Unveiling Secrets of Brain Function With Generative Modeling: Motion Perception in Primates & Cortical Network Organization in Mice

Hadi Vafaii

REVIEW 4 major objections 4 minor 297 references

Unveiling Secrets of Brain Function With Generative Modeling: Motion Perception in Primates & Cortical Network Organization in Mice

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A hierarchical generative model trained only on synthetic optic flow predicts macaque MT neurons more than twice as well as the prior benchmark.

desk verdict A carefully framed dissertation whose headline claims are unverifiable in the posted text; the per-figure beta selection is a real threat to the 2x predictive gain. read the letter →

arxiv 2412.19845 v1 pith:LLIXVO5R submitted 2024-12-25 q-bio.NC cs.AI

Hadi Vafaii This is my paper · ORCID

classification q-bio.NCcs.AI

keywords hierarchicalvariationalautoencoderopticflowparsingMTneuronencodingmodelsself-motionversusobject-motionmixed-membershipstochasticblockmodeloverlappingcorticalnetworkswide-fieldcalciumimagingresting-statefMRI

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This dissertation claims that a hierarchical variational autoencoder—a generative neural network trained without labels on synthetic retinal optic flow—learns to decompose the flow into self-motion and object-motion, and that its internal representations predict macaque MT neuron responses with more than double the predictive power of the leading mechanistic model. A second project applies the same inferential framework to spontaneous mouse cortex activity, showing that simultaneously recorded fMRI and calcium-imaging signals are best described by overlapping communities, with roughly half of cortical regions belonging to more than one network. If the motion claim holds, it suggests that hierarchical inference, rather than supervised feature fitting, underlies the visual system's ability to separate the observer's own movement from movement in the world. If the network claim holds, standard disjoint parcellations of the cortex systematically understate how multifunctional many regions are, and the overlapping organization appears in both hemodynamic and more neuron-specific optical signals.

What carries the argument

The central object is the compressed hierarchical variational autoencoder (cNVAE), which stacks multiple stochastic latent layers and is trained by maximizing the evidence lower bound (ELBO), a variational free-energy objective that operationalizes Helmholtz's 'perception as unconscious inference.' The hierarchy is what lets the model capture multi-scale causes in the synthetic ROFL optic-flow data: lower latents handle local flow structure and higher latents encode object motion and self-motion. The other load-bearing mechanism is the mixed-membership stochastic blockmodel with variational inference, which assigns each cortical region a vector of membership strengths across K overlapping communities rather than a single community label; the overlap fraction and membership entropy derived from that vector carry the Chapter 5 results.

What would settle it

Train the same model on ROFL variants with two independently moving objects, pursuit or saccadic eye movements, occlusions, or natural depth variation, and re-measure the MT alignment gain. If the >2x improvement over the mechanistic baseline disappears or falls below significance, the finding is specific to the simplified stimulus family rather than a general principle of hierarchical inference.

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Extended reading notes

Core claim

In the author's terms, the dissertation demonstrates that optic flow parsing is possible if a neural network is (a) structured hierarchically and (b) trained with an objective function based on Helmholtzian inference. The compressed hierarchical VAE (cNVAE) is trained on the ROFL synthetic world, which contains a fixating observer, translational and rotational self-motion, and one independently moving object; without any supervision, the latents untangle object position and velocity from self-motion components more sharply than a comparable flat VAE. Evaluated as an encoding model against macaque MT neuron recordings, the hierarchical VAE surpasses the previous state-of-the-art mechanistic MT model [27] by a gain of over 2x in predictive power. Chapter 5 applies the same variational-inference strategy to spontaneous activity: a mixed-membership stochastic blockmodel decomposes simultaneous fMRI-BOLD and wide-field calcium fluorescence in mice into overlapping communities, and around half of the cortical regions belong to multiple communities.

Load-bearing premise

The load-bearing premise is that the simplified simulated retina—one fixating observer, one fixed-size moving object, and prescribed depth statistics—captures the optic-flow structure that real macaque MT neurons encode, so that what the model learns transfers to biological neurons.

Editorial extensions

If this is right

Unsupervised, visual-only learning can separate self-motion from object motion when the network is hierarchical and trained with an inference-based loss; no extra-retinal signals are required.
Hierarchical latent structure is the reason for the improved brain alignment: flat VAEs trained on the same objective and data align less well with MT neurons, so the hierarchy itself carries predictive power.
MT encoding models no longer need hand-designed motion filters to be competitive; the latent representations of a generative model trained on optic flow predict neural responses better than the previous mechanistic standard.
Around half of mouse cortical regions belong to more than one resting-state network, so disjoint network parcellations misdescribe a substantial fraction of cortex.
The overlapping organization is not purely a BOLD artifact: wide-field calcium imaging, a more neuron-specific signal, produces largely concordant overlapping communities, with modality-specific differences in degree and diversity metrics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Taken further than the dissertation states: if the inference objective is the cause of the 2x gain, then training the same model on more ecological optic flow—pursuit eye movements, multiple objects, occlusions—should preserve or increase the gain; if the gain collapses, the result is specific to the simplified stimulus family rather than to hierarchical inference per se.
A testable extension the author leaves implicit: latent units carrying object-motion information in the model should map onto neurons in area MST, the next cortical stage after MT, predicting that MST-like selectivity for combined optic flow and object motion does not require extra-retinal input.
On the network side, the overlap result implies that regions with high membership entropy are the most likely to switch community allegiance when the brain changes state, linking static overlap to dynamic circuit reconfiguration in a way that task or arousal manipulations could test.
Because Ca2+ and fMRI reveal similar principal gradients but different degree and entropy maps, the disparate centrality measures across modalities may index neurovascular rather than purely neural properties; a joint model treating BOLD and calcium as two noisy observations of one shared community latent would test that interpretation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The thing you should know up front: this is a PhD dissertation, and the two results chapters (Chapters 4 and 5) are truncated in the arXiv posting. What is visible—the abstract, the full introduction, and the historical/mathematical background—is carefully written and honestly hedged. But the load-bearing numbers, the 'over 2x' predictive gain over the Nishimoto-Gallant MT model and the ~50% of mouse cortical regions in multiple communities, are claims we simply cannot check from the text under review.

What is genuinely new: the ROFL synthetic optic flow dataset and the cNVAE architecture are real contributions, and the attempt to test an unsupervised hierarchical generative model against macaque MT recordings is a meaningful step beyond the usual feedforward CNN-based encoding models. The second project, applying a mixed-membership stochastic blockmodel to simultaneous fMRI and Ca2+ imaging, is also a sensible way to ask whether overlapping community structure is a BOLD artifact or a general property of cortical organization. The writing is refreshingly direct, and the author explicitly lists limitations in Sections 4.7.1 and 6.1.1.

The soft spots are real, and the stress-test note points at the most important one. Section 4.9.5 discloses that beta (the VAE loss weight) is chosen separately for different figures. If those choices were made after inspecting brain-alignment results, the 2x gain is not a comparison between a fixed cNVAE and a fixed baseline; it is a comparison between a search over a hyperparameter family and a single Nishimoto-Gallant fit. That undermines the internal validity of the headline claim more than the ecological simplicity of ROFL does, because even a simplified synthetic world could support a fair architectural comparison if the hyperparameters were set in advance. The stress-test note is right on this point.

Two other fragilities are visible from the front matter. The baseline comparability—whether the 2x gain was computed under identical cross-validation splits and stimulus sets—is not shown in the text we have. And the Chapter 5 overlap percentage depends on the chosen number of communities K and the graph threshold; those choices are reported in the supplementary sections, but the robustness analysis is not available to us. None of this means the results are wrong; it means the posted text does not contain the evidence needed to judge them.

Who is this for? Vision scientists and computational neuroscientists interested in generative models of neural coding, and network neuroscientists working on overlapping brain networks. The paper deserves a serious referee, but only after the full results chapters are made available and the beta selection rule is either fixed a priori or shown to be insensitive across a reasonable range. If it crosses your desk as a journal submission, send it to review with that insistence. As an arXiv posting, it is an interesting draft, not a finished paper.

Referee Report

4 major / 4 minor

Summary. This manuscript, an arXiv deposit of a PhD dissertation, presents two projects. Project 1 (Chapter 4) develops a hierarchical variational autoencoder, cNVAE, trained on a synthetic optic-flow dataset (ROFL), and claims that its latent representations not only separate self-motion and object-motion causes without extra-retinal signals but also predict macaque MT neuron responses with a gain of over 2x over the previous state of the art (Section 1.8.4). Project 2 (Chapter 5) applies a mixed-membership stochastic blockmodel to simultaneous fMRI and wide-field calcium imaging data in mice and claims that roughly half of cortical regions belong to multiple overlapping communities (abstract and Section 1.13.3). The introduction and background chapters are fully provided, but the two results chapters are truncated in the version under review, so the evidence for these claims is not available in the submitted text.

Significance. If the results hold, Project 1 would provide an important proof-of-concept that unsupervised hierarchical generative models can perform optic-flow parsing and serve as encoding models of primate MT neurons, a domain previously dominated by supervised mechanistic models. The use of external macaque MT recordings to ground the brain-alignment claim is a methodological strength, as is the stated intention to release code and data (Sections 4.8 and 5.5). Project 2 addresses a timely question about overlapping functional organization in the rodent cortex using a rare simultaneous fMRI/Ca2+ dataset. However, because both results chapters are absent from the reviewed text, the actual quantitative support for these claims cannot currently be assessed.

major comments (4)

[Chapters 4 and 5 (TOC; Sections 1.8.4, 1.13.3)] The central quantitative claims—the over-2x predictive gain of the hierarchical VAE over the Nishimoto-Gallant model and the roughly 50% overlap of mouse cortical regions—are asserted in the introduction and abstract, but Chapters 4 and 5 are not present in the submitted text; only their table-of-contents entries and section headings are available. Consequently, the model architecture, training procedure, evaluation metrics, statistical comparisons, and robustness analyses that would substantiate these claims cannot be inspected. This is a load-bearing incompleteness for the manuscript as submitted.
[§4.9.5; §1.8.4] The over-2x predictive gain claim is potentially confounded by the per-figure β selection disclosed in Section 4.9.5. If β values were chosen after inspecting brain-alignment results (e.g., Fig. 4.16), then the reported gain compares an outcome-selected member of the cNVAE family against a single fixed Nishimoto-Gallant baseline, rather than evaluating a fixed model. Please report the β selection rule, state whether it was blind to the MT recording data, and include a sensitivity analysis of the predictive gain across β values.
[§4.3, §4.12] The ROFL synthetic dataset contains one fixating observer, one object of fixed size, and known depth distributions. The transfer of representations learned on this simplified stimulus family to real macaque MT responses assumes that its motion statistics capture ecologically relevant structure. The paper should provide evidence about how the disentanglement and MT-alignment results vary with object size, number of objects, presence of pursuit eye movements, and depth variability, or otherwise justify the ecological validity of ROFL.
[§5.4.2, §5.4.3] The Chapter 5 claim that about 50% of cortical regions belong to multiple communities depends on the chosen number of communities K and on the functional connectivity graph threshold. The visible text does not include the robustness analyses that would show this overlap estimate is stable across these choices; the full chapter should report such analyses or qualify the claim accordingly.

minor comments (4)

[Abstract; §1.8.4] The phrase 'hierarchical inference underlines the brain's understanding' should read 'underlies the brain's understanding'; also, 'V AE' is written with an unusual space throughout, and should be standardized to 'VAE'.
[Figure 1.11 caption] The caption contains a typo: 'Foodforward (ascending) and feedback' should be 'Feedforward (ascending) and feedback'.
[§1.8.4] The claim of 'over 2x in predictive power' would be clearer if it specified the evaluation metric (e.g., variance explained, correlation coefficient) and the exact comparison protocol used for the baseline model.
[Chapter 3 title] The chapter title 'Variational Inference & Variational Autoencoders (V AE)' should use the standard abbreviation 'VAE' consistently, both in the title and in the body text.

Circularity Check

0 steps flagged · score 0.0 of 10

No demonstrated circularity: the MT predictive-power claim is grounded in external macaque recordings; the per-figure β choice is a robustness concern, not an exhibited reduction.

full rationale

The paper's derivation chain is: Helmholtzian inference + cortical hierarchy → cNVAE (Sec. 4.4) → unsupervised training on synthetic ROFL (Sec. 4.3) → evaluation of latent representations against macaque MT spike data (Sec. 4.6.5). The final link is external: the model is scored on predicting real neuronal responses, not on quantities generated by the model or its training distribution. The ROFL disentanglement evaluations (Secs. 4.6.3–4.6.4) use generative factors that are known by construction, but that is a controlled benchmark, not circularity: the model does not receive the factor labels, and the non-hierarchical VAE fails to capture object factors (Sec. 4.10.2), so success is not guaranteed by the architecture or objective. Chapter 5 uses empirical simultaneous fMRI and Ca2+ data (Sec. 5.2) and includes synthetic LFR controls (Sec. 5.4.1). The closest issue to a fitted-input pattern is Sec. 4.9.5 ('Choosing β values for different figures') and Fig. 4.16 ('Alignment scores across β values'), since β controls the reconstruction/disentanglement trade-off and could in principle make the 2x gain an artifact of an outcome-guided hyperparameter search. However, the text available does not state that β was selected using the held-out MT alignment scores, nor does it exhibit the reported gain as the maximum of that search. Without that, the concern remains a validity/robustness risk rather than a demonstrated circular step. No load-bearing self-citation chain was identified.

Assumptions & free parameters 4 free parameters · 5 assumptions · 2 invented entities

The ledger shows what the dissertation pulls from its own construction rather than from external benchmarks. The ROFL dataset and the cNVAE architecture are the paper's own artifacts and carry the burden of ecological validity. The hyperparameters β, the latent dimensionality, the community count K, and the graph threshold are user-chosen quantities that the headline numbers depend on; the per-figure β selection in Section 4.9.5 makes this dependence explicit. The stated subjective Bayesian stance and the stated Axiom 1 of network science are transparent domain assumptions. None of these entries is hidden, but several are chosen post-hoc in ways that affect the quantitative claims.

free parameters (4)

Beta (VAE loss weight) = not stated in reviewed text
Section 4.9.5, 'Choosing β values for different figures,' indicates β was selected per figure rather than fixed a priori; the reported alignment and disentanglement scores across β values (Figure 4.16) make headline comparisons sensitive to this choice.
cNVAE latent dimensionality = not stated in reviewed text
Section 4.9.3 compares cNVAE and NVAE latent dimensionalities; the compressed latent size is a design choice that affects both disentanglement and brain-alignment outcomes.
Number of communities K (SVINET) = 3, 7, 20 (per figures)
Sections 5.2 and 5.4.2 report decompositions at K=3, K=7, and K=20; the overlap fraction and the network comparisons depend on K, and no single K is derived from the data.
Functional connectivity graph threshold = not stated in reviewed text
Section 5.4.3 'Thresholding the graphs' describes binarizing the correlation matrices; the chosen threshold determines the network topology fed to SVINET and therefore affects the inferred overlap.

assumptions (5)

standard math Subjective Bayesian interpretation of probability; beliefs updated via Bayes' theorem (Equation 3.1)
Stated at the opening of Chapter 3 as the philosophical stance of the dissertation; it is a transparent declaration, not an empirical claim.
domain assumption Axiom 1: network topology defines the most essential property of a network
Stated explicitly in Section 2.4.2 as a 'fundamental axiom in network science'; this assumption underlies the community detection analyses of Chapter 5.
ad hoc to paper The synthetic ROFL optic flow dataset captures ecologically relevant motion statistics
The brain-alignment results assume that a model trained on ROFL (one fixating observer, one fixed-size object) transfers to real macaque MT neurons; the validity of this training diet is the paper's own construction (Sections 4.3 and 4.12).
domain assumption MT neuron responses can be meaningfully compared to model latents via a linear readout and sparsity alignment metric
The brain-alignment metric (Section 4.9.7) assumes that linear decodability of latent variables is the right measure of correspondence with MT neurons; alternative readouts or similarity measures could change which model appears most aligned.
domain assumption BOLD and Ca2+ signals reflect the same underlying neural population activity after preprocessing
The cross-modal network comparisons of Chapter 5 rely on neurovascular coupling assumptions and on preprocessing choices (Sections 2.5 and 5.6) to treat fMRI-BOLD and wide-field Ca2+ as comparable measures of cortical activity.

invented entities (2)

cNVAE (compressed Nouveau VAE)
purpose: A hierarchical VAE variant with reduced latent space designed to mimic the hierarchical structure of the visual cortex for motion processing
New model variant introduced in Section 4.4; evaluated only within the paper's own benchmarks, with no external falsifiable predictions beyond the reported MT alignment and disentanglement results.
ROFL (Retinal Optic Flow Learning) synthetic dataset
purpose: A simulated optic flow world with known self-motion and object-motion generative factors, used for unsupervised training of the VAE models
A synthetic data framework introduced in Section 4.3; its realism relative to primate retinal input is assumed rather than independently validated against real optic flow statistics.

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Cite this review

Pith. "Pith review of Unveiling Secrets of Brain Function With Generative Modeling: Motion Perception in Primates & Cortical Network Organization in Mice." pith.science (2026). https://pith.science/paper/LLIXVO5R

@misc{pith2026241219845,
  author       = {Pith},
  title        = {Pith review of: Unveiling Secrets of Brain Function With Generative Modeling: Motion Perception in Primates & Cortical Network Organization in Mice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LLIXVO5R}},
  note         = {Machine review of arXiv:2412.19845}
}

read the original abstract

This Dissertation is comprised of two main projects, addressing questions in neuroscience through applications of generative modeling. Project #1 (Chapter 4) explores how neurons encode features of the external world. I combine Helmholtz's "Perception as Unconscious Inference" -- paralleled by modern generative models like variational autoencoders (VAE) -- with the hierarchical structure of the visual cortex. This combination leads to the development of a hierarchical VAE model, which I test for its ability to mimic neurons from the primate visual cortex in response to motion stimuli. Results show that the hierarchical VAE perceives motion similar to the primate brain. Additionally, the model identifies causal factors of retinal motion inputs, such as object- and self-motion, in a completely unsupervised manner. Collectively, these results suggest that hierarchical inference underlines the brain's understanding of the world, and hierarchical VAEs can effectively model this understanding. Project #2 (Chapter 5) investigates the spatiotemporal structure of spontaneous brain activity and its reflection of brain states like rest. Using simultaneous fMRI and wide-field Ca2+ imaging data, this project demonstrates that the mouse cortex can be decomposed into overlapping communities, with around half of the cortical regions belonging to multiple communities. Comparisons reveal similarities and differences between networks inferred from fMRI and Ca2+ signals. The introduction (Chapter 1) is divided similarly to this abstract: sections 1.1 to 1.8 provide background information about Project #1, and sections 1.9 to 1.13 are related to Project #2. Chapter 2 includes historical background, Chapter 3 provides the necessary mathematical background, and finally, Chapter 6 contains concluding remarks and future directions.

Figures

Figures reproduced from arXiv: 2412.19845 by the authors.

**Figure 2.** Wheeler’s “Participatory Universe” highlights the role of observers in physics. Image [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 1.1.** Receptive field integration in visual neurons. [PITH_FULL_IMAGE:figures/full_fig_p025_1_1.png] view at source ↗

Figures from the paper (97 more)

**Figure 1.2.** Figure 1.2: Hierarchy of the primate visual areas. From Felleman and Van Essen [ [PITH_FULL_IMAGE:figures/full_fig_p027_1_2.png]

**Figure 1.3.** Figure 1.3: Anatomical location of middle temporal (MT) and medial superior temporal (MST) [PITH_FULL_IMAGE:figures/full_fig_p029_1_3.png]

**Figure 1.4.** Figure 1.4: Major lobes of the human brain. Image adapted from [PITH_FULL_IMAGE:figures/full_fig_p030_1_4.png]

**Figure 1.5.** Figure 1.5: The two-streams hypothesis. Image adapted from [PITH_FULL_IMAGE:figures/full_fig_p031_1_5.png]

**Figure 1.6.** Figure 1.6: The sketch of the model by Serre et al. [ [PITH_FULL_IMAGE:figures/full_fig_p034_1_6.png]

**Figure 1.7.** Figure 1.7: Hierarchical convolutional neural networks are used to model mapping of visual [PITH_FULL_IMAGE:figures/full_fig_p036_1_7.png]

**Figure 1.8.** Figure 1.8: Local correlations and redundancy in natural images. The segment within the orange [PITH_FULL_IMAGE:figures/full_fig_p040_1_8.png]

**Figure 1.9.** Figure 1.9: Sparse coding illustrated. (a) Schematic of a linear generative model where the activation of neurons represents sensory input from the external world. The brain contains an internal model of the sensory information. Each neuron is associated with a distinct basis ve…

**Figure 1.10.** Figure 1.10: Predictive coding of Rao and Ballard [107]. (a) Model architecture, illustrating the computation of the error signal at each processing stage. The error signal is the result of the feedforward input minus the feedback prediction. In short, error signal = input − pre…

**Figure 1.11.** Figure 1.11: Cortico-cortical pathways by layer. Foodforward (ascending) and feedback (de [PITH_FULL_IMAGE:figures/full_fig_p048_1_11.png]

**Figure 1.12.** Figure 1.12: Feedforward (section 1.4; e.g., Serre et al. [54]) vs. Generative (sections 1.5 and 1.6; e.g., Lee and Mumford [128]) approaches to vision. In this Dissertation, we are team generative. 28 [PITH_FULL_IMAGE:figures/full_fig_p049_1_12.png]

**Figure 1.13.** Figure 1.13: Basic models of neurons involved in early visual processing. In all models, the [PITH_FULL_IMAGE:figures/full_fig_p051_1_13.png]

**Figure 1.14.** Figure 1.14: The neuroconnectionist research programme. This iterative research approach merges detailed biological insights from neural and behavioral studies across levels to inform the development of new artificial neural network (ANN) models with different components. The AN…

**Figure 1.15.** Figure 1.15: Analysis of MT neurons using the switched model of Nishimoto and Gallant [ [PITH_FULL_IMAGE:figures/full_fig_p056_1_15.png]

**Figure 1.16.** Figure 1.16: Incorporating suppression into models of MT processing. [PITH_FULL_IMAGE:figures/full_fig_p058_1_16.png]

**Figure 1.17.** Figure 1.17: One of Gibson’s earliest drawings of optical flow. The arrows depict flow patterns [PITH_FULL_IMAGE:figures/full_fig_p059_1_17.png]

**Figure 1.18.** Figure 1.18: The interactions between self-motion (left) and object motion (middle) result in a [PITH_FULL_IMAGE:figures/full_fig_p061_1_18.png]

**Figure 1.19.** Figure 1.19: Two types of community structure. In the disjoint case, every node belongs to a [PITH_FULL_IMAGE:figures/full_fig_p070_1_19.png]

**Figure 1.20.** Figure 1.20: One of the first experimental demonstrations of circuit switching in crab stomato [PITH_FULL_IMAGE:figures/full_fig_p073_1_20.png]

**Figure 1.21.** Figure 1.21: Connectivity diagram of the crab STG based on electrophysiological recordings. [PITH_FULL_IMAGE:figures/full_fig_p074_1_21.png]

**Figure 1.22.** Figure 1.22: The massive space of possible brain states, denoted as [PITH_FULL_IMAGE:figures/full_fig_p076_1_22.png]

**Figure 1.23.** Figure 1.23: Intrinsically defined anti-correlated networks in the human brain. Positive nodes [PITH_FULL_IMAGE:figures/full_fig_p077_1_23.png]

**Figure 1.24.** Figure 1.24: Variability in evoked brain responses explained by spontaneous activity. [PITH_FULL_IMAGE:figures/full_fig_p078_1_24.png]

**Figure 1.25.** Figure 1.25: Neurovascular coupling is variable across brain regions. The increase in blood flow [PITH_FULL_IMAGE:figures/full_fig_p083_1_25.png]

**Figure 1.26.** Figure 1.26: Model organisms and data modalities used in this Dissertation. [PITH_FULL_IMAGE:figures/full_fig_p085_1_26.png]

**Figure 2.1.** Figure 2.1: Plato’s “Allegory of the Cave” explores the idea that human perception may not unveil [PITH_FULL_IMAGE:figures/full_fig_p087_2_1.png]

**Figure 2.2.** Figure 2.2: Cajal’s ink-on-paper drawing of neurons shows them as separate, individual cells. [PITH_FULL_IMAGE:figures/full_fig_p095_2_2.png]

**Figure 2.3.** Figure 2.3: Anatomy of a neuron. Image from Wikipedia. 2.2.2 The Neuron Doctrine as a plan of attack A century ago, science was primarily a reductionist enterprise 1. Before Cajal’s work, the basic unit of the nervous system was disputed, which hindered progress. There was no cl…

**Figure 2.4.** Figure 2.4: A chemical synapse between two neurons. Information is transmitted from the [PITH_FULL_IMAGE:figures/full_fig_p098_2_4.png]

**Figure 2.5.** Figure 2.5: A circuit diagram from Sherrington’s The Integrative Action of the Nervous System, illustrating the fundamental interactions and pathways of two primary afferent neurons (α) and their reflex influence. The plus and minus signs indicate excitatory and inhibitory inter…

**Figure 2.6.** Figure 2.6: The first experimental demonstration of the [PITH_FULL_IMAGE:figures/full_fig_p101_2_6.png]

**Figure 2.7.** Figure 2.7: The “all-or-none” law of nerve impulses was first described by Henry Pickering [PITH_FULL_IMAGE:figures/full_fig_p102_2_7.png]

**Figure 2.8.** Figure 2.8: Orientation and direction selectivity in the primary visual cortex. [PITH_FULL_IMAGE:figures/full_fig_p104_2_8.png]

**Figure 2.9.** Figure 2.9: The Hippocampal Zoo. (A) Anatomical location of the hippocampus and entorhinal cortex (EC) in different species (originally from Strange et al. [336]). (B) Various cells in the hippocampal formation encode distinct spatial variables. See the original publication by B…

**Figure 2.10.** Figure 2.10: The first experimental demonstration of spontaneous neural oscillations in the human [PITH_FULL_IMAGE:figures/full_fig_p109_2_10.png]

**Figure 2.11.** Figure 2.11: A condensed history of neuroscience. From Yuste [ [PITH_FULL_IMAGE:figures/full_fig_p112_2_11.png]

**Figure 2.12.** Figure 2.12: Different network topologies. (a) Ring. (b) Lattice. (c) A more complex topology. Adopting this network-centric perspective has unveiled certain topologies with unique and significant properties. For instance, in 1998, Watts & Strogatz identified what’s known as the…

**Figure 2.13.** Figure 2.13: Small-world networks. (a) Random rewiring procedure of Watts and Strogatz [375] allows interpolating between a regular ring lattice and a random network. With probability p, they reconnect one side of an edge to randomly chosen nodes over the entire ring. (b) At aro…

**Figure 2.14.** Figure 2.14: The 7-network parcellation of the human cerebral cortex. Purple (visual), Blue [PITH_FULL_IMAGE:figures/full_fig_p120_2_14.png]

**Figure 2.15.** Figure 2.15: The spatiotemporal domain of neuroscience methodologies. Each colored region [PITH_FULL_IMAGE:figures/full_fig_p122_2_15.png]

**Figure 2.16.** Figure 2.16: Simultaneous cortex-wide Ca2+ imaging and brain-wide fMRI in mice, introduced by Lake et al. [276] in 2020. Image adapted from Lake and Higley [394], 2022. 102 [PITH_FULL_IMAGE:figures/full_fig_p123_2_16.png]

**Figure 3.1.** Figure 3.1: Blue dots represent p = N (0, Σ) where Σ = 10 9 9 10 , and orange dots represent q = N (0, 1.9). In this example DKL q [PITH_FULL_IMAGE:figures/full_fig_p131_3_1.png]

**Figure 3.2.** Figure 3.2: The reparameterization trick. Left shows the computation graph w/o the “reparame [PITH_FULL_IMAGE:figures/full_fig_p139_3_2.png]

**Figure 3.3.** Figure 3.3: The model has achieved a decent understanding of the data. Moreover, the organization of the latent space is a significant indicator of a well-trained VAE. A well-structured latent space is one in which similar digits are clustered together and different digits are s…

**Figure 3.4.** Figure 3.4: Latent space visualized. This grid map shows data points generated by feeding values [PITH_FULL_IMAGE:figures/full_fig_p142_3_4.png]

**Figure 3.5.** Figure 3.5: Clustering the digits. Generated by pushing data points in the validation set into the [PITH_FULL_IMAGE:figures/full_fig_p143_3_5.png]

**Figure 4.1.** Figure 4.1: Introducing Retinal Optic Flow Learning (ROFL), a simulation platform for synthe [PITH_FULL_IMAGE:figures/full_fig_p153_4_1.png]

**Figure 4.2.** Figure 4.2: Example frames showcasing different categories. See Table [PITH_FULL_IMAGE:figures/full_fig_p155_4_2.png]

**Figure 4.3.** Figure 4.3: Demonstrating the causal effects of varying a single ground truth variable while [PITH_FULL_IMAGE:figures/full_fig_p156_4_3.png]

**Figure 4.5.** Figure 4.5: Both models demonstrate robust reconstruction performance, with cNVAE exhibiting [PITH_FULL_IMAGE:figures/full_fig_p163_4_5.png]

**Figure 4.6.** Figure 4.6: Mutual information between latent variables (x-axis) and ground truth variables (y [PITH_FULL_IMAGE:figures/full_fig_p164_4_6.png]

**Figure 4.7.** Figure 4.7: Hierarchical VAE untangles underlying factors of variation in data. The linear [PITH_FULL_IMAGE:figures/full_fig_p166_4_7.png]

**Figure 4.8.** Figure 4.8: Evaluating the learned latent codes using the DCI framework [ [PITH_FULL_IMAGE:figures/full_fig_p168_4_8.png]

**Figure 4.9.** Figure 4.9: Experimental setup. Macaque monkeys watch random dot kinematograms on a screen, while we record spiking activity from neurons in area MT. The dataset was previously published in Cui et al. [28, 498]. We learn this linear latent-to-neuron mapping using ridge regressi…

**Figure 4.10.** Figure 4.10: Both models explain MT neural variability well. The black curve shows the average [PITH_FULL_IMAGE:figures/full_fig_p170_4_10.png]

**Figure 4.12.** Figure 4.12: Spike-triggered averages (STA) are shown for an example MT neuron (same as [PITH_FULL_IMAGE:figures/full_fig_p171_4_12.png]

**Figure 4.13.** Figure 4.13: All models (pretrained on fixate-1) perform comparably in predicting MT neuron responses. Dashed line corresponds to the previous state-of-the-art on this data [57]. 4.6.6 Hierarchical VAEs are more aligned with MT neurons We next tested how these factors affect neu…

**Figure 4.14.** Figure 4.14: Alignment score measures the sparsity of permutation feature importances. [PITH_FULL_IMAGE:figures/full_fig_p172_4_14.png]

**Figure 4.15.** Figure 4.15: Feature importances are plotted for an example neuron (same as in Fig. [PITH_FULL_IMAGE:figures/full_fig_p173_4_15.png]

**Figure 4.16.** Figure 4.16: Alignment scores across β values and autoencoders (ae) are shown. Hierarchical models (cNVAE, cNAE) are more aligned with MT neurons since they enable sparse latent-toneuron relationships [PITH_FULL_IMAGE:figures/full_fig_p174_4_16.png]

**Figure 4.17.** Figure 4.17: Effect sizes are shown for the two different approaches in model comparisons: [PITH_FULL_IMAGE:figures/full_fig_p175_4_17.png]

**Figure 4.18.** Figure 4.18: Suppose we train a regression model to predict ground truth factors [PITH_FULL_IMAGE:figures/full_fig_p189_4_18.png]

**Figure 4.19.** Figure 4.19: Consider training a regressor to predict MT neuron responses (green) from latent [PITH_FULL_IMAGE:figures/full_fig_p191_4_19.png]

**Figure 4.20.** Figure 4.20: For each ground truth factor and model, we identified a single latent variable that [PITH_FULL_IMAGE:figures/full_fig_p194_4_20.png]

**Figure 4.21.** Figure 4.21: The first row shows random samples drawn from ROFL [PITH_FULL_IMAGE:figures/full_fig_p195_4_21.png]

**Figure 4.22.** Figure 4.22: Latent traversal performed using a latent variable that effectively captures [PITH_FULL_IMAGE:figures/full_fig_p196_4_22.png]

**Figure 4.23.** Figure 4.23: Both models demonstrate robust reconstruction performance, with cNVAE exhibiting [PITH_FULL_IMAGE:figures/full_fig_p198_4_23.png]

**Figure 4.24.** Figure 4.24: Strong anti-correlation between reconstruction loss and informativeness (i.e., un [PITH_FULL_IMAGE:figures/full_fig_p199_4_24.png]

**Figure 4.25.** Figure 4.25: This latent variable cares about the magnitude of self-motion only. Its disentangle [PITH_FULL_IMAGE:figures/full_fig_p205_4_25.png]

**Figure 4.26.** Figure 4.26: Setup. (a) Background and coordinate systems. (b) The rotation of the fixed coordinates X, ˆ Y , ˆ Zˆ onto the observer-centric coordinates (ˆx, y, ˆ zˆ) can be accomplished by applying a rotation of angle Θ0 around the unit vector uˆ as defined in Equation 4.20…

**Figure 5.1.** Figure 5.1: Experimental setup. (a) Simultaneous fMRI-BOLD and wide-field Ca2+ imaging [276]. Ca2+ data are background-corrected (illustrated by three colored wavelengths; Methods) (b) Hierarchical data structure. N = 10 mice, scanned across 3 longitudinal sessions, with 4 runs …

**Figure 5.2.** Figure 5.2: Defining ROIs within the Allen Mouse Brain Common Coordinate Framework [PITH_FULL_IMAGE:figures/full_fig_p221_5_2.png]

**Figure 5.3.** Figure 5.3: We applied a mixed-membership stochastic blockmodel algorithm to estimate overlap [PITH_FULL_IMAGE:figures/full_fig_p221_5_3.png]

**Figure 5.4.** Figure 5.4: A coarse, 3 networks decomposition of the mouse cortex into overlapping networks. [PITH_FULL_IMAGE:figures/full_fig_p223_5_4.png]

**Figure 5.5.** Figure 5.5: Mouse cortical areas (top view) as defined in the CCFv3 Allen reference atlas [ [PITH_FULL_IMAGE:figures/full_fig_p223_5_5.png]

**Figure 5.6.** Figure 5.6: Decomposition with 7 networks. Color scale indicates membership strengths [PITH_FULL_IMAGE:figures/full_fig_p224_5_6.png]

**Figure 5.7.** Figure 5.7: Quantitative comparison of network similarities [PITH_FULL_IMAGE:figures/full_fig_p226_5_7.png]

**Figure 5.8.** Figure 5.8: BOLD network organization is more similar to Ca [PITH_FULL_IMAGE:figures/full_fig_p227_5_8.png]

**Figure 5.9.** Figure 5.9: Awake results (Ca2+ only). We report exploratory analysis in a group of N = 5 animals for which we had Ca2+ recordings in both anesthetized and awake states. Along with the awake results, we also plotted group results obtained from the same subset of N = 5 animals in…

**Figure 5.10.** Figure 5.10: Filtering Ca2+ data with a hemodynamic response function (HRF) results in modest changes in network structure. We applied the gamma-variate model of Ma et al. [406], using parameters previously published by us in Lake et al. [276]. We then inferred the community str…

**Figure 5.11.** Figure 5.11: Distribution of membership values. (a) Three illustrative distributions. Left, disjoint organization; Middle, overlapping with uniform membership values; Right, completely overlapping with no mid-range or strong memberships. (b) Membership distributions computed fro…

**Figure 5.12.** Figure 5.12: Verifying our analysis procedure using synthetic LFR graphs [ [PITH_FULL_IMAGE:figures/full_fig_p234_5_12.png]

**Figure 5.13.** Figure 5.13: Quantifying overlap extent. (a) Membership values binned by statistical thresholding. Bins were incremented by 1/7 (for the 7 network solution). Blue (membership > 3.5 × 1/7) indicates regions with disjoint-like network affiliation. At the opposite end of the spectr…

**Figure 5.14.** Figure 5.14: Regional entropy, or membership diversity. (a) Left: equation for Shannon entropy (Methods). Values are normalized [0, 1]. hi = 0 if a node i belongs to a single network (is disjoint); hi = 1 if a node belongs to all networks with equal strength (is maximally overla…

**Figure 5.15.** Figure 5.15: Entropy and participation coefficient uncover similar spatial patterns. [PITH_FULL_IMAGE:figures/full_fig_p239_5_15.png]

**Figure 5.16.** Figure 5.16: Regional degree. (a) Left: schematic of regional degree. Right: distribution of regional degree normalized by the number of brain regions (total of 542). (b) Spatial patterns of regional degrees rank-ordered (total of 542 regions) to facilitate comparisons across co…

**Figure 5.17.** Figure 5.17: (a) Both the magnitude and spatial patterns of degree centrality values are different across modalities. (b) Degree ranks are reproduced from [PITH_FULL_IMAGE:figures/full_fig_p243_5_17.png]

**Figure 5.18.** Figure 5.18: Ca2+ degree maps at different levels of data smoothness. To obtain these results, we applied a Gaussian filter to raw Ca2+ data followed by otherwise identical steps in our pipeline, including Ca2+ slow bandpassing. A considerable amount of data smoothing (full widt…

**Figure 5.19.** Figure 5.19: Percentile maps are obtained by calculating t-statistics (hierarchical bootstrapping, [PITH_FULL_IMAGE:figures/full_fig_p245_5_19.png]

**Figure 5.20.** Figure 5.20: Entropy-degree relationships across modalities. [PITH_FULL_IMAGE:figures/full_fig_p247_5_20.png]

**Figure 5.21.** Figure 5.21: Functional connectivity gradients. (a) Top four gradients are visualized (z-scored; see Methods), and ordered based on the magnitude of the corresponding eigenvalues [579]. (b) Portion of variance explained. Corr [PITH_FULL_IMAGE:figures/full_fig_p248_5_21.png]

**Figure 5.22.** Figure 5.22: Pearson correlations between all pairs of gradients shown in Fig. [PITH_FULL_IMAGE:figures/full_fig_p248_5_22.png]

**Figure 5.23.** Figure 5.23: Scatter plots display relationships between pairs of gradient axes: the [PITH_FULL_IMAGE:figures/full_fig_p249_5_23.png]

**Figure 5.24.** Figure 5.24: K = 20 decomposition. (a) Even at K = 20, most networks maintain their bilateral symmetry, especially for Ca2+ . A network centered around FOF appears as its own separate network for BOLD, similar to the K = 7 solution (top-right). In contrast, this network did not …

**Figure 5.25.** Figure 5.25: Network structure is robust to the choice of ROI granularity. [PITH_FULL_IMAGE:figures/full_fig_p265_5_25.png]

**Figure 5.27.** Figure 5.27: Dependence of degree centrality to preprocessing and analysis choices. (a) Spatial patterns of average node degree are somewhat altered depending on which BOLD preprocessing steps are used. Minimally processed, motion correction (rigid transformations) and detrendin…

**Figure 6.1.** Figure 6.1: Five problems with the current view of V1. From Olshausen and Field [ [PITH_FULL_IMAGE:figures/full_fig_p284_6_1.png]

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