Explainable Runtime Dependency Tracking for AI-RAN Conflict Monitoring

# Explainable Runtime Dependency Tracking for AI-RAN Conflict Monitoring
Source: [https://arxiv.org/html/2606.06663](https://arxiv.org/html/2606.06663)
###### Abstract

Future AI\-integrated Radio Access Networks \(AI\-RAN\) will combine open programmability with learning\-enabled xApps, rApps, and control functions that act on shared parameters and key performance indicators \(KPIs\)\. For conflict monitoring, it is not enough to know which applications are deployed; the system must also know whether the parameter–KPI dependencies assumed by runtime diagnosis remain valid under the current operating regime\. This paper studies a lightweight monitoring primitive for that purpose: tracking an interpretable dependency representation from streaming telemetry events\.

We represent active dependencies by a Boolean matrix and use Boolean matrix multiplication to check whether recent parameter\-activity and KPI\-response events are consistent with the current estimate\. We propose a sliding\-window inference procedure that reuses the estimate when it remains consistent and recomputes it when recent observations indicate structural change\. The tracker is intended as an explainable signal for conflict diagnosis and slow\-loop model refresh, not as an autonomous mitigation mechanism\. Experiments on controlled Boolean event streams show efficient and accurate tracking under dependency changes and Boolean observation noise\.

## IIntroduction

Radio access networks are moving toward open, programmable, and increasingly AI\-integrated architectures\. This transition is a clear priority for both commercial and defense communities\. Open Radio Access Network \(O\-RAN\) exposes control interfaces to enable independently developed third\-party applications, termed xApps and rApps\. These applications optimize mobility, slicing, load balancing, energy consumption, and resource allocation\[[1](https://arxiv.org/html/2606.06663#bib.bib1),[2](https://arxiv.org/html/2606.06663#bib.bib2)\]\. The OUSD\(R&E\) FutureG Office has identified programmable, open\-interface RANs as foundational infrastructure for future defense communications\. This office actively funds open\-source RAN stacks, security\-focused xApp and rApp development, and resilient tactical deployments under its Spectrum Forward initiative\[[3](https://arxiv.org/html/2606.06663#bib.bib3),[4](https://arxiv.org/html/2606.06663#bib.bib4)\]\. The FutureG\-backed OCUDU initiative is producing an open, carrier\-grade, AI\-native RAN software stack for both commercial and mission\-critical defense operations\[[5](https://arxiv.org/html/2606.06663#bib.bib5),[6](https://arxiv.org/html/2606.06663#bib.bib6)\]\. AI\-RAN further develops learning, prediction, and adaptive decision\-making as core parts of the control loop\[[7](https://arxiv.org/html/2606.06663#bib.bib7),[8](https://arxiv.org/html/2606.06663#bib.bib8)\]\. Future networks trend toward multiple adaptive control functions that change with traffic, context, policy, and the operating environment\.

This flexibility creates a runtime reasoning problem that is especially acute in military scenarios\. Control functions operating in the same RAN may interact through shared parameters, shared KPIs, or feedback through observed network state\. These interactions allow conflicts that erode the ability to achieve intended objectives\. In a commercial setting, conflicts may degrade throughput or energy efficiency\. In a tactical setting, undetected control\-function conflicts can degrade mission\-critical links, mask adversarial interference signatures, or prevent adaptive responses from taking effect\. Prior FutureG SBIR solicitations have specifically identified xApps and rApps as a priority for achieving the agility and resilience necessary to support Warfighter communications\[[3](https://arxiv.org/html/2606.06663#bib.bib3)\]\.

Some conflicts may be visible from application subscriptions or control objectives\. Others arise only through the propagation of parameter changes to KPIs and then subsequent control decisions\. These indirect interactions are difficult to identify in advance because the relevant parameter–KPI relationships may be hidden, nonlinear, or operating\-regime dependent\. In a tactical context, regime changes may be abrupt; node loss, jamming onset, or dynamic insertion of new control functions can shift the parameter–KPI relationships within seconds\. As highlighted in FutureG FRONTIER workshop, adversarial actions further complicate tactical environments with dependency shifts that conventional monitoring cannot anticipate\[[9](https://arxiv.org/html/2606.06663#bib.bib9)\]\. Runtime tracking must therefore ask whether dependencies used by monitoring logic are consistent with recent telemetry and, if not, flag a possible regime shift or slow\-loop refresh\.

Much of the existing work represents O\-RAN relationships using graph\-based models, such as conflict graphs, GNNs, graph convolutional networks, and hypergraphs\[[10](https://arxiv.org/html/2606.06663#bib.bib10),[11](https://arxiv.org/html/2606.06663#bib.bib11),[12](https://arxiv.org/html/2606.06663#bib.bib12),[13](https://arxiv.org/html/2606.06663#bib.bib13),[14](https://arxiv.org/html/2606.06663#bib.bib14),[15](https://arxiv.org/html/2606.06663#bib.bib15)\]\. These graph representations are useful for visualization, link prediction, conflict labeling, and structural learning\. However, these methods are designed for periodic or offline analysis\. PACIFISTA reports conflict\-evalution times on the order 20 seconds\[[11](https://arxiv.org/html/2606.06663#bib.bib11)\]\. GNN\-based reconstruction requires training over hundreds of epochs\[[10](https://arxiv.org/html/2606.06663#bib.bib10)\]\. These timescales are poorly matched to tracking parameter–KPI shifts in dynamic tactical contexts\.

In this paper, we use a Boolean representation of parameter–KPI relationships to enable dynamic runtime monitoring within a fast/slow\-loop workflow\. A slowerlearning looplearns a bolleanization model for detecting significant parameter\-activit and KPI response events\[[16](https://arxiv.org/html/2606.06663#bib.bib16)\]\. Theruntime loopapplies this model to streaming telemetry to maintain and update parameter–KPI dependencies\. This separation keeps the heavier continuous\-data learning problem in the slow loop and leaves the fast loop with a compact algebraic tracking problem\.

The main contributions of this paper are as follows:

1. 1\.We frame runtime parameter–KPI dependency tracking as an AI\-RAN conflict\-monitoring primitive for detecting stale dependency assumptions in evolving control environments, including contested tactical settings where shifts may be abrupt and adversarially induced\.
2. 2\.We introduce a Boolean\-algebraic dependency representation in which checking whether recent observations match the current dependency model reduces to a Boolean matrix equation\.
3. 3\.We define a fast/slow\-loop workflow in which a slower learning stage provides Boolean event indicators, while the runtime loop maintains an interpretable dependency matrix online\.
4. 4\.We develop and evaluate a sliding\-window reuse\-and\-recompute inference procedure, quantifying tracking accuracy, false alarms, detection delay, and per\-event processing cost on controlled Boolean event streams\.

## IIMethods

This section defines the runtime telemetry abstraction, Boolean dependency model, sliding\-window inference rule, controlled Boolean event generator, and tracking metrics\.

### II\-ARuntime Telemetry and Boolean Event Model

Letp​\(c\)∈ℝnPp\(c\)\\in\\mathbb\{R\}^\{n\_\{P\}\},k​\(c\)∈ℝnKk\(c\)\\in\\mathbb\{R\}^\{n\_\{K\}\}denote real\-valued control\-parameter and KPI telemetry at observation indexcc\. HerenPn\_\{P\}is the number of control parameters andnKn\_\{K\}is the number of KPIs\. At runtime, each observation is converted into Boolean event indicators using a booleanization model learned by a slower stage\[[16](https://arxiv.org/html/2606.06663#bib.bib16)\]:

𝒬θ:\(p​\(c\),k​\(c\),ℋc\)↦\(bP​\(c\),bK​\(c\)\),\\mathcal\{Q\}\_\{\\theta\}:\(p\(c\),k\(c\),\\mathcal\{H\}\_\{c\}\)\\mapsto\\left\(b\_\{P\}\(c\),b\_\{K\}\(c\)\\right\),whereℋc\\mathcal\{H\}\_\{c\}denotes any recent history or baseline information used by the converter,bP​\(c\)∈\{0,1\}nPb\_\{P\}\(c\)\\in\\\{0,1\\\}^\{n\_\{P\}\}, andbK​\(c\)∈\{0,1\}nKb\_\{K\}\(c\)\\in\\\{0,1\\\}^\{n\_\{K\}\}\. The entrybP​\[i\]​\(c\)=1b\_\{P\}\[i\]\(c\)=1indicates a significant activity event in parameterPiP\_\{i\};bK​\[j\]​\(c\)=1b\_\{K\}\[j\]\(c\)=1indicates a significant response in KPIKjK\_\{j\}\. This paper focuses on the dependency\-tracking step after this conversion; learning the booleanization model is addressed as part of the slow loop\[[16](https://arxiv.org/html/2606.06663#bib.bib16)\]\.

### II\-BBoolean Dependency Representation

The active parameter–KPI dependency structure at observationccis represented by a latent Boolean matrixL∗​\(c\)∈\{0,1\}nK×nPL^\{\\\!\*\}\(c\)\\in\\\{0,1\\\}^\{n\_\{K\}\\times n\_\{P\}\}, whereL∗​\(c\)​\[j,i\]=1L^\{\\\!\*\}\(c\)\[j,i\]=1means that activity in parameterPiP\_\{i\}can influence KPIKjK\_\{j\}in the current operating regime\. In the ideal noiseless case:

bK​\(c\)=L∗​\(c\)⊙𝖡bP​\(c\),b\_\{K\}\(c\)=L^\{\\\!\*\}\(c\)\\odot\_\{\\mathsf\{B\}\}b\_\{P\}\(c\),\(1\)where⊙𝖡\\odot\_\{\\mathsf\{B\}\}denotes Boolean matrix multiplication:\(L∗​\(c\)⊙𝖡bP​\(c\)\)j=⋁i=1nP\(L∗​\(c\)​\[j,i\]∧bP​\[i\]​\(c\)\)\\left\(L^\{\\\!\*\}\(c\)\\odot\_\{\\mathsf\{B\}\}b\_\{P\}\(c\)\\right\)\_\{j\}=\\bigvee\_\{i=1\}^\{n\_\{P\}\}\\left\(L^\{\\\!\*\}\(c\)\[j,i\]\\wedge b\_\{P\}\[i\]\(c\)\\right\)\. Given a candidate matrixLL, the corresponding predicted KPI\-event vector isb^K​\(c\)=L⊙𝖡bP​\(c\)\\widehat\{b\}\_\{K\}\(c\)=L\\odot\_\{\\mathsf\{B\}\}b\_\{P\}\(c\)\. A single observation is explained byLLwhen

b^K​\(c\)=bK​\(c\)\.\\widehat\{b\}\_\{K\}\(c\)=b\_\{K\}\(c\)\.\(2\)Otherwise, the observation produces a mismatch, see[Figure1](https://arxiv.org/html/2606.06663#S2.F1)\. The runtime objective is to maintain an estimateL^​\(c\)∈\{0,1\}nK×nP\\widehat\{L\}\(c\)\\in\\\{0,1\\\}^\{n\_\{K\}\\times n\_\{P\}\}that tracksL∗​\(c\)L^\{\\\!\*\}\(c\)without treating every single mismatch as a structural change\.

\(a\) MatrixLLP1P\_\{1\}P2P\_\{2\}P3P\_\{3\}K1K\_\{1\}K2K\_\{2\}1101101111\(b\) Boolean checkp​\(t\)p\(t\)k^​\(t\)\\widehat\{k\}\(t\)k​\(t\)k\(t\)P1P\_\{1\}P2P\_\{2\}P3P\_\{3\}11011Observed→\\rightarrowK1K\_\{1\}K2K\_\{2\}1111Predicted≠\\neqK1K\_\{1\}K2K\_\{2\}110Observedk^​\(t\)≠k​\(t\)\\widehat\{k\}\(t\)\\neq k\(t\)\(c\) Graph viewP1P\_\{1\}P2P\_\{2\}P3P\_\{3\}K1K\_\{1\}K2K\_\{2\}\!ParametersKPIsPi=1P\_\{i\}=1Pi=0P\_\{i\}=0Ki=1K\_\{i\}=1Ki=0K\_\{i\}=0Mismatch

Figure 1:Single\-step Boolean dependency consistency check\. \(a\) A binary matrixLLencodes parameter–KPI dependencies\. \(b\) The Boolean predictionk^​\(t\)=L⊙𝖡p​\(t\)\\widehat\{k\}\(t\)=L\\odot\_\{\\mathsf\{B\}\}p\(t\)is compared with the observed KPI\-event vectork​\(t\)k\(t\)\. \(c\) The same mismatch is shown on the corresponding dependency graph\. Persistent mismatches over a window may indicate a change inLL\.For a sliding window of lengthWW, defineBP\(c,W\)=\[bP​\(c−W\+1\),…,bP​\(c\)\]∈\{0,1\}nP×WB\_\{P\}^\{\(c,W\)\}=\\left\[b\_\{P\}\(c\-W\+1\),\\ldots,b\_\{P\}\(c\)\\right\]\\in\\\{0,1\\\}^\{n\_\{P\}\\times W\}andBK\(c,W\)=\[bK​\(c−W\+1\),…,bK​\(c\)\]∈\{0,1\}nK×WB\_\{K\}^\{\(c,W\)\}=\\left\[b\_\{K\}\(c\-W\+1\),\\ldots,b\_\{K\}\(c\)\\right\]\\in\\\{0,1\\\}^\{n\_\{K\}\\times W\}as the stacked Boolean parameter and KPI \(respectively\) event matrices over the window\. A candidate dependency matrixLLis consistent with the window if

BK\(c,W\)=L⊙𝖡BP\(c,W\)\.B\_\{K\}^\{\(c,W\)\}=L\\odot\_\{\\mathsf\{B\}\}B\_\{P\}^\{\(c,W\)\}\.\(3\)

### II\-CRow\-Wise Boolean Inference

The window\-level consistency condition in[equation3](https://arxiv.org/html/2606.06663#S2.E3)decomposes by KPI row\. For each rowℓj∈\{0,1\}nP\\ell\_\{j\}\\in\\\{0,1\\\}^\{n\_\{P\}\}, the row\-inference problem is:

ℓ^j=argminℓ∈\{0,1\}nP‖BK,j\(c,W\)−ℓ⊙𝖡BP\(c,W\)‖0,\\widehat\{\\ell\}\_\{j\}=\\operatorname\*\{argmin\}\_\{\\ell\\in\\\{0,1\\\}^\{n\_\{P\}\}\}\\left\\\|B\_\{K,j\}^\{\(c,W\)\}\-\\ell\\odot\_\{\\mathsf\{B\}\}B\_\{P\}^\{\(c,W\)\}\\right\\\|\_\{0\},\(4\)where∥⋅∥0\\\|\\cdot\\\|\_\{0\}denotes the number of nonzero entries\. Ties are broken by minimum Hamming distance from the current row estimate\. Each row ofL^\\widehat\{L\}can be inferred independently and in parallel, so wall\-clock time does not grow withnKn\_\{K\}\. For the small matrices studied here, we use exhaustive search over2nP2^\{n\_\{P\}\}candidates; larger deployments can apply standard 0–1 optimization methods\[[17](https://arxiv.org/html/2606.06663#bib.bib17)\]\.

### II\-DSliding\-Window Runtime Inference

[algorithm1](https://arxiv.org/html/2606.06663#alg1)maintains a sliding window of theWWmost recent Boolean event observations\. At each new observation indexcc, the loop receives real\-valued telemetry, converts it into Boolean event vectors, updates the window, and tests whether the current dependency estimate remains consistent with the recent window\. If the estimate is consistent, the current matrix is reused\. If not, the matrix is recomputed from the current window using the row\-wise inference rule in[equation4](https://arxiv.org/html/2606.06663#S2.E4)\.

Input:Telemetry streams,

𝒬θ\\mathcal\{Q\}\_\{\\theta\}, window size

WW
Initialize window buffers and current estimate

L^c​u​r\\widehat\{L\}\_\{cur\}
for*c=1,…,Tc=1,\\ldots,T*do

\(bP​\(c\),bK​\(c\)\)←𝒬θ​\(p​\(c\),k​\(c\),ℋc\)\(b\_\{P\}\(c\),b\_\{K\}\(c\)\)\\leftarrow\\mathcal\{Q\}\_\{\\theta\}\(p\(c\),k\(c\),\\mathcal\{H\}\_\{c\}\)
Update

BP\(c,W\)B\_\{P\}^\{\(c,W\)\}and

BK\(c,W\)B\_\{K\}^\{\(c,W\)\}
if*window is fulland\(L^c​u​r\\widehat\{L\}\_\{cur\}is emptyor[equation2](https://arxiv.org/html/2606.06663#S2.E2)fails\)*then

Recompute

L^c​u​r\\widehat\{L\}\_\{cur\}using[equation4](https://arxiv.org/html/2606.06663#S2.E4)

Set

L^​\(c\)←L^c​u​r\\widehat\{L\}\(c\)\\leftarrow\\widehat\{L\}\_\{cur\}

Algorithm 1Sliding\-window dependency trackingThis reuse\-and\-recompute rule is designed to avoid unnecessary inference\. Recomputation is triggered only when recent observations are inconsistent with the current matrix\. The window sizeWWcontrols the main stability–adaptability tradeoff\. A smallWWcan react quickly to structural changes but may be underdetermined and sensitive to isolated booleanization errors\. A largeWWprovides more evidence for each inferred dependency matrix but can mix observations from multiple dependency regimes after a change\.

### II\-EDependency\-Tracking Data Generator

The experimental evaluation isolates the runtime tracking layer\. Therefore, we directly generate controlled Boolean event streams with known ground\-truth dependency changes\. This allows us to study the behavior of the sliding\-window tracker independently of errors introduced by the continuous\-to\-Boolean conversion stage\.

An initial sparse matrixL∗​\(1\)∈\{0,1\}nK×nPL^\{\\\!\*\}\(1\)\\in\\\{0,1\\\}^\{n\_\{K\}\\times n\_\{P\}\}is perturbed everyDDobservations to produce a piecewise\-constant ground\-truth sequenceL∗​\(1\),…,L∗​\(T\)L^\{\\\!\*\}\(1\),\\ldots,L^\{\\\!\*\}\(T\)\. Larger values ofDDcorrespond to slower structural change, while smaller values ofDDcreate a more dynamic tracking problem\. Parameter\-event vectorsbP​\(c\)b\_\{P\}\(c\)are sampled at each step\. The corresponding noiseless KPI\-response vector isbK​\(c\)=L∗​\(c\)⊙𝖡bP​\(c\)b\_\{K\}\(c\)=L^\{\\\!\*\}\(c\)\\odot\_\{\\mathsf\{B\}\}b\_\{P\}\(c\)\. Boolean noise is added by independently flippingbK​\(c\)b\_\{K\}\(c\)entries with probabilityϵ\\epsilon\.

### II\-FEvaluation Metrics

We evaluate the inferred sequenceL^​\(c\)\\widehat\{L\}\(c\)against the ground\-truth sequenceL∗​\(c\)L^\{\\\!\*\}\(c\)using both edge\-level and change\-detection metrics\. For edge\-level tracking, each entry of the dependency matrix is treated as a binary edge decision between one parameter and one KPI\. We flatten these matrix entries across all evaluated observations and compute standard binary precision, recall, and F1 score\[[18](https://arxiv.org/html/2606.06663#bib.bib18)\]\.

We also report matrix\-level structural error using the Hamming distancedH​\(L^​\(c\),L∗​\(c\)\)=∑j=1nK∑i=1nP𝟏​\{L^​\(c\)​\[j,i\]≠L∗​\(c\)​\[j,i\]\}d\_\{H\}\(\\widehat\{L\}\(c\),L^\{\\\!\*\}\(c\)\)=\\sum\_\{j=1\}^\{n\_\{K\}\}\\sum\_\{i=1\}^\{n\_\{P\}\}\\mathbf\{1\}\\\{\\widehat\{L\}\(c\)\[j,i\]\\neq L^\{\\\!\*\}\(c\)\[j,i\]\\\}\.

For change detection, a true change occurs whenL∗​\(c\)≠L∗​\(c−1\)L^\{\\\!\*\}\(c\)\\neq L^\{\\\!\*\}\(c\-1\), and a detected change occurs whenL^​\(c\)≠L^​\(c−1\)\\widehat\{L\}\(c\)\\neq\\widehat\{L\}\(c\-1\)\. Letτ\\taudenote the change\-matching tolerance in observations\. A detected change atc^\\widehat\{c\}is matched to a true change atc0c\_\{0\}only if

c0≤c^≤c0\+τ\.c\_\{0\}\\leq\\widehat\{c\}\\leq c\_\{0\}\+\\tau\.The first such detected change is counted as the detection for that true change, with delayc^−c0\\widehat\{c\}\-c\_\{0\}\. Additional inferred changes during the same post\-change adaptation period are counted separately as adaptation updates rather than as additional successes\. Detected changes outside any allowed post\-change region are counted as false alarms\. We report change recall, change precision, change F1, false\-alarm fraction, and mean/median detection delay in observations\. This avoids over\-crediting unstable inference that changes frequently: frequent updates may increase raw recall, but they also increase false alarms and adaptation updates\.

## IIIExperimental Results and Discussion

This section evaluates the runtime dependency\-tracking loop under controlled dynamic conditions\. The experiments use Boolean event streams with known dependency matrices and planted structural changes, so the inferred dependency sequence can be compared against a known reference\. All reported plots use the representative moderate\-noise settingϵ=0\.02\\epsilon=0\.02, so the discussion focuses on the interaction between structural\-change rate and sliding\-window tracking\. A broader sweep over event\-noise levels is left for future evaluation\.

### III\-AExperimental Setup

Unless otherwise stated, the experiments usenP=5n\_\{P\}=5parameters,nK=4n\_\{K\}=4KPIs, and sparse dependency matrices, generated across multiple random seeds, with at most three active parameter parents per KPI row\. We vary the dependency\-change intervalD∈\{32,64,75,100,150,300\}D\\in\\\{32,64,75,100,150,300\\\}, and the sliding\-window sizeW∈\{4,8,16,32\}W\\in\\\{4,8,16,32\\\}\. Each configuration is repeated across multiple random seeds\. For each run, we generate a dynamic Boolean stream, infer the dependency sequence with Algorithm[1](https://arxiv.org/html/2606.06663#alg1), and compute the metrics described above\.

For the change\-detection metrics, we set the matching tolerance toτ=W\\tau=Wobservations after each true dependency change, and use the sameWW\-observation interval as the adaptation grace period for counting repeated post\-change updates\.

Two diagnostic considerations are especially important when interpreting the results\. First, the sliding\-window sizeWWshould be interpreted relative to the dependency\-change intervalDD\. Larger windows provide more evidence for each inferred dependency matrix, but they are also more likely to include observations from before and after a dependency change, weakening the approximate stationarity assumption inside the window\. Second, the false\-alarm and adaptation\-update metrics are reported together with change recall to distinguish genuine change detection from unstable repeated updating\.

### III\-BRuntime Cost of Reuse and Recomputation

Fig\.[2](https://arxiv.org/html/2606.06663#S3.F2)reports the measured processing cost of the two runtime paths in Algorithm[1](https://arxiv.org/html/2606.06663#alg1)\. The timing results show that reuse events are essentially independent of the sliding\-window sizeWW\. This is expected because the reuse path only evaluates the current matrix on the newest parameter\-event column\. Across all tested window sizes, the measured reuse cost remains well below0\.010\.01ms per event\. By contrast, recomputation is substantially more expensive and increases withWW, since the update path solves the row\-wise inference problem over the full window\. Thus, the measured runtime behavior supports the intended reuse\-and\-recompute design: most observations can be handled by a very fast single\-column consistency check, while the more expensive window\-level inference step is reserved for observations that are inconsistent with the current dependency estimate\.

![Refer to caption](https://arxiv.org/html/2606.06663v1/x1.png)Figure 2:Measured per\-event processing cost for the no\-update/reuse and update/recompute paths atϵ=0\.02\\epsilon=0\.02\. Error bars show bootstrapped 10th–90th percentile ranges\.Existing O\-RAN conflict\-management methods address broader graph\-reconstruction or conflict\-evaluation tasks that are heavier than the per\-event consistency check studied here\. For example, PACIFISTA profiles applications in sandbox environments and reports that its prototype conflict\-evaluation procedure takes approximately 20 s\[[11](https://arxiv.org/html/2606.06663#bib.bib11)\]\. GNN\-based conflict\-graph reconstruction methods require training over hundreds of epochs\[[10](https://arxiv.org/html/2606.06663#bib.bib10)\]to recover hidden xApp–parameter–KPI relationships\. These methods are complementary rather than direct baselines: they reconstruct or evaluate conflicts, whereas the proposed Boolean tracker assumes Boolean events are available and tests whether the current dependency support remains consistent with each new observation\. Thus, the timing value of the proposed method is as an always\-on guard that can trigger slower graph\-reconstruction or conflict\-evaluation procedures only when recent telemetry suggests a stale dependency model\.

### III\-CTracking Accuracy

Fig\.[3](https://arxiv.org/html/2606.06663#S3.F3)reports both edge\-level tracking accuracy and matrix\-level structural error\. Panel \(a\) shows edge\-level F1, where each parameter–KPI matrix entry is treated as one binary dependency prediction\. Panel \(b\) shows mean Hamming distance, which measures how many entries of the inferred matrix are incorrect on average\.

Together, these metrics distinguish average edge recovery from the severity of matrix\-level errors\. A high edge\-level F1 indicates that most dependencies are recovered correctly, while a low Hamming distance indicates that the inferred matrix is usually only a few entries away from the true matrix\. The results show the same stability–adaptability trend observed throughout the paper: moderate windows provide enough evidence for inference, while overly large windows can mix observations from multiple dependency regimes after a structural change\.

### III\-DChange Detection, False Alarms, and Delay

Fig\.[4](https://arxiv.org/html/2606.06663#S3.F4)summarizes the change\-detection behavior for the representative moderate\-noise conditionϵ=0\.02\\epsilon=0\.02\. Panel \(a\) reports change recall, panel \(b\) reports the false\-alarm fraction, and panel \(c\) reports mean detection delay\. These metrics must be interpreted jointly\. A method can obtain high change recall simply by changing its inferred matrix very often, but such behavior is not operationally useful if it also produces many false alarms\. The updated evaluation therefore matches at most one detected change to each true dependency change and counts extra updates during the adaptation region separately\.

In the representative condition shown, larger windows tend to reduce false alarms because the inferred matrix is based on more evidence\. However, larger windows also increase detection delay\. This is the central dynamicity result of the paper: window size controls a tradeoff between stable tracking and fast responsiveness\. Small windows react quickly but may update too often; large windows are more stable but react later and can mix observations from before and after a dependency change\.

![Refer to caption](https://arxiv.org/html/2606.06663v1/x2.png)\(a\)Edge\-level F1
![Refer to caption](https://arxiv.org/html/2606.06663v1/x3.png)\(b\)Mean Hamming distance

Figure 3:Tracking accuracy and structural error versus sliding\-window size atϵ=0\.02\\epsilon=0\.02: \(a\) edge\-level F1 and \(b\) mean Hamming distance\.![Refer to caption](https://arxiv.org/html/2606.06663v1/x4.png)\(a\)Change recall,ϵ=0\.02\\epsilon=0\.02
![Refer to caption](https://arxiv.org/html/2606.06663v1/x5.png)\(b\)False\-alarm fraction,ϵ=0\.02\\epsilon=0\.02
![Refer to caption](https://arxiv.org/html/2606.06663v1/x6.png)\(c\)Mean detection delay,ϵ=0\.02\\epsilon=0\.02

Figure 4:Change\-detection tradeoff atϵ=0\.02\\epsilon=0\.02\. Larger windows generally reduce false alarms but increase detection delay\.Overall, these results show that the Boolean tracker is most useful when the dependency structure remains stable long enough for the window to collect informative observations\. LargerWWimproves stability and reduces false alarms, but increases detection delay and can mix dependency regimes\. In an AI\-RAN/O\-RAN setting, the tracker should therefore be interpreted as an explainable runtime monitor that flags possible dependency shifts or model\-refresh needs, rather than as an autonomous mitigation mechanism\.

### III\-ELimitations

The present study is intentionally scoped\. The experiments use synthetic Boolean streams with planted dependency changes\. The Boolean model captures only the support of parameter–KPI influence, not direction, magnitude, timing, causal strength, or multi\-parameter interaction effects\. Noise is modeled as independent Boolean flips in KPI events, and the experiments do not yet include a continuous telemetry source or a full RAN simulator\. The reported plots use a representative moderate Boolean KPI\-noise setting,ϵ=0\.02\\epsilon=0\.02\. A broader sweep over booleanization error rates is left for future work\. The row\-wise exhaustive inference procedure is appropriate for the small matrices studied here, but larger deployments will require constrained or approximate search\. A direct empirical comparison with graph\-reconstruction or full conflict\-evaluation frameworks is left for future work, since those methods solve broader tasks than the per\-event dependency\-consistency check isolated here\. These limitations do not invalidate the tracking formulation, but they define the next steps required before the approach can be evaluated as a practical AI\-RAN monitoring component\.

## IVConclusion

This paper studied interpretable runtime dependency tracking as one step toward explainable monitoring for AI\-RAN control loops\. Assuming that continuous telemetry has already been converted into Boolean parameter\-activity and KPI\-response events, we formulated runtime dependency maintenance as a streaming tracking problem over a time\-varying Boolean parameter–KPI matrix\. We proposed a lightweight reuse\-and\-recompute sliding\-window inference rule and evaluated tracking quality under controlled dependency changes\.

The results emphasize the stability–adaptability tradeoff\. Longer dependency\-change intervals make tracking easier because the active structure remains stable for more observations\. Larger windows provide more stable inference and reduce false alarms, but they also increase detection delay and can mix multiple dependency regimes\. These trends indicate that runtime Boolean dependency tracking is most useful when window size is chosen relative to the expected rate of structural change\.

The tracker is therefore best viewed as a compact runtime monitoring component rather than a complete AI\-RAN conflict\-mitigation system\. Future work will connect it to continuous\-data learning, evaluate richer AI\-RAN\-inspired traces or simulators, compare against streaming baselines, and study how detected dependency shifts support conflict diagnosis, mitigation, and policy adaptation\.

## References

- \[1\]A\. S\. Abdalla, P\. S\. Upadhyaya, V\. K\. Shah, and V\. Marojevic, “Toward next generation open radio access networks: What O\-RAN can and cannot do\!”*IEEE Network*, vol\. 36, no\. 6, pp\. 206–213, 2022\.
- \[2\]M\. Polese, L\. Bonati, S\. D’Oro, S\. Basagni, and T\. Melodia, “ColO\-RAN: Developing machine learning\-based xApps for open RAN closed\-loop control on programmable experimental platforms,”*IEEE Transactions on Mobile Computing*, vol\. 22, no\. 10, pp\. 5787–5800, 2023\.
- \[3\]FutureG & 5G Office, OUSD\(R&E\), “Security\-focused xApp and rApp solutions for open RAN,” Office of the Under Secretary of Defense for Research and Engineering, Tech\. Rep\. SBIR 24\.4, Topic OSD\-244\-R2, 2024, available: https://media\.defense\.gov/2024/May/16/2003467177/\-1/\-1/0/OSD\_FUTUREG\_SBIR\_244\_R2\.PDF\.
- \[4\]B\. Pimentel and M\. Weiss, “DOD leaders highlight key technologies shaping the future of network operations,” GovCon Wire, Feb\. 2024, available: https://www\.govconwire\.com/2024/02/dod\-leaders\-highlight\-key\-technologies\-shaping\-the\-future\-of\-network\-operations/\.
- \[5\]Linux Foundation, “Linux foundation launches OCUDU ecosystem foundation to accelerate open source AI\-RAN innovation,” ExecutiveGov, Mar\. 2026, available: https://www\.executivegov\.com/articles/ocudu\-ecosystem\-foundation\-launch\-ai\-6g\-ran\.
- \[6\]DeepSig and Software Radio Systems, “DeepSig and SRS chosen by DOD FutureG office to lead OCUDU: The open\-source 5G/6G RAN initiative,” Business Wire, Sep\. 2025, available: https://www\.businesswire\.com/news/home/20250930836266/en/DeepSig\-and\-SRS\-Chosen\-by\-DOD\-FutureG\-Office\-to\-Lead\-OCUDU\-The\-Open\-Source\-5G6G\-RAN\-Initiative\.
- \[7\]S\. Montebugnoli, A\. Sabbioni, F\. Callegati, L\. Foschini, and P\. Bellavista, “CLO5ER: A composable lightweight observability for 5G RAN environment inside near\-RT RIC,” in*ICC 2025 – IEEE International Conference on Communications*\. IEEE, 2025, pp\. 1900–1905\.
- \[8\]I\. Lindra, H\. Hendrawan, A\. Subekti, and E\. Mulyana, “Integration of artificial intelligence into radio access network \(AI\-RAN\): Architecture, classification, and development focus,” in*2025 11th International Conference on Wireless and Telematics \(ICWT\)*\. IEEE, 2025, pp\. 305–308\.
- \[9\]K\. Chowdury, S\. Shakkottai, and D\. Bharadia, “FRONTIER: FutureG\-Compliant Resilient Open Tactical & Emerging RANs,” IEEE, Tech\. Rep\., 2024, available: https://milcom2024\.ieee\-milcom\.org/program/frontier\-futureg\-compliant\-resilient\-open\-tactical\-emerging\-rans\.
- \[10\]A\. Zolghadr, J\. F\. Santos, L\. A\. DaSilva, and J\. Kibiłda, “Learning and reconstructing conflicts in O\-RAN: A graph neural network approach,” in*2025 IEEE Wireless Communications and Networking Conference \(WCNC\)*\. IEEE, 2025, pp\. 1–6\.
- \[11\]P\. Brach del Prever, S\. D’Oro, L\. Bonati, M\. Polese, M\. Tsampazi, H\. Lehmann, and T\. Melodia, “PACIFISTA: Conflict evaluation and management in open RAN,”*IEEE Transactions on Mobile Computing*, vol\. 24, no\. 10, pp\. 10 590–10 605, 2025\.
- \[12\]A\. E\. Giannopoulos, S\. T\. Spantideas, G\. Levis, A\. S\. Kalafatelis, and P\. Trakadas, “COMIX: Generalized conflict management in O\-RAN xApps–architecture, workflow, and a power control case,”*IEEE Access*, vol\. 13, pp\. 116 684–116 700, 2025\.
- \[13\]M\. Al Shami, J\. Yan, and E\. T\. Fapi, “O\-RAN xApps conflict prediction using graph convolutional networks,”*IEEE Transactions on Mobile Computing*, 2026\.
- \[14\]S\. Henna and U\. Rathnayake, “Hypergraph representation learning\-based xApp for traffic steering in 6G O\-RAN closed\-loop control,”*IEEE Transactions on Network and Service Management*, 2026\.
- \[15\]A\. G\. Bermúdez, M\. Farreras, M\. Groshev, J\. A\. Trujillo, I\. de la Bandera, and R\. Barco, “Graph neural networks for open radio access network mobility management: A link prediction approach,”*IEEE Vehicular Technology Magazine*, vol\. 20, no\. 4, pp\. 66–74, 2025\.
- \[16\]C\. Djidjev and N\. Kaminski, “Learning control\-to\-KPI dependencies in AI\-RAN with Boolean event detection,” 2026, arXiv preprint\. \[Online\]\. Available: https://arxiv\.org
- \[17\]G\. L\. Nemhauser and L\. A\. Wolsey,*Integer and Combinatorial Optimization*\. Wiley, 1988\.
- \[18\]D\. M\. W\. Powers, “Evaluation: From precision, recall and F\-measure to ROC, informedness, markedness and correlation,”*Journal of Machine Learning Technologies*, vol\. 2, no\. 1, pp\. 37–63, 2011\.