DyMo: Adaptive Dynamic Systems

• DyMo is a family of dynamic adaptive systems whose definitions vary across networking, wireless feedback, multimodal selection, diffusion alignment, and robotics.
• In networking and LTE contexts, DyMo enables reactive routing and low-overhead QoS feedback through stochastic group instructions and adaptive route discovery.
• In machine learning and robotics, DyMo drives inference-time modality selection, training-free diffusion alignment, and state prediction for effective tool use and manipulation.

The designation DyMo, and the related capitalization DYMO, is used in several technically distinct research contexts rather than for a single canonical method. In ad hoc networking it denotes Dynamic MANET On-Demand, a reactive routing protocol for MANETs and VANETs; in LTE multicast it denotes Dynamic Monitoring for low-overhead eMBMS feedback; in recent machine learning literature it names an inference-time modality-selection framework for incomplete multimodal classification, a training-free diffusion alignment method based on dynamic multi-objective scheduling, and a dynamics-modelling augmentation for tool-using LLMs; in robotics it appears as DYMO-Hair, a model-based system for robot hair care (Kumar et al., 2012, Bejerano et al., 2017, Du et al., 30 Jan 2026, Xie et al., 2024, Guo et al., 3 Jun 2025, Zhao et al., 7 Oct 2025). The shared label does not imply a shared formalism: each usage defines its own state space, update rule, and evaluation protocol.

1. Nomenclature and scope

In the cited literature, the name spans networking, wireless systems, multimodal learning, generative modeling, tool use, and robot manipulation.

Designation	Expansion and domain	Representative source
DYMO	Dynamic MANET On-Demand; reactive routing in MANETs/VANETs	(Mahmood et al., 2012)
DyMo	Dynamic Monitoring; LTE-eMBMS QoS feedback and control	(Bejerano et al., 2017)
DyMo	Inference-time dynamic modality selection for incomplete multimodal classification	(Du et al., 30 Jan 2026)
DyMo	Dynamic multi-objective scheduling for training-free diffusion alignment	(Xie et al., 2024)
DyMo	Dynamics Modelling for LLM tool use in stateful environments	(Guo et al., 3 Jun 2025)
DYMO-Hair	Generalizable volumetric dynamics modeling for robot hair manipulation	(Zhao et al., 7 Oct 2025)

The term is therefore best treated as a family of acronymic usages. In the networking literature, DYMO usually refers to a protocol lineage related to AODVv2; in later systems papers, DyMo typically denotes a dynamic inference or monitoring mechanism. This suggests a naming convention centered on adaptive behavior, but the underlying mathematical objects differ substantially across domains.

2. DYMO as a reactive routing protocol

DYMO, or Dynamic MANET On-Demand, is described as a purely reactive routing protocol designed to discover and maintain unicast routes in highly dynamic wireless multi-hop networks without requiring periodic route advertisements. Its control plane is organized around Route Request (RREQ), Route Reply (RREP), and Route Error (RERR) messages, with link-break detection provided either by link-layer notification or by periodic HELLO messages when enabled. Protocol state typically includes a routing table, a request-seen cache or RREQ table for duplicate suppression, and optionally a neighbor cache; route entries carry destination address, destination sequence number, next hop, hop count, lifetime, and precursor information. Several descriptions also emphasize path accumulation, in which intermediate nodes append address information to RREQ or RREP packets so that other nodes can learn routes passively (Kumar et al., 2012, Gupta et al., 2013).

Route discovery begins when a source lacks a valid route and broadcasts an RREQ, often under Expanding Ring Search (ERS). Intermediate nodes record reverse-path information, suppress duplicates, and either rebroadcast or return an RREP if permitted by the specific model or implementation. Route maintenance invalidates broken routes and propagates RERR messages upstream so that sources can initiate a new discovery if the route is still needed. Sequence numbers are used throughout to express freshness and to prefer strictly newer or equally fresh but shorter routes (Sagar et al., 2012).

The routing-overhead literature models DYMO through explicit discovery and maintenance terms. One simplified derivation treats DYMO as having no intermediate RREP, sets the intermediate-reply probability to zero, and gives the per-discovery and per-route overhead as

$R_{disc}(H)=2(3^H-1)+H,$

$$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$

where $H$ is average hop count, $T$ is mean route lifetime, and $t$ is the HELLO interval (Mahmood et al., 2012). A more general control-overhead model decomposes total cost into $O_{\rm RREQ}$, $O_{\rm RREP}$, and $O_{\rm HELLO}$, and reports $\partial O/\partial n>0$, $\partial O/\partial H>0$, $$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$0, and $$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$1, so overhead rises with network size, route length, and route lifetime, and decreases with longer HELLO intervals (Mahmood et al., 2013).

Comparative performance results are notably scenario-dependent. In one ns-2 study against AODV and DSR, DYMO had the lowest end-to-end delay under mobility, but the worst throughput and the highest normalized routing load under mobility; under scalability tests, however, its routing load stayed near 2.5 packets/data packet even at 50 nodes, lower than AODV and DSR in that setting (Mahmood et al., 2013). In VANET-oriented comparisons against DSDV and OLSR, default DYMO and MOD-DYMO were reported to achieve higher Packet Delivery Ratio (PDR), Average End-to-End Delay (AE2ED) performance, link duration, and path stability than DSDV and OLSR, but at the cost of higher Normalized Routing Overhead (NRO) (Kumar et al., 2012). Under IEEE 802.11 versus 802.11p, one study concluded that DYMO gives outstanding performance with 802.11, while modified DYMO performs better under 802.11p (Wasiq et al., 2013). Another implementation-oriented paper reported DYMO as having the highest throughput, high PDR, lowest AEED, and lowest routing overhead among DSDV, AODV, DSR, and DYMO in its configuration (Gupta et al., 2013). These results are not mutually reducible to a single ranking; they arise from different simulators, parameterizations, and protocol variants.

A recurring source of ambiguity concerns what counts as “DYMO behavior.” Some descriptions allow the destination or an intermediate node with a fresh enough route to return an RREP, whereas one analytical model explicitly characterizes DYMO as having no gratuitous RREP and no intermediate reply in its overhead analysis (Kumar et al., 2012, Mahmood et al., 2012). A plausible implication is that parts of the literature combine draft-level DYMO behavior, implementation-specific choices, and model simplifications.

The strongest controversy concerns loop freedom. A formal critique of AODV-based protocols argues that monotonically increasing sequence numbers do not, by themselves, guarantee loop freedom, and specifically notes that AODVv2 (DYMO) inherits the same issue. The analysis identifies hidden assumptions on overwrite rules, RERR handling, and self-entries; proposed hardening measures include accepting updates only when fresher or shorter, using the $$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$2 rule for invalidation, and banning or sealing self-entries (Glabbeek et al., 2015). This directly challenges the common informal claim that sequence numbers alone suffice.

3. DyMo as Dynamic Monitoring for LTE-eMBMS

In LTE evolved Multimedia Broadcast/Multicast Service, DyMo denotes a low-overhead, real-time feedback and control system for large-scale eMBMS deployments. The motivating problem is that eMBMS does not provide continual per-UE QoS reports, while modulation and coding, FEC, and related parameters must be tuned across a Single Frequency Network (SFN) for a very large user population. DyMo addresses this using Stochastic Group Instructions (SGIs) broadcast over eMBMS to all UEs; each instruction specifies reporting probabilities as a function of observed QoS, and each UE sends a unicast report only with the probability assigned to its QoS range. The design therefore implements an importance-sampling scheme concentrated around the low-SNR tail that drives outage guarantees (Bejerano et al., 2017).

The central inference target is the low-tail SNR percentile

$$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$3

where $$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$4 is the SFN-combined SNR CDF over active UEs and $$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$5 is the tolerated outlier fraction, such as $$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$6. The paper develops both a two-step static estimator and an iterative dynamic estimator. The static scheme chooses

$$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$7

under the constraint $$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$8 and $$R_{\rm total\;(per\;route)}=2(3^H-1)+2H+2\frac{T}{t}H,$$9. The iterative scheme assumes each UE’s SNR moves at most $H$0 dB per interval and focuses reporting on the window that can cross the threshold, with optional exponential smoothing $H$1 for stable tracking (Bejerano et al., 2017).

DyMo operates as a closed loop. At each reporting interval, the server broadcasts new SGIs, UEs measure an individual SNR value $H$2 defined so that 95% of eMBMS packets in the interval exceed it, and a small number of UEs report according to their assigned probabilities. A Feedback Collection module aggregates the reports, a QoS Evaluation module estimates the target percentile, and an MCS Control module selects the highest MCS index whose required SFN SNR is below the estimate, with coordinated synchronized updates across MCEs and base stations (Bejerano et al., 2017).

The reported efficiency is unusually aggressive. For $H$3, DyMo detects the eMBMS SNR experienced by the 0.1% percentile of the UEs with RMSE of 0.05% using only 5 to 10 reports per second regardless of the number of UEs. The same study reports error below 0.3 dB in SFN-combined SNR for the 0.1% percentile, robustness from 5 k to 50 k UEs, convergence in $H$4 interval under mobility, and one-interval recovery after a simulated base-station failure with a 10 dB local SNR drop (Bejerano et al., 2017). The system is also framed as standards-compatible because it uses existing MBMS-MTCH for SGI broadcast and unicast MDT for feedback.

4. DyMo for incomplete multimodal classification

In multimodal deep learning, DyMo is introduced as an inference-time dynamic modality selection framework for incomplete multimodal classification. The motivating problem is the discarding-imputation dilemma: existing methods either discard missing modalities, losing task-relevant information, or recover them and risk injecting irrelevant noise. DyMo assumes an observed modality set $H$5 and access to recovered modalities $H$6, and then adaptively selects a subset of those recovered modalities at test time (Du et al., 30 Jan 2026).

Its theoretical justification is an information-theoretic one. The framework aims to maximize the task-relevant information $H$7 between representation $H$8 and label $H$9, starting from

$T$0

Because the true cross-entropy loss satisfies $T$1, the method uses a reduction in CE loss as a tractable proxy for an increase in task-relevant information:

$T$2

At inference time this becomes an empirical decision rule based on the observed loss drop when a recovered modality is added (Du et al., 30 Jan 2026).

The resulting reward for a candidate recovered modality $T$3 is the CE-loss reduction between the representation with the observed set $T$4 and the representation with $T$5:

$T$6

Because labels are unavailable at test time, DyMo substitutes a predicted label and further stabilizes the reward using class prototypes $T$7 in representation space. A calibrated reward $T$8 then drives a greedy selection algorithm: at each iteration, DyMo computes rewards for all remaining recovered modalities, adds the modality with maximal positive reward, and removes modalities whose reward is non-positive (Du et al., 30 Jan 2026).

The backbone is designed to support arbitrary modality combinations. Each modality has its own encoder, a learnable [CLS] token is prepended, visible-modality tokens are concatenated with dummy tokens for missing ones, and a shared multimodal Transformer applies self-attention with masks that block information flow from dummy tokens. Training combines an incomplete-modality simulation classification loss with a missing-agnostic contrastive loss so that the representation space remains meaningful under many missingness patterns (Du et al., 30 Jan 2026).

Empirically, DyMo is reported to outperform recovery-free methods, recovery-based methods, and dynamic-fusion baselines across natural and medical image datasets. The reported gains include 96.8% on PolyMNIST at 80% missing versus a best prior near 91.1%; 85.3% on MST under missing $T$9 versus 82.1%; 93.1% on DVM with full table missing $t$0 versus 89.9%; 81.2% AUC on UKBB CAD at $t$1 versus 77.7%; and 77.9% AUC on UKBB MI at $t$2 versus 75.7% (Du et al., 30 Jan 2026). Ablations attribute gains to the MTIR reward, prototype-based calibration, iterative selection, incomplete-simulation training, and the contrastive loss.

5. DyMo for training-free diffusion alignment

In text-to-image generation, DyMo denotes a plug-and-play, training-free alignment framework that steers pre-trained diffusion models toward human-preferred outputs during inference. The method is motivated by the gap between expensive training-based alignment methods and prior training-free approaches that rely on a single objective and inaccurate guidance in early noisy steps. DyMo therefore combines a semantic alignment objective and a human preference objective, and schedules them dynamically over the diffusion trajectory (Xie et al., 2024).

The total guided loss at timestep $t$3 is

$t$4

where $t$5 are cross-attention maps and $t$6 is the one-step predicted clean image. The dynamic weight is

$t$7

with $t$8 for very high noise $t$9 and $O_{\rm RREQ}$0 for low noise $O_{\rm RREQ}$1. Early guidance relies entirely on semantic structure because cross-attention maps remain informative even when the one-step image estimate is too noisy for reliable preference scoring (Xie et al., 2024).

The semantic loss is built from an LLM-parsed prompt graph of entities and attributes. Positive edges correspond to correct entity-attribute pairs, and negative edges correspond to distinct entities; the loss encourages high cosine similarity for positive pairs and low similarity for negative pairs in the cross-attention maps. Human preference guidance is taken from a pre-trained, step-aware preference model derived from SPO. To stabilize optimization, the latent update uses a Polyak-style step size, and DyMo further performs dynamic time travel with

$O_{\rm RREQ}$2

so larger gradient norms trigger more recurrent refinement steps (Xie et al., 2024).

The paper reports gains on multiple backbones and metrics. On SD V1.5, DyMo increases PickScore from 20.73 to 23.07, HPSv2 from 0.2341 to 0.2755, ImageReward from 0.1697 to 0.7170, and Aesthetic from 5.337 to 5.831. On SDXL, it raises PickScore from 21.91 to 24.90, with similar gains on the other alignment metrics. In user studies over 100 prompts, DyMo variants win more than 60% of pairwise comparisons for prompt alignment and visual appeal (Xie et al., 2024).

The method’s stated limitations are also structurally important. Prompt-graph extraction by an LLM can omit subtle relations, recurrent sampling increases per-image runtime, and hyperparameters such as $O_{\rm RREQ}$3, $O_{\rm RREQ}$4, and the timestep thresholds were obtained by grid search. These caveats position DyMo as an inference-time control policy rather than a universally parameter-free alignment rule (Xie et al., 2024).

6. DyMo as dynamics modelling for tool-using LLMs

In the LLM tool-use literature, DyMo stands for dynamics modelling: a post-training augmentation that teaches an LLM not only to emit a tool call but also to predict the next environment state that the call would induce. The motivating setting is the stateful environment, where repeated real-world trials are unsafe or impossible because an executed action irreversibly changes the world. DyMo therefore adds an internal environment model to the usual function-calling policy (Guo et al., 3 Jun 2025).

The formulation separates the two learned distributions:

$O_{\rm RREQ}$5

where $O_{\rm RREQ}$6 is the input state or user prompt, $O_{\rm RREQ}$7 is a JSON-formatted function call, and $O_{\rm RREQ}$8 is the predicted next state or API response. Supervised post-training combines a function-call loss over correct calls with a state-prediction loss over logged responses. Optional online RL further combines a two-sample REINFORCE Leave-One-Out (RLOO) loss with a DyMo state-prediction loss so that policy improvement and world-model learning proceed jointly (Guo et al., 3 Jun 2025).

At inference time, DyMo enables Self-Verification Sampling (SVS). For a budget of $O_{\rm RREQ}$9 mental trials, the model samples candidate actions, predicts their outcomes, scores each candidate by the internal pass probability

$O_{\rm RREP}$0

and executes only the highest-scoring real action. This allows test-time compute scaling without repeated oracle-environment interaction. The same pass probability can also drive refusal when confidence falls below a threshold $O_{\rm RREP}$1 (Guo et al., 3 Jun 2025).

The evaluation uses the Berkeley Function Calling Leaderboard V2. Reported state-prediction performance reaches 93.62% overall accuracy, 90.00% precision, 87.71% recall, and 88.84% F1, which the authors contrast with a 72.77% raw SFT pass rate. In supervised fine-tuning, adding DyMo raises overall performance from 66.35% to 70.87% unweighted and 73.89% weighted, with the largest gain of +18.27 points on irrelevance prompts. In the RL setting, RLOO reaches 80.31% overall, while RL + DyMo reaches 82.13% unweighted / 83.16% weighted; a stronger SFT baseline with DyMo reaches 83.62% / 86.68% (Guo et al., 3 Jun 2025).

SVS provides the largest test-time gains. Without SVS, the best RL+DyMo model attains 85.77% pass@1; with SVS at $O_{\rm RREP}$2 mental trials, pass@1 increases to 90.69%. The reported pass^k also exceeds the non-SVS version by 1–7 points for $O_{\rm RREP}$3 up to 32. In refusal experiments with $O_{\rm RREP}$4, the precision of accepted calls remains near 94.5% across $O_{\rm RREP}$5, while the refusal rate falls from 23.8% at $O_{\rm RREP}$6 to 13.3% at $O_{\rm RREP}$7 (Guo et al., 3 Jun 2025). The core claim is therefore not only better tool use, but a test-time planning mechanism that does not repeatedly query the real environment.

7. DYMO-Hair and volumetric dynamics modelling in robotics

DYMO-Hair is a model-based robot hair care system for visual goal-conditioned hair styling. The state at time $O_{\rm RREP}$8 is a volumetric representation

$O_{\rm RREP}$9

where $O_{\rm HELLO}$0 is a 3D occupancy grid with $O_{\rm HELLO}$1 and $O_{\rm HELLO}$2 is a per-voxel unit-vector field. This state is encoded into a latent code $O_{\rm HELLO}$3, while each action is a 3D combing motion represented by a short trajectory of tool poses. Planning seeks an action sequence that minimizes the cumulative distance to a target hairstyle, using a strand-level Chamfer cost (Zhao et al., 7 Oct 2025).

The distinctive modeling device is an action-conditioned latent state editing mechanism in a compact pre-trained 3D latent space of diverse hairstyles. The architecture uses pre-trained volumetric encoders for state, trainable motion encoders for the comb action, zero-initialized 3D convolutions plus cross-attention for voxel-aligned fusion, VQ-VAE quantization, and a decoder back to volumetric state. During editing, only the motion path and fusion layers are trainable; the pre-trained encoders, decoders, and codebooks remain frozen to preserve the learned representation (Zhao et al., 7 Oct 2025).

The latent space is pre-trained at scale using a novel hair physics simulator built on Genesis with a Position-Based Dynamics (PBD) hair model. Each strand is represented by particles with stretch, bend, and approximate twist constraints. Dynamics training minimizes a one-step latent prediction loss and may include a two-step rollout loss plus $O_{\rm HELLO}$4 weight decay on motion encoders. Closed-loop control is provided by a Model Predictive Path Integral (MPPI) planner with horizon $O_{\rm HELLO}$5, operating directly in latent space (Zhao et al., 7 Oct 2025).

The reported empirical gains are substantial. In simulation, DYMO-Hair’s dynamics model outperforms baselines on capturing local deformation for diverse unseen hairstyles, and in closed-loop styling it achieves 22% lower final geometric error and 42% higher success rate than the state-of-the-art system over 7 unseen hairstyles × 3 messiness levels × 5 seeds. In real-world tests on two physical wigs, including one long-length style where the prior fails completely, DYMO-Hair achieves 100% success in the reported trials, while the rule-based baseline attains 0% success (Zhao et al., 7 Oct 2025).

Across its disparate meanings, the DyMo/DYMO label recurrently marks systems that adapt online to incomplete information: missing routes, missing QoS reports, missing modalities, noisy diffusion trajectories, uncertain tool outcomes, or partially observed deformable state. This suggests a shared rhetorical motif—dynamic decision-making under uncertainty—even though the concrete algorithms range from reactive routing and percentile estimation to Transformer-based selection, diffusion guidance, model-based planning, and internal world models.