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REVIEW 3 major objections 5 minor 59 references

Learning to cluster neuronal function

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read By adding an explicit clustering bias to neural-response models, the paper argues that excitatory neurons in mouse V1 form a functional continuum rather than discrete cell types.

desk verdict A genuinely useful clustering method with solid retina validation, but the mouse V1 continuum conclusion rests on an unvalidated ARI-peak assumption. read the letter →

arxiv 2506.03293 v1 pith:6HHFABMB submitted 2025-06-03 q-bio.NC

Nina S. Nellen , Polina Turishcheva , Michaela Vystrčilová , Shashwat Sridhar , Tim Gollisch , Andreas S. Tolias , Alexander S. Ecker This is my paper · ORCID
classification q-bio.NC
keywords functionalcelltypesneuronalembeddingsdeepembeddingclusteringexpectationmaximizationStudent'st-mixturemodelclusterconsistencyAdjustedRandIndexmousevisualcortex
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

Predictive deep networks learn one embedding per neuron, and those embeddings have not shown clear clusters in mouse V1. This paper asks whether the missing clusters are a true property of the cortex or a limitation of the models. It introduces DECEMber, a clustering loss that trains the embeddings together with cluster centers and per-cluster scale matrices, and shows that the loss improves cluster consistency while preserving predictive accuracy. Applied to mouse V1, consistency improves but never peaks at any cluster count, which the authors read as evidence that excitatory neurons there form a functional continuum. On marmoset retina, where discrete cell types are known, the same method separates the types almost perfectly, supporting the method's sensitivity.

What carries the argument

The load-bearing object is the DECEMber loss, $L_{\mathrm{cluster}}=\mathrm{KL}(Q\|P)$, where $q_{ij}$ is the soft assignment of neuron $i$ to cluster $j$ under a multivariate Student's $t$-mixture with center $\mu_j$ and diagonal scale matrix $\Sigma_j$, and $p_{ij}\propto q_{ij}^2/f_j$ sharpens confident assignments. Cluster centers and scales are updated by expectation-maximization after each batch, while the core and readout weights are updated by gradient descent on the full loss. The learned per-cluster scale matrices are what prevent the degenerate fixed-scale solution in which every center collapses to the same point; this mechanism is what allows cluster consistency to improve without sacrificing prediction quality.

What would settle it

Train DECEMber on synthetic populations with known discrete cluster structure, including unbalanced and overlapping clusters whose embeddings have the same dimensionality and scale as mouse V1 readouts, and measure the Adjusted Rand Index across cluster counts; if ARI does not peak at the true number, the absence of a peak in mouse V1 cannot be taken as evidence of a continuum.

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Extended reading notes

Core claim

The central claim is that the lack of clustered structure in state-of-the-art mouse V1 embeddings is not a modeling artifact: when an explicit clustering bias is added, the model can be made to produce more consistent clusters, yet no particular number of clusters is singled out. This is the pattern the authors expect if the neurons form a continuum rather than discrete types. The supporting evidence is that on marmoset retinal ganglion cells DECEMber recovers known discrete types with an Adjusted Rand Index of 0.96 and a near-perfect confusion matrix, whereas on mouse V1 ARI roughly doubles but stays flat over 5 to 60 clusters, and on mouse retina and macaque V4 it also improves consistency. The paper therefore concludes that functional cell types in mouse V1 are better described as a continuum, and that asking for discrete types may be the wrong question.

Load-bearing premise

The load-bearing premise is that the Adjusted Rand Index (ARI), a score for how consistently neuron pairs land in the same cluster across runs, would peak noticeably at the true number of clusters if discrete functional types existed in mouse V1.

Editorial extensions

If this is right

  • Known cell types become recoverable: on marmoset retinal ganglion cells, DECEMber reaches an Adjusted Rand Index of $0.96\pm0.01$ with a nearly perfect confusion matrix, so the method exposes discrete structure when it exists.
  • The flat ARI profile across 5 to 60 clusters for mouse V1, together with higher consistency than baseline, is evidence for a functional continuum and against a preferred discrete number of excitatory types.
  • The method also improves cluster consistency on mouse retina and macaque V4, so the benefit is not tied to one species, stimulus type, or readout architecture.
  • When the clustering loss dominates, predictive performance drops and consistency stops improving, so the useful operating regime is where consistency rises while performance stays at baseline.

Reading between the lines

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

  • The paper's interpretive step, that ARI would peak noticeably at the true cluster count if discrete types existed, could be checked directly on synthetic data with known discrete and unbalanced types; if that peak does not appear there, the mouse V1 continuum conclusion loses support.
  • A flat ARI profile is consistent with a continuum, but also with hierarchical or heavily overlapping discrete types, and the reported experiments do not distinguish those alternatives.
  • The same loss could serve as a general diagnostic in other brain areas: a sharp ARI peak would argue for discrete functional types, while a flat profile would argue for a gradient.
  • Because DECEMber learns per-cluster scale matrices, the fitted scales could be interpreted as within-type functional variability, potentially connecting model clusters to morphological or transcriptomic continua.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper introduces DECEMber, an auxiliary clustering loss for predictive models of neural activity. The loss extends the deep embedding clustering (DEC) objective by modeling each cluster with a multivariate Student-t distribution and updating cluster centers and diagonal scale matrices via EM steps during training. The authors evaluate cluster consistency using the Adjusted Rand Index across different random seeds and report improved consistency with preserved predictive performance on marmoset retina (where discrete cell types are known), mouse V1, mouse retina, and macaque V4. From the absence of a clear peak in ARI as a function of the number of clusters in mouse V1, the paper concludes that excitatory neurons in mouse V1 form a functional continuum rather than discrete clusters.

Significance. If the conclusions hold, DECEMber would be a useful methodological contribution to a debated question in neuroscience, and the result on mouse V1 would be an important data point. The paper's strengths include making the code available, validating the method on marmoset retina with known cell types, and benchmarking against post-hoc GMM and k-means baselines. The main weakness is that the central biological conclusion depends on an unvalidated diagnostic: the claim that a true discrete cluster structure would produce a sharp ARI peak at the correct cluster count. Since the retina validation fixes the number of clusters to the known number of types, it does not calibrate this diagnostic, and the toy example is not an ARI-vs-K sweep with known ground truth. The manuscript is therefore best viewed as a solid methods paper whose strongest interpretive claim requires additional control experiments.

major comments (3)
  1. [Section 5, Fig. 4H (mouse V1 results)] The central conclusion that mouse V1 excitatory neurons form a functional continuum rests on the statement 'We would expect ARI to peak noticeably at the true number of clusters if such a structure existed' (Sec. 5, mouse V1 results). This expectation is not validated anywhere in the paper. ARI measures agreement between two partitions, not the match to a latent ground truth; for unbalanced or hierarchical clusterings the ARI-vs-K curve need not peak at the true K, and with finite noisy samples it can be flat or increasing. The marmoset retina validation (Fig. 3A) fixes J=4 to the known number of types and therefore does not calibrate the diagnostic, and the toy example (Fig. 2) is a two-cluster demonstration of the collapse failure, not an ARI-vs-J sweep under known ground truth. I request a synthetic calibration experiment: generate embeddings with known discrete structure (e.g., balanced and unbalanced clusters, several true K, overlapping or hierarchical geometry), apply DECEMber across the same J range used for mouse V1, and show that the ARI curve indeed peaks at the true K under the same embedding/model settings. Without such a control, the absence of a peak in Fig. 4H supports the continuum claim only under an untested assumption.
  2. [Algorithm 1, step (3); Eq. (2.2)] The definition of the target distribution P in Algorithm 1 is inconsistent with Eq. (2.2). Eq. (2.2) defines p_ij = (q_ij^2 / f_j) / sum_j' (q_ij'^2 / f_j'), whereas Algorithm 1 writes p_ij = (q_ij^2 / f_j) / sum_k (q_ik / f_k), with the denominator lacking the square on q_ik. Since the clustering loss depends directly on P, this discrepancy changes the objective and affects reproducibility. Please correct the algorithm box to match Eq. (2.2) or state explicitly if the unsquared version is intended and why.
  3. [Section 5, Figs. 4H and 5C] The absence of a sharp peak in ARI is assessed visually from curves that appear to be means over three seeds, with no error bars or statistical comparison. Given that ARI is computed from only three model fits per condition, the difference between a flat curve and a weak peak cannot be judged without variance estimates or a permutation-based test. Please report mean plus/minus standard deviation or confidence intervals across seeds for the key ARI curves, and if possible include per-seed curves for the mouse V1 analysis.
minor comments (5)
  1. [Algorithm 1] The label 'Gradiet step' should read 'Gradient step'.
  2. [Section 4] 'which alloed for different variances' should be 'which allowed for different variances'.
  3. [Figure 2] The caption lists panels A-D only, but the text refers to 'Fig. 2E'; either add panel E or correct the reference.
  4. [Appendix B.1] The section title 'Retina gagnlion cells' should be 'Retinal ganglion cells'.
  5. [Introduction] 'One could view it as model-driven hypothesis testing' is a fragment; consider integrating it into a complete sentence.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the continuum conclusion rests on an unvalidated ARI-peak diagnostic, not on a reduction of the output to the clustering loss.

full rationale

DECEMber's clustering loss (Eq. 3.2) is an explicit inductive bias, so the observation that it raises ARI relative to a post-hoc GMM baseline is a verification that the bias does what it is designed to do, not an independent biological prediction; this is not a circular reduction because cross-seed ARI is not the optimized objective and no fitted quantity is later renamed as a result. The central continuum conclusion is drawn from the absence of an ARI peak across J=5..60 (Fig. 4H), under the stated expectation that ARI 'would peak noticeably at the true number of clusters if such a structure existed.' That expectation is not validated on synthetic data with known discrete, unbalanced, or hierarchical clusters, so the inference is risky; but the risk is an unvalidated diagnostic assumption about ARI behavior, not a definitional equivalence or a fitted-parameter-as-prediction. Independent checks exist: marmoset RGCs with ground-truth types (Fig. 3), mouse retina and macaque V4 generalization, and preservation of predictive performance. Self-citations to Turishcheva et al. [13] (baseline and pretraining) and Weis et al. [6] (corroborating continuum work) are methodological or corroborative, not uniqueness theorems, and do not carry the argument. Score 2 only for the mild self-referential flavor of evaluating a clustering loss by cluster consistency and same-group citations; no load-bearing circular step was identified.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The paper's central claims depend on several fitted hyperparameters (beta, J, learning rate, pretraining length) and on two assumptions that are not independently validated: the faithfulness of readout embeddings as functional descriptors, and the diagnostic power of an ARI peak. The cluster scale matrices are learned via EM but are not free parameters in the conventional sense; they are part of the model.

free parameters (5)
  • clustering strength beta = 1e1 to 1e7 (mouse V1); 0.001 (retina, V4)
    Controls the weight of the clustering loss relative to the predictive loss; tuned per dataset to balance ARI and predictive performance (Sec. 4, Fig. 4F-H).
  • number of clusters J = 5 to 60 (mouse V1); 4 (marmoset RGC); varied for retina/V4
    Must be specified; paper searches a range and finds no peak, which is central to the continuum claim.
  • degrees of freedom nu = 2.1
    Fixed by hand, just above the threshold where variance is defined; not tuned.
  • pretraining length m = 5, 9, 10, 11, 20, 30, 40 epochs
    Explored; 10 epochs gives best ARI for mouse V1 (Fig. 5C).
  • learning rate = tuned; examples 0.003-0.008 with beta=1e4-1e7
    Learning rate is tuned on validation set for each combination of beta and pretraining length (Fig. 5A-B).
assumptions (3)
  • domain assumption The readout weights z_i in the trained predictive model constitute a faithful functional embedding of each neuron.
    Invoked throughout; the entire clustering analysis is performed on these weights (Sec. 3.1). If the embeddings miss functionally relevant dimensions, cluster structure would be invisible.
  • ad hoc to paper The expectation that a true discrete cluster structure would produce a sharp peak in ARI as a function of the number of clusters.
    Used to interpret the mouse V1 results (Sec. 5, Fig. 4H). Not derived and not validated on synthetic data.
  • ad hoc to paper The Student-t mixture model with EM updates for cluster parameters, combined with the KL clustering loss, avoids degenerate solutions and recovers true clusters.
    Shown on a toy example (Sec. 5, Fig. 2) but no general proof; the composite objective is not a single well-defined optimization problem.

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Pith. "Pith review of Learning to cluster neuronal function." pith.science (2026). https://pith.science/paper/6HHFABMB

@misc{pith2026250603293,
  author       = {Pith},
  title        = {Pith review of: Learning to cluster neuronal function},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6HHFABMB}},
  note         = {Machine review of arXiv:2506.03293}
}
abstract

Deep neural networks trained to predict neural activity from visual input and behaviour have shown great potential to serve as digital twins of the visual cortex. Per-neuron embeddings derived from these models could potentially be used to map the functional landscape or identify cell types. However, state-of-the-art predictive models of mouse V1 do not generate functional embeddings that exhibit clear clustering patterns which would correspond to cell types. This raises the question whether the lack of clustered structure is due to limitations of current models or a true feature of the functional organization of mouse V1. In this work, we introduce DECEMber -- Deep Embedding Clustering via Expectation Maximization-based refinement -- an explicit inductive bias into predictive models that enhances clustering by adding an auxiliary $t$-distribution-inspired loss function that enforces structured organization among per-neuron embeddings. We jointly optimize both neuronal feature embeddings and clustering parameters, updating cluster centers and scale matrices using the EM-algorithm. We demonstrate that these modifications improve cluster consistency while preserving high predictive performance and surpassing standard clustering methods in terms of stability. Moreover, DECEMber generalizes well across species (mice, primates) and visual areas (retina, V1, V4). The code is available at https://github.com/Nisone2000/sensorium/tree/neuroips_version.

Figures

Figures reproduced from arXiv: 2506.03293 by the authors.

Figure 1
Figure 1. A: Model architecture: The model consists of a neuronwise shared core outputting a feature map of size (height × width × feature channels) and neuron specific Gaussian readouts. They consist of a receptive field position and a weight vector. The RF position chooses the vector in the feature map which is then combined with the neuron’s weight vector by a dot product to get the neuron’s response. B: Clustering procedu… view at source ↗
Figure 2
Figure 2. A: PDF of z1 (blue) and z2 (orange) of the underlying true uniform distribution and t-distribution with unit scale estimated by DEC-loss. The two t-distributions are highly overlapping whereas there is a clear separation in the uniform distributions. B+C t-SNE projection of toy data after training with DEC loss (B) vs our method (C). We first pretrain a simple linear regression model by minimizing an MSE-loss for 25… view at source ↗
Figure 3
Figure 3. A: ARI across 3 seeds for GMM, k￾means and DECEMber. B: DECEMber predictions. Pretraining length: 25 epochs. Corresponding test correlation: 0.805 ± 0.068 (std). As we observed substantial differences between the two retinas’ temporal response features (po￾tentially due to temperature variation [49]), we followed Vystrcilová et al. [ ˇ 16] and trained a separate model for each retina to avoid clus￾tering by retina. … view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: A: t-SNE of baseline model without clustering loss. B-E: t-SNE projections of our model with clustering bias for different multipliers β and tuned learning rates (lr). All models use 15 clusters, PE = 10 and seed 100. B: β = 104 and lr = 0.008. C: β = 105 and lr = 0.00…
Figure 5
Figure 5. Figure 5: A–B: Learning rate tuning for β (A) and length of pretraining (B). We fixed amount of clusters to 15. If the learning rate is too high the clustering loss starts oscillating due to learning rate scheduling leading to a massive drop in performance. C ARI for different n…
Figure 6
Figure 6. Figure 6: The choice of pretrain epoch doesn’t influence perfor￾mance when we’re using an op￾timal learning rate. Consistency of embeddings depends on length of pretraining. To validate our conclusions that mouse V1 lacks discrete func￾tional cell types, we performed extensive t…
Figure 7
Figure 7. Figure 7: ARI on A mouse retina [19], weighted across six models. B monkeys V4 [51]. For macaque V4 data we used spiking extracellular multi￾electrode recorded responses of neurons to gray-scale nat￾ural images shown to awake macaque monkeys [51] and the model from Pierzchlewicz…
Figure 8
Figure 8. Figure 8: A: DECEMber predictions. Pretraining length: 20 epochs. Same predictions for GMM and k-means. All methods have ARI 1. B: t-SNE projections of the corresponding cells. To select reliable cells from the marmoset RGCs dataset [48], we used the same reliability assess￾ment…
Figure 9
Figure 9. Figure 9: All plots show evaluations of seed 4 of the trained marmoset RGC model [ [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Clustering stability of k-means and GMM on retina 1 for marmoset RGC. We started with a single baseline RGC model of retina 1 (seed 2) and performed k-means and GMM clustering (4 clusters each), varying the random seed (42, 10, 100) for both algorithms. Clustering was…
Figure 11
Figure 11. Figure 11: Clustering stability of GMM on mouse V1. We trained a baseline model of mouse V1 for one seed (seed=42). We then did GMM for clusters ranging from 5 to 60 with a step size of 5 as the ground truth is not known varying just the seed for the initialization of the GMM bu…
Figure 12
Figure 12. Figure 12: Different clustering consistency metrics for monkey V4 and mouse retina datasets. Same [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]
Figure 13
Figure 13. Figure 13: V-measure and Fowlkes-Mallows-score for PE 10, 15 clusters. [PITH_FULL_IMAGE:figures/full_fig_p019_13.png]
Figure 14
Figure 14. Figure 14: DECEMber, with PE = 10; DECEMber cluster consitency matches the rotation-equivariant [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]
Figure 15
Figure 15. Figure 15: ARI per retina. n is the number of neurons in the model B.9 Further analysis of monkeys data 10 20 Number of clusters 0.2 0.3 0.4 0.5 0.6 ARI A baseline PE:5 PE:10 PE:20 0 1 2 3 4 5 6 7 8 9 10 11 Predicted Labels 0 1 2 3 4 5 6 7 8 9 10 11 True Labels 0 0 2 0 2 3 1 0 1…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.