Unidirectional Dynamic Interaction (UDI)

• UDI is a concept defining a one-way, nonreciprocal dynamic influence where one subsystem or modality drives another without reverse feedback.
• In multimodal learning, UDI uses a sequential training scheme by first converging on an anchor modality to proactively guide and balance weaker modalities.
• Across fields such as thermodynamics, network dynamics, and wave physics, UDI’s irreversible transitions simplify complex interactions into tractable, efficient models.

to=arxiv_search.search 񹚓json {"query":"id:(Wang et al., 2 Sep 2025) OR id:(Lokhov et al., 2014) OR id:(Yuan et al., 2022)","max_results":10,"sort_by":"submittedDate","sort_order":"descending"} to=arxiv_search.search 彩票主管 to=arxiv_search.search 人人中彩票json {"query":"(Wang et al., 2 Sep 2025)","max_results":5,"sort_by":"relevance","sort_order":"descending"} to=arxiv_search.search 玩彩神争霸 to=arxiv_search.search 下载彩神争霸json {"query":"(Lokhov et al., 2014) dynamic message-passing equations for models with unidirectional dynamics","max_results":5,"sort_by":"relevance","sort_order":"descending"} Unidirectional Dynamic Interaction (UDI) denotes a directed, nonreciprocal dynamical influence in which one subsystem, state, or mode affects another without an equivalent reverse action in the same channel. In the explicit terminology of multimodal learning, UDI is introduced as a strategy that abandons the conventional joint loss in favor of a proactive, sequential training scheme: an anchor modality is first trained to convergence, and its learned representations then guide another modality via unsupervised loss (Wang et al., 2 Sep 2025). Across other literatures, closely related structures appear as unidirectional transitions in stochastic thermodynamics, local unidirectional coupling in oscillator networks, unidirectional magnetic coupling in bilayers, and unidirectional destructive interference in wave systems (Oliveira, 2024, Chew et al., 2019, Yuan et al., 2022, 1804.00185). This suggests that UDI is best treated as a cross-domain structural motif rather than as a single universally standardized formalism.

1. Terminology, scope, and competing usages

The expression “Unidirectional Dynamic Interaction” is not used uniformly across fields. In "Balanced Multimodal Learning: An Unidirectional Dynamic Interaction Perspective" (Wang et al., 2 Sep 2025), UDI is the name of a multimodal training strategy. In "Incident Direction Independent Wave Propagation and Unidirectional Lasing" (1804.00185), by contrast, the acronym UDI refers specifically to unidirectional destructive interference, not to “interaction” in the multimodal-learning sense. Several other works do not use the acronym explicitly, but formalize the same one-way structure through expressions such as unidirectional transitions, local unidirectional coupling, or unidirectional magnetic coupling (Oliveira, 2024, Chew et al., 2019, Yuan et al., 2022).

Domain	Term in source	One-way feature
Multimodal learning	Unidirectional Dynamic Interaction	anchor modality guides another modality
Stochastic thermodynamics	unidirectional transitions	$W_{x'x}>0,\ W_{xx'}=0$
Wave physics	UDI = unidirectional destructive interference	resonator decouples for one incidence direction
Oscillator networks	local unidirectional coupling	oscillator $i$ is influenced only by $i-1$
Spintronics	unidirectional magnetic coupling	left layer drives right layer, but not vice versa

A common source of confusion is therefore terminological rather than technical. UDI can name a specific algorithm, a specific interference condition, or a broader pattern of irreversible or nonreciprocal coupling. The stable common denominator is directed dynamical asymmetry: a privileged propagation, transition, or guidance direction.

2. UDI in balanced multimodal learning

In multimodal learning, the immediate target of UDI is modality imbalance. The source describes the standard setting as one in which multimodal learning “typically utilizes multimodal joint loss to integrate different modalities and enhance model performance,” but also states that this joint learning strategy can induce imbalance because “strong modalities overwhelm weaker ones and limit exploitation of individual information from each modality and the inter-modality interaction information” (Wang et al., 2 Sep 2025).

The proposed response is explicitly proactive rather than reactive. Existing remedies listed in the source include dynamic loss weighting, auxiliary objectives, and gradient modulation, but these are characterized as strategies that “mitigate modality imbalance based on joint loss” and “remain fundamentally reactive, detecting and correcting imbalance after it arises” (Wang et al., 2 Sep 2025). UDI instead “abandons the conventional joint loss in favor of a proactive, sequential training scheme.” Its abstract-level workflow has two defining stages: it “first trains the anchor modality to convergence,” and then “uses its learned representations to guide the other modality via unsupervised loss.” The source further states that “the dynamic adjustment of modality interactions allows the model to adapt to the task at hand, ensuring that each modality contributes optimally,” and that by “decoupling modality optimization and enabling directed information flow, UDI prevents domination by any single modality and fosters effective cross-modal feature learning” (Wang et al., 2 Sep 2025).

The same source claims empirical superiority, stating that “UDI outperforms existing methods in handling modality imbalance” and yields “performance improvement in multimodal learning tasks” (Wang et al., 2 Sep 2025). However, the available source details also state that the LaTeX file contains no sections, equations, methods, experiments, or other body text, and therefore no extractable formulation of the exact losses, training stages, architectural choices, datasets, ablations, or quantitative results. As a result, the multimodal-learning meaning of UDI is presently available only at the level of the abstract: a sequential, anchor-guided alternative to joint-loss optimization.

3. Unidirectional transitions and thermodynamic formulations

A mathematically precise formulation of one-way dynamics appears in stochastic thermodynamics. In "Entropy production in continuous systems with unidirectional transitions" (Oliveira, 2024), a unidirectional transition in the discrete-state setting is defined by

$W_{x'x} > 0,\qquad W_{xx'} = 0,$

so the forward transition exists but the reverse transition does not. The source emphasizes that the standard Schnakenberg formula fails in this case because it contains a logarithm with the reverse rate in the denominator.

The continuous-space construction uses jumps

$$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$

with state-dependent rates $w_\nu(x)$, leading to the master equation

$$\frac{dP(x)}{dt} = \frac{1}{\varepsilon}\sum_\nu \left[ w_\nu(x-\varepsilon c^\nu)\,P(x-\varepsilon c^\nu) - w_\nu(x)\,P(x)\right]. \tag{25}$$

The associated drift field is

$f_i(x) = \sum_\nu c_i^\nu\,w_\nu(x). \tag{26}$

In the Fokker–Planck limit, the probability density obeys

$$\frac{\partial P}{\partial t} = -\frac{\partial}{\partial x_i}\big[f_i(x)P(x)\big] + \frac{\partial^2}{\partial x_i\partial x_j}\big[T_{ij}(x)P(x)\big], \tag{36}$$

with

$$T_{ij}(x)= \frac{\varepsilon}{2}\sum_\nu c_i^\nu c_j^\nu\,w_\nu(x). \tag{37}$$

The entropy production rate becomes

$i$0

which is manifestly nonnegative because $i$1 is positive semi-definite (Oliveira, 2024).

The paper’s central deterministic-limit result is geometric: $i$2 Thus the entropy flux is the negative divergence of the drift vector field. The source interprets this as a statement about volume contraction or expansion in state space: contraction corresponds to entropy flux from the system to the environment. It also makes a sharp limiting distinction: for Hamiltonian dynamics,

$i$3

because Hamiltonian flows are volume-preserving. A plausible implication is that UDI, in this thermodynamic sense, is not merely directional influence but directional influence that renders the effective flow compressible.

4. Ordered-state network dynamics and dynamic message passing

A second rigorous formalization appears in "Dynamic message-passing equations for models with unidirectional dynamics" (Lokhov et al., 2014). There, each node state belongs to an ordered set

$i$4

with allowed transitions only of the form

$i$5

Backward transitions are forbidden. This irreversibility is the paper’s key structural assumption.

The analytic consequence is decisive. Because trajectories are monotone, a node trajectory can be encoded by a small number of flipping times rather than by an arbitrary time sequence. For $i$6, a single time $i$7 suffices; for SIR-type $i$8 processes, two times $i$9 encode $i-1$0 and $i-1$1. This reduction makes dynamic belief propagation tractable and yields dynamic message-passing (DMP) equations that are exact on trees and asymptotically exact on locally tree-like graphs (Lokhov et al., 2014).

For SIR, the source gives the characteristic DMP structure

$i-1$2

$i-1$3

together with a recursion for $i-1$4 that incorporates both non-transmission and recovery. The same framework is developed for the zero-temperature random-field Ising model, generalized SI, rumor spreading, and a four-state process $i-1$5 (Lokhov et al., 2014).

The computational scaling given in the source underscores the importance of irreversibility. Generalized SI and SIR admit $i-1$6 algorithms; rumor spreading requires $i-1$7; the four-state example requires $i-1$8. The paper further conjectures that a model with $i-1$9 non-trivial transitions yields complexity $W_{x'x} > 0,\qquad W_{xx'} = 0,$0. In this setting, UDI is not just a modeling choice: it is the condition that turns exponentially large trajectory inference into polynomial-time recursion.

5. Wave, magnonic, and spin realizations of one-way dynamics

In wave physics, UDI has an explicit and narrower meaning. "Incident Direction Independent Wave Propagation and Unidirectional Lasing" defines UDI as unidirectional destructive interference (1804.00185). For a side-coupled resonator with synthetic flux $W_{x'x} > 0,\qquad W_{xx'} = 0,$1, destructive interference occurs for

$W_{x'x} > 0,\qquad W_{xx'} = 0,$2

where $W_{x'x} > 0,\qquad W_{xx'} = 0,$3 is the Bloch wave vector. At $W_{x'x} > 0,\qquad W_{xx'} = 0,$4, the side resonator is isolated for left incidence and active for right incidence. In the special case $W_{x'x} > 0,\qquad W_{xx'} = 0,$5, the scattering matrix is

$W_{x'x} > 0,\qquad W_{xx'} = 0,$6

The source further identifies unidirectional perfect absorption at $W_{x'x} > 0,\qquad W_{xx'} = 0,$7 and unidirectional lasing at $W_{x'x} > 0,\qquad W_{xx'} = 0,$8 (1804.00185). This usage is physically narrower than the multimodal-learning one, but structurally similar: one incidence direction is effectively decoupled from a degree of freedom that remains active in the opposite direction.

In magnetic bilayers, "Unidirectional magnetic coupling" presents a dynamical nonreciprocity engineered by interlayer Dzyaloshinskii–Moriya interaction (DMI) and non-local Gilbert damping (Yuan et al., 2022). At the tuned field

$W_{x'x} > 0,\qquad W_{xx'} = 0,$9

the equations of motion reduce so that $$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$0 precesses independently of $$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$1, whereas $$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$2 is driven by $$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$3. In the multilayer extension,

$$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$4

so spin $$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$5 is driven only by its left neighbor (Yuan et al., 2022). The same paper derives asymmetric susceptibilities and transmission functions $$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$6, yielding spin-current and spin-wave diode behavior.

A related but distinct chiral selection mechanism appears in "Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction" (Shi et al., 2023). There, the XXZ model admits two degenerate helix towers with pitches $$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$7 and $$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$8 in the absence of DMI. Under the resonant condition

$$x \to x' = x + \varepsilon c^\nu,\qquad \nu=1,\dots,n,$$9

the DMI preserves only the $w_\nu(x)$0 tower exactly, while the $w_\nu(x)$1 tower is shifted away from zero energy. In the Holstein–Primakoff mapping, the bosonic dispersion is

$w_\nu(x)$2

and at resonance $w_\nu(x)$3. The source concludes that DMI acts as a filter with high efficiency (Shi et al., 2023). This suggests a spectrally protected version of UDI: one chirality remains dynamically stationary, while the opposite chirality is destabilized.

6. Nonlinear transport, synchronization, and conceptual limits

Nonlinear wave transport supplies another family of examples. In the coupled nonlinear Schrödinger/Manakov system studied in "Unidirectional flow of composite bright-bright solitons through asymmetric double potential barriers and wells," asymmetric double barriers or wells produce direction-dependent transmission of two-component bright-bright solitons (Javed et al., 2021). For Rosen–Morse barriers with $w_\nu(x)$4, the source identifies a window $w_\nu(x)$5 with right-moving transmission and left-moving reflection. It also reports polarity reversal under attractive inter-component coupling $w_\nu(x)$6, and unidirectional segregation under weak repulsive coupling $w_\nu(x)$7, where one component is transmitted and the other reflected only for one incidence direction (Javed et al., 2021). Here UDI manifests as direction-dependent nonlinear scattering history.

Directed synchronization models make the same structure explicit at the network level. "Stability of anti-bunched buses and local unidirectional Kuramoto oscillators" studies the ring dynamics

$w_\nu(x)$8

with periodic indexing $w_\nu(x)$9 (Chew et al., 2019). Each oscillator is influenced only by its predecessor. For identical frequencies, the source states that a completely phase-locked solution with all neighboring phase differences less than $$\frac{dP(x)}{dt} = \frac{1}{\varepsilon}\sum_\nu \left[ w_\nu(x-\varepsilon c^\nu)\,P(x-\varepsilon c^\nu) - w_\nu(x)\,P(x)\right]. \tag{25}$$0 is asymptotically stable, and that stable anti-bunched states can exist if the number of oscillators is at least five (Chew et al., 2019). The same paper contrasts this with the bus-loop system, whose native average-velocity dependence on headway is monotonically decreasing and therefore bunching-prone; no-boarding and holding policies are then interpreted as mechanisms for reshaping the effective coupling into a more stabilizing, sine-like form.

A common misconception is that unidirectionality always requires an explicit asymmetry along the coordinate of motion. "Unidirectional Magnon-Driven Domain Wall Motion Due to the Interfacial Dzyaloshinskii-Moriya Interaction" states the opposite: the domain wall moves along the same direction regardless of magnon-flow direction, and this “counterintuitive behavior originates from a combined action of two intrinsic asymmetries in the other two directions” (Kim et al., 2018). The paper decomposes the velocity as

$$\frac{dP(x)}{dt} = \frac{1}{\varepsilon}\sum_\nu \left[ w_\nu(x-\varepsilon c^\nu)\,P(x-\varepsilon c^\nu) - w_\nu(x)\,P(x)\right]. \tag{25}$$1

with the odd-order contributions in $$\frac{dP(x)}{dt} = \frac{1}{\varepsilon}\sum_\nu \left[ w_\nu(x-\varepsilon c^\nu)\,P(x-\varepsilon c^\nu) - w_\nu(x)\,P(x)\right]. \tag{25}$$2 unidirectional. Its analytic expression separates a conventional bidirectional term from a DMI-induced unidirectional term,

$$\frac{dP(x)}{dt} = \frac{1}{\varepsilon}\sum_\nu \left[ w_\nu(x-\varepsilon c^\nu)\,P(x-\varepsilon c^\nu) - w_\nu(x)\,P(x)\right]. \tag{25}$$3

so the same-direction response arises from the dampinglike magnon-mediated DMI torque (Kim et al., 2018).

Taken together, these formulations show that UDI is not tied to any single ontology. It may describe a sequential optimization protocol, an irreversible state ordering, a direction-selective interference condition, a chiral magnetic coupling, or a predecessor-only network interaction. What unifies these cases is a privileged dynamical direction that survives formalization at the level of transition rules, response matrices, or reduced equations of motion. A plausible implication is that UDI is best understood as a structural asymmetry in dynamical dependence: not merely nonreciprocity in outcomes, but nonreciprocity in the rule by which states, modes, or modalities influence one another.