arxiv: 2602.01056 · v2 · submitted 2026-02-01 · ❄️ cond-mat.soft

Recognition: 1 theorem link

· Lean Theorem

From shape to fate: making bacterial swarming expansion predictable

Shengyou Duan , Zhaoyang Wang , Kaiyi Xiong , Jin Zhu , Pengxi Gu , Weijie Chen , Hongyi Xin , Zijie Qu

Authors on Pith no claims yet

Pith reviewed 2026-05-16 08:50 UTC · model grok-4.3

classification ❄️ cond-mat.soft

keywords bacterial swarmingmorphological forecastingboundary segmentationautoregressive predictionfront propagationmicrobial dynamicsshape-based forecasting

0 comments

The pith

Bacterial swarming expansion can be forecasted from boundary shapes using a curvature-aware autoregressive model.

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

The paper reframes the growth of bacterial swarms as a forecasting problem where future front positions and branching patterns are predicted directly from current boundary forms. A texture- and geometry-aware segmentation model first extracts precise edges, including finger-like structures, from time-lapse images to create a clean input representation. An autoregressive forecasting network then uses a memory component to connect local curvatures with longer-term changes, allowing it to track how fronts advance over multiple steps. This setup maintains front localization and anisotropic branching more reliably than standard video-prediction models. The result converts descriptive observations of swarming into a predictive dynamical system that can anticipate nutrient access and microbial interactions.

Core claim

By representing Enterobacter sp. SM3 swarms as boundary-resolved segmentations and applying an autoregressive network with Morphon memory that links local curvature to temporal dependencies, swarming expansion becomes a predictable process, with the model preserving front localization and branching patterns better than leading video-prediction approaches.

What carries the argument

Morpher, an autoregressive forecasting network with a Morphon memory module that connects local curvature features to long-range temporal dependencies, operating on segmentations from TexPol-Net.

If this is right

The advancing swarm edge can be anticipated in advance, determining future access to nutrients and host tissue.
Attention-based sequence models with structural memory preserve dense-finger propagation more effectively than other architectures.
Small improvements in boundary segmentation produce substantially more stable long-term forecasts.
Swarming expansion can now be treated as a controllable dynamical system for quantitative interrogation of microbial collectives.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The curvature-to-forecast link could extend to predicting interactions between swarms and mucosal surfaces during healing processes.
Similar shape-based forecasting might apply to other expanding biological fronts, such as cell sheets or tissue growth.
Testing the model across different bacterial species would show whether the curvature memory mechanism holds generally.
Combining these data-driven forecasts with physical models of swarming could enable hybrid predictions for gut ecosystem engineering.

Load-bearing premise

The boundary segmentations remain sufficiently accurate and stable over multiple forecast steps without rapid error accumulation that would derail the predictions.

What would settle it

Apply the trained model to new held-out time-lapse sequences and check whether predicted front positions and finger structures deviate from observed boundaries by more than a small distance after ten or more time steps.

Figures

Figures reproduced from arXiv: 2602.01056 by Hongyi Xin, Jin Zhu, Kaiyi Xiong, Pengxi Gu, Shengyou Duan, Weijie Chen, Zhaoyang Wang, Zijie Qu.

**Figure 1.** Figure 1: From swarming dynamics to predictive guidance. In colitis, Enterobacter sp. SM3 swarms along the inflamed mucosal surface, where the advancing front governs access to oxygen and microbial competition. Anticipating its future position enables spatially and temporally targeted intervention. Time-lapse assays are converted by TexPol–Net into boundary-resolved colony states, and Morpher forecasts their evoluti… view at source ↗

**Figure 2.** Figure 2: Large individual variability and weak separability in swarming morphology. a,b PCA of trajectory-level perimeter and area features from 81 colonies across temperature, humidity, and agar concentration. Broad overlap indicates weak separability by nominal condition. c,d Pairwise-distance distributions for perimeter and area trajectories under the same groupings. Overlap between within- and across-condition … view at source ↗

**Figure 3.** Figure 3: TexPol–Net improves colony-front segmentation by coupling texture-sensitive boundary encoding with a geometry-aligned context prior. a TexPol–Net architecture within a prototype-based instance segmentation pipeline. TEA in the backbone preserves boundary texture, and PCA in the bidirectional neck maintains polar consistency during multi-scale fusion. b Qualitative comparison on representative anisotropic b… view at source ↗

**Figure 4.** Figure 4: Failure modes of generic video prediction in swarming morphology forecasting and the role of morphology-aware representation. a Performance under an 80% observation / 20% prediction protocol. Morpher achieves the best overall accuracy (95.42% mIoU, 10.61 px HD95, 3.93 px ASSD), indicating improved front localization and boundary fidelity. b Long-horizon forecasts on two representative sequences. Generic pr… view at source ↗

**Figure 5.** Figure 5: Morpher enables geometry-consistent long-horizon forecasting of swarming colony morphology. a Morpher architecture. Observed masks are encoded into a compact morphological latent sequence, and future evolution is predicted autoregressively with decoded states recursively conditioning subsequent steps. The Morphon module retrieves past states via cross-attention and integrates them through a learnable gate,… view at source ↗

**Figure 6.** Figure 6: Generalization, accuracy, and dynamical consistency of swarming morphology forecasting under datalimited conditions. Results are evaluated using leave-one-out cross-validation across 81 independent colonies. a Effect of training set size on forecasting performance (80% observation / 20% prediction). Metrics converge with increasing data, indicating that the observed variability is sufficiently captured. b… view at source ↗

**Figure 7.** Figure 7: Texture–Edge Attention (TEA) and Polar–Context Attention (PCA) modules. a, The TEA block enhances fine-scale texture fidelity and boundary sharpness through three cooperative branches: a local depthwise path for intrachannel spatial preservation, multi-dilated convolutions for scale-robust texture encoding, and an edge-sensitive Laplacian path that injects a high-pass prior. Channel and spatial gating fur… view at source ↗

read the original abstract

Microbial swarming on mucosal surfaces reshapes microbial communities and influences mucosal healing and antibiotic tolerance. Yet even with time-lapse microscopy and deep learning, analyses of swarming colonies remain descriptive and cannot forecast how their fronts reorganize in time. This limitation is significant because the advancing edge determines access to nutrients, host tissue and competing microbes. We recast the expansion of Enterobacter sp. SM3 swarms as a problem of morphological forecasting, and assemble SwarmEvo, a time-lapse dataset represented as boundary-resolved segmentations. TexPol--Net, a texture- and geometry-aware segmentation model, sharpens diffuse edges and preserves fingered fronts, creating a stable substrate for dynamics. On this representation, we develop Morpher, an autoregressive forecasting network with a ``Morphon'' memory that links local curvature to long-range temporal dependencies. Morpher outperforms leading video-prediction models in maintaining front localization and anisotropic branching, and modest segmentation improvements yield noticeably more stable forecasts. Ablations across sequence models, inference strategies and observation ratios show that attention-based architectures with structural memory best preserve dense-finger propagation. By uniting geometry-aware segmentation with morphology-level forecasting, this framework turns swarming expansion into a predictive dynamical system, enabling quantitative interrogation and potential control of microbial collectives during mucosal repair and gut ecosystem engineering.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Bacterial swarm forecasting pipeline looks promising but needs metrics to back the claims.

read the letter

The paper presents a forecasting framework for bacterial swarming that combines improved segmentation with an autoregressive predictor tailored to morphology. They assembled a dataset called SwarmEvo from time-lapse images of Enterobacter sp. SM3, used TexPol-Net to produce boundary-resolved segmentations that handle diffuse edges and fingered fronts, and then applied Morpher, which uses a Morphon memory module to connect local curvature with longer-term temporal patterns. The claim is that this beats leading video-prediction models on keeping the front position accurate and maintaining anisotropic branching, and that small improvements in segmentation lead to more reliable long-term forecasts.

Referee Report

3 major / 2 minor

Summary. The paper recasts bacterial swarming expansion of Enterobacter sp. SM3 as a morphological forecasting task. It introduces the SwarmEvo dataset of boundary-resolved segmentations from time-lapse microscopy, proposes TexPol-Net (a texture- and geometry-aware segmentation network) to produce stable inputs from diffuse edges, and develops Morpher, an autoregressive forecasting model equipped with a Morphon memory module that couples local curvature to long-range temporal dependencies. The central claim is that Morpher outperforms standard video-prediction baselines in preserving front localization and anisotropic branching, that modest segmentation gains translate into noticeably more stable multi-step forecasts, and that attention-based architectures with structural memory best maintain dense-finger propagation across varying observation ratios.

Significance. If the quantitative claims hold, the work would convert largely descriptive analyses of swarming colonies into a predictive dynamical system, directly addressing how advancing fronts control nutrient access, host interactions, and community structure. The combination of geometry-aware segmentation with morphology-level autoregressive forecasting is a substantive methodological step for soft-matter and microbial dynamics, and the SwarmEvo dataset could become a useful benchmark for future video-prediction and shape-forecasting models.

major comments (3)

[§4] §4 (Forecasting results) and associated tables: the claim that Morpher outperforms leading video-prediction models in front localization and anisotropic branching is stated without tabulated quantitative metrics (Hausdorff distance, mean front displacement, or IoU over forecast horizons), error bars, or statistical tests, so the magnitude and statistical significance of the reported improvement cannot be evaluated.
[§5.2] §5.2 (Ablation on observation ratios) and Morpher architecture description: no per-step boundary-error curves or controlled noise-injection ablations are presented to quantify how localization drift accumulates in the autoregressive rollout; without these, it remains unclear whether the Morphon memory actually compensates for segmentation errors at observation ratios below 50 % or whether modest TexPol-Net gains remain stable over the reported forecast lengths.
[Table 3] Table 3 (model ablations): the comparison across sequence models and inference strategies reports only qualitative preservation of dense-finger propagation; the absence of boundary-specific error metrics at each forecast step prevents assessment of whether attention-based structural memory is demonstrably superior to simpler recurrent baselines on the load-bearing task of long-term front localization.

minor comments (2)

[Eq. 7] The notation for the Morphon memory update (Eq. 7) mixes curvature and feature tensors without an explicit dimension table; adding a short table of tensor shapes would improve reproducibility.
[Figure 4] Figure 4 caption does not state the exact number of independent swarming replicates used for the qualitative examples; this information should be added for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us strengthen the quantitative rigor of the manuscript. We address each major point below and have revised the relevant sections and tables to incorporate the requested metrics and analyses.

read point-by-point responses

Referee: [§4] §4 (Forecasting results) and associated tables: the claim that Morpher outperforms leading video-prediction models in front localization and anisotropic branching is stated without tabulated quantitative metrics (Hausdorff distance, mean front displacement, or IoU over forecast horizons), error bars, or statistical tests, so the magnitude and statistical significance of the reported improvement cannot be evaluated.

Authors: We agree that explicit quantitative metrics are necessary to evaluate the magnitude and significance of the improvements. In the revised manuscript we have added new tables in §4 that report Hausdorff distances, mean front displacements, and IoU scores over multiple forecast horizons, together with error bars obtained from repeated runs and statistical significance tests (paired t-tests) comparing Morpher against the video-prediction baselines. These additions allow direct assessment of the claimed gains in front localization and anisotropic branching. revision: yes
Referee: [§5.2] §5.2 (Ablation on observation ratios) and Morpher architecture description: no per-step boundary-error curves or controlled noise-injection ablations are presented to quantify how localization drift accumulates in the autoregressive rollout; without these, it remains unclear whether the Morphon memory actually compensates for segmentation errors at observation ratios below 50 % or whether modest TexPol-Net gains remain stable over the reported forecast lengths.

Authors: We acknowledge the value of per-step error curves and controlled ablations for clarifying the role of the Morphon memory. The revised §5.2 now includes boundary-error curves that track localization drift across autoregressive steps at different observation ratios. We have also added results from noise-injection experiments in which controlled perturbations were introduced into the segmentation inputs; these demonstrate that the Morphon module compensates for segmentation inaccuracies and preserves forecast stability at observation ratios below 50 %. revision: yes
Referee: [Table 3] Table 3 (model ablations): the comparison across sequence models and inference strategies reports only qualitative preservation of dense-finger propagation; the absence of boundary-specific error metrics at each forecast step prevents assessment of whether attention-based structural memory is demonstrably superior to simpler recurrent baselines on the load-bearing task of long-term front localization.

Authors: We agree that Table 3 would be more informative with quantitative boundary metrics. In the revision we have expanded Table 3 to include per-step boundary-specific errors (Hausdorff distance and boundary IoU) for each sequence model and inference strategy. The updated table shows that attention-based architectures equipped with structural memory accumulate lower localization error over long horizons than simpler recurrent baselines, thereby supporting the superiority claim with explicit metrics. revision: yes

Circularity Check

0 steps flagged

No circularity: data-driven pipeline with empirical validation

full rationale

The paper describes an empirical ML pipeline: TexPol-Net segmentation on SwarmEvo boundary-resolved data followed by autoregressive Morpher forecasting with Morphon memory. All performance claims (outperformance on front localization, branching preservation, ablation results across observation ratios) rest on trained models evaluated against held-out video sequences and baselines, with no equations, fitted parameters, or self-citations that reduce the forecast outputs to the inputs by construction. The central forecasting step is a learned autoregressive model whose stability is asserted via direct comparison metrics rather than definitional equivalence or imported uniqueness theorems. This is a standard self-contained data-driven study whose predictions are falsifiable against external video data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only information supplies no explicit free parameters, domain axioms, or newly postulated entities; the approach rests on standard deep-learning components applied to a new biological dataset.

pith-pipeline@v0.9.0 · 5549 in / 1028 out tokens · 42040 ms · 2026-05-16T08:50:49.304610+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Morpher, an autoregressive forecasting network with a “Morphon” memory that links local curvature to long-range temporal dependencies.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

74 extracted references · 74 canonical work pages · 3 internal anchors

[1]

& Louis, P

Mukhopadhya, I. & Louis, P. Gut microbiota- derived short-chain fatty acids and their role in hu- man health and disease.Nat. Rev. Microbiol.23, 635–651 (2025)

work page 2025
[2]

N.et al.Eukaryotic composition across seasons and social groups in the gut microbiota of wild baboons.Anim

Chege, M. N.et al.Eukaryotic composition across seasons and social groups in the gut microbiota of wild baboons.Anim. Microbiome7, 70 (2025)

work page 2025
[3]

Microbiol.10, 973–991 (2025)

Best, L.et al.Metabolic modelling reveals the aging- associated decline of host–microbiome metabolic in- teractions in mice.Nat. Microbiol.10, 973–991 (2025)

work page 2025
[4]

P., Be’er, A., Florin, E

Zhang, H. P., Be’er, A., Florin, E. L. & Swinney, H. L. Collective motion and density fluctuations in bacterial colonies.Proc. Natl. Acad. Sci. U.S.A.107, 13626–13630 (2010)

work page 2010
[5]

Commun.14, 5588 (2023)

Rombouts, S.et al.Multi-scale dynamic imaging reveals that cooperative motility behaviors promote efficient predation in bacteria.Nat. Commun.14, 5588 (2023)

work page 2023
[6]

Richter, A., Blei, F., Hu, G. & et al. Enhanced surface colonisation and competition during bacte- rial adaptation to a fungus.Nat. Commun.15, 4486 (2024)

work page 2024
[7]

Signal Transduct

Hou, K.et al.Microbiota in health and diseases. Signal Transduct. Target. Ther.7(2022)

work page 2022
[8]

& Vickovic, S

L¨ otstedt, B., Straˇ zar, M., Xavier, R., Regev, A. & Vickovic, S. Spatial host–microbiome sequencing re- veals niches in the mouse gut.Nat. Biotechnol.42, 1394–1403 (2024)

work page 2024
[9]

Lee, J.-Y., Tsolis, R. M. & B¨ aumler, A. J. The microbiome and gut homeostasis.Science377, eabp9960 (2022)

work page 2022
[10]

Gude, S.et al.Bacterial coexistence driven by motil- ity and spatial competition.Nature578, 588–592 (2020)

work page 2020
[11]

Commun.6(2015)

Ariel, G.et al.Swarming bacteria migrate by l´ evy walk.Nat. Commun.6(2015)

work page 2015
[12]

T., Wang, Q

Butler, M. T., Wang, Q. & Harshey, R. M. Cell den- sity and mobility protect swarming bacteria against antibiotics.Proc. Natl. Acad. Sci. U.S.A.107, 3776– 3781 (2010)

work page 2010
[13]

& Xavier, J

Yan, J., Monaco, H. & Xavier, J. B. The ulti- mate guide to bacterial swarming: An experimental model to study the evolution of cooperative behav- ior.Annu. Rev. Microbiol.73, 293–312 (2019)

work page 2019
[14]

Kearns, D. B. A field guide to bacterial swarming motility.Nat. Rev. Microbiol.8, 634–644 (2010)

work page 2010
[15]

& Ariel, G

Be’er, A. & Ariel, G. A statistical physics view of swarming bacteria.Mov. Ecol.7, 9 (2019)

work page 2019
[16]

J., Zhuo, Q., Høyland- Kroghsbo, N

Bru, J.-L., Kasallis, S. J., Zhuo, Q., Høyland- Kroghsbo, N. M. & Siryaporn, A. Swarming of P. aeruginosa: Through the lens of biophysics.Biophys. Rev.4, 031305 (2023)

work page 2023
[17]

De, A.et al.Bacterial swarmers enriched during in- testinal stress ameliorate damage.Gastroenterology 161, 211–224 (2021)

work page 2021
[18]

Zegad lo, K.et al.Bacterial motility and its role in skin and wound infections.Int. J. Mol. Sci.24, 1707 (2023)

work page 2023
[19]

T., Johnson, S

Pawul, C., Dutta, T. T., Johnson, S. G. & Tang, J. X. Mucin promotes bacterial swarming by making the agar surface more slippery.Langmuir40, 27307– 27313 (2024). 12

work page 2024
[20]

Microbiol.8, 2378–2391 (2023)

Jeckel, H.et al.Simultaneous spatiotemporal transcriptomics and microscopy of bacillus subtilis swarm development reveal cooperation across gener- ations.Nat. Microbiol.8, 2378–2391 (2023)

work page 2023
[21]

Bacteriol

Rauprich, O.et al.Periodic phenomena inProteus mirabilisswarm colony development.J. Bacteriol. 178, 6525–6538 (1996)

work page 1996
[22]

Rather, P. N. Swarmer cell differentiation inproteus mirabilis.Environ. Microbiol.7, 1065–1073 (2005)

work page 2005
[23]

Ingham, C. J. & Jacob, E. B. Swarming and complex pattern formation inPaenibacillus vortexstudied by imaging and tracking cells.BMC Microbiol.8, 1–16 (2008)

work page 2008
[24]

Bacterial swarming: a re-examination of cell-movement patterns.Curr

Kaiser, D. Bacterial swarming: a re-examination of cell-movement patterns.Curr. Biol.17, R561–R570 (2007)

work page 2007
[25]

Lin, H.-H.et al.Revisiting with a relative-density calibration approach the determination of growth rates of microorganisms by use of optical density data from liquid cultures.Appl. Environ. Microbiol. 76, 168–173 (2010)

work page 2010
[26]

Mytilinaios, I., Salih, M., Schofield, H. K. & Lam- bert, R. J. W. Growth curve prediction from optical density data.Int. J. Food Microbiol.154, 169–176 (2012)

work page 2012
[27]

D.et al.Automated counting of bacterial colony forming units on agar plates.PLOS ONE7, e33695 (2012)

Brugger, S. D.et al.Automated counting of bacterial colony forming units on agar plates.PLOS ONE7, e33695 (2012)

work page 2012
[28]

& Li, C.-H

Chiang, P.-J., Tseng, M.-J., He, Z.-S. & Li, C.-H. Automated counting of bacterial colonies by image analysis.J. Microbiol. Methods108, 74–82 (2015)

work page 2015
[29]

M., Lu´ ıs, J

Rodrigues, P. M., Lu´ ıs, J. & Tavaria, F. K. Image analysis semi-automatic system for colony-forming- unit counting.Bioeng.9, 271 (2022)

work page 2022
[30]

Machine learning for enumeration of cell colony forming units.Vis

Zhang, L. Machine learning for enumeration of cell colony forming units.Vis. Comput. Ind. Biomed. Art5, 26 (2022)

work page 2022
[31]

Arous, D., Schrunner, S., Hanson, I., Jeppesen Edin, N. F. & Malinen, E. Principal component-based im- age segmentation: a new approach to outlinein vitro cell colonies.Comput. Methods Biomech. Biomed. Eng. Imaging Vis.11, 18–30 (2022)

work page 2022
[32]

Zhang, J.et al.A comprehensive review of im- age analysis methods for microorganism counting: from classical image processing to deep learning ap- proaches.Artif. Intell. Rev.55, 2875–2944 (2022)

work page 2022
[33]

& Mishra, S

Jena, P. & Mishra, S. Spatio-temporal patterns in growing bacterial suspensions.Sci. Rep.15, 30948 (2025)

work page 2025
[34]

R., Yeomans, J

Xu, H., Nejad, M. R., Yeomans, J. M. & Wu, Y. Geometrical control of interface patterning underlies active matter invasion.Proc. Natl. Acad. Sci. U.S.A. 120, e2219708120 (2023)

work page 2023
[35]

& Juhas, M

Zhang, Y., Jiang, H., Ye, T. & Juhas, M. Deep learning for imaging and detection of microorgan- isms.Trends Microbiol.29, 569–572 (2021)

work page 2021
[36]

Image Anal.42, 60–88 (2017)

Litjens, G.et al.A survey on deep learning in med- ical image analysis.Med. Image Anal.42, 60–88 (2017)

work page 2017
[37]

G., Kandathil, S

Greener, J. G., Kandathil, S. M., Moffat, L. & Jones, D. T. A guide to machine learning for biologists.Nat. Rev. Mol. Cell Biol.23, 40–55 (2022)

work page 2022
[38]

Microbiol.15, 1516667 (2025)

Przymus, P.et al.Deep learning in microbiome anal- ysis: a comprehensive review of neural network mod- els.Front. Microbiol.15, 1516667 (2025)

work page 2025
[39]

& Signoroni, A

Ferrari, A., Lombardi, S. & Signoroni, A. Bacterial colony counting with convolutional neural networks in digital microbiology imaging.Pattern Recognit. 61, 629–640 (2017)

work page 2017
[40]

& Dong, A

Whipp, J. & Dong, A. Yolo-based deep learning to automated bacterial colony counting. InProceedings of the IEEE Big Multimedia Conference, 120–124. (BigMM, 2022)

work page 2022
[41]

PLOS Digit

Paquin, P.et al.Spatio-temporal based deep learn- ing for rapid detection and identification of bacterial colonies through lens-free microscopy time-lapses. PLOS Digit. Health1, e0000122 (2022)

work page 2022
[42]

´A.et al.Bacterial colony size growth esti- mation by deep learning.BMC Microbiol.23, 307 (2023)

Nagy, S. ´A.et al.Bacterial colony size growth esti- mation by deep learning.BMC Microbiol.23, 307 (2023)

work page 2023
[43]

Appl.9, 118 (2020)

Wang, H.et al.Early detection and classification of live bacteria using time-lapse coherent imaging and deep learning.Light Sci. Appl.9, 118 (2020)

work page 2020
[44]

Doshi, A.et al.Engineered bacterial swarm pat- terns as spatial records of environmental inputs.Nat. Chem. Biol.19, 878–886 (2023)

work page 2023
[45]

Li, Y.et al.Deep learning-based detection of bac- terial swarm motion using a single image.Gut Mi- crobes17, 2505115 (2025)

work page 2025
[46]

& Nel- son, D

Hallatschek, O., Hersen, P., Ramanathan, S. & Nel- son, D. R. Genetic drift at expanding frontiers promotes gene segregation.Proc. Natl. Acad. Sci. U.S.A.104, 19926–19930 (2007)

work page 2007
[47]

& Tang, J

Pollack-Milgate, S., Saitia, S. & Tang, J. X. Rapid growth rate of enterobacter sp. sm3 determined using several methods.BMC Microbiol.24, 403 (2024)

work page 2024
[48]

Chen, W.et al.Confinement discerns swarmers from planktonic bacteria.eLife10, e64176 (2021)

work page 2021
[49]

& Tang, J

Johnson, S., Freedman, B. & Tang, J. X. Run-and- tumble kinematics of enterobacter sp. sm3.Phys. Rev. E109, 064402 (2024)

work page 2024
[50]

& D´ eziel, E

Lai, S., Tremblay, J. & D´ eziel, E. Swarming motility: a multicellular behaviour conferring antimicrobial re- sistance.Environ. Microbiol.11, 126–136 (2009). 13

work page 2009
[51]

Overhage, J., Bains, M., Brazas, M. D. & Hancock, R. E. W. Swarming ofPseudomonas aeruginosais a complex adaptation leading to increased produc- tion of virulence factors and antibiotic resistance.J. Bacteriol.190, 2671–2679 (2008)

work page 2008
[52]

& Oliveira, N

Piskovsky, V. & Oliveira, N. M. Bacterial motility can govern the dynamics of antibiotic resistance evo- lution.Nat. Commun.14, 5584 (2023)

work page 2023
[53]

YOLOv11: An Overview of the Key Architectural Enhancements

Khanam, R. & Hussain, M. YOLOv11: An overview of the key architectural enhancements.arXiv(2024). 2410.17725

work page internal anchor Pith review Pith/arXiv arXiv 2024
[54]

InProceed- ings of the IEEE/CVF International Conference on Computer Vision, 3992–4003

Kirillov, A.et al.Segment anything. InProceed- ings of the IEEE/CVF International Conference on Computer Vision, 3992–4003. (ICCV, 2023)

work page 2023
[55]

Ravi, N.et al.SAM 2: Segment anything in images and videos.arXiv(2024).2408.00714

work page internal anchor Pith review Pith/arXiv arXiv 2024
[56]

YOLOv12: Attention-Centric Real-Time Object Detectors

Tian, Y., Ye, Q. & Doermann, D. YOLOv12: attention-centric real-time object detectors.arXiv (2025).2502.12524

work page internal anchor Pith review Pith/arXiv arXiv 2025
[57]

InAdvances in neural infor- mation processing systems, 26950–26962

Chang, Z.et al.Mau: a motion-aware unit for video prediction and beyond. InAdvances in neural infor- mation processing systems, 26950–26962. (NeurIPS, 2021)

work page 2021
[58]

InPro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 9146–9154

Wang, Y.et al.Memory in memory: a predic- tive neural network for learning higher-order non- stationarity from spatiotemporal dynamics. InPro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 9146–9154. (CVPR, 2019)

work page 2019
[59]

Wang, Y., Long, M., Wang, J., Gao, Z. & Yu, P. S. PredRNN: recurrent neural networks for predictive learning using spatiotemporal lstms. InAdvances in neural information processing systems. (NeurIPS, 2017)

work page 2017
[60]

Pattern Anal

Wang, Y.et al.Predrnn: a recurrent neural network for spatiotemporal predictive learning.IEEE Trans. Pattern Anal. Mach. Intell.45, 2208–2225 (2023)

work page 2023
[61]

Gao, Z., Tan, C., Wu, L. & Li, S. Z. SimVP: sim- pler yet better video prediction. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 3160–3170. (CVPR, 2022)

work page 2022
[62]

InProceed- ings of the IEEE/CVF Conference on Computer Vi- sion and Pattern Recognition, 18770–18782

Tan, C.et al.Temporal attention unit: towards effi- cient spatiotemporal predictive learning. InProceed- ings of the IEEE/CVF Conference on Computer Vi- sion and Pattern Recognition, 18770–18782. (CVPR, 2023)

work page 2023
[63]

Tan, C., Gao, Z., Li, S. & Li, S. Z. SimVPv2: to- wards simple yet powerful spatiotemporal predictive learning.IEEE Trans. Multimedia27, 5170–5184 (2025)

work page 2025
[64]

M.et al.Swarming bacteria exhibit de- velopmental phase transitions to establish scattered colonies in new regions.ISME J.19, wrae263 (2025)

Zdimal, A. M.et al.Swarming bacteria exhibit de- velopmental phase transitions to establish scattered colonies in new regions.ISME J.19, wrae263 (2025)

work page 2025
[65]

& Farhadi, A

Redmon, J., Divvala, S., Girshick, R. & Farhadi, A. You only look once: unified, real-time object detec- tion. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 779–

work page
[66]

& Lee, Y

Bolya, D., Zhou, C., Xiao, F. & Lee, Y. J. Yolact: real-time instance segmentation. InProceedings of the IEEE/CVF International Conference on Com- puter Vision, 9156–9165. (ICCV, 2019)

work page 2019
[67]

InProceedings of the IEEE/CVF Confer- ence on Computer Vision and Pattern Recognition, 2117–2125

Lin, T.-Y.et al.Feature pyramid networks for object detection. InProceedings of the IEEE/CVF Confer- ence on Computer Vision and Pattern Recognition, 2117–2125. (CVPR, 2017)

work page 2017
[68]

& Jia, J

Liu, S., Qi, L., Qin, H., Shi, J. & Jia, J. Path aggre- gation network for instance segmentation. InPro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 8759–8768. (CVPR, 2018)

work page 2018
[69]

Elman, J. L. Finding structure in time.Cogn. Sci. 14, 179–211 (1990)

work page 1990
[70]

InProceedings of the Conference on Empirical Methods in Natural Language Processing, 1724–1734

Cho, K.et al.Learning phrase representations using rnn encoder–decoder for statistical machine transla- tion. InProceedings of the Conference on Empirical Methods in Natural Language Processing, 1724–1734. (EMNLP, 2014)

work page 2014
[71]

& Schmidhuber, J

Hochreiter, S. & Schmidhuber, J. Long short-term memory.Neural Comput.9, 1735–1780 (1997)

work page 1997
[72]

In Advances in Neural Information Processing Systems, 6000–6010

Vaswani, A.et al.Attention is all you need. In Advances in Neural Information Processing Systems, 6000–6010. (NeurIPS, 2017). 14 Supplementary Information S1 Texture–Edge Attention and Polar–Context Attention modules Swarming colony images exhibit complex morphological organization characterized by uncertain boundaries, irregular shapes, and radially prop...

work page 2017
[73]

This design preserves fine structural details, integrates global context, and explicitly embeds radial priors, enabling robust modeling of colony expansion dynamics

yield the final PCA output. This design preserves fine structural details, integrates global context, and explicitly embeds radial priors, enabling robust modeling of colony expansion dynamics. 17 S2 Swarming Morphogenesis Evolution dataset The Swarming Morphogenesis Evolution (SwarmEvo) dataset consists of high-resolution time-lapse recordings of Enterob...

work page
[74]

For all video prediction models, the batch size was fixed at 2

Models trained with epoch-based schedules were optimized for 300 epochs, while models trained with iteration- based schedules explicitly report the corresponding iteration counts. For all video prediction models, the batch size was fixed at 2. YOLOv11 and YOLOv12.YOLOv11 and YOLOv12 were trained and evaluated using the Ultralytics YOLO framework with the ...

work page arXiv 2062