Factorized visual representations in the primate visual system and deep neural networks

  1. Jack W. Lindsey
  2. Elias B. Issa

  • Curated by eLife

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    eLife assessment

    The study makes a valuable empirical contribution to our understanding of visual processing in primates and deep neural networks, with a specific focus on the concept of factorization. The analyses provide solid evidence that high factorization scores are correlated with neural predictivity, yet more evidence would be needed to show that neural responses show factorization. Consequently, while several aspects require further clarification, in its current form this work is interesting to systems neuroscientists studying vision and could inspire further research that ultimately may lead to better models of or a better understanding of the brain.

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Abstract

Object classification has been proposed as a principal objective of the primate ventral visual stream and has been used as an optimization target for deep neural network models (DNNs) of the visual system. However, visual brain areas represent many different types of information, and optimizing for classification of object identity alone does not constrain how other information may be encoded in visual representations. Information about different scene parameters may be discarded altogether (“invariance”), represented in non-interfering subspaces of population activity (“factorization”) or encoded in an entangled fashion. In this work, we provide evidence that factorization is a normative principle of biological visual representations. In the monkey ventral visual hierarchy, we found that factorization of object pose and background information from object identity increased in higher-level regions and strongly contributed to improving object identity decoding performance. We then conducted a large-scale analysis of factorization of individual scene parameters – lighting, background, camera viewpoint, and object pose – in a diverse library of DNN models of the visual system. Models which best matched neural, fMRI and behavioral data from both monkeys and humans across 12 datasets tended to be those which factorized scene parameters most strongly. Notably, invariance to these parameters was not as consistently associated with matches to neural and behavioral data, suggesting that maintaining non-class information in factorized activity subspaces is often preferred to dropping it altogether. Thus, we propose that factorization of visual scene information is a widely used strategy in brains and DNN models thereof.

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  1. Version published to 10.1101/2023.04.22.537916v3 on bioRxiv
  2. Version published to 10.7554/elife.91685.1 on eLife
  3. Version published to 10.7554/elife.91685 on eLife
  4. eLife

    eLife assessment

    The study makes a valuable empirical contribution to our understanding of visual processing in primates and deep neural networks, with a specific focus on the concept of factorization. The analyses provide solid evidence that high factorization scores are correlated with neural predictivity, yet more evidence would be needed to show that neural responses show factorization. Consequently, while several aspects require further clarification, in its current form this work is interesting to systems neuroscientists studying vision and could inspire further research that ultimately may lead to better models of or a better understanding of the brain.

  5. eLife

    Reviewer #1 (Public Review):

    Summary:
    The paper investigates visual processing in primates and deep neural networks (DNNs), focusing on factorization in the encoding of scene parameters. It challenges the conventional view that object classification is the primary function of the ventral visual stream, suggesting instead that the visual system employs a nuanced strategy involving both factorization and invariance. The study also presents empirical findings suggesting a correlation between high factorization scores and good neural predictivity.

    Strengths:

    1. Novel Perspective: The paper introduces a fresh viewpoint on visual processing by emphasizing the factorization of non-class information.

    2. Methodology: The use of diverse datasets from primates and humans, alongside various computational models, strengthens the validity of the findings.

    3. Detailed Analysis: The paper suggests metrics for factorization and invariance, contributing to a future understanding & measurements of these concepts.

    Weaknesses:

    1. Vagueness (Perceptual or Neural Invariance?): The paper uses the term 'invariance', typically referring to perceptual stability despite stimulus variability [1], as the complete discarding of nuisance information in neural activity. This oversimplification overlooks the nuanced distinction between perceptual invariance (e.g., invariant object recognition) and neural invariance (e.g., no change in neural activity). It seems that by 'invariance' the authors mean 'neural' invariance (rather than 'perceptual' invariance) in this paper, which is vague. The paper could benefit from changing what is called 'invariance' in the paper to 'neural invariance' and distinguish it from 'perceptual invariance,' to avoid potential confusion for future readers. The assignment of 'compact' representation to 'invariance' in Figure 1A is misleading (although it can be addressed by the clarification on the term invariance). [1] DiCarlo JJ, Cox DD. Untangling invariant object recognition. Trends in cognitive sciences. 2007 Aug 1;11(8):333-41.

    2. Details on Metrics: The paper's explanation of factorization as encoding variance independently or uncorrelatedly needs more justification and elaboration. The definition of 'factorization' in Figure 1B seems to be potentially misleading, as the metric for factorization in the paper seems to be defined regardless of class information (can be defined within a single class). Does the factorization metric as defined in the paper (orthogonality of different sources of variation) warrant that responses for different object classes are aligned/parallel like in 1B (middle)? More clarification around this point could make the paper much richer and more interesting.

    3. Factorization vs. Invariance: Is it fair to present invariance vs. factorization as mutually exclusive options in representational hypothesis space? Perhaps a more fair comparison would be factorization vs. object recognition, as it is possible to have different levels of neural variability (or neural invariance) underlying both factorization and object recognition tasks.

    4. Potential Confounding Factors in Empirical Findings: The correlation observed in Figure 3 between factorization and neural predictivity might be influenced by data dimensionality, rather than factorization per se [2]. Incorporating discussions around this recent finding could strengthen the paper.

    [2] Elmoznino E, Bonner MF. High-performing neural network models of the visual cortex benefit from high latent dimensionality. bioRxiv. 2022 Jul 13:2022-07.

    Conclusion:
    The paper offers insightful empirical research with useful implications for understanding visual processing in primates and DNNs. The paper would benefit from a more nuanced discussion of perceptual and neural invariance, as well as a deeper discussion of the coexistence of factorization, recognition, and invariance in neural representation geometry. Additionally, addressing the potential confounding factors in the empirical findings on the correlation between factorization and neural predictivity would strengthen the paper's conclusions.

  6. eLife

    Reviewer #2 (Public Review):

    Summary:
    The dominant paradigm in the past decade for modeling the ventral visual stream's response to images has been to train deep neural networks on object classification tasks and regress neural responses from units of these networks. While object classification performance is correlated to the variance explained in the neural data, this approach has recently hit a plateau of variance explained, beyond which increases in classification performance do not yield improvements in neural predictivity. This suggests that classification performance may not be a sufficient objective for building better models of the ventral stream. Lindsey & Issa study the role of factorization in predicting neural responses to images, where factorization is the degree to which variables such as object pose and lighting are represented independently in orthogonal subspaces. They propose factorization as a candidate objective for breaking through the plateau suffered by models trained only on object classification. They claim that (i) maintaining these non-class variables in a factorized manner yields better neural predictivity than ignoring non-class information entirely, and (ii) factorization may be a representational strategy used by the brain.

    The first of these claims is supported by their data. The second claim does not seem well-supported, and the usefulness of their observations is not entirely clear.

    Strengths:
    This paper challenges the dominant approach to modeling neural responses in the ventral stream, which itself is valuable for diversifying the space of ideas.

    This paper uses a wide variety of datasets, spanning multiple brain areas and species. The results are consistent across the datasets, which is a great sign of robustness.

    The paper uses a large set of models from many prior works. This is impressively thorough and rigorous.

    The authors are very transparent, particularly in the supplementary material, showing results on all datasets. This is excellent practice.

    Weaknesses:
    1. The primary weakness of this paper is a lack of clarity about what exactly is the contribution. I see two main interpretations: (1-A) As introducing a heuristic for predicting neural responses that improve over-classification accuracy, and (1-B) as a model of the brain's representational strategy. These two interpretations are distinct goals, each of which is valuable. However, I don't think the paper in its current form supports either of them very well:

    (1-A) Heuristic for neural predictivity. The claim here is that by optimizing for factorization, we could improve models' neural predictivity to break through the current predictivity plateau. To frame the paper in this way, the key contribution should be a new heuristic that correlates with neural predictivity better than classification accuracy. The paper currently does not do this. The main piece of evidence that factorization may yield a more useful heuristic than classification accuracy alone comes from Figure 5. However, in Figure 5 it seems that factorization along some factors is more useful than others, and different linear combinations of factorization and classification may be best for different data. There is no single heuristic presented and defended. If the authors want to frame this paper as a new heuristic for neural predictivity, I recommend the authors present and defend a specific heuristic that others can use, e.g. [K * factorization_of_pose + classification] for some constant K, and show that (i) this correlates with neural predictivity better than classification alone, and (ii) this can be used to build models with higher neural predictivity. For (ii), they could fine-tune a state-of-the-art model to improve this heuristic and show that doing so achieves a new state-of-the-art neural predictivity. That would be convincing evidence that their contribution is useful.

    (1-B) Model of representation in the brain. The claim here is that factorization is a general principle of representation in the brain. However, neural predictivity is not a suitable metric for this, because (i) neural predictivity allows arbitrary linear decoders, hence is invariant to the orthogonality requirement of factorization, and (ii) neural predictivity does not match the network representation to the brain representation. A better metric is representational dissimilarity matrices. However, the RDM results in Figure S4 actually seem to show that factorization does not do a very good job of predicting neural similarity (though the comparison to classification accuracy is not shown), which suggests that factorization may not be a general principle of the brain. If the authors want to frame the paper in terms of discovering a general principle of the brain, I suggest they use a metric (or suite of metrics) of brain similarity that is sensitive to the desiderata of factorization, e.g. doesn't apply arbitrary linear transformations, and compare to classification accuracy in addition to invariance.

    Overall, I suggest the authors clarify exactly what their claim is, then focus on that claim and present results to justify it. If neither of the claims above can be supported by evidence, then this paper still has value as an idea that they spent effort trying to test, but they should not suggest these claims in the paper. In that case, it may also be possible to increase the value of the contribution by characterizing how the structure of class-free variable representations impacts correlation with neural fit, instead of just comparing existence vs absence (invariance) of this information. For example, evaluate the degree to which local or global orthogonality matters, or the degree to which curvature of the embedding matters.

    2. I think the comparison to invariance, which is pervasive throughout the paper, is not very informative. First, it is not surprising that invariance is more weakly correlated with neural predictivity than factorization, because invariant representations lose information compared to factorized representations. Second, there has long been extensive evidence that responses throughout the ventral stream are not invariant to the factors the authors consider, so we already knew that invariance is not a good characterization of ventral stream data.

    3. The formalization of the factorization metric is not particularly elegant, because it relies on computing top K principal components for the other-parameter space, where K is arbitrarily chosen as 10. While the authors do show that in their datasets the results are not very sensitive to K (Figure S5), that is not guaranteed to be the case in general. I suggest the authors try to come up with a formalization that doesn't have arbitrary constants. For example, one possibility that comes to mind is E[delta_a x delta_b], where 'x' is the normalized cross product, delta_a, and delta_b are deltas in representation space induced by perturbations of factors a and b, and the expectation is taken over all base points and deltas. This is just the first thing that comes to mind, and I'm sure the authors can come up with something better. The literature on disentangling metrics in machine learning may be useful for ideas on measuring factorization.

    4. The authors defined the term "factorization" according to their metric. I think introducing this new term is not necessary and can be confusing because the term "factorization" is vague and used by different researchers in different ways. Perhaps a better term is "orthogonality", because that is clear and seems to be what the authors' metric is measuring.

    5. One general weakness of the factorization paradigm is the reliance on a choice of factors. This is a subjective choice and becomes an issue as you scale to more complex images where the choice of factors is not obvious. While this choice of factors cannot be avoided, I suggest the authors add two things: First, an analysis of how sensitive the results are to the choice of factors (e.g. transform the basis set of factors and re-run the metric); second, include some discussion about how factors may be chosen in general (e.g. based on temporal statistics of the world, independent components analysis, or something else).

  7. eLife

    Reviewer #3 (Public Review):

    Summary:
    Object classification serves as a vital normative principle in both the study of the primate ventral visual stream and deep learning. Different models exhibit varying classification performances and organize information differently. Consequently, a thriving research area in computational neuroscience involves identifying meaningful properties of neural representations that act as bridges connecting performance and neural implementation. In the work of Lindsey and Issa, the concept of factorization is explored, which has strong connections with emerging concepts like disentanglement [1,2,3] and abstraction [4,5]. Their primary contributions encompass two facets: (1) The proposition of a straightforward method for quantifying the degree of factorization in visual representations. (2) A comprehensive examination of this quantification through correlation analysis across deep learning models.

    To elaborate, their methodology, inspired by prior studies [6], employs visual inputs featuring a foreground object superimposed onto natural backgrounds. Four types of scene variables, such as object pose, are manipulated to induce variations. To assess the level of factorization within a model, they systematically alter one of the scene variables of interest and estimate the proportion of encoding variances attributable to the parameter under consideration.

    The central assertion of this research is that factorization represents a normative principle governing biological visual representation. The authors substantiate this claim by demonstrating an increase in factorization from macaque V4 to IT, supported by evidence from correlated analyses revealing a positive correlation between factorization and decoding performance. Furthermore, they advocate for the inclusion of factorization as part of the objective function for training artificial neural networks. To validate this proposal, the authors systematically conduct correlation analyses across a wide spectrum of deep neural networks and datasets sourced from human and monkey subjects. Specifically, their findings indicate that the degree of factorization in a deep model positively correlates with its predictability concerning neural data (i.e., goodness of fit).

    Strengths:
    The primary strength of this paper is the authors' efforts in systematically conducting analysis across different organisms and recording methods. Also, the definition of factorization is simple and intuitive to understand.

    Weaknesses:
    This work exhibits two primary weaknesses that warrant attention: (i) the definition of factorization and its comparison to previous, relevant definitions, and (ii) the chosen analysis method.

    Firstly, the definition of factorization presented in this paper is founded upon the variances of representations under different stimuli variations. However, this definition can be seen as a structural assumption rather than capturing the effective geometric properties pertinent to computation. More precisely, the definition here is primarily statistical in nature, whereas previous methodologies incorporate computational aspects such as deviation from ideal regressors [1], symmetry transformations [3], generalization [5], among others. It would greatly enhance the paper's depth and clarity if the authors devoted a section to comparing their approach with previous methodologies [1,2,3,4,5], elucidating any novel insights and advantages stemming from this new definition.

    Secondly, in order to establish a meaningful connection between factorization and computation, the authors rely on a straightforward synthetic model (Figure 1c) and employ multiple correlation analyses to investigate relationships between the degree of factorization, decoding performance, and goodness of fit. Nevertheless, the results derived from the synthetic model are limited to the low training-sample regime. It remains unclear whether the biological datasets under consideration fall within this low training-sample regime or not.

    [1] Eastwood, Cian, and Christopher KI Williams. "A framework for the quantitative evaluation of disentangled representations." International conference on learning representations. 2018.
    [2] Kim, Hyunjik, and Andriy Mnih. "Disentangling by factorising." International Conference on Machine Learning. PMLR, 2018.
    [3] Higgins, Irina, et al. "Towards a definition of disentangled representations." arXiv preprint arXiv:1812.02230 (2018).
    [4] Bernardi, Silvia, et al. "The geometry of abstraction in the hippocampus and prefrontal cortex." Cell 183.4 (2020): 954-967.
    [5] Johnston, W. Jeffrey, and Stefano Fusi. "Abstract representations emerge naturally in neural networks trained to perform multiple tasks." Nature Communications 14.1 (2023): 1040.
    [6] Majaj, Najib J., et al. "Simple learned weighted sums of inferior temporal neuronal firing rates accurately predict human core object recognition performance." Journal of Neuroscience 35.39 (2015): 13402-13418.

  8. Version published to 10.1101/2023.04.22.537916v2 on bioRxiv
  9. Version published to 10.1101/2023.04.22.537916v1 on bioRxiv