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A Peer-Relative Representation Learning Framework for Energy Inefficiency Identification in Mobile Network Sites

Eliud Nyakweba Koto, Jaco du Toit, Adham Stoltz, Johan du Preez

arXiv:2609.03809v1cs.LG

TL;DR

Mobile-site inefficiency is hard to identify without verified labels because historical energy data may already contain abnormal behaviour. The paper introduces an unsupervised energy-aware MDE that displaces high-consuming sites from structural peers, and reports improved detection and field-investigation prioritisation, with limitations from controlled injection, cross-sectional data, fixed hyperparameters, and weak peer comparability.

  • Problem

    Operational networks lack verified inefficiency labels, and historical consumption may embed persistent inefficiencies into site-specific baselines.

  • Method

    An energy-aware MDE embeds structurally comparable sites while using energy deviations to displace inconsistent sites and derive peer-relative anomaly scores.

  • Results

    The framework outperformed standard unsupervised detectors at every contamination rate, improved detectors in the learned embedding, and transferred rankings to lightweight classifiers through pseudo-labels.

  • Takeaways & Limitations

    The framework converts heterogeneous, unlabelled site data into a prioritisation signal for field investigations, with several high-ranking candidates confirmed as inefficient.

  • Takeaways & Limitations

    Evaluation relies on controlled injections and one observation per site, while uncommon configurations may have weakly comparable peers and less reliable scores.

Abstract

from arXiv · show

Energy consumption is one of the largest operational expenditure items for mobile network operators, yet site-level energy inefficiencies such as faulty cooling controllers, idle radio equipment, and parasitic auxiliary loads often remain undetected because no ground-truth inefficiency labels exist and historical measurements may already contain embedded inefficiencies. This study proposes an unsupervised peer-relative approach based on the premise that sites with similar structural and operational characteristics should exhibit comparable energy consumption. To capture these relationships, a novel energy-aware Minimum Distortion Embedding (MDE) formulation is introduced that extends the standard MDE objective with an energy-based repulsion mechanism. This encourages sites with anomalously high energy consumption relative to comparable peers to become displaced from their local neighbourhoods in the embedding space. The resulting low-dimensional representation simultaneously preserves structural similarity and encodes energy-related deviations, enabling the identification of potentially inefficient sites through peer-relative comparison. The derived anomaly scores provide a practical mechanism for prioritising field investigations, allowing mobile network operators to focus engineering resources on sites most likely to yield energy savings. Experimental results demonstrate that the proposed approach outperforms conventional anomaly detection baselines and provides a robust foundation for large-scale energy-efficiency optimisation in mobile networks.

1 Introduction

Mobile-site energy inefficiency is difficult to detect because sites are heterogeneous, labels are absent, and historical baselines may already include abnormal consumption. The paper addresses this with an energy-aware peer-relative embedding and evaluates it using controlled operational-data experiments.

  • Motivation: Mobile networks combine RAN equipment with cooling, power conversion, and other supporting systems across thousands of distributed sites.Supporting subsystems contribute substantially to site energy consumption.
  • Motivation: Cooling and other subsystem faults can waste energy persistently without interrupting service, allowing inefficiencies to remain unnoticed.Cooling accounted for approximately 40% of total site energy at one operational South African site while an air conditioner was active.
  • Problem: Site-specific equipment, layout, environmental exposure, weather, and traffic make broad energy optimisations difficult to apply uniformly.The supplied passage introduces site heterogeneity as a constraint on traditional engineering interventions.
  • Problem: Operational detection lacks reliable labels, while historical predictive models can absorb long-standing inefficiencies into their expected-consumption baselines.A continuously operating air conditioner may therefore appear normal in a site’s own history.
  • Approach: The proposed energy-aware MDE embeds structurally comparable sites while repelling those with unusually high peer-relative consumption.This converts energy inconsistency into a geometric signal for identifying candidate sites.
  • Evaluation: An embedding-relative displacement score ranks sites by distance from their structural peer groups and supports pseudo-label generation for downstream supervised models.The study evaluates the framework on 5,372 live sites with four injected inefficiency classes and contamination rates from 1% to 99%.

2 Related Work

Related work has focused on modelling and optimising network energy use, but site-level inefficiency requires accounting for structural context. The paper positions peer-relative representation learning as a response to missing labels, contaminated historical baselines, and misleading global outlier comparisons.

  • Existing energy-efficiency research: Mobile-network energy research has primarily modelled RAN demand and optimised sleep modes, carrier design, resource allocation, and traffic-aware management.Site-level energy also includes cooling and auxiliary infrastructure.
  • Site context: Energy consumption cannot be interpreted independently of site structure because high use may be normal for a complex site while lower use may still be peer-relative inefficiency.Relevant context includes equipment, traffic, transmission, architecture, cooling, and auxiliary systems.
  • Labels and baselines: Historical inefficiencies can become part of the observed baseline, causing predictive models trained on past consumption to encode abnormal behaviour as expected.This is framed as an imperfect proxy between observed energy and underlying efficiency state.
  • Anomaly detection gap: Unsupervised anomaly detection is appropriate when operational networks lack ground-truth inefficiency labels, but generic methods capture population-level abnormality rather than peer-relative inconsistency.Isolation Forest and LOF illustrate contrasting notions of abnormality.
  • Paper positioning: The paper fills this gap by encoding structural comparability and energy deviation together in a representation-learning framework.This distinguishes the approach from predictive modelling and global anomaly detection.

3 Proposed Peer-Relative Energy-Aware Embedding Framework

The framework separates structural attributes from observed energy, constructs structural peer graphs, and modifies MDE attraction using local energy deviations. Its push–pull objective preserves comparable relationships while displacing energy-inconsistent sites.

  • Problem formulation: Each site is represented by structural attributes and observed monthly energy, allowing peers to be defined structurally and deviations assessed energetically.The feature dimension is d = d_s + 1.
  • Structural graph construction: A structural kNN graph connects each site to predefined numbers of nearest structural peers, using reciprocal-neighbour agreement for edge weights.Weights are 1 for one-way selection and 2 for reciprocal selection; structural distance determines edges, not weights.
  • Standard MDE: Standard MDE minimises distortion over graph edges, with the graph selecting comparable pairs and the distortion function penalising their embedded distances.The embedding matrix contains the learned low-dimensional coordinates.
  • Energy-aware weight adjustment: The energy-aware adjustment uses a percentile baseline from baseline-neighbour consumption, with positive log-ratio deviations indicating excess energy.A 1 kWh floor stabilises ratios, while q controls baseline conservativeness.
  • Energy-aware weight adjustment: Energy-aware weights reduce attraction for elevated deviations and can become negative, converting connected-pair interactions into repulsion.The parameter β controls adjustment strength, forming the method’s push–pull mechanism.
  • Push–pull objective: The final objective combines adjusted structural edges with randomly sampled non-adjacent pairs that provide additional repulsive scaffolding.The sampled set contains μ|E^(s)| pairs, with fixed negative weight w−.
  • Optimisation: The embedding is obtained by minimising the push–pull objective over coordinates using first-order PyMDE routines.The supplied implementation passage describes iterative coordinate updates along descent directions.

3.4 Embedding-Relative Anomaly Scoring

Anomaly scoring measures how far a site lies from its structural peers in the learned embedding, normalised by the peers’ intrinsic spread. Higher scores indicate stronger evidence of potential energy inefficiency.

  • Displacement measure: For each site, the scoring signal begins with its mean embedded distance to a designated scoring neighbourhood.The neighbourhood is defined over the learned representation.
  • Normalisation: The mean distance is normalised by average pairwise distance among neighbours to account for differing natural neighbourhood spreads.This makes displacement relative to the local geometry rather than an unscaled distance.
  • Ranking: A small ε prevents division by zero in degenerate neighbourhoods, and sites are ranked by their resulting peer-relative anomaly score.Higher scores indicate stronger evidence of potential energy inefficiency.

3.5 Pseudo-Label Distillation

The framework converts ranked anomaly scores into pseudo-labels for downstream supervised models. These labels identify strongly displaced sites as candidate inefficient examples and transfer the embedding-derived anomaly structure to conventional classifiers.

  • Pseudo-label construction: Anomaly rankings become supervisory targets by thresholding the top-ψ fraction of sites, where ψ is the assumed anomaly proportion.The threshold τψ corresponds to the top-ψ fraction of ranked sites.
  • Pseudo-label construction: The resulting binary pseudo-labelled dataset treats strongly displaced sites as candidate inefficient examples.The pseudo-labels are derived from embedding geometry rather than external annotation.
  • Downstream transfer: Embedding-derived labels transfer the discovered anomaly structure to conventional classifiers.The complete pipeline produces anomaly scores, a ranked site list, and pseudo-labels for downstream use.

3.6 Complexity

The pipeline is designed to scale to national-network populations. Its main costs arise from kNN graph construction, edge-based embedding iterations, and neighbour-spread scoring.

  • Computational cost: O(N log N) is the graph-construction cost when tree- or index-based kNN search is used.Baseline and edge-weight computation add O(Nkgraph).
  • Computational cost: Each first-order MDE solver iteration evaluates distances and gradients over |E(∗)| edges.The passage identifies this edge-based evaluation as the dominant per-iteration operation.
  • Computational cost: O(Nk_score^2) is the worst-case scoring cost because of pairwise neighbour spread.Despite this component, the pipeline scales to tens of thousands of sites on commodity hardware.
  • Scalability: The complete pipeline scales to national-network populations of tens of thousands of sites on commodity hardware.This supports deployment at large operator network sizes.

4 Controlled Evaluation Methodology

The evaluation uses synthetic populations grounded in live-network data because verified operational inefficiency labels are unavailable. Structural profiles and group-specific energy baselines are preserved, then heterogeneous inefficiencies are injected for controlled measurement.

  • Evaluation design: Verified inefficiency labels are unavailable in operational data, so controlled injections provide ground truth only for evaluation.Injected labels are excluded from graph construction, embedding optimisation, and scoring.
  • Reference data: The reference dataset contains 5,372 live sites represented by cross-sectional observations with structural, traffic, and monthly energy features.The observations span January 2024 to January 2026, with most from January 2026.
  • Reference data: The data contain 1,336 unique site structures, including 587 repeated configurations suitable for comparable peer groups.The structures combine vendor, sharing status, mast type, cell count, and non-RAN equipment count.
  • Synthetic population generation: Synthetic sites preserve the empirical structural composition and receive group-specific linear baseline energy models.The baseline uses cell count and non-RAN equipment count within vendor, sharing, and mast groups; traffic is excluded from this baseline.
  • Synthetic population generation: The synthetic reference population contains 5,000 efficient sites with expected energy ranging from approximately 500 to 9,000 kWh and a median of 3,654 kWh.Multiplicative log-scale noise preserves positive energy and produces larger absolute deviations for larger sites.
  • Controlled inefficiency injection: A randomly selected fraction ρ receives elevated consumption through four heterogeneous mechanisms: overload, cooling overhead, idle-RF load, and another controlled injection type.At ρ = 10%, 500 sites are injected, balanced across the four types.
  • Controlled inefficiency injection: Figure 2 compares log-scale simulated energy distributions and metered-to-baseline energy ratios for efficient and injected inefficient sites.Injected sites generally have higher consumption, while efficient-site ratios concentrate near one and injected-site ratios shift higher.

5 Experimental Setup

The experiments evaluate an unsupervised, transductive framework using held-out synthetic labels only for hyperparameter selection and final assessment. Comparisons span standard detectors, residual methods, representation transfer, and pseudo-label distillation across contamination rates.

  • Configuration: The MDE embedding is fitted jointly on 5,000 synthetic sites without injected inefficiency labels.Stratified validation and test partitions are used for selection and final evaluation, respectively.
  • Configuration: Independent tuning yields kgraph = 300, kbase = 10, and kscore = 50, with q = 35 and traffic down-weighting fixed in graph construction.The three neighbourhood sizes serve graph construction, local energy comparison, and displacement scoring.
  • Configuration: β = 20 maximises validation ROC-AUC among the tested repulsion strengths.The sweep uses β ∈ {0, 5, 10, 20, 35, 50, 75, 100} with other settings held fixed.
  • Configuration: 0.68 is the ROC-AUC of the purely structural embedding at β = 0, while test ROC-AUC remains 0.847–0.857 for β ∈ [20, 100].The reported partition-level values are not directly comparable to full-population results in Section 6.
  • Comparators: The proposed score is compared with Isolation Forest, LOF, GMM, autoencoder, linear, Huber, and random-forest residual detectors.A physics residual reference is included as a privileged upper bound unavailable during deployment.
  • Teacher–student experiment: Pseudo-label students train on the top ψ = 10% of ranked training sites and are evaluated on a held-out test set.The student models are logistic regression, random forest, and XGBoost using a 70/30 stratified split.
  • Evaluation metrics: ROC-AUC, PR-AUC, and Precision@K measure ranking quality and inspection-oriented performance.Precision@K uses K equal to the top 10% of ranked sites.

6 Results and Discussion

The proposed energy-aware MDE score consistently outperforms unsupervised and practical supervised baselines, especially as contamination increases. Its learned embedding also improves generic detectors and supports lightweight deployment through teacher–student distillation, while evaluation remains limited by controlled injection and weak peer comparability for uncommon sites.

  • Comparison With Unsupervised Feature-Space Methods: 0.84 ROC-AUC at ρ = 1% and 0.71 at ρ = 99% show the proposed score remains strongest and degrades gradually across contamination rates.LOF reaches approximately 0.60 at low rates, while Isolation Forest, GMM, and AE remain near random for most of the sweep.
  • Comparison With Supervised Residual Methods: 0.05 ROC-AUC at ρ = 99% separates the proposed score from the RF residual, 0.714 versus 0.665, after overtaking it from ρ = 20%.The RF residual leads at low contamination by 0.02–0.03 ROC-AUC but decays steeply as contamination grows.
  • Comparison With Supervised Residual Methods: Beyond ρ = 25%, the proposed score achieves higher PR-AUC at every evaluated rate and leads in 8 of 14 sampled scenarios.RF has the slightly higher full-sweep mean PR-AUC, 0.741 versus 0.713, driven entirely by the low-contamination regime.
  • Effect of the Embedding on Standard Detectors: At ρ = 10%, learned embeddings raise ROC-AUC from 0.569 to 0.906 for Isolation Forest, 0.577 to 0.897 for GMM, and 0.724 to 0.889 for AE.The proposed displacement score performs best overall with ROC-AUC 0.911 and Precision@10% = 0.554; LOF is the exception.
  • Teacher–Student Distillation: On the 1,500-site held-out test set, RF and XGBoost student models reach Precision@10% = 0.587 versus 0.567 for the teacher, while XGBoost attains PR-AUC 0.642.The student models retain most of the teacher signal and operate on raw site features, avoiding repeated embedding optimization for new sites.
  • Discussion and Limitations: The evaluation uses controlled injection rather than real ground truth, is cross-sectional, and may yield less reliable scores for sites with uncommon structural configurations.Injected inefficiencies are based on documented failure modes and calibrated to operational data, but real inefficiencies may have more complex temporal and environmental behaviour.

7 Conclusion

The paper develops an unsupervised peer-relative framework that embeds energy-inconsistent sites away from comparable peers and ranks them for investigation. In evaluation and field investigations, it outperformed baseline detectors and identified confirmed inefficiencies associated with measurable energy savings, while several deployment limitations remain.

  • The energy-aware MDE formulation displaces energy-inconsistent sites from peer neighbourhoods and scores them by normalised displacement.
  • 5,372 live sites supported a controlled evaluation in which the proposed score outperformed standard unsupervised detectors across contamination rates and transferred rankings to lightweight classifiers.
  • Field investigations confirmed previously undetected inefficiencies, including a DAS control fault whose correction reduced energy consumption by approximately 600 kWh per month.
  • Evaluation remains limited by injected rather than fully validated ground truth, cross-sectional observations, fixed hyperparameters, and weaker peer comparability for uncommon site configurations.

Appendix: Controlled Inefficiency Injection Specification

The controlled injection specification simulates four inefficiency mechanisms by modifying noisy site-level baseline energy. The mechanisms use configuration-, traffic-, mast-group-, and unit-dependent terms before final metered energy is rounded to two decimals.

  • Injected sites are selected by random permutation, independently of site configuration, and assigned four inefficiency mechanisms in equal proportion.
  • Cooling overhead adds a mast-group-dependent uniformly sampled amount to baseline energy, with bounds ranging from 80–200 to 200–400 kWh.
  • Idle-RF load scales with the squared cell count, a traffic-dependent idle factor, and a uniformly sampled coefficient, subject to a signal-to-noise floor of 2σi.
  • Non-RAN parasitic load is defined using the number of non-RAN units, while final simulated metered energy is rounded to two decimals.
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