ReDirector: Controlled Redirection Systems

• ReDirector is a unified framework that employs domain-specific, parametric control signals for dynamic redirection across various computational domains.
• It integrates innovations such as shared 3D RoPE with camera-conditioned phase shifts for video retakes and degree-based redirection rules to generate scalable, clustered networks.
• Applications extend to ML-driven predictive rerouting in airspace, magnetic gradient–controlled quantum photonic routing, and redirected walking in VR, demonstrating enhanced controllability and performance.

ReDirector denotes a set of principled algorithms and systems for controlled redirection, retargeting, and rerouting across diverse computational domains, unified by the explicit use of parametric control signals to steer processes dynamically. Contemporary usage spans camera-conditioned video retake synthesis, network topology growth via probabilistic redirection, quantum photonic routing, predictive rerouting in airspace operations, and redirected walking in virtual reality. The defining feature of ReDirector frameworks is the integration of domain-specific control—such as rotary camera encoding, forecasted user trajectories, or redirection probabilities—directly into the generative, predictive, or routing mechanism, yielding improved controllability, efficiency, and often a quantifiable advance in metric consistency or cost.

1. Camera-Controlled Video Retakes: Rotary Camera Encoding

The "ReDirector" framework in camera-conditioned video generation implements a novel solution for synthesizing any-length video retakes under arbitrary user-specified camera trajectories. This is achieved by amending two core aspects:

1. Corrected Use of Shared 3D Rotary Positional Encoding (RoPE): Prior models' misapplication of RoPE (using partial or absolute encodings) limited generalization and forced fixed-length constraints. ReDirector applies the same 3D RoPE rotation matrix to both source and target tokens. Given the $f \times h \times w$ tokens, the shared phase ensures that spatial-temporal alignment is length-agnostic, preserving the relative position necessary for robust, scalable retakes.

2. Rotary Camera Encoding (RoCE):

ReDirector injects a camera-conditioned phase shift into the self-attention mechanism. Let $\mathbf{c} \in \mathbb{R}^{2N \times d}$ denote Plücker-ray camera extrinsics. Per-token phase shifts $\Delta^q, \Delta^k, \Delta^v$ are computed by MLPs, producing unitary matrices $\exp(i \Delta)$ that modulate the queries, keys, and values in attention:

$$\bar{\mathbf{q}}' = \bar{\mathbf{q}} \circ \mathbf{R} \circ \exp(i\Delta^q),$$

with analogous forms for keys and values. The attention kernel thereby encodes relative camera differences directly in its phase, boosting correspondence between tokens sharing spatial-temporal and geometric relationships, and enhancing generalization to new camera paths and video lengths (Park et al., 25 Nov 2025).

Extensive evaluation demonstrates best-in-class geometric consistency (Dyn-MEt3R↑0.8477, MEt3R↓0.3073), translation/rotation error ($0.0165$m, $1.666^\circ$), and superior robustness to video length and camera-pose distribution. Ablations confirm the necessity of shared RoPE and RoCE, with accuracy degrading severely under naïve additive or fixed-index embedding schemes.

2. Enhanced Redirection in Network Growth Algorithms

The ReDirector principle manifests in network science via enhanced redirection rules in generative models of complex networks. Here, each new node selects an attachment point either directly or, with redirection probability $r(a, b) = 1 - b^{-\lambda},\, \lambda>0$, to the parent of the target node, biasing attachment toward higher-degree ("hub") nodes:

• Master Equation: The average degree distribution $N_k(N)$ obeys

$N_k(N) \sim N^{\nu-1}/k^\nu, \, 1 < \nu < 2.$

This scaling results in multiple "macrohubs" whose degrees $\propto N$, non-extensivity of $N_k$, and a lack of self-averaging, yielding highly variable macrostructure across runs.

• Clustering Extension: Allowing double attachment leads to strong clustering, with average local clustering coefficient $\langle C\rangle = 4\ln 2 - 2 \approx 0.77258$ (Gabel et al., 2013).

This model provides a purely local, tunable mechanism for constructing scale-free, highly clustered, and non-self-averaging networks, with implications for understanding real-world systems with dominant hubs and persistent sample-to-sample fluctuations.

3. Predictive Rerouting in Airspace Systems

In operational logistics, ReDirector designates machine learning-based microservices for large-scale prediction of reroute advisories, primarily in air traffic management:

• System Architecture: Containerized microservices ingest streaming FAA and NCEP data, partition airspace into ARTCC polygons and/or coarse grid cells, and maintain sliding-window feature aggregations per spatial unit.
• Learning and Inference: Feature extractor services emit time-bucketed, sliding statistics, enabling training of ML algorithms (RF, ET, GBM, MLP, SVM) after class-imbalance correction (SMOTE+Tomek). Models are validated via cross-validation and custom Reroute Detection Score (RDS), with overall mean accuracy exceeding 90% in experiments.
• Operational Integration: The system supports scalable, cloud-native deployment, with full API surface for retraining, prediction, and model registry updates. The modular infrastructure allows dynamic adaptation to concept drift, inclusion of new input features, and fine-resolution spatial modeling (Oliveira et al., 2023).

A plausible implication is that feature engineering based on temporal aggregations and spatial tiling is essential for high performance in reroute prediction, and ReDirector-style architecture is adaptable to other streaming, spatiotemporal forecasting domains.

4. Quantum Photonic Routing by Wavevector Control

In quantum information and nanophotonics, ReDirector refers to the deterministic and fast routing of photonic qubits by direct manipulation of quantum memories:

• Mechanism: A weak quantum signal is stored in an atomic ensemble as a spin-wave coherence with wavevector $\boldsymbol{\kappa}$. The application of a magnetic field gradient shifts $$\boldsymbol{\kappa} \rightarrow \boldsymbol{\kappa}' = \boldsymbol{\kappa} + \Delta \boldsymbol{k}$$, steering the subsequent collective reemission (on retrieval) into any desired direction, with the angle $\Delta \theta \simeq |\Delta k_\perp|/|k_c|$.
• Performance: Simulated total efficiencies remain $\gtrsim80\%$ for deflection angles up to 180°, with switching times from a few to $\sim100\ \mu$s, and full in-plane angular control in solid-state systems.
• Physical Interpretation: The entire process is all-electric, uses no moving optics, and leverages the phase-encoded geometry of the spin-wave for routing (Korzeczek et al., 2020).

This suggests the ReDirector protocol delivers high-speed, loss-minimized single-photon routing scalable for future quantum networks.

5. Predictive Redirection in Virtual and Physical Navigation

ReDirector concepts underpin redirected walking (RDW) frameworks where future user state forecasting enables safer and more efficient navigation in limited or complex physical environments:

• F-RDW Mechanism: An LSTM module predicts future user positions based on real-time inputs (gaze, head orientation, velocity). The predicted state is then integrated into controllers such as MPCRed, S2C, TAPF, or ARC, typically by blending present and predicted control vectors or cost weights. For example:

$r = (1-\mu)\,d_c + \mu\,d_f,\quad \mu=0.5,$

where $d_c$ and $d_f$ are current and forecasted center-vectors.

• Performance: Simulation in small or obstacle-dense arenas reveals consistent reductions in resets ($p<0.03$ for all methods in dense environments), with up to 40% fewer resets and greater traversed distance per reset. User studies corroborate these findings, with subjective presence, sickness, and comfort metrics unchanged (Jeon et al., 2023).
• Generalizability: F-RDW functions as a wrapper, requiring no modification of controller internals and incurring negligible computational cost.

A plausible implication is that ReDirector-style predictive redirection could generalize further to dynamic environments, non-rectangular layouts, or multi-user collision avoidance, provided the forecasting module adapts to broader sensory signals and temporally varying scene structure.

6. Comparative Table: Main Features Across ReDirector Systems

Domain	Control Signal/Mechanism	Principal Benefit
Video retake	Shared 3D RoPE + RoCE phase shift	Variable length, geometric control
Network growth	Degree-dependent redirection probability	Macrohubs, clustering, heavy-tails
Airspace rerouting	Sliding-window aggregation + ML	High-accuracy, adaptive prediction
Quantum routing	Magnetic gradient–induced $\Delta k$	Electronic, fast, loss-minimized
Physical navigation	Forecasted user state + gain fusion	Fewer resets, efficient locomotion

Each ReDirector instance is domain-optimized, but all leverage local or global control signals to modulate redirection in space, time, or information flow.

7. Significance, Limitations, and Outlook

ReDirector methods exemplify the convergence of local encoding of control cues—spatiotemporal, probabilistic, physical, or predictive—inside high-capacity generative or routing systems. They have redefined state-of-the-art in controlled video synthesis (Park et al., 25 Nov 2025), scale-free network design (Gabel et al., 2013), human-in-the-loop VR locomotion (Jeon et al., 2023), and systematic routing in both quantum and operational infrastructures (Korzeczek et al., 2020, Oliveira et al., 2023). While limitations persist—such as generalization with rapidly moving occluding objects in video retakes, incomplete support for dynamic or non-uniform spatial environments in redirected walking, or lack of self-averaging in network macrostructure—ReDirector paradigms are driving advances in efficient, controllable, and scalable redirection across computational science. Further generalization may require hybridization with explicit world models, dynamic parameter adaptation, or integration of multi-modal control signals for robust operation under previously unseen conditions.