FLOWER: Botany, Sensing & ML Integration

• FLOWER is a polysemous term referring both to botanical flowers—with structured whorls, gene regulatory networks, and spatial dynamics—and to various machine learning frameworks.
• Recent studies model flower sensing via electrostatic and image-based techniques, achieving high performance in petal reconstruction, pose estimation, and geometric inference under uncertainty.
• In federated learning, the FLOWER framework demonstrates scalability and secure aggregation, supporting diverse applications from simulation to robotic pollination and edge deployments.

“FLOWER” is a polysemous term in recent arXiv literature. It denotes the angiosperm flower as a developmental, physiological, ecological, sensing, and robotic target, but it also names a federated learning framework and several acronymic methods in continual learning, recommendation, speech restoration, inverse problems, and neural PDE solving. Across these usages, the term is repeatedly associated with spatial organization, transport, uncertainty propagation, and geometry-aware inference (Poza et al., 2018, Beutel et al., 2020, Ma'sum et al., 2023, Gao et al., 10 Mar 2025, Yang et al., 3 May 2025, Pourya et al., 30 Sep 2025, Muser et al., 17 Feb 2026).

1. Developmental organization and inter-organ physiology

Angiosperm flowers are organized in four concentric whorls from outside to inside—sepals, petals, stamens, and carpels—and arise from a floral meristem whose cells progressively acquire organ identity. In a spatially continuous model for Arabidopsis thaliana, the underlying Boolean gene regulatory network has 13 nodes and $2^{13}$ initial conditions, converges to 10 attractors, and yields floral attractors with counts $c_S = 152$, $c_P = 160$, $c_T = 3744$, and $c_C = 3608$. Those attractors are projected into a two-dimensional plane and assembled into a Waddington landscape,

$$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$

which is then coupled to reaction–diffusion dynamics on an annular domain. The stationary solutions recover the wild-type order sepals $\rightarrow$ petals $\rightarrow$ stamens $\rightarrow$ carpels, and also reproduce the spatial patterns of the AP1, PI, and AG homeotic mutants (Poza et al., 2018).

Recent work also treats the flower as an internal volatile-transport system rather than only a display organ. In petunia, the tube-specific terpene synthase PhTPS1 (GenBank MK159027) produces a suite of sesquiterpenes, with major products germacrene D, bicyclogermacrene, $\beta$-cadinene, and germacrene D-4-ol. About $c_S = 152$0 of each PhTPS1 product is emitted from the inner, adaxial tube surface into the enclosed bud headspace, from which the compounds accumulate in the stigma. RNAi knockdown of PhTPS1 by $c_S = 152$1 drastically reduces tube emission and pistil accumulation, produces pistils weighing $c_S = 152$2 of wild type, and lowers seed yield per flower by up to $c_S = 152$3; on day 2 post-anthesis, the most abundant bacterial OTU, from the family Pseudomonadaceae, increases significantly in the knockdown lines (Boachon et al., 2024).

This suggests that current flower research treats floral organs not only as morphogenetic outputs of gene regulation, but also as coupled chemical compartments in which development, defense, and reproduction are linked through spatial transport.

2. Non-visual flower sensing and electrostatic morphology

A distinct line of work studies flowers as electrostatic objects whose morphology can be inferred from field perturbations rather than images. In the BeeNet formulation, a positively charged bee approaches an uncharged, polarisable flower modeled as a linear dielectric in the quasi-static limit, with piecewise homogeneous permittivity and a two-dimensional logarithmic point-charge potential. The flower occupies an analytic boundary, petals vary in number, shape, thickness, elongation, and orientation, and the perturbation fields are computed by a two-domain AAA–least squares solver on an $c_S = 152$4 grid. The generated dataset contains 1,979 simulated scenarios, later downsampled to $c_S = 152$5, encoded as a 16-bit RGB image with channels $c_S = 152$6, $c_S = 152$7, and $c_S = 152$8, and used to train a Dynamic U-Net with a ResNet101 encoder, 318,616,725 parameters, and 121 layers (Turley et al., 15 Aug 2025).

The reported performance is explicitly morphology dependent. On validation data with familiar shapes but unseen rotations, the mean $c_S = 152$9 score is $c_P = 160$0; the mean is $c_P = 160$1 for 1 rounded petal, $c_P = 160$2 for 2 petals, and $c_P = 160$3 for 3 petals. Reconstruction peaks at the intermediate bee–flower distance $c_P = 160$4, where mean $c_P = 160$5, compared with $c_P = 160$6 at $c_P = 160$7 and $c_P = 160$8 at $c_P = 160$9. Increasing the permittivity ratio from $c_T = 3744$0 to $c_T = 3744$1 improves mean $c_T = 3744$2 from $c_T = 3744$3 to $c_T = 3744$4. On the held-out 4-petal test set, mean $c_T = 3744$5, indicating generalization to more complex morphologies not seen during training (Turley et al., 15 Aug 2025).

The same study reports failure patterns that are structurally informative. Rounded petals achieve mean $c_T = 3744$6, whereas pointed petals fall to $c_T = 3744$7, with the largest errors at tips. For elongated 3-petal flowers, mean $c_T = 3744$8 decreases from $c_T = 3744$9 to $c_C = 3608$0. The model also tends to “re-add” a missing petal, which the authors attribute to learned priors and field symmetries. A plausible implication is that electrostatic flower sensing is strongest when the geometry leaves a smooth, redundant signature in the external field, and weakest when the target contains sharp local features or structural asymmetries.

3. Robotic pollination, 3D registration, and pose estimation

Recent robotic literature treats flowers as manipulable spatial targets whose geometry must be estimated robustly under growth, occlusion, and robot-induced motion. Three representative systems cover cluster re-identification, single-flower pose estimation, and low-cost urban-farm phenotyping.

Study	Core representation	Reported outcome
Robust flower cluster matching (Chu et al., 26 Mar 2025)	$c_C = 3608$1 from RGB-D detections; Unscented Transform covariance and $c_C = 3608$2-gated Mahalanobis matching	Correct Match $c_C = 3608$3 within Dataset 1; Matches $c_C = 3608$4 when Dataset 1 tolerance is applied to Dataset 2
FloPE pose estimation (Shrestha et al., 8 Mar 2025)	3D Gaussian Splatting synthetic data, Grounding DINO + SAM teacher, YOLOv11-nano student, PoseNet rotation regression, EKF refinement	Mean translational error $c_C = 3608$5 cm, mean rotational error $c_C = 3608$6, success rate $c_C = 3608$7; UR5 pollination success $c_C = 3608$8
FarmBot flower pose estimation (Muriki et al., 2 Sep 2025)	Translating occupancy-grid projection to six 2D views, 2D detection, 3D lifting, plane/superellipsoid/paraboloid fitting	49 of 61 GT-labeled flowers detected $c_C = 3608$9; plane mean angular error $$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$0

The cluster-matching system is explicitly uncertainty-aware. Flower centers are detected in RGB with Grounding DINO, lifted to 3D with ray-normalized depth, transformed to world coordinates, and summarized by a centroid-relative descriptor with two scalar features,

$$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$1

The descriptor uncertainty is propagated from flower-position uncertainty through the nonlinear mapping $$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$2 using the Unscented Transform, with $$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$3, $$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$4, and $$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$5. Matching is accepted when the squared Mahalanobis distance satisfies $$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$6; in experiments, a threshold of $$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$7 is used. Monte Carlo validation over 10,000 iterations and noise levels $$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$8 m yields Frobenius-norm differences from $$F(u,v)=\min_k a_k\big[(u-u_k)^2+(v-v_k)^2\big], \qquad a_k=\frac{1}{c_k},$$9 to $\rightarrow$0, with outlier percentages $\rightarrow$1 down to $\rightarrow$2, supporting the UT covariance estimates (Chu et al., 26 Mar 2025).

FloPE addresses a different bottleneck: embedded real-time flower pose estimation in precision pollination. It synthesizes photorealistic training data by rendering novel views from a 3D Gaussian Splatting model reconstructed with COLMAP, distills Grounding DINO + SAM labels into a YOLOv11-nano student, regresses rotation in $\rightarrow$3 and projects it to $\rightarrow$4 by SVD, then smooths both translation and rotation with an Extended Kalman filter. Before filtering, the student reaches $\rightarrow$5 cm translational error, $\rightarrow$6 rotational error, and $\rightarrow$7 pose success; after filtering, the complete FloPE system reaches $\rightarrow$8 cm and $\rightarrow$9, and pollination experiments report $\rightarrow$0 success on StickBug and $\rightarrow$1 on a UR5 (Shrestha et al., 8 Mar 2025).

The FarmBot pipeline emphasizes accessibility rather than teacher-student distillation. A custom camera end-effector scans strawberry plants, Polycam reconstructs a 3D model, six orthogonal occupancy-grid sweeps generate 2D views, and YOLOv10 or Roboflow 3.0 detections are deterministically lifted back into 3D. DBSCAN segmentation $\rightarrow$2 isolates flower clouds, and pose is recovered by fitting planes, superellipsoids, or paraboloids. The plane fit is the most robust, with mean angular error $\rightarrow$3, median $\rightarrow$4, and standard deviation $\rightarrow$5, whereas superellipsoids and paraboloids are more vulnerable to local minima and $\rightarrow$6 flips when petals curve downward (Muriki et al., 2 Sep 2025).

Across these systems, the dominant technical theme is not generic detection but geometry under uncertainty: world-frame consistency, explicit priors on motion or noise, and representations chosen to survive occlusion, branch motion, or sensing limitations.

4. Image-based recognition, segmentation, and retrieval

Flower perception in computer vision spans pixelwise detection in orchards, fine-grained species classification, organ-aware retrieval, and mobile inference.

System	Dataset/task	Reported result
Orchid CBIR with flower + lip features (Apriyanti et al., 2014)	30 orchid species; shape and HSV descriptors on flower and labellum	Validation accuracy $\rightarrow$7; testing accuracy $\rightarrow$8; flower-only validation $\rightarrow$9
Multispecies flower detection (Dias et al., 2018)	Apple, peach, pear semantic segmentation with DeepLab-ResNet + RGR	AppleA $\rightarrow$0, IoU $\rightarrow$1; Pear $\rightarrow$2, IoU $\rightarrow$3
DeepFlorist (Khadangi, 2023)	104-species flower classification on Kaggle TPU challenge	Macro $\rightarrow$4; 4th out of over 800 teams
Mobile CNN flower recognition (Yurdakul et al., 22 Jan 2026)	16-species mobile application with on-device TFLite inference	DenseNet121 + SGD + GAP: accuracy $\rightarrow$5, precision $\rightarrow$6, recall $\rightarrow$7, $\rightarrow$8-score $\rightarrow$9

The orchid system is organ-aware by design. It segments both the whole flower and the labellum with MSRM, extracts centroid contour distance, moment invariant, aspect ratio, roundness, fractal dimension, SF1, SF2, and HSV features while ignoring the $\beta$0 channel, and concatenates flower-region and lip-region descriptors into a 111-dimensional vector. With LIBSVM and an RBF kernel $\beta$1, combining flower and lip features improves validation accuracy from $\beta$2 to $\beta$3 and test accuracy from $\beta$4 to $\beta$5. The most dominant features are reported as Centroid Contour Distance, Moment Invariant, and HSV Color (Apriyanti et al., 2014).

For orchard-scale detection, the dominant formulation is semantic segmentation. A refined DeepLab-ResNet system fine-tuned only on apple flowers and post-processed with region growing refinement yields $\beta$6, precision $\beta$7, recall $\beta$8, and IoU $\beta$9 on AppleA; $c_S = 152$00 on AppleB; $c_S = 152$01 on peach; and $c_S = 152$02 on pear. The same paper emphasizes that the method is applied to apple, peach, and pear “without any pre-processing or dataset-specific training,” which is notable because the peach flowers are pink and the pear scenes have high branch clutter (Dias et al., 2018).

At the classification end of the spectrum, DeepFlorist combines DenseNet201 with EfficientNet-B4, B5, and B6 as base models, then applies stacking or weighted averaging. On the Kaggle “Flower Classification with TPUs” task, which contains 104 flower species, the system reaches Macro $c_S = 152$03 and ranks 4th out of over 800 teams. The paper reports that the meta-classifier consistently outperformed the individual base models and that weighted probability aggregation improved leaderboard $c_S = 152$04 relative to equal-weight averaging (Khadangi, 2023).

The mobile application paper shifts the emphasis from leaderboard performance to deployment. Using a balanced 16-class, 15,742-image dataset, it compares MobileNet, DenseNet121, and Xception under seven optimizers, finding that DenseNet121 with SGD, 0% freezing, and GAP is best at $c_S = 152$05 accuracy and $c_S = 152$06 macro precision, recall, and $c_S = 152$07. Deployed through TensorFlow Lite in an Android application, the model reports average inference times of $c_S = 152$08 ms on a Casper Via S, $c_S = 152$09 ms on a Xiaomi Redmi Pro, $c_S = 152$10 ms on a Xiaomi Redmi, and $c_S = 152$11 ms on a Samsung Galaxy A70 (Yurdakul et al., 22 Jan 2026).

A common misconception in this literature is that flower recognition is primarily a color-classification problem. The papers collectively argue otherwise: radial contour geometry, shape invariants, and organ-specific segmentation are repeatedly reported as decisive, especially when class boundaries involve subtle petal morphology, dense clutter, or species-specific structures such as the orchid labellum.

5. Flower as a federated learning framework

In machine learning systems, “Flower” denotes a federated learning framework designed to bridge small, homogeneous simulations and realistic, heterogeneous deployments. Its core abstractions are the Server, Client, Strategy API, and ClientProxy, with a Virtual Client Engine for large-scale simulation and an Edge Client Engine for on-device execution in Python, Java, C++, and other languages. The framework is open-source under Apache 2.0, ML framework- and language-agnostic, and includes tested implementations of FedAvg, Fault-Tolerant FedAvg, FedProx, QFedAvg, and the FedOptim family. In the original systems paper, Flower demonstrates FL experiments up to 15M in client size using a pair of NVIDIA V100 GPUs on an Amazon Book Reviews DistilBERT workload, while also supporting secure aggregation through SecAgg and SecAgg+ and compatibility with differential privacy approaches (Beutel et al., 2020).

The programming model is intentionally server–client centric. Strategy implementations control client sampling, round configuration, aggregation of model updates, and optional evaluation; clients expose fit and evaluate functions; and the transport layer is communication-agnostic, implemented by default through bi-directional gRPC with efficient binary serialization. Later work rearticulates this architecture as Flower Next, introducing SuperLink and SuperNodes to decouple communication from application logic and to support multi-run orchestration, analytics, evaluation, and hybrid deployments. The same paper shows an initial integration with NVIDIA FLARE in which unmodified Flower applications run inside the FLARE runtime via Local gRPC Server and Local gRPC Client components, while FLARE provides ReliableMessage, startup kits with certificates, authentication and authorization, flexible communication backends, and confidential computing (Roth et al., 2024).

A separate medical-imaging benchmark positions Flower differently. In a five-client PathMNIST experiment using standard FedAvg, three communication rounds, and two local epochs per round, Flower reaches “Final Accuracy (%) ~70,” with “Communication Overhead” rated “Low,” “Training Time (hrs)” rated “Medium,” “Setup Complexity” rated “Low,” and “Deployment Readiness” rated “Low.” The same study characterizes Flower as a “research-oriented platform enabling lightweight simulations, fast prototyping, and flexible integration into existing ML codebases” (Gupta et al., 27 Oct 2025).

These descriptions are not contradictory, but they are scoped differently. The benchmark explicitly states that secure aggregation, differential privacy, and encryption were not implemented in its Flower runs, and it therefore rates “Privacy and Security Features” as “Low.” By contrast, the framework paper documents SecAgg and SecAgg+, and the FLARE integration paper emphasizes certificate-based runtime security and access control. A plausible implication is that “Flower” occupies two positions simultaneously: it is a research framework with low setup complexity, and it is a substrate that can be paired with enterprise runtimes when stronger orchestration, security, and compliance are required (Gupta et al., 27 Oct 2025, Beutel et al., 2020, Roth et al., 2024).

6. Acronyms, derived methods, and the spread of the FLOWER name

Beyond botany and federated learning, “FLOWER” and “Flowers” recur as method names across modern machine learning.

Name	Domain	Core mechanism or reported result
FLOWER (FLat-tO-WidE AppRoach) (Ma'sum et al., 2023)	Few-shot continual learning	Flat-wide minima, feature-space ball generator, and PMAS regularization; Avg $c_S = 152$12 on MiniImageNet with 60 base classes
Flower (Flow-guided fine-tuning recommender) (Gao et al., 10 Mar 2025)	LLM recommendation	GFlowNet process supervision with token-level rewards; on Movie & TV, Title JS $c_S = 152$13
FLOWER (Flow-Based Estimated Gaussian Guidance) (Yang et al., 3 May 2025)	General speech restoration	Conditional normalizing flow guidance injected into diffusion/flow-matching U-Nets; matched PESQ $c_S = 152$14, SI-SDR $c_S = 152$15
FLOWER inverse solver (Pourya et al., 30 Sep 2025)	Linear inverse problems	Three-step flow-consistent destination estimation, proximal refinement, and time progression; CelebA deblurring runtime $c_S = 152$16 s, $c_S = 152$17 GB
Flowers (Muser et al., 17 Feb 2026)	Neural PDE operators	Multihead warps with linear-cost adaptive global interactions; 17.3M model outperforms similarly sized Fourier, convolution, and attention baselines

In few-shot continual learning, FLOWER denotes a no-replay method that seeks “flat-wide minima” and combats data scarcity through feature-space augmentation inside a smallest enclosing ball. It uses a ResNet backbone, SGD, a ball generator implemented as a 3-layer fully connected transformation $c_S = 152$18, and Projection-based Memory Aware Synapses. On moderate-base MiniImageNet, CIFAR100, and CUB-200-2011, the reported average accuracies are $c_S = 152$19, $c_S = 152$20, and $c_S = 152$21, with the strongest gains appearing in small-base-task settings (Ma'sum et al., 2023).

In recommendation, Flower replaces supervised fine-tuning with a GFlowNet-based objective over item-title prefix trees. Item-level rewards are decomposed into token-level process rewards,

$c_S = 152$22

and Subtrajectory Balance aligns token generation probabilities with those rewards. On Movie & TV, it yields Title KL$c_S = 152$23, Title KL$c_S = 152$24, and Title JS $c_S = 152$25, substantially lower than the BIGRec, DPO, and PPO baselines reported in the same study. On Amazon datasets, it also improves fairness metrics such as DGU@10 and MGU@10 while retaining competitive NDCG@5 and HR@5 (Gao et al., 10 Mar 2025).

In speech restoration, FLOWER introduces Gaussian guidance from a conditional normalizing flow trained on clean speech. During training, the NF maps clean speech and latent conditioning into a Gaussian prior; during inference, the NF is removed and $c_S = 152$26 is sampled directly, projected, and injected into the last two upsampling blocks of a multi-resolution U-Net. On matched WSJ+CHiME4 data, FLOWER on SGMSE+ improves PESQ from $c_S = 152$27 to $c_S = 152$28, SRMR from $c_S = 152$29 to $c_S = 152$30, SI-SDR from $c_S = 152$31 to $c_S = 152$32, and LSD from $c_S = 152$33 to $c_S = 152$34; on mismatched VCTK+DEMAND, it improves PESQ from $c_S = 152$35 to $c_S = 152$36 and SI-SDR from $c_S = 152$37 to $c_S = 152$38 (Yang et al., 3 May 2025).

In inverse problems, FLOWER uses a pretrained flow model as an unconditional prior and turns it into a measurement-consistent posterior sampler through three recurrent steps: destination estimation,

$c_S = 152$39

proximal refinement against $c_S = 152$40, and time progression along the flow path. The paper proves that the first step estimates $c_S = 152$41 under optimal training and that the overall update approximates ancestral posterior sampling under linear-Gaussian assumptions. On CelebA deblurring, the method reports $c_S = 152$42 s runtime and $c_S = 152$43 GB memory, while outperforming or matching OT-ODE, D-Flow, Flow-Priors, and PnP-Flow across deblurring, super-resolution, inpainting, and denoising (Pourya et al., 30 Sep 2025).

Finally, “Flowers” in the plural names a neural PDE solver built entirely from multihead warps. Each head predicts a displacement field pointwise, samples features at $c_S = 152$44, and composes these sparse pullbacks inside a multiscale residual scaffold. The resulting operator has linear cost, is motivated through conservation-law flow maps, waves in inhomogeneous media, and a kinetic-theoretic continuum limit, and a compact 17.3M-parameter model outperforms similarly sized Fourier, convolutional, and attention-based baselines on The Well, PDEGym, PDEBench, and WaveBench. A 155.8M-parameter Flower-Medium also improves over a 628.6M scOT-based foundation model on Euler multi quadrants (Muser et al., 17 Feb 2026).

Taken together, these namesakes show that “FLOWER” has become a recurrent label for methods centered on flow, transport, geometric structure, or multistage refinement. This suggests that the term now operates in the literature as both a botanical object of study and a compact brand for algorithms that model structured movement through physical, latent, or probabilistic spaces.