representational similarity analysis), our method focuses on the dimensions that are relevant for a behavioral task and is invariant to variability along other task-irrelevant dimensions.
3.1 Decision variable correlations (DVC) of two neural representations
Signal detection theory is fundamental in the study of perceptual behavior. The idea is that, for binary- choice tasks, observer uses a continuous decision variable (DV) to make a choice (Fig. [p. Recently,
20 proposed to generalize signal detection theory to study the correlation of decision variables of two observers (Fig. [b). Their method inferred the DVC from binary choice data. Here, we develop a simple new strategy to infer triai-by-trial DVCs from high-dimensional internal representations (Fig. For a pair of image categories and an observer (a brain area or a particular layer from neural network), we can take its neural representation and find the optimal decision axis for solving the categorization task. We then project the high-dimensional representation for each image onto the decision axis and obtain its decision variable. Now consider the case of two observers. By performing the analysis on both observers, we obtaín two decision variables for each image. We can compute
the correlation of the decision variables (DVC) for the two observers (Fig. [o). This correlation
captures the similarity of the encoding and the decoding into a decision for the two observers in this classification task.
Note that the method of inferring DVC from behavioral responses only applies to binary choice tasks. Our new method does not suffer this limitation. Given N (>2) image classes, we can focus on each pair of categories at time, and infer the DVC for that particular classification task.
3.2 Implementation of the DVC method
We next discuss how we implement the DVC framework to amalyze the high-dimensional neural representations. The code is available at abbttps///ggttho..om///eebbbbbb www.wwi-bbww---eeeeeeeeooeeeeeee
Lab/DVC
Decoding decision variables (DVs) from neural representations For each pair of classes (c.g.. cats v.s. dogs), we use Linear Discriminant Analysis (LDA) to find the axis that maximizes class separation decode the DVs from the brain or model representations. The projection onto the LDA axis reflects the model's 's tendency to classify the image as one class versus the other; values near the midpoint indicate greater classification uncertainty. One important practical issue is that LDA can be unstable under high dimensions with few samples. The reason is that there are many noisy feature directions with similar class separation, but the projections of image representations along these dimensions can be different. Consequently, even if two models have the same underlying
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Figure The computational framework of decision variable correlation (DVC) for neural representations. (a) Traditional signal detection theory models how a single observer solve binary classification task. The idea is that the observer use a decision variable together with a criterion (dash line) make choice. (b) Decision variable correlation generalizes the signal detection theory to study the trial-by-trial consistency the decision variables two observers. The two panels illustrate two cases with the same accuracy in solving the task, but with drastically different correlations in the decision variabless (DVs). (c) We further generalize DVC to compare two neural representations. optimal linear classifier infer the decision variables of individual observers
The basic idea and then quantify the consistency of the decision variables.
representations, LDA projections may show low correlation. Note that models examined in this paper have a wide range of dimensionality in their penultimate layer (10 107).
To address this problem, we use dimensionality reduction (e.g., PCA) to reduce the representations to the same number of features before using LDA to decode the underlying DV We measure the similarity between decoded DVs using Pearson Correlation. A DVC value is obtained for each class in each pair of classes. The final reported number is taken as the average of all DVC values.
Normalization address mcasurement noise DV Measurement noise may limit the accuracy of the inferred DVC. The otherwise perfect correlation between two identical representations would be corrupted by adding noise. Low correlation might therefore reflect true underlying dissimilarity or high noise level. To correct for the under-estimation of DVCs due to measurement noise, we develop a split-half procedure to infer the impact of noise.
We aim to estimate the true correlation between two decision variable (DV) signals, DV and DV each of which contaminated by independent noise. To correct for the attenuation bias introduced
25 PC dimensions. See Appendix C.3 and C.4 for experiments that demonstrate the robustness of the results.

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by noise, we split each DV into two independent halves: DV DV and DV B1 DV For neural recordings, this would indicate splitting into two sets of neurons, and for model representations, two sets of hidden units. We then compute a noise-corrected Pearson correlation as follows:
Tcross
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Tself
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T Teross = [p(DV DV. p(DV A1, DV B2) p(VV A2. DV)1) 1 p(DV A2. A2, DV
(2)
and the denominator normalizes by the geometric mean of the within-ebserver (split-half) reliabilities:
Tself = (D(DV AVA2) (DV B1. DV DV
(3)
This correction removes the bias introduced by independent, additive symmetric noise in the estimated decision variable, yielding an unbiased estimate of the true underlying correlation between the latent signals driving A and DVg B How best recover DVC under more general noise conditions remains an interesting question for future work.
4 DVCs reveal the divergence between deep networks and brains
We apply the new DVC-based methodology to examine (i) the trial-by-trial consistency of the neural representation of the high-level visual areas (V4/TT) between macaque brains, (ii) the consistency be- tween individual neural network models & the IT//V4 neural representations, and (iii) the consistency between different deep neural network models. We specifically consider three classes of deep network models: (i) models that were pre-trained on ImageNet- k using standard network training (i.e., no adversarial training); (ii) "robust models" that were fine-tuned on ImageNet- Ik using adversarial training: (iii) "data-rich models" that were pre-trained on even larger datasets such as ImageNet-2Ik and JFT-300M.
4.1 High trial-by-trial consistency of V4 & IT representations across monkey brains
We evaluate the consistency of neural representations in different macaque monkeys. We used the publicly available dataset of objects rendered on naturalistic scenes 38) In these experiments, they used images from eight classes (animals, boats, cars, chairs, faces, fruits, planes, tables), with 400 images each, totaling 400 x 8 = 3200 images. Recordings were taken from V4 and IT areas of two adult macaque monkeys passively viewing these images. The brain representation is taken to be the time-binned spike counts averaged over 50 repeats. 100 neurons from V4 and IT combined were obtained from each monkey.
We first examine the classification accuracy based on V4 and IT response, and find that the accuracy based on LDA is high (0.94 and 0.92, respectively). We combine the neural data from areas V4 and IT, and compute the DVCs. We find that the DVC between the monkeys is about 0.57. We further compute the DVCs for V4 and IT separately, and find the DVC values to be 0.63 and 0.41, respectively. Overall, these results suggest that DVCs across the monkeys' brain are generally high, implying that the encoding and the decision strategies used by different monkeys are consistent on an image-by image basis.
4.2
Deep networks with higher accuracy ImageNet exhibit lower DVCs with brains
We study a set of models (n=43, obtained from Torchvision, 33 pretrained on ImageNet-1k, an influential benchmark image classification. This also offers fair comparison between models by controlling for confounding factors related to different training data. We use the same neural datasets from 388 as above. We feed the images in (38) into deep vision-based neural networks, subject to standard transforms. The model representation for an image is defined as the activation taken from the penultimate layer the last layer before the final logit layer.
Brain vs. network Evaluating the DVCs between models and monkey brains, we find that the consistency between models and monkeys are modest, and generally lower than that of monkeys. For the 43 models we tested, the average is 0.29 + 0.05. Given the differences in the training data,
"See Appendix A for proof, and Appendix C for discussions on the validity of DVC under different conditions. including behaviors of split normalization at boundary conditions.
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Figure 2: Results on models trained on ImageNet-Ik: (a) Heatmap: DVCs inferred for pairs of models. Different colors used to indicate models from different model families. 15 models selected to represent this cohort in later analysis.
(b) 2D t-SNE embedding of the models using their dissimilarities, measured as 1 DVC. (c) There is strong negative correlation between the classification performance (top-1 accuracy) of a network and its DVC correlation to the V4/IT representation. (d) Networks belonging the same family exhibit higher DVCs compared those belonging to different model families (p = 1.33e-56).
learning algorithm, and loss functions between deep networks and brains, this is perhaps not too surprising. The models we tested differ in their ability to solve image categorization tasks. One influential hypothesis has been that the more accurate network can solve the task, the more similar its representation would be when compared to that of primate visual cortex. Earlier results [19] supported this hypothesis. This motivated us examine whether networks with higher performance on ImageNet- 1k also have higher DVC with macaque ITT/44. Surprisingly, we find the opposite, that is, networks with higher top-1 accuracy on ImageNet- Ik generally have lower DVC with IT/V4 representation (Pearson correlation = -0.70, p 2.28c-07; Fig. (bb).
Network vs. network We next examine the DVCs between different deep neural networks. Specif- ically, we evaluate DVCs between deep networks from different model families Using DVC, models from the same family otherwise share architectural similarities are clearly clustered to- gether(Fig. b). We find that DVCs between pairs of models within the same family (similar model structures and training processes) are substantially higher than pairs from different families (p
*e define a model family as a set of architectures sharing a canonical computational graph such as residual, attention, or convolutional block structures with variation limited to hyperparameters like depth, width, patch size, token embedding dimension. See Appendix B for more model details

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1.33e-56, Fig. 2 consistent with previous findings [40]. We also find DVCs between models not to be exceedingly high. Despite being trained on the same dataset, they do not seem to converge to single solution, at least not significantly higher compared to the similarity between the two monkeys (Fig- ( These results imply that model structures and training processes still play significant roles in the task solutions found by the models. Notably, these results differ substantially from results obtained by computing error consistency. These studies [13 [4] reported that (i) the consistency between model and brain is very low; (ii) the consistency between network models is much higher than the consistency between humans, Later, we will address the difference between the methodologies.
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Figure 3: Results on robustly trained deep networks on ImageNet-Ik. (a) Networks based on adversarial training has lower DVC with V4/TT compared the representative models (introduced
in Fig. 2) without adversarial training. (b) Heatmap showing the inferred DVCs between pairs of
models. (c) Robustness networks have high DVCs among themselves, and they have relatively low DVCs with the representative models.
4.3 Adversarially trained networks, while highly consistent, have low DVCs to the brain
Robustness represents one important difference between deep networks and our perceptual systems. Small perturbations to images that are imperceptible to humans can lead to qualitative errors in deep networks (i.e., adversarial examples) [1]]. Adversarial examples reflect the misalignment between representations in deep networks and brains, given certain local perturbations in the inputs. Adversarial robustness
be increased by using adversarial training, c.g., by finding adversarial examples and adding them to the training set. Studies suggest that features learned through adversarial training may be more aligned with human perception [27 28 posing an intriguing hypothesis that by making networks locally consistent with human perception, network representations may be better aligned with brain representations globally.
To test this hypothesis, we examine the DVCs of set of adversarially trained networks and macaque V4/IT. We obtain robust models fine-tuned for adversarial robustness on TaageNet-1kk(n-)) from Robustbench, 42 Evaluating the DVCs of these models to V4/IT representations, we observe no improvement in the similarity to the brain. In fact, observe slight decrease of the DVC values 0.02, Fig.344. 33).. Furthermore, we observe that models based on similar adversarial training procedures show a high similarity with each other (0.69 0.09, Fig. Bt). Mcanwhile, their similarities to models without adversarial robustness drop substantially (p- = 5.203e-37, Fig. Bbg. These results suggest that adversarially trained models converge common solution (despite that these models have different architectures). Their representations diverge from the non-adversse aon-avvessrilllyy trained deep networks, yet they also diverge from the neural representation in macaque V4/IT.
4.4 Networks trained on rich datasets exhibit no increase DVC to the brain
Whereas ImageNet-1k has been an important benchmark dataset for the image classification commu- nity for decade, recent state-of-the ahe- models are trained on larger datasets such as ImageNet-22 2 which is a scaled-up version of ImageNet- 1k, and JFT-300M, which is proprietary. Models trained on larger, more diverse datasets may generalize within a larger domain, and may show better out- of-distribution generalization ability. A recent study showed that models trained on these larger datasets may exhibit better alignment with human behavior [14.. Furthermore, the negative correla- tions between classification performance and DVCs to the brains (Fig. 2?) suggest the possibility of overfitting to particular dataset that is much smaller than what brains are trained on evolutionarily,
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developmentally. and during the experiments 43.. Therefore, it is of particular interest to investigate whether models trained on the richer datasets exhibit higher DVCs to the brain.
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Figure 4: Results on deep networks trained on richer datasets. (a) Networks we examined that were pre-trained on richer datasets exhibit lower DVC with V4/IT compared to the representative models (trained on ImageNet- 1k). (b) Heatmap showing the inferred DVCs between pairs of models. (c) DVCs between lower data-rich models and representative models are generally lower than those within representative models or data-rich models.
We examine models pre-trained on bigger, or multimodal datasets (n=13), namely, 5 SWAG models
44 from Torchvision and 6 BiT (Big (ransfer)[45 models, Noisy Student[46) and CLIP [47] from Timm (for details, see Appendix B) [39 48). Briefly, BiT (Big Transfer) a supervised pretraining approach that trains ResNetV2 models on large-scale datasets like ImageNet-21k, Noisy Student semi-supervised learning framework that iteratively trains a student model on both labeled (ImageNet- 1k) and unlabeled (JFM-300M) data using uoise-augmented inputs. CLIP is contrastive laniunel model that jointly learns aligned image and text embeddings from web-scale paired data. SWAG is training strategy introduced by Meta that improves supervised learning by using large-scale weak supervision from hashtAGs. All of these models enjoy better performance on ImageNet-1k 1k than their vanilla counterparts. Comparing these models V4/IT, surprisingly, find that the DVCs to the brains are lower than those trained on ImageNet- (0.24 0.05, Fig. 4b). Given that these models generally have high ImageNet- 1k accuracy, it seems follow the previously reported trend that better performing models tend to show less consistency with brains. These data-rich models are less similar the representative models trained on ImageNet- Ik compared to the similarity among themselves (Fig. 4.).
4.5 Comparison to error consistency based Cohen's Kappa
One method that highly relevant DVC Cohen's Kappa. As a classic statistical measure of inter-rater consistency [50], Cohen's 's Kappa was recently applied to quantify the eтror consistency of deep networks and brains [33 14). These studies examined numan-model alignment using categorical judgements on assorted out-of-distributin stimuli. For example, 'edges' where only the edges are illustrated, or "silhouettes" which are filled outlines of objects. These studies arrived at very different conclusions, namely that (i) model-model similarity is significantly higher than suman-human similarity, (ii) model--huaan similarity extremely low and that (iii) models trained on rich datasets are more aligned with humans. At high level, these results seem to be inconsistent with our findings, because we found that (i) deep networks exhibit modest consistency with the brain; (ii) DVCs between different deep networks trained on Image 1k are not exceedingly large; (iii) models trained on rich datasets have lower DVCs with brains.
To understand these potential discrepancies, we performed several analyses. We start by applying Cohen's Kappa to study the neural dataset used above. We used 5-fold cross-validated logistic regression to obtain model decisions as well as monkey 'decisions'. Using this decoder, we find that DVC shows a high correlation with Cohen's Kappa, consistent with the theoretical analysis in (20 (Fig Sp.c). We find that Cohen's Kappa between deep networks and the brain is modest (0. + 0.04), and generally larger than the typical values reported in [33. Furthermore, Cohen's Kappa between different deep networks (0.23 + 0.07) is not substantially larger than that between the monkeys (0.22). These results suggest that Cohen's Kappa applied optimal linear classifiers leads to generally consistent results on this dataset. What then is causing the difference in network-
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Figure 5: Comparsion to Cohen's Kappa. (a) Heatmaps showing the DVC and Cohen's 's Kappa for pairs of representative models. (b) There is strong positive correlation between Cohen's 's Kappa and DVC on model-model consistency (evaluated on this dataset) (c) There a decent positive correlation between Cohen's Kappa and DVC on model-monkey consistency. (d) The values of Cohen's Kappa between models (blue) and human subjects (green) are low while Cohen's Kappa between models and between human subjects are high, consistent with the original report. Re-analyzed based on data from [49]. (e) Scatter plot showing the relationship between Cohen's Kappa and the difference in accuracy of pairs of observers, and the theoretical upper bound. (f) The response histogram to 'edges' distortion based on the model and decision rules used in [3] and the original study [49]. Different colors represent different nerual networks. (g) Simulation results show that Cohen's Kappa sensitive to decision biases, while DVC is invariant to decision biases.
network and network- consistency between the results reported in 13 and DVC? To address this question, we next analyze the behavioral data used in [13]
Accuracy difference While Cohen's 's Kappa was originally proposed to disentangle the accuracy and consistency of the observers under certain conditions, it remains possible that the two intermingled in practice [3]. To assess this issue, we examine the behavioral responses to 'edges' stimuli from |4 From the results shown in Fig. 5l.e it is evident that Cohen's 's Kappa is strongly affected by the difference in the accuracy of the two observer
H When the difference in accuracy is high, Cohen's
*Thcoretical upper-hound is given by S (1-d)² observers. See Appendix A.2 for the derivation.
1+4 where is the accuracy difference between two

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kappa is low. This suggests that the low error consistency between humans and models reported in [3] is at least partially due to the large differences in accuracy between the two observers. It also potentially explains why models trained on 'rich' datasets, which enjoy better out-of- performance, also exhibit better alignment with human behavior based on Cohen's 's Kappa [1].
Decoder bias According to signal detection theory, Cohen's Kappa is determined by both the correlation of the decision variables and decision criterion. Thus, we wondered if the extremely high Cohen's ' Kappa values between different networks as reported in [ are due to biases in the decisions. We thus perform second analysis to further investigate the data from
49 and analysis
used in [3]. Consistent with our hypothesis, we find that the approach in [33] introduces high
decision bias (see Fig. [5) and reduced accuracy, especially when target categories do not align cleanly with the original training labels. We also find that the origin of this large decision bias is because the analysis in 13 based on an aggregated decoder that estimates class probabilities by combining probabilities from related ImageNet- k classes. Once we substituted the original decoder with cross- validaedd logisitic regression classifier, the estimated Cohen's Kappa values become largely consistent with the DVC we obtained on the main dataset we analyzed. These results suggest that the large Cohen's 's Kappa values between different networks are due to the biases in the decoder F
These results highlight the advantages of the DVC method. DVC is insensitive to the decision biases, while the error consistency quantified based on Cohen's ' Kappa captures both shared behavior biases and consistency in their underlying decision variables. This point is further demonstrated using a simple simulation (see Fig. (5)). Here, we add behavioral biases to the two observers by shifting the decision criteria consistently, so that they both prefer one category over another. Naturally, as the bias increases, the accuracy drops. Cohen's Kappa strongly reflects these decision biases, whereas DVC remains consistent (b) Furthermore, DVC can effectively decouple accuracy v.s. trial-by-trial consistency of the decision variables (20)
Discussion
We have developed a method, DVC, to quantify the consistency of two neural representations. The focus on task-relevant features makes DVC different from other popular approaches such as RSA[I5] or linear regression ( Two representations may have high DVC yet low consistency according to RSA, or vice versa. For behavioral metrics that aim to characterize trial-by-trial consistency, one challenge has been to decouple task performance and trial-by-trial consistency. DVC provides a principled way to do so. For future work, it would be interesting to combine the analysis of DVC at the behavioral level [20) and the neural representation level to dissect the contribution of consistency of DVs and the shared biases of the observers. It would also be interesting systematically compare Applying the DVC method, we find that there surprising negative correlations between (i) the classification performance of the deep networks trained on ImageNet- 1k and (ii) the consistency with the neural representation in V4/IT. Furthermore, training the deep network adversarially or using rich datasets seems to evoke decrease, rather than increase of DVCs. While it is unclear how to close the gap between the image-by-image consistency of deep networks to that of the brain, the following directions might be promising: (i) training networks using datasets that better resemble the stimulus statistics that drives the evolution of the primate visual system [31]; (ii) develop training procedures that better capture the stimulus noise and internal noise of the brain [11], as well as low level properties of the visual system (e.g..
DVC to other proposed similarity measures [[5] 5 19
optics and foveation).
Limitations First, our results are limited by the number of monkey subjects in the datasets and the number of neurons recorded simultaneously from V4 and IT. Future larger neural datasets would allow for more accurate estimates of DVCs. Second, despite various adjustments in dimensionality reduction and DV decoding that we have experimented with, there may be factors that we have not taken into account that limit the scope and applicability of the results. For example, It is possible that the high-dimensionality of the feature space of some models affected the estimation of the DV. However, the DVCs of these models with the monkeys are not systematically lower, thus it is unlikely that they are underestimated. Third, while monkeys provide access neural recordings, the objects shown in the experiments might not have the same behavioral relevance for them as they do for humans. Thus, caution should be taken when attempting to generalize the result to humans.
$ SSee Appendix D.3 for results on the 'edges' data using logistic regression classifier.
SSee Appendix E for some preliminary results on comparison to RSA.
10

---

Review and Acknowledgments We thank Nikolaus Kriegeskorte for helpful discussions. This research was supported by the National Institute Of Neurological Disorders And Stroke of the National Institutes of Health (Award Number ROINS133924), the NIH BRAIN Initiative and National Institute On Drug Abuse (Award Number R01DA060742) and Sloan Research Fellowship (to X.-X. Wei). The content is solely the responsibility of the authors and does not necessarily represent the official views of the funding agencies.
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14

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A Method details
A.1
Split normalization recovers true DVC
Assume the noisy DVs:
AV 3,4 + EA
DV sB +
Assume mean-centered and all signal- and noise-noise covariances vanish:
E[sa] E[sn] B|s a B[ =0 0
Cov(SA, Cov EB) = = =
Note:
Var(sA) a
Var(sB) o Cov SB) A0B
Var(ea) des Var(eg) dep
Then:
DV DV Cov(SA, AB
Var(DV = 03 + o
Var(DV = σ + o²
So the observed correlation is:
OΛOB
Pobs
Pirue
( + (o +
Now split both DVs:
DV 8A + EAI,
DV = 8A + E,2
DV B1 = 8B + +
DV B2 =8 + E
Assuming independent, identically distributed splits, and zero-mean and zero-covariances as before: Var(DV A1) a oe. Cov A1, DV D2 oA
So the reliability is:
0
pDV DV A2)
O
Likewise for B:
pDV B1. DV B2)
B
8 0
And the cross-observer split correlations are:
p(DV A:. DV By) Purue
10% + 03 (og 02
where i.j = (1,
Taking the geometric mean of the cross-observer split correlation gives better estimate of Pahc:
Teross jDVV DV p(DV DV B2) p(DV A2, DV p(DV 42, DV
Pobs.
While the geometric mean of the within-observer split correlation gives the normalization factor:
d
of
Yself [p(DV AL, DV A2) p(DV B1. DV 1/2
1/2
0
02
o
Vi02 + oz + 02
Then the correcce correlation is:
Piree AOB/ (03 + 02 (0 + +22))
Peross
Pcotrected
Pirue
Tself
OAOB/ (03 d2 (0 + o2.)
15

---

A.2 Upper bound on Cohen's Kappa with respect to accuracy difference between the two observers
Let I.J E }
} be the correctness indicators of two decision makers on the same N items, with
accuracies Pj P(I- 1). Ps [PJ 1). and d Pyl. Define
Cobs Cexp
Cobs P(I = J),
Cexp
P.Pj (1 P:)(1 p5), K
(Cexp < 1).
1 Cexp
Cobs maximized when 7, maximally agree, and pi, Pj only differ by d. Hence Cobs S d, and
mobs,max
For Cexps parametrize the accuracies by their mean puttii 2
pi m 1
Pj m 4.
E
[d.
1-4]
--2
Then
d²
Cexp(m) (m) = PiPs + (1 p1) p3)
(ps ps) 2p:p;
2m 2m
2
the expression is minimized at mn* = 2. yielding
d²
Cexp.min
Since & (Cobs ((1x))(11 Cexp) is increasing in Cobs and decreasing in Cexp (for Cexp < 1), combining the results gives
d)
d²
da
(1-d)²
2
2
2
1 d2
2
3
T
Tightness is achieved by m (i.e., Pi
1td
2
Pj
I-d
and maximum agreement between J,
which realizes Cobs = 1 - d and Cexp
A.3 Simulation demonstrates the relationship between bias, accuracy and Cohen's Kappa
In order demonstrate that this decision bias could influence Cohen's Kappa, we did a simple simulation. Suppose that there are 10 classes with 100 samples each. The observers output a vector which corresponds to the 10 classes. An unbiased perfect observer outputs 'DV (decision variable)' I for the corresponding class and ( for all other classes (a one-hot vector). For realism, as observers make mistakes, we simply added gaussian noise the DV output, which results in both lower Cohen's Kappa and lower DVC. To model a biased imperfect observer, bias is applied after DV, which is the same for all samples in the same class (e.g. 0. for the first class, 0.2 for the second class) etc. Varying bias levels is achieved by scaling the bias added to the output. The final output is one-hot + noise + bias.
Here, Cohen's 's Kappa is directly inflated by the shared bias between two observers. On the other hand, because the bias does affect the underlying DVs, the pre-normalization DVC unaffected by the addition of bias. However, DVC does become systematically lower when the DVs are dominated by noise. Therefore, Cohen's Kappa and DVC are distinct that the former cares about the decision criterion and the latter do not. They can be seen as complementary in certain scenarios. The simple simulation also hints the relationship between accuracy, bias, and Cohen's 's Kappa. We continue this discussion in section D, where we reiterate that Cohen's 's Kappa is intimately linked to accuracy.
16

---

B Model and dataset details
B.1 Model performances and choices of the penultimate layers
Table A.1; Models Trained ImageNet-1k
Model Name
Top-1 1 Acc
Top-5 Acc
Model Family
Layer
alexnet
56.522
79.066
AlexNet
classifier 33
vgg11 1 bn
70.37
89.81
VGG
classifier [3]
vgg13_bn bn
71.586
90.374
VGG
classifier[-3)
vgg16 bn
73.36
91.516
VGG
classifier[331
vgg19_bn
74.218
91.842
VGG
classifier[-31
squeezenetl_0 _0
58.092
80.42
SqueezeNet
features[-1]
squeezenet1_1
58.178
80.624
SqueezeNet
features[-1]
densenet121
74.434
91.972
DenseNet
features.norm5
densenet
75.6
92.806
DenseNet
features.norms
densenet201
76.896
93.37
DenseNet
features.norm3
inception_y v3
77.294
93.45
Inception
avgpool
resnet18
69.758
89.078
ResNet
avgpool
resnet34
73.314
91.42
ResNet
avgpool
resnet50
76.13
92.862
ResNet
avgpool
resnet101
77.374
93,546
ResNet
avgpool
resnet152
78.312
94.046
ResNet
avgpool
shufflenettv2_xX11
60.552
81.746
ShuffleNet
conv5
mobilenet_v2 v2
71.878
90.286
MobileNet
classifier(O]
resnext50_
77.618
93,698
ResNet
avgpool
resnext101 __xxd
79.312
94.526
ResNet
avgpool
wide vide_resnet50_2
78,468
94.086
ResNet
avgpool
wide cecde_resnet11_11
78.848
94.284
ResNet
avgpool
mnasnetO_ _
67.734
87.49
MNASNet
classifier(0]
mnasnetl
73.456
91.51
MNASNet
classifier(0]
googlenet
69.778
89.53
Googl LeNet
avgpool
convnext_base
84.062
96.87
ConvNeXt
avgpool
convnext_tiny
82.52
96.146
ConyNeXt
avgpool
convnext small
83.616
96.65
ConvNeXt
avgpool
convnext_aare Jarge
84.414
96.976
ConvNeXt
avgpool
efficientnet_Bb b0
77.692
93.532
EfficientNet
avgpool
efficientnet__1 b4
83.384
96.594
EfficientNet
avgpool
efficientnet
84.122
96.908
EfficientNet
avgpool
efficientnet v2.
84.228
96,878
EfficientNet
avgpool
efficientnet v2 m
85.112
97.156
EfficientNet
avgpool
regnet_y_8ge
82.828
96.33
RegNet
avgpool
regnet_y __6gf
82,886
96.328
RegNet
avgpool
swin
83.582
96.64
Swin
avgpool
swin_v2 v2_b
84.112
96,864
Swin
avgpool
twin_v2_s
83.712
96.816
Swin
avgpool
swin_v2_1
82.072
96.132
Swin
avgpool
vit 16
81.072
95.318
ViT
encoder.In
vit b_32
75.912
92.466
VIT
encoder.
vit 16
79.662
94.638
ViT
encoder.In
17

---

Table A.2: Robust Models
Model ID
Architecture
Clean Acc
Robust Ace
Layer
Li20023Comprrheessiee --trapprreeeeiieSSSSiLLL
Swin-L
78.92
59.56
norm
Liu2023Comprrheensve
-ot ConvNeXI-L
ConvNeXI-L
78.02
58.48
norm
Liu2023Comprehensive Swin-BB
Swin-B
76. 16
56. 16
norm
Singh2023Revisitnnng ViT-B-ConvStem
VIT-B ConvStem
76.3
54.66
norm
Peng2023Robust
Wid-ResNat-101-2
73.44
48.94
avgpool
Chen2024Data WRN _0_2
WideResNet-50+
68.76
40.6
avgpool
Salman2020Do _0_0__00__
WideResNeet50-22
68.46
38.14
avgpool
Salman2020Do_PP
ResNet-50
64.02
34.96
avgpool
Engstrom2219Robustnes
ResNet-50
62.56
29.22
avgpool
Salman2020Do_Rie
ResNet-18
52.92
25.32
avgpool
Table A.3: Data-rich Models
Model Name
Architecture
Top-1 Acc
Training
Layer
resnetv2_500 __50x 1_bim
ResNetV2 (BiT-M)
80
ImageNet-21K norm
resnetv2 50x3 bitm
ResNetV2 (BiT-M)
82.6
ImageNet-211K norm
resnctv2_1011 1 1_itm bitm
ResNetV2 (BiT-M)
81.5
ImageNet-21k norm
resnetv2 101x3 bitm
ResNetV2 (BiT-M)
84
ImageNet-21K
norm
resnetv2_ 1_____1222__bb_________ resnetv2 152x4 bitm
ResNetV2 (BiT-M)
83.7
ImageNet-21k
ResNetV2 (BiT-M)
84.3
ImageNet-21k
tf efeffccienteet _2.ns__22_____t 475
EfficientNet-L22
88.4
Noisy Student JFT
pool
regnet_y s_______swaa_______________
swag_es e2e
RegNetY-16GF
86
hashtAGs
avgpool
pygnet_y32gff @uge_yy_2gfsswaa_eee _2e
RegNetY-32GF
86.8
hashtAGs
avgpool
regnet_y y 128gf swag ele vit hit_b16_swaag
RegNetY-128GF
88.2
hashtAGs
avgpool
ViT-B/16
85.3
hashtAGs
encoder.In
vit 1 16 swag e2e
ViT-L/16
88.1
hashtAGs
encoder.In
CLIP
ViT-B/32
NA
Image-text pairs
NA
While we do not have a strict criterion for selecting which models to test, we do follow certain principles. First of all, we try cover diverse of model architectures and span the range of model accuracy, which why we included older models with mediocre performances. Secondly, we try to include models that other studies have previously examined, so it casier to compare our study with the previous studies. We did exclude some models due to time limits. We intend to examine an even more comprehensive of models in future work.
B.2 Licenses for Third-Party Assets
The models used in this study were sourced from RobustBench, Torchvision, and Timm (PyTorch Image Models). We these pretrained models cohort to study representational similarity, without referring to their individual implementation details.
We make use of publicly available datasets and pretrained models in accordance with their respective licenses:
Brain-Score/ Sww./////////oonnnno Vision dataset (Majjj al., 2015) were used solely for non-commercial aca- demic research. We follow the terms use as outlined.
Models from Torchvision are provided under the BSD 3-Clause License.
Robustbench models are used under the MIT License.
Timm models used under the Apache License 2.0.
18

---

C Implementation and verification
For detailed implementation used in analysis, refer to httpp:///gihuuu..om/ee-bbbbbb
C.1 General information the DVC framework
The DVC method is computationally efficient and stable, as dimensionality reduction applied before attempting decode the DV using L.A.. All experiments i7-14700K CPU without resorting to GPU usage. Computing DVC between pair of models takes 30 seconds on average, with the total compute rounding 30 hours.
performed Intel(R) Core
b
Split model activations into two halves
PCA
LDA
Pearson's
DVC between splits across models
Normalize for noise using splits
1/4
Average between pairs classes
1/2
DVC between splits within models
Figure A.1: Implementation of the DVC framework. (a) The diagram of our anlaysis pipeline. To increase the accuracy of the decision variable inferred in the regime of huge dimensionality and few samples, we first reduce the dimensionality of the neural representation (or hidden layer representations in neural networks) before applying the optimal linear classifier to infer the decision variables. (b) To correct for the under-estimation of the magnitude of the inferred decision variable due to noise, we develop normalization procedure based on estimating the effective noise from two splits of the data. See text for more details.
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C.2 Verification of the robustness of DVC results
While the guiding principle behind DVC is general and intuitive, specific implementation choices carry implications on the numerical stability and robustness to different data distributions. We thus experimented with different algorithms and hyperparameter choices and found that they do not affect the main conclusions drawn in this study. Specifically, we want to verify if the choice of PC dimensions might change the conclusions in this study. First we note that with PC dimensions (for each split), all the monkey recordings and model representations achieve high binary linear seprability (Fig- p)2 and that 8 8-way logistic regression accuracy plateaus early on (Fig. p.2p) main result is robust with varying PC dimensions (Fig. A.3j.bb.
p). addition, the
Other choices also do affect the results. Pearson's correlation easily biased by extreme values. Although the DVs appear normally distributed, we substituted Pearson's 's correlation with Spearman rank correlation and found that the trend persists (Fig. A.3 addition, we tested shrink regularization for LDA, which could enhance stability of the procedure, and find that the result is robust the choice of I.DA solver (Fig. A.3
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Figure A.2: Dimensionality reduction retains task-relevant information. (a) LDA score of all monkeys (red) and networks high. (b) As the dimensionality increases, decoding performance using logistic regression plateaus.
C.3 Consistency of the DVC results across different linear decoders
The choice of using LDA decoder is not coincidental. Under the assumption of Gaussian distribution and in the setting of pairwise classification, linear decoder provides the best classifier. We calculated DVC between the two monkey subjects using logistic regression and linear support vector machine (SVM). We find that the DVC is highly consistence across different linear decoders. In addition, across repeats (random split normalization), DVC estimation varied little. On the other hand, DVC values calculated using nonlinear decoders such as kernel SVM and multi-layer perceptron are significantly lower, suggesting overfitting (Fig. A.3e).
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Figure A.3: The main results are robust to particular choices in the implementation. We tested the result in Fig. 2 where networks with better ImageNet- performance are less alignment under different conditions when (a) using the top 10 principal components (PCs) instead 25, (b) Using the top 50 PCs instead of 25. (c) Using Spearman's 's rank correlation instead of Pearson's correlation. (d) Using eigen SVD solver with shrinkage instead of SVD solver for LDA. (e) Measure of monkey-monkey DVC is consistent across linear decoders and across random splits. Error bar indicates the standard deviation.
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C.4 DVC results are consistent in another neural datasets
To alleviate concern that the dataset from which we derived the main results contains only two monkeys, we verified the result on an additional dataset from Bashivan et al [52]. The dataset contains three monkey subjects viewing natural and synthesized images. Among the three subjects, only one ('monkey M') has sufficient neuron count for this test (n = 168). The neurons are pooled across four recording sessions. We used data from monkey M viewing naturalistic images and calculated its DVC against neural networks viewing the same images. The main results are also significant in this case (Pearson's correlation -0.84, p = 0.87e-05, Fig A.4a).
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Figure A.4: The main result is confirmed in an additional dataset from 52
(a) DVC of monkey M against representative models. Again, these is a strong negative correlation between the top-1 accuracy of the deep networks and the DVC to the monkey brain. (b) DVC between representative models.
C.5 DVC between representations and raw image pixels
We calculated the DVC between the V4/TT representations and model hidden representations to flattened image pixels and found that the DVC between the two monkeys and raw image pixels are 0.153 and 195, respectively. The DVC between model hidden representations and network DVC are generally lower but still substantial (Fig. A.5 The results suggest that part of the DVC results might come from remnants of linear separability the image pixels, which is reduced by nonlinearity in the brain and models. Indeed, the LDA score for categorization using raw image pixels is 0.70, which is smaller than that of brain and model representations (>0.90) but still very high. We plotted the LDA axis for classifying 'chair' and "car' in image pixel space and see clear silouettes of the objects (Fig. A.5p), suggesting that high DVC to image pixels may be due to simplicity of generated image samples. It would be interesting to test the result on datasets with more complex and diverse images.
C.6 Split normalization under uncommon conditions
The split normalization procedure could behave counterintuitively under extreme conditions. For example, it could result in DVC value larger than I when the internal noise is high. None of the normalized correlations between different representations reached the cap. In addition, we took the absolute value before calculating the geometric means. When there is no correlation between two representations, this would bias the normalized DVC to a small positive value. None of the representations in this study fall this range.
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2002
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Figure A.5: DVC between the monkey and model representations and raw image pixels. (a) The DVC between models and raw image pixels are markedly lower than DVC between models and monkeys yet still substantial. (b) The LDA axis between categories 'chair' and 'car' in image pixel space.
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D Additional results on the effect of behavioral decoding on Cohen's Kappa
Geirhos al. [33 have discussed several caveats of applying Cohen's Kappa, including that Cohen's Kappa is bounded by error overlap expected by chance Ceap. We also explicitly showed that the accuracy difference d = Ps Pyl provides an upper bound on Cohen's 's Kappa (see Section A.2). When the accuracy difference is high, one subject is often right, while the other is often wrong, then their behaviors cannot be consistent. From original behavioral data, it clear that human subjects perform with high accuracy but models perform (Fir,y(Fig, [A.6). While Geirhos et al used simulations to show that under the condition that the subjects act independently, accuracy is not necessarily correlated with model performance, Cohen's 's Kappa may still depend accuracy under more general conditions.
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Figure A.6: Re-plotting of the data (based on "edge" stimuli from 13.. Red: accuracy of human subjects. Blue: accuracy deep network models tested. Overall, the accuracy of the deep network models are much lower than that of human subjects.
We would like verify whether the high model-model consistency reported in the original work might be inflated by the low-accuracy high-bias condition caused by the choice decoder (directly aggregating the probabilities). To test this, we take the original stimuli provided by Geirhos et al., and calculate Cohen's ' Kappa between the models by (i) taking the average of the probability of the corresponding ImageNet-Ik subclasses or (ii) training 5-fold cross-validated logistic regression decoder on the representations in the penultimate layer. The result shows that compared to (i), approach (ii) achieves higher accuracy (Fig. AA.p..c) exhibits less bias towards certain categories (Fig. (A77lee) and results in significantly lower model-modes consistency as measured by Cohen's 's Kappa (Fig. A.7.).
While the shared behavioral bias that results from aggregating probabilities from the original ImageNet-1k 1k classes is very interesting, it does make the human-model consistency and the model- model consistency a lot more ambiguous. Thus, it may be more appropriate to use a stronger decoder for classification or use DVC when applicable.
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b
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Figure A.7: Using logistic regression decoder results in higher accuracy, lower bias and lower Cohen's 's Kappa estimate compared mean probability decoder, estimated on the 'edges' images. (a) Cohen's Kappa estimated using a mean probability decoder is significantly higher than that estimated by logistic regression decoder. (b) Behavioral accuracy mean probability decoder. (c) Behavioral accuracy of logistic regression decoder. (d) Choice histogram of the mean probabilities decoder. (e)
Choice histogram logistic regression decoder.
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E Comparison to Representational Similarity Analysis
Representational similarity analysis (RSA) measures the similarity between the general arrangement of categories (or samples) between two representations. Under appropriate conditions, it can be as equivalent to centered kernel alignment (CKA) and canonical correlation analysis (CCA) [53]. In the monkey dataset that tested, RSA is positively correlated with DVC when measuring both model-monkey alignments and model-model alignments (see Fig. A.8
While RSA may contain information about the correlations of task-related dimensions, they may be confounded by task-irrelevant correlations. We demonstrate this point using simple simulation. Given the same baseline decision variables ("task-relevant correlation') ) we introduced independent fluctuations ("noise") and shared fluctuations ("task-irrelevant correlation", ). We find that while DVC generally unaffected by the introduction of stronger task-irrelevant correlation (Fig, A.8 In contrast, RSA quickly plateaus as task-irrete irreleeant correlation overshadows task meskvreleaant ones. This simulation demonstrates that RSA and DVC capture different aspects of the representation. The ability DVC to focus on only task-relevant dimensions makes it suitable when applied to scenarios with high shared fluctuation based common stimulus input, where only some dimensions encode task-relevant information.
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Figure A.8: Comparison to Representational Similarity Analysis (RSA). (a) Heatmaps showing the DVC and representational similarity (RS) for pairs of representative models. (b) There a strong positive correlation between DVC and RS on model-model consistency (evaluated on this dataset). (c) The correlation between category-level RSA. (d) Category-level RSA recreates the main result that alignment between model and brain declines with ImageNet top-1 accuracy. (c) Simulation results show that RSA is conflated with mnsk-rreleevant correlations whereas DVC only cares about task-relevant ones.
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Broader Impacts
We expect DVC to be a broadly applicable approach to study the similarity of brain and neural network models. On the positive side, the method and results discussed in this paper could redirect community focus away from brute-force scaling and toward more targeted investigations into task- relevant representation alignment and model-brain convergence. It could in the long term lead to models that are more brain-like, thus greatly facilitating research in fields like neuroscience, cognitive science and Al interpretability and safety. However, while DVC offers biologically grounded lens for comparing model and brain representations, promoting alignment with biological brains might inadvertently constrain models in certain domains where brain cognition suboptimal.
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Reviews:
[{"review_id": "juNUBvmBY0", "reviewer": "Reviewer_7UD3", "summary": "This paper introduces a novel method, Decision Variable Correlation (DVC), to measure the similarity between the decision strategies of different observers (e.g., brains and deep neural networks). Grounded in Signal Detection Theory, DVC quantifies the trial-by-trial consistency of task-relevant representations by correlating the decision variables decoded from two observers for a binary classification task. Applying this method to compare monkey V4/IT neural recordings with a wide range of deep learning models, the authors uncover several surprising findings. They report that model-monkey similarity is consistently lower than monkey-monkey similarity and, counter-intuitively, decreases as models' ImageNet performance increases. Furthermore, neither adversarial training nor pre-training on larger datasets appears to close this gap. These results lead the authors to suggest a fundamental divergence between the representations learned by current models and those in the primate visual cortex.", "questions": "**Missing Citations:** The findings that adversarial training increases model-model similarity but decreases model-brain alignment are consistent with other recent work. Have the authors considered citing papers like Subramanian et al. (2023) and Linsley et al. (2023) to better contextualize their results and show how they fit into a broader emerging consensus?\n\n**Generalizability of Claims:** The claim of a \"fundamental divergence\" is quite strong. How confident are the authors in this conclusion given that the neural data comes from only two monkeys? Could the observed model-monkey gap be partially explained by inter-animal variability that a larger sample of primate data might clarify?\n\n**Robustness of the DVC Method:** The DVC calculation relies on an optimal linear classifier (LDA) to define the decision axis. How sensitive are the reported DVC results to this specific methodological choice? Have the authors explored whether using a non-linear decoder or a different linear classifier would significantly alter the observed correlations and the paper's main conclusions?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n\n**Novel and Principled Method:** The paper introduces DVC, a methodologically sound approach for comparing representations that is well-grounded in Signal Detection Theory. The careful consideration of potential confounds, such as the use of PCA to stabilize the decoder and the development of a split-half procedure to correct for measurement noise, demonstrates rigor (Section 3).\n\n**Comprehensive Experimental Scope:** The study's conclusions are supported by an extensive evaluation across a diverse set of 65 models, including standard ImageNet-trained networks, adversarially robust models, and models trained on web-scale datasets (Section 4). This breadth makes the findings less likely to be an artifact of a specific architecture or training scheme.\n\n**Significant and Counter-intuitive Findings:** The paper's central results challenge common assumptions in the field. The strong negative correlation between ImageNet accuracy and DVC to monkey V4/IT (Fig. 2c) and the observation that adversarial training actually reduces model-monkey similarity (Fig. 3a) are important, surprising findings that should stimulate further research.\n\n**Strong Baselines and Contextualization:** The use of monkey-monkey DVC provides a clear biological benchmark, giving crucial context to the model-monkey similarity scores. Furthermore, the direct comparison to Cohen's Kappa, a related behavioral metric, helps to situate DVC within the literature and highlights its specific advantages, such as its insensitivity to decision bias (Section 4.5, Fig. 5e).\n\n### Weaknesses and Possible Improvements\n**Insufficient Contextualization with Recent Literature:** The paper's findings, particularly regarding adversarial training, align with a growing body of work suggesting that standard robustness metrics do not guarantee better alignment with biological vision. Citing recent, highly relevant papers (e.g., Subramanian et al., 2023; Linsley et al., 2023) would strengthen the authors' claims and better situate their contribution within the current scientific discourse.\n\n**Limited Neural Dataset:** The strong claim of a \"fundamental divergence\" between models and the primate brain is based on neural recordings from only two macaque monkeys. While the authors acknowledge this in the limitations section, the forcefulness of their main claims could be tempered by this constraint. The potential for inter-subject variability in the primate data might be a larger factor than is currently accounted for.\n\n**Sensitivity to Decoder Choice:** The entire DVC framework relies on using an optimal linear classifier (LDA) to find the \"decision axis\" for each observer. The paper does not explore how sensitive the final DVC values are to this specific choice. It is possible that a different decoder (e.g., a non-linear one, or even a different linear method) could yield different correlation patterns.\n\n**References:**\n\n1. Linsley, D., Feng, P., Boissin, T., Ashok, A. K., Fel, T., Olaiya, S., & Serre, T. (2023). Adversarial alignment: Breaking the trade-off between the strength of an attack and its relevance to human perception. arXiv preprint arXiv:2306.03229.\n\n2. Subramanian, A., Sizikova, E., Majaj, N., & Pelli, D. (2023). Spatial-frequency channels, shape bias, and adversarial robustness. Advances in neural information processing systems, 36, 4137-4149.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your encouraging comments and constructive feedback. We find the criticisms to be very on point and have worked on addressing them with additional data.\n\n(1)Missing citations: Thank you for giving context to some of the findings. Subramanian et al. discovered that artificial neural networks use wider channels than human observers and robust networks use even wider channels. Linsley et al. show that harmonized networks are attacked on features that are more detectable and human-aligned. In future versions of the paper, we will provide the context in the vein of “There has been an emerging consensus that even though adversarial training increased model robustness, these robust networks do not use human-like features unless explicitly aligned”.\n\n(2)Generalizability/limited neural dataset: \nIn the current version, we only reported data from Majaj et al., 2015, which is one of the best datasets that are available to us when considering the neurons recorded, trials repeated and data format.\n\nTo address the reviewer’s concern, we have performed additional analysis and examined  more datasets. In particular, we have analyzed the dataset collected in Bashivan et al., 2019. This dataset contains only V4 neurons and a smaller number of recorded neurons – only one of the monkeys (monkey m) had sufficient neurons. As a result, the monkey-monkey DVC and monkey-model DVC concerning the monkey subjects with only ~20 neurons are lower due to insufficient sample size, but the relative scale of the DVC remains consistent. In addition, the observation that DVC drops with increasing ImageNet accuracy holds for monkey m (rho=-0.76, p=9.89e-04). We will edit the manuscripts so the words reflect the scope of implications accurately. Specifically, instead of “fundamental divergence”, we will use “substantial divergence”\n\n(3)Robustness to decoder choice: \nThis is a good question. To address the reviewer’s concern, we have now additionally tested the DVC with other linear decoders such as logistic regression and linear SVM and found that the estimate remained stable (for DVC between monkeys: LDA 0.567 ± 0.014, logistic regression 0.562 ± 0.017, linear SVM 0.554 ± 0.017). \n\nRegarding nonlinear decoder, in the current work, we deliberately chose to focus on linear decoding because we are interested in understanding the trial-by-trial correlation of the linearly decodable information for classification tasks. The approach can be incorporated to deal with nonlinear decoder, however, the results obtained would be more difficult to interpret. For reference, using SVM with RBF kernel or MLP with ReLU activation seems to result in lower DVC across the board.\n\nWe will incorporate these new results in the final version of the paper. Thank you again for your thoughtful and constructive advice which further strengthens the paper. We hope the additional results we provided above help mitigate your concerns."}, {"review_id": "B5MH2OKJSj", "reviewer": "Reviewer_4PbU", "summary": "1. New approach (Decision Variable Correlation) to characterize the similarity of the decision strategies of two modalities referred to as observers in this paper\n2. Model-monkey similarity is consistently lower than monkey-monkey or model-model relationship\n3. Adversarial training , Improved accuracy on Imagenet or pretraining on larger dataset does not increase model-monkey similarity \n\nThe study demonstrates divergenece between task relevant representations in monkey V4/IT and models trained on image classification tasks.", "questions": "Did you consider applying DVC to opensource human neuroimaging datasets?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "**Strength**\n\n1. DVC quantifies task relevant similarities and is insensitive to the observer’s biases and independent of behavioral accuracy. It’s a nice bridge between methods purely based on behavior and methods comparing neural representations and it focuses only on those dimensions which are relvant for the behavioral task\n2. Comprehensive Evaluations:\n    1. Large set of models to identify correlation between imagenet accuracy and model-monkey DVC\n    2. Robustly trained models vs. representative models\n    3. Dependency of monkey-model DVC on scale of data used for model training\n3. Interesting findings:\n    1. Data rich and robustly trained model show lower DVC than representative models. The finding is surprising and reveals difference between how monkeys and models solve classification tasks\n    2. Comparison with Cohen’s Kappa measure shows that DVC is insensitive to decision biases.\n4. Clear description of methods, results and figures\n\n**Weakness**\n\n1. A theoretical/data-driven experiment using some simulated data to demonstrate the key differences between different measures would have revealed the pros and cons of different behavioral and representational similarity methods.", "was_revised": true, "final_justification": "The authors addressed all my concerns. I will maintain the original rating. The authors may consider THINGS dataset for furture experiments", "rebuttal": "Thank you for your positive evaluation of our paper and for providing great ideas to help further strengthen it. We address your suggestions below.\n\n(1)Simulation to show difference between methods\nThis is a great suggestion. The difference between unsupervised shape metrics such as RSA and DVC is that DVC focuses on the task dimension and ignores similarities that are irrelevant to the task. To demonstrate this, we simulated two observers with representations that consisted of 1D decision variable, individual noise and shared noise. As shared noise increases, RSA quickly increases and saturates towards 1, while DVC remains stable. We feel this is a great point to add to the paper because it makes the motivation of our method more clear. We will incorporate this point to the revised version of the paper.\n\n(2)DVC to neuroimaging datasets: The existing neuroimaging datasets (e.g. Horikawa & Kamitani, 2017) typically contain hundreds or thousands of image categories, but only a handful of exemplar images in each category, which is the opposite of what we are looking for in this case (more images per category). We were looking at the popular Natural Scenes Dataset (NSD Dataset) which uses COCO images, which has no fixed number of images per category, and each image has multiple labels. This makes the NSD dataset not ideal for our purpose. \nIf the reviewer can think of any publicly available datasets that would be appropriate for the application of our approach, please share them with us. It would be greatly appreciated and would be eager to test these out."}, {"review_id": "R8tH702Tuv", "reviewer": "Reviewer_9A6o", "summary": "This paper introduces a new representational similarity measure for stimulus-driven neural activity. The method is based on a multidimensional generalization of signal detection theory. Neural responses to different stimuli with a known class structure are projected onto the LDA (linear discriminant analysis) axis. The Pearson correlation between the projections of these stimuli for two observers (modulo a noise correction factor) is the proposed similarity score between the neural representations of the corresponding observers. Some advantages of the proposed measure over purely behavioral measures (Cohen’s kappa) are discussed (e.g. insensitivity to decision biases, dependence on internal (neural) representations) and a seeming discrepancy with an earlier study using a purely behavioral measure (Cohen’s kappa) is resolved by taking into account the decision biases affecting Cohen’s kappa.", "questions": "Please address the issues raised under the \"weaknesses\" section above. In particular, the authors need to do a much better job motivating their approach: why exactly it is needed and what it offers over the multitude of current methods.", "limitations": "I think the issues raised above are limitations of the work that aren't adequately addressed by the authors.", "rating": 2, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths:** \n\nI think this is a technically solid paper overall. The experimental demonstration in section 4.5 that Cohen’s kappa used in earlier analyses can be affected by decision biases is a nice contribution. It’s also nice to see error bars in a NeurIPS submission for a change.\n\n**Weaknesses:** \n\nI guess my main concern about this work is that I’m not sure if we really needed another representational similarity measure. In the first two sections of the paper, the authors complain about the multiplicity of representational similarity measures and how they can sometimes give seemingly contradictory results. But they are making this problem worse by introducing (without any good justification) yet another similarity measure that is not going to always agree with previous measures. \n\nWhat exactly is the problem with RSA or regression-based metrics (like Brain-Score), for example, that this new method is addressing? In section 3, the authors write (lines 96-98):\n> ... in contrast to methods for analyzing the similarity of two neural representations (such as representational similarity analysis), our methods focus on the dimensions that are relevant for a behavioral task and is invariant to variability along other task-irrelevant dimensions.\n\nI’m not sure if this is a win for the proposed approach. The proposed approach can’t be applied to cases where there is no obvious class structure in the stimuli or where the class structure is irrelevant (*e.g.* passive viewing of natural videos or images). \n\nEven in cases where there is a class structure and it is relevant to the task, somewhat counterintuitively, the proposed method actually doesn’t say anything about the observer’s actual behavior in the task (it only says something about the behavior of an ideal linear classifier based on the neural responses, which may be completely different from the observer’s own behavior). Whatever its problems, Cohen’s kappa at least doesn’t suffer from this particular issue: it says something about the observer’s actual behavior. \n\nSo, it appears that the proposed method is intended more as an alternative to neural similarity measures, such as RSA or regression-based metrics, as opposed to behavioral similarity measures like Cohen's kappa, but the authors haven't really shown any particular problems with these neural similarity measures that their approach is addressing. The problem they identify only affects Cohen's kappa. So, we're left wondering what exactly is the pressing need or the real motivation behind this new neural representational similarity measure.\n\nIf I’m interested in quantifying the similarity between neural responses and model responses, I can use RSA or a regression-based metric. These are general methods I can use for any type of stimuli or task. Their application is not limited to classification tasks. If I don’t have access to neural responses or if I just want to quantify the behavioral similarity between an observer and a model, I can use kappa or some bias corrected version of it. I haven’t really read anything in this paper that made me question these choices and convinced me that a new similarity measure was desperately needed.", "was_revised": true, "final_justification": "The proposed method has a rather severe limitation: it only applies to classification tasks. This limitation does not hold for alternative methods like RSA or various flavors of regression: these are universally applicable methods for any type of task or stimuli. **The authors have not shown any deficiencies in these alternative methods that their own method is addressing.** \n\nMoreover, the authors misleadingly pit their method against Cohen's kappa, which is a well-established measure of **decision correlations** for different observers. The paper and the rebuttal persistently (and again misleadingly to my mind) refer to the method as measuring the correlation between \"decision strategies of two observers\" or variations thereof, but actually, unlike Cohen's kappa, **the proposed method has nothing to do with the actual decisions of the observers** (only with the \"decisions\" of an optimal linear classifier), so these methods are not directly comparable. The proposed method is rather more accurately thought of as an alternative to representational similarity measures like RSA or regression, but as mentioned before, the authors have not shown any deficiencies in these particular methods; on the contrary, the proposed method has a severe limitation compared to these alternative representational similarity measures. \n\nSo, in my opinion, the proposed method is unmotivated and unnecessary. I'm sorry for being a bit harsh here, but my honest judgment is that it is simply cluttering an already cluttered literature on representational similarity.", "rebuttal": "Thank you for your thoughtful review on our work. The main criticism is why our method is needed given there are already several prior methods to modeling the alignment of neural/behavioral responses across different observers/models. This is an important point that requires further clarification.\n\n(1)Reason to adopt DVC over other methods: As a representational similarity measure, DVC is a supervised method that utilizes labels for task-specific comparisons, which distinguishes it from the methods that focus on general geometry. In addition, it is less biased and more principled. We think it should be able supersede previous methods where the conditions for its application are met.\n\nDVC can be also applied strictly to behavior such as comparing models to behavior, comparing two behaving animals, or the same behaving animal on multiple occasions. In all cases, it provided an unbiased principled measure of decision correlations. For more on how DVC may be inferred from behavior, see Sebastian & Geisler, 2018.\n\n(2)Scope of application: Biological vision systems evolve to perform two kinds of specific tasks that are relevant for survival: categorization tasks, and estimation tasks. DVC can be measured for both kinds of tasks. We are interested in understanding biological vision. Most of the rigorous studies of biological vision have been some form of categorization or estimation task. A rigorous unbiased measurement technique should find plenty of applications.\n\nIt is true that there are tasks that the DVC methods would not apply, but we have deliberatively developed our method to study a specific kind of question, in particular, how well the decision strategies of two observers are correlated on a trial-by-trial basis in classification tasks. This is a unique feature of our method that distinguishes our work from other methods, such as RSA which quantifies the similarity of the geometry of two representations.\n\nWe appreciate your thoughtful comments and will revise the paper to incorporate the key points above."}, {"review_id": "oVPbzGut0a", "reviewer": "Reviewer_4fv6", "summary": "This paper proposes Decision Variable Correlation (DVC) as a new method to measure task-relevant similarity between neural representations in brains and deep networks.  DVC focuses on the trial-by-trial correlation of inferred decision variables, isolating task-relevant information while being robust to noise and decision bias. Applying DVC to monkey V4/IT and various deep networks, the authors find that model–model consistency is comparable to monkey–monkey, but model–monkey consistency is lower and decreases with higher ImageNet accuracy. Neither adversarial training nor larger datasets improve model–brain alignment, suggesting a divergence between artificial and biological representations.", "questions": "**Questions and Suggestions for the Authors**\n\n1. **Comparison to RSA/CKA**: The abstract and introduction motivate DVC by highlighting the limitations of standard representational similarity methods (e.g., RSA, CKA). However, the paper does not empirically compare DVC to these methods. Can the authors include such comparisons—ideally using the same model and brain representations? These metrics can also be applied to the output (decision) layer, allowing for a fairer comparison to DVC, which is decoded via LDA from the same representations.\n\n2. **Clarifying Novelty**: Several of the qualitative findings (e.g., that adversarial training or dataset scale does not improve brain alignment) have been previously reported using other similarity metrics. Can the authors clarify what new insights DVC provides beyond replicating existing conclusions?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n- **Clarity and Motivation:** The paper is clearly written and well-motivated. It introduces a conceptually principled method (DVC) that isolates task-relevant similarity, avoiding confounds like accuracy and decision bias. The derivation from signal detection theory is elegant and intuitive.\n- **Sound Methodology:** The method is grounded in theory, and the implementation accounts for practical issues such as noise correction and high-dimensional instability. The authors take care to validate that DVC behaves sensibly under these conditions.\n- **Conservative Claims:** The paper avoids overclaiming and discusses its limitations transparently, including dataset size and generalizability beyond monkeys.\n\n**Weaknesses**\n\n- **No Empirical Comparison to RSA/CKA:** While the paper argues that DVC improves on representational similarity methods like RSA, it does not empirically compare DVC to RSA, CKA, or CCA. This weakens the case for DVC as a superior alternative, especially since RSA-based methods have also reported similar qualitative conclusions (e.g., limited brain-model alignment).\n- **Overlap with Prior Findings:** Many key takeaways—such as the failure of adversarial training or larger datasets to improve alignment—have been reported previously using other similarity metrics. Without a side-by-side comparison, it remains unclear how much new insight DVC offers.", "was_revised": true, "final_justification": "I still think that more experiments could be helpful to make the use case of this method more distinguishable compared to the existing methods. However, based on clarifications provided by authors, and their promises to add clarifications to the text, I am now more confident to recommend this work for publication.", "rebuttal": "Thank you for your constructive feedback. The concerns you have are very representative and we have worked on addressing them.\n\n(1)Comparisons to other methods: Thank you for raising this great point. RSA, CKA and CCA are all useful correlation-based metrics and equivalent under certain conditions. We have compared these metrics in this dataset and find that DVC is indeed positively correlated with all the aforementioned metrics, albeit to different degrees. Of course, DVC is a supervised method that utilizes the labels to discern task-relevant dimensions from task-irrelevant ones, which distinguishes it from other correlation-based methods. The RSA between two simulated representations may be arbitrarily inflated while DVC remains the same. The fact that they are positively correlated, and the degree to which they are correlated, could help us pick apart how much of the variance in the representation is useful for task-solving. We will incorporate the new results on the comparison to relevant other methods in the final version of the paper. Thank you for your valuable suggestion which helped us improve the paper.  \n\n(2)Clarifying novelty: While the main contribution of the paper is the DVC method, we hope that we could use a principled, task-driven approach to examine the topics where other methods have been giving contradictory accounts. Take for example, the relationship between brain alignment and Imagenet accuracy, papers have reported increasing, saturating, peaking then dropping etc. While DVC reports show that the alignment has been dropping consistently since early days, with the exception of some noteworthy outliers. The finding that alignment between brains are on par with the alignment between models also contradicts previous results. We think additional novelty of these findings lies in the method used to derive them and the principles behind the method, making the findings more grounded than previous reports. We agree with the reviewer that these points regarding the novelty should be made more clear in the paper. We will revise the paper to make these points more salient."}, {"review_id": "Wl3ed79tVs", "reviewer": "Reviewer_4tHi", "summary": "The paper proposes a novel method for measuring the similarity of decision strategies between two observers, as is frequently done between DNNs and primate brains in the field of NeuroAI. The method is called decision variable correlation (DVC), which aggregates the trial-level correlations between the decision variables of the observers, which is basically the distance a sample in embedding space has to the separatrix of a linear classifier.\nUsing this method, the authors find low between-group similarity between monkeys and models despite high within-group similarity. This low between-group similarity is not increased by increased classification performance on ImageNet, by more training data, or by higher adversarial robustness, which suggests profound representational differences between monkey brains and image classification models.", "questions": "- What is the effect of the split normalization (sec. 3.2 second paragraph / Appendix A) on results? How would results look like without this normalization? If the point of this step is to reduce noise, wouldn't it be better to split the images into different sets, rather than the neurons?\n- What is the motivation behind checking all pairwise decision variables, rather than just looking at the class-vs-all-others separatrix, which would scale much nicer to large numbers of classes, like 1k ImageNet classes?\n- What is the uncertainty in a DVC-value? You currently just report a point estimate without specifying a CI around these values. This could be achieved by bootstrapping, i.e. if a value is calculated over 1,000 images, draw 1,000 images from the set with replacement for N times and re-calculate DVC for each set, then report the range in which 95% of values end up.\n- What is a model's self-DVC? For example, train a ResNet-50 from scratch on ImageNet with two different random seeds and evaluate their DVC on the validation set.\n- Similarly, what is the DVC between two randomly initialized networks, is it really 0 as expected, and what is the variance?\n- What is the classification accuracy that an optimal linear classifier on top of the monkey representatins achieves?\n- (section 4.5, second paragraph) I'm surprised that logistic regression on top of network representations does not beat the aggregation strategy proposed by Geirhos et al,  shouldn't it be at least as good?", "limitations": "The authors have written a limitation-section, but I think missed one point which they maybe thought was obvious: The method is limited to datasets that have class labels, like ImageNet. This is not true for all image datasets, and other methods like RSA work independently of known class labels, hence I think it should be explicitly mentioned.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n- The paper addresses a relevant problem and is fairly clearly written.\n- The idea of only using those parts of the representation that are relevant for the task is valuable.\n- The conducted analysis is very thorough, sufficiently many models were investigated and the selection of models is reasonable.\n\n## Weaknesses\nMy main gripe with the paper is that they propose yet another method for measuring brain-model similarity, and immediately jump to deriving conclusions, instead of first sanity-checking the method itself. I propose a few of these sanity checks in the Questions-block.\n\n- The description of the method lacks rigor, the authors never properly define what the decision variable is. I understood it to be the length of the projection onto the separatrix, but I'm not even sure if this is correct.\n- I find the split-normalization highly dubious. The authors just assume that within the two randomly drawn subpopulations of neurons of a layer, the same signal is represented, plus different noise, which can essentially be averaged out. I don't share this intuition, because if the different subgroups represent different features, the signal may be different.\n- The comparison to Cohen's Kappa (especially how figure 5e was obtained) is missing details, e.g. why does a low decision bias enforce a low kappa? \n- I have some concerns about the dependence of DVC on the accuracy of the two classifiers, which are not addressed by the paper. I suspect that two classifiers with very different accuracy cannot have a high DVC, just like two classifiers with different accuracies cannot have a high Error Consistency (as measured by Cohen's kappa over correctness values). It does not surprise me that increased accuracy on ImageNet-1k does not yield increased DVC to monkeys, because I doubt that an optimal linear classifier on top of the monkey representations would perform very well. I fear that such a dependency on accuracy could also explain the findings in figure 2d, because (as seen in figure 2c) models from the same family tend to have similar accuracy. This is problematic, as it would mean that I gain no more knowledge from DVCs than I would trivially get from accuracy.\n\n## Conclusion\nOverall, I find the method interesting and could imagine accepting the paper, because it meaningfully adds to the discourse. But there are too many issues that make me feel uneasy about the method, so I don't trust the results yet. If the authors address these concerns and other reviewers agree, I'm open to increasing my score.", "was_revised": true, "final_justification": "In my initial review, I had some concerns about the paper, mostly because there are already too many metrics of alignment rather than too few. There were also some choices that were not properly ablated. However, during the rebuttal period, the authors have addressed the specific concerns I had raised and clarified some details of the method. It seems that this approach is comparatively well-grounded in signal detection theory, and results seem to be robust. At this stage, I have no good arguments against accepting this paper, so vote to accept, which generally also seems to be the consensus among reviewers.", "rebuttal": "Thank you for your very detailed feedback and questions on our work. For several of these points, we have now performed additional analysis to address them. We feel that by addressing these critiques, the paper has been greatly improved.\n\n(1) Explain the decision variable: Your intuition is not far off! The decision variable is a term derived from signal detection theory that is frequently adopted by behavioral psychologists as a model for decision making, which is why it is the perfect base ingredient for this method. It is a continuous variable that represents the sensory evidence of the observer. A threshold (the separatrix) is further used to make the decision. So here it is the projection onto the axis orthogonal to the separatrix.\n\n(2)Justify split normalization: Your question about if the split halves are truly two copies of the same information (decision variable) contaminated by independent noise is an interesting one. \nFollowing your suggestion, we have performed additional analysis by decoding the individual splits. Although there is no ground truth available for the decision variable, we find the decoding performance to be high for the individual splits. In addition the DVC estimates with random splits are very consistent across repeats (normalized DVC for monkey vs. monkey is 0.568 ± 0.014), showing that it is likely that splits contain the same copy of task-relevant information. This result is consistent with the general idea that information about the task is distributed in the network. The split normalization, as you would expect, rescues DVC relating to noisier observers, making the monkey-monkey, monkey-model DVC higher than would otherwise be. As the math (described in the Supplementary Information section A1) shows, under the correct (if somewhat restrictive) assumptions, the procedure recovers the ground truth DV.\n\nThe splits are on the neurons instead of the images because we are trying to account for the overall noise in the representation instead of the image sampling noise. The sample size is large enough in this case (400 images in each category) that the latter is miniscule. However this could be useful in cases where the sample size is smaller.\n\n(3)The relationship between Kappa and bias: This is a good question. The details on the simulation that addresses the relation between Cohen’s Kappa and decision biases are provided in the Supplementary Materials Section A2. We apologize if the description has been unclear. The general intuition is that DVC is agnostic to the behavioral biases of the observers while Kappa is inflated when there is a shared bias between observers. Low bias does not enforce a low Kappa.\n\n(4)Accuracy of linear decoder on monkey recordings: Thank you for this suggestion. An optimal linear decoder on monkey V4/IT recordings actually performs very well (average pairwise LDA score 0.92 & 0.94 for the two monkeys respectively, which is at a similar level as the networks ~0.96) so it is very unlikely to be the cause of differences in DVC. The accuracy for the logistic regression classifier for all the classes (instead of binary classification) is 0.80 & 0.81, respectively. With cross validation it drops to 0.74 & 0.71. In addition, the decision variable is conceptually decoupled from accuracy, since it cares about the information used to make the decision, not the decision itself. Which makes it great for addressing behavioral differences by different observers. We will include this result into the revised version of the paper. \n\n(5)Pairwise or one vs. the others: Our choice of focusing on pairwise classification instead of one vs. the others classification is in part due to the fact that we use a smaller dataset. However, also consider that between two (e.g. gaussian) distributions with equal covariances, the best classifier is linear. But in the case of one vs. many gaussian distributions, it can be very hard, or even impossible, to find a good linear classifier depending on the arrangement of the classes, especially in settings where the effective signal dimension is low.\n\n(6)The uncertainty of DVC: DVC estimate with split is very robust with the amount of samples in this dataset. As previously mentioned, normalized DVC for monkey vs. monkey is 0.568 ± 0.014, where the uncertainty comes from different splits. The uncertainty of DVC with respect to sampling can be estimated using bootstrap procedure. Thank you for this suggestion.\n\n(7)DVC between networks initiated with different seeds: As established in studies such as Mehrer et al. 2020 (Nat Comm), networks with varying initiation can learn very different intermediate representations, therefore should be viewed as different models. To address your question, we tested DVC on Resnet50 variants trained using different initialization, augmentations, training recipes etc. Notably, DVC between models with different initialization but otherwise underwent the same training procedure is 0.80.\n\n(8)DVC results with randomly initialized networks: We have since examined DVC on randomly initialized networks. Under special circumstances where networks of the same family are initialized using the same seed, DVC reports could be quite high. However in general DVC between randomly initialized networks fall in the 0.10 - 0.20 range.\n\nThank you again for taking time to carefully examine our manuscript. We hope our new analyses and the clarification above address your concerns. Please feel free to follow up with further inquiries."}]

Author rebuttal:

Meta-review: This work proposes a representational similarity metric that is grounded in signal detection theory. They evaluate their metric on monkey V4/IT recordings and find the model-monkey similarity decreases with the model's performance on a ImageNet classification task, which is surprising given that other metrics (namely, linear regression) suggest the opposite. 

Four of the reviewers recommended acceptance, while Reviewer 9A6o recommended rejection. Reviewer 9A6o's main concerns are that (1) the method is limited to classification tasks, and (2) the interpretation of their metric as a behavioral readout is misleading. During the discussion period, two of the other reviewers commented that they did not find (1) to be a significant limitation and that (2) could be addressed by the authors in their revision.

Given this, I recommend acceptance and urge the authors to clarify the issues raised by the reviewers.
Decision: Accept (poster)