Transient State Reorganization and Cell Differentiation in the Developmental Dynamics of Growing Neural Cellular Automata

Atsushi Masumori; Hiroki Sato; Takashi Ikegami

REVIEW 3 major objections 5 minor 17 references

Transient State Reorganization and Cell Differentiation in the Developmental Dynamics of Growing Neural Cellular Automata

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read GNCA development is a staged, coordinated reorganization of transient states rather than incremental refinement toward a target morphology.

desk verdict Useful first look at GNCA development with credible morphological and state-space findings, but the cell-type community analysis is methodologically shaky and undercuts the stronger 'reorganization' framing. read the letter →

arxiv 2607.15726 v2 pith:TVP3FXYL submitted 2026-07-17 cs.NE

Hiroki Sato , Atsushi Masumori , Takashi Ikegami This is my paper · ORCID

classification cs.NE

keywords growingneuralcellularautomatacelldifferentiationtransientstatesdevelopmentaldynamicscommunitydetectionintrinsicdimensionalityself-organizationtrajectory

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 paper traces the full developmental trajectory of trained Growing Neural Cellular Automata (GNCA) from a single seed cell to a target emoji image and argues that development unfolds as a coordinated reorganization of transient states, not as monotonic refinement. Within roughly the same early window (about steps 5–30), the whole morphology overshoots or undershoots the target, hidden channels self-organize into modular groups, cell states fan out across a low-dimensional smooth manifold, and coarse cell-type communities expand and then contract before finer stable types appear. The authors conclude that a purely local shared rule with no global coordinator spontaneously produces a staged developmental phase with internal structure, and they offer GNCA as a minimal model for studying how such phases arise.

What carries the argument

The central object is the 16-dimensional cell state carried by each GNCA cell (4 visible RGBA channels plus 12 hidden channels), updated by a shared local neural-network rule. To see cell types in the continuous state space, the authors collect all living cells over all time steps, L2-normalize their states, build an epsilon-neighbour graph where edges connect cells whose cosine distance is at most epsilon=0.1, and apply a standard modularity-maximizing community-detection algorithm. Each community is interpreted as a cell type, and tracking community sizes and spatial maps over time exposes the expansion, contraction, and subdivision pattern. Supporting measures include channel-wise cosine

What would settle it

Recompute the community trajectories across a fine sweep of epsilon, and also with a density-based clustering method that does not fix a radius; if the early expansion-and-contraction of coarse communities appears only in a narrow window around epsilon=0.1, the reorganization story loses its main support. As a secondary check, the UR=1.0 smiley overshoot at steps 10–15 is a specific point prediction: if it disappears under a different optimizer or longer training while the channel and community timing stays unchanged, the coordination argument weakens.

Watch

Extended reading notes

Core claim

The central claim is that GNCA growth proceeds through a recognizable developmental stage in which cell states first differentiate into a few widely separated types, overshoot in state-space variance and morphological error, and then contract and subdivide into a larger set of finer-grained, spatially coherent, stable cell types. The evidence is temporal coordination across four independent measures: non-monotonic MSE trajectories, the appearance of block structure in inter-channel cosine-distance matrices, growth of intrinsic dimensionality from roughly 2–3 to 3–6 along a smooth manifold, and community-detection trajectories whose early broad communities are replaced by stable finer communi

Load-bearing premise

The central claim collapses if the transient-then-stable pattern is an artifact of defining cell types with a fixed epsilon=0.1 threshold on cosine distances — the paper itself notes that a fixed epsilon interacts with the rising intrinsic dimensionality and that density-based clustering could change the picture.

Editorial extensions

If this is right

If the claim holds, evaluating a GNCA only by its output image misses most of development; the internal channel organization and transient cell communities are established in the same early window as morphological convergence.
The same shared rule produces a hierarchical differentiation pattern — a few coarse types first, then fine stable subtypes — suggesting that staged development can emerge from purely local interactions without a global program.
The MSE overshoot/undershoot should be understood as a structural transition, not training noise, so analyses and training schedules that assume monotonic convergence may be mis-specified.
The developmental phase is dynamically distinct from the maintenance/self-repair regime that follows it; the paper leaves the connection between these two regimes as an open problem.

Reading between the lines

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

Editorial extension: the transient-community trajectories are a falsifiable handle on causation — one could ablate or perturb a specific transient community during steps 5–30 and predict that the final morphology or later cell-type layout changes, whereas perturbing a stable late community should produce only local, repairable damage.
Editorial extension: the two epsilon resolutions (0.1 and 0.005) hint that the 'cell types' are hierarchical; applying a density-based or hierarchical clustering method could make that hierarchy explicit and remove the fixed-radius assumption.
Editorial extension: if staged reorganization is a general property, then training objectives that penalize deviation from the target at every step may fight the system's natural dynamics; allowing or even scheduling transient overshoot could change training speed and outcome.
Editorial extension: the update-rate differences (broader variance peak and higher mature diversity under asynchronous updating) are based on eight seeds per condition and would need larger samples to distinguish a robust property from seed variation.

Share X Bluesky LinkedIn Reddit HN

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

Quick take: this is a useful first systematic look at how GNCAs actually develop, and the non-monotonic convergence and state-space overshoot findings are worth knowing. But the community-analysis evidence for 'cell types' is weaker than the paper suggests, and the central 'reorganization' claim leans on it more than it should.

What's new: it's the first paper to track the whole trajectory from seed to mature form, combining morphological loss, channel-wise correlation, intrinsic dimensionality, and community detection. The MSE overshoot for the smiley and the variance peak across all models are credible and nicely documented, with 8 seeds and percentile bands. The ID analysis with a random baseline is solid. The smoothness measure with a spatial-shuffle baseline is a good idea. And the epsilon sweep shows some robustness of the overall graph structure.

The soft spot is the cell-type section. The epsilon-NN graph pools cells from all time steps into one point cloud and then runs Louvain once. The resulting communities are a static partition of a moving cloud. Because early cells are compact and later cells are more spread out, a fixed epsilon will naturally split early cells into a few big communities and late cells into many small ones. The growing-then-shrinking transient communities are exactly what you'd expect from the density change, not necessarily from any true differentiation process. The paper acknowledges the fixed-epsilon/ID interaction in a paragraph and a limitation sentence, but still treats the community curves as independent evidence for coordination. A simple null model—shuffling time labels, or clustering each time step separately—would settle this. Without it, the 'transient cell types' interpretation doesn't carry weight.

The other two pillars (variance overshoot, channel block formation) stand on their own, so the paper is not without value. But the coordination claim is overstated. Also, three targets is a small sample, no code or data is released, and the epsilon values (0.1, with a special 0.005 for smiley) feel post-hoc.

Bottom line: this is a well-written descriptive study that should be sent to reviewers. The authors need to address the community-analysis issue before the 'reorganization' framing can be accepted. If you work on NCA or artificial life, it's worth reading. I'd cite the morphological and state-space results, but not the cell-type claim.

Recommendation: yes to peer review, expect substantial revision on the community analysis.

Referee Report

3 major / 5 minor

Summary. The paper analyzes the developmental trajectories of trained Growing Neural Cellular Automata (GNCA) models, using three emoji targets (lizard, smiley, spider-web) under synchronous and asynchronous update rates, with n=8 seeds each. The authors report four main observations: (1) morphological convergence, measured by MSE to the target image, is sometimes non-monotonic (overshoot, undershoot, or plateau); (2) hidden channels self-organize into modular blocks during development; (3) cell states diversify within a low-dimensional, smooth manifold, with intrinsic dimensionality growing from about 2–3 to 3–6; and (4) community detection on an epsilon-nearest-neighbour graph of L2-normalized cell states reveals transient early communities and stable, finer-grained late communities. The central claim is that these signatures are temporally coordinated within roughly Steps 5–30, indicating that GNCA development is a staged reorganization of transient states rather than incremental refinement toward the target.

Significance. If the central claim holds, the paper would provide a useful and non-obvious characterization of GNCA development: a purely local, shared rule produces an intermediate developmental phase with internal structure, not merely a monotonic approach to the target. The study has clear strengths: it uses multiple independent measures; it reports n=8 seeds with percentile bands; it includes calibration baselines for intrinsic dimensionality and transition smoothness; and it performs an epsilon sweep with several summary metrics for the community detection. The distinction between 'reorganization' and 'incremental refinement' is an interesting and potentially important one for the GNCA community and for artificial-life comparisons to biological development. However, as discussed below, the community-detection evidence—which is load-bearing for the cell-differentiation and coordination claims—currently lacks a control that separates genuine transient cell types from artifacts of the fixed-epsilon graph on a progressively spreading point cloud.

major comments (3)

[Cell Differentiation – Community detection method and Developmental dynamics of cell types] The community analysis pools one node per cell-time instance across all 128 steps into a single epsilon-NN graph and then applies one Louvain partition. The temporal curves in Figures 6–7 therefore describe how a static partition of a moving point cloud is populated over time, not an independent dynamic developmental process. The manuscript itself notes in the 'Characterization of the epsilon-NN structure' subsection that a fixed epsilon interacts with the increasing intrinsic dimensionality, and the Discussion mentions this as a limitation. But the paper still treats the transient-then-stable community curves as evidence of reorganization. Under a fixed epsilon, an expanding point cloud that monotonically spreads from low intrinsic dimensionality (ID≈2–3) to higher ID (≈3–6) will naturally have a few coarse, connected communities early and many fine, fragmented communities late. The obs
[Characterization of the epsilon-NN structure (Figure 5)] The operating point epsilon=0.1 is chosen post hoc from global summary metrics, with an additional exceptional value of 0.005 for smiley at UR=1.0. The summary metrics in Figure 5—number of communities, modularity, isolation rate, spatial coherence, and final-step community fraction—do not establish that the temporal growth/contraction pattern of communities is stable across epsilon. A robustness check that directly examines the temporal community curves over a range of epsilon values, or an adaptive/density-based method that avoids the fixed-epsilon/ID interaction, is needed. As written, the choice of epsilon could be selecting the regime that exhibits the desired transient-then-stable narrative, especially since the authors acknowledge that small epsilon yields fine-grained communities and large epsilon yields coarse ones.
[Discussion – temporal coordination] The central claim that the phenomena are 'temporally coordinated' and constitute a single process is supported only by qualitative visual alignment (approximately Steps 5–30). No quantitative measure of alignment is provided, and the non-monotonic MSE signature is not universal: the text reports a clear overshoot for smiley at UR=1.0, an undershoot for spider-web at UR=1.0, a rugged plateau for spider-web at UR=0.5, and monotonic decrease for lizard at both update rates and smiley at UR=0.5. The coordination claim is important because the Discussion uses it to argue that the transient phase is not optimizer noise. Without a quantitative cross-measure analysis (e.g., event timing per seed, cross-correlation, or a combined null test), the claim that MSE non-monotonicity, variance peaks, channel block formation, and community transience are all manifestations of one process remains an asser

minor comments (5)

[Figure 2] The channel cosine distance matrices are shown for only selected seeds (one seed for most conditions, two for lizard UR=0.5), while the text says 'for all targets (n=8)' in several places. Clarify how the displayed seeds were selected and note that the figure is illustrative, not aggregate.
[Equation (1) and Figure 4] The transition-smoothness baseline uses spatially shuffled states at time t+1. A time-shuffle baseline (permuting the time labels while preserving spatial structure) would be a more direct control for the claim that transitions are temporally continuous, and would complement the spatial shuffle.
[References] Two references are 'under review' (Masumori et al.) or personal blog (Greydanus). The 'under review' citation is used as if it were a citable source for the information-propagation claim; please either describe the result in the text or cite a public version.
[Discussion – limitations] The limitation paragraph correctly identifies the fixed-epsilon/ID issue, but the main text and Conclusion state the cell-type findings strongly ('successfully extracted','discrete cell types'). Please soften or qualify these statements until the control analysis is provided.
[Methods – training] The statement 'All subsequent analyses are performed on these recorded trajectories, which correspond to the ontogeny of the trained model at inference time' is clear, but it would help to state explicitly that the development is not re-run with different initial random seeds for inference; only the training seed is used. If multiple inference trajectories per model were generated, please state the number.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the analyses are descriptive and no central claim reduces to its inputs by construction.

full rationale

The paper's central claim is that GNCA development is a staged, coordinated process of transient state reorganization. All supporting analyses—MSE trajectories, channel-wise cosine distance matrices, state-space variance and intrinsic dimensionality, transition distances, and Louvain community detection—are descriptive measurements of recorded developmental trajectories. No parameter is fitted to reproduce the claimed pattern, and no equation is shown to be equivalent to another by construction. The only self-citations (Masumori et al., under review) support background statements about local information propagation and post-developmental fluctuations; these are not load-bearing, since the local nature of NCA updates is already evident from the architecture. The MSE measure is the training objective, but the paper uses its non-monotonic time course as an observation, not as a fitted prediction; a trained model can converge monotonically or non-monotonically, and the paper reports both. The acknowledged interaction between fixed epsilon and increasing intrinsic dimensionality is a methodological limitation of the community analysis, not a circularity: the paper sweeps epsilon, reports robustness, and explicitly suggests density-based alternatives. Even if the community curves were later shown to be artifacts of the fixed threshold, that would be a validity concern, not a reduction of the conclusion to its inputs. The temporal-coordination argument is interpretive rather than derivational. Therefore no circular step can be exhibited, and the score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The analysis is purely descriptive and does not introduce new theoretical entities or fitted predictive models. The main free parameters are analysis thresholds (epsilon, k). The central claim rests on domain assumptions about the meaningfulness of the chosen metrics and the representativeness of the trained models.

free parameters (2)

epsilon (epsilon-NN threshold) = 0.1 (default; swept over 0.005–0.2)
Selected post-hoc after sweeping to balance isolation rate, modularity, and spatial coherence; the specific choice affects community granularity and thus the transient-vs-stable narrative. An additional 0.005 was used for smiley at UR=1.0.
k (nearest neighbors for intrinsic dimensionality) = 15
Fixed for the Levina-Bickel estimator with no sensitivity analysis; the choice influences ID estimates, though the qualitative low-dimensional result is probably robust.

assumptions (4)

domain assumption Louvain communities on an epsilon-neighbour graph of L2-normalized cell states correspond to meaningful cell types.
Interpretation of communities as cell types is assumed throughout the Cell Differentiation section; no external validation or stability analysis beyond epsilon sweeps.
domain assumption Cosine distance on L2-normalized state vectors is an appropriate state space metric.
Used for all geometric and community analyses; discards magnitude information, which could hide important developmental differences.
domain assumption The trained GNCA models (3 emojis, 8 seeds, 2 update rates) are representative of GNCA development in general.
Generalization to other targets, architectures, or training regimes is not established; the authors acknowledge this limitation.
domain assumption The spatially shuffled baseline is a valid null model for transition smoothness.
Used to claim continuity of state transitions; assumes shuffling preserves the marginal distribution and only destroys spatial structure.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Transient State Reorganization and Cell Differentiation in the Developmental Dynamics of Growing Neural Cellular Automata." pith.science (2026). https://pith.science/paper/TVP3FXYL

@misc{pith2026260715726,
  author       = {Pith},
  title        = {Pith review of: Transient State Reorganization and Cell Differentiation in the Developmental Dynamics of Growing Neural Cellular Automata},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TVP3FXYL}},
  note         = {Machine review of arXiv:2607.15726}
}

abstract

Growing Neural Cellular Automata (GNCA) develop complex morphologies from a single seed cell through shared local rules, yet the internal dynamics of this process remain poorly understood. To investigate how GNCA grows, the full developmental trajectory of trained GNCA models was traced. The trajectory of cell state development revealed that morphological convergence often proceeds non-monotonically through transient intermediate configurations. In addition, channel-wise analysis showed that the hidden channels self-organize into modular groups in parallel with the visible form. Furthermore, geometric analysis of the cell state space indicated that cell states diversify within a low-dimensional, smooth manifold. To examine cell development in more detail, community detection on an $\epsilon$-neighbour network of cells was conducted. This analysis successfully extracted discrete cell types from this continuous space, and identified transient cell-type communities during early development and stable, finer-grained types corresponding to spatially coherent regions of the mature morphology. The temporal coordination of these phenomena across multiple independent measures indicates that the developmental process of GNCA is a reorganization of transient states rather than incremental refinement.

Figures

Figures reproduced from arXiv: 2607.15726 by the authors.

**Figure 2.** Inter-channel cosine distance matrices at devel [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Left: intrinsic dimensionality over developmental steps (grey: random baselines; dashed: ambient dimensional [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

Figures from the paper (2 more)

**Figure 6.** Figure 6: Cell type dynamics during GNCA development. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Cell type dynamics during GNCA development. [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

17 extracted references · 3 canonical work pages

[1]

Growing Neural Cellular Automata

Mordvintsev, Alexander and Randazzo, Ettore and Niklasson, Eyvind and Levin, Michael. Growing Neural Cellular Automata. Distill. doi:10.23915/distill.00023

doi:10.23915/distill.00023
[2]

Studying Growth with Neural Cellular Automata

Greydanus, Sam. Studying Growth with Neural Cellular Automata. Natural Intelligence by Sam Greydanus
[3]

Neural cellular automata -why, what, and how

Obinwa, Chiadika and Fridovich-Keil, David and Coleman, Tyler. Neural cellular automata -why, what, and how
[4]

Learning About Growing Neural Cellular Automata

Catrina, Sorana and Catrina, Mirela and Băicoianu, Alexandra and Plajer, Ioana Cristina. Learning About Growing Neural Cellular Automata. IEEE access: practical innovations, open solutions. doi:10.1109/access.2024.3382541

arXiv 2024
[5]

Neural Cellular Automata Can Respond to Signals

Stovold, James. Neural Cellular Automata Can Respond to Signals. arXiv [cs.NE]. arXiv:2305.12971

arXiv
[6]

Physical Review Letters , Month =

Schreiber, Thomas , Doi =. Physical Review Letters , Month =. 2000 , Bdsk-Url-1 =

2000
[7]

Texture Generation with Neural Cellular Automata

Mordvintsev, A and Niklasson, Eyvind and Randazzo, E. Texture Generation with Neural Cellular Automata. arXiv.org. 2105.07299

arXiv
[8]

Towards self-organized control: Using neural cellular automata to robustly control a cart-pole agent

Variengien, Alexandre and Nichele, Stefano and Glover, Tom and Pontes-Filho, Sidney. Towards self-organized control: Using neural cellular automata to robustly control a cart-pole agent. arXiv [cs.NE]. arXiv:2106.15240

arXiv

Show all 17 references

[9]

Developmentally Morpho-motor coupled systems using neural cellular automata

Sato, Hiroki and Masumori, A. Developmentally Morpho-motor coupled systems using neural cellular automata. ALIFE 2024: Proceedings of the 2024 Artificial Life Conference. doi:10.1162/isal\_a\_00710

2024 doi
[10]

Regenerating Soft Robots Through Neural Cellular Automata

Horibe, Kazuya and Walker, Kathryn and Risi, Sebastian. Regenerating Soft Robots Through Neural Cellular Automata. Genetic Programming. doi:10.1007/978-3-030-72812-0\_3

doi
[11]

A single neural cellular automaton for body-brain co-evolution

Pontes-Filho, Sidney and Walker, Kathryn and Najarro, Elias and Nichele, Stefano and Risi, Sebastian. A single neural cellular automaton for body-brain co-evolution. Proceedings of the Genetic and Evolutionary Computation Conference Companion. doi:10.1145/3520304.3529002
[12]

2023 , month =

Masumori, Atsushi and Maruyama, Norihiro and Ikegami, Takashi , title =. 2023 , month =. doi:10.1162/isal_a_00634 , url =

2023 doi
[13]

Maximum likelihood estimation of intrinsic dimension

Levina, Elizaveta and Bickel, Peter J. Maximum likelihood estimation of intrinsic dimension. Advances in Neural Information Processing Systems
[14]

Fast unfolding of communities in large networks

Blondel, Vincent D and Guillaume, Jean-Loup and Lambiotte, Renaud and Lefebvre, Etienne. Fast unfolding of communities in large networks. Journal of Statistical Mechanics. doi:10.1088/1742-5468/2008/10/p10008

2008 doi
[15]

Growing 3D Artefacts and Functional Machines with Neural Cellular Automata

Sudhakaran, Shyam and Grbic, Djordje and Li, Siyan and Katona, Adam and Najarro, Elias and Glanois, Claire and Risi, Sebastian. Growing 3D Artefacts and Functional Machines with Neural Cellular Automata. arXiv [cs.LG]. arXiv:2103.08737

arXiv
[16]

Variational Neural Cellular Automata

Palm, Rasmus Berg and González-Duque, Miguel and Sudhakaran, Shyam and Risi, Sebastian. Variational Neural Cellular Automata. arXiv [cs.NE]. arXiv:2201.12360

arXiv
[17]

The Dynamical and Information-Theoretic Basis of Internal Dynamics in Self-Repairing Growing Neural Cellular Automata

Masumori, Atsushi and Sato, Hiroki and Ikegami, Takashi. The Dynamical and Information-Theoretic Basis of Internal Dynamics in Self-Repairing Growing Neural Cellular Automata. doi:10.3390/e1010000

doi

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

[1] [1]

Growing Neural Cellular Automata

Mordvintsev, Alexander and Randazzo, Ettore and Niklasson, Eyvind and Levin, Michael. Growing Neural Cellular Automata. Distill. doi:10.23915/distill.00023

doi:10.23915/distill.00023

[2] [2]

Studying Growth with Neural Cellular Automata

Greydanus, Sam. Studying Growth with Neural Cellular Automata. Natural Intelligence by Sam Greydanus

[3] [3]

Neural cellular automata -why, what, and how

Obinwa, Chiadika and Fridovich-Keil, David and Coleman, Tyler. Neural cellular automata -why, what, and how

[4] [4]

Learning About Growing Neural Cellular Automata

Catrina, Sorana and Catrina, Mirela and Băicoianu, Alexandra and Plajer, Ioana Cristina. Learning About Growing Neural Cellular Automata. IEEE access: practical innovations, open solutions. doi:10.1109/access.2024.3382541

arXiv 2024

[5] [5]

Neural Cellular Automata Can Respond to Signals

Stovold, James. Neural Cellular Automata Can Respond to Signals. arXiv [cs.NE]. arXiv:2305.12971

arXiv

[6] [6]

Physical Review Letters , Month =

Schreiber, Thomas , Doi =. Physical Review Letters , Month =. 2000 , Bdsk-Url-1 =

2000

[7] [7]

Texture Generation with Neural Cellular Automata

Mordvintsev, A and Niklasson, Eyvind and Randazzo, E. Texture Generation with Neural Cellular Automata. arXiv.org. 2105.07299

arXiv

[8] [8]

Towards self-organized control: Using neural cellular automata to robustly control a cart-pole agent

Variengien, Alexandre and Nichele, Stefano and Glover, Tom and Pontes-Filho, Sidney. Towards self-organized control: Using neural cellular automata to robustly control a cart-pole agent. arXiv [cs.NE]. arXiv:2106.15240

arXiv