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Collaborative In-Context Learning for Indoor Radio Map Estimation

Yuanzhe Peng, Jie Xu

arXiv:2610.31702v1cs.LGcs.AI

TL;DR

Indoor RME methods often depend on costly labeled data and task-specific training, while building information may be too private to centralize. POLY-RIPPLE formulates RME as collaborative ICL, using private client demonstrations, ripple-ordered prediction, and importance-aware aggregation. On a public benchmark, it consistently outperforms representative ICL baselines, with results aligning with the theoretical analysis.

  • Problem

    Supervised indoor RME requires costly labeled data and task-specific training, while privacy-sensitive building information may not be centralized.

    Source: §I · p. 1

  • Method

    POLY-RIPPLE uses frozen LAVMs for client-side ICL with private demonstrations, ripple-ordered prediction, and importance-aware server aggregation.

    Source: §I · p. 2

  • Results

    POLY-RIPPLE consistently outperforms representative ICL baselines on a public RME benchmark, and the empirical results support the theoretical analysis.

    Source: §I · p. 2, §VII · p. 9

  • Takeaways & Limitations

    Collaborative ICL combines distributed contextual knowledge without sharing private demonstrations or processing them all within one context.

    Source: §I · p. 2

Abstract

from arXiv · show

Indoor radio map estimation (RME) is essential for wireless applications such as coverage planning, localization, and network deployment. However, most existing methods follow a supervised learning paradigm that requires costly labeled data and task-specific model training. Moreover, indoor environments involve privacy-sensitive information, such as building layouts and structures, that often cannot be centralized. To address these challenges, we make the first attempt to formulate indoor RME as a collaborative in-context learning (ICL) problem. We propose Poly-Ripple, a framework in which multiple clients perform ICL using large autoregressive vision models (LAVMs) without model updates. Each client is prompted by its private demonstrations and predicts the radio map for the same scene query. To capture the causal structure of wireless propagation outward from the transmitter (Tx), we adopt ripple-ordered autoregressive modeling. We further introduce importance-aware aggregation to exploit heterogeneous contextual knowledge distributed across clients under the context length constraint. We provide theoretical analysis and conduct extensive experiments on a public indoor RME benchmark. The experimental results show that Poly-Ripple consistently outperforms representative ICL baselines, while aligning with our theoretical analysis.

I. INTRODUCTION

Indoor RME remains difficult to deploy because labeled maps are costly to obtain and private building information often cannot be centralized. POLY-RIPPLE addresses these constraints by using collaborative ICL with ripple-ordered predictions and importance-aware aggregation.

I. INTRODUCTION

  • Costly labeled maps and privacy-sensitive building layouts limit supervised indoor RME, motivating inference without task-specific training or centralized demonstrations.The paper identifies ray-tracing simulations or field measurements as costly sources of labeled maps, while layouts and structures may not be shared across sites.Source: §I · pp. 1–2
  • POLY-RIPPLE combines client-side ICL, ripple-ordered autoregressive prediction, and server-side importance-aware aggregation of distributed contextual knowledge.The ripple order is motivated by outward signal propagation from the transmitter; aggregation uses query relevance to combine client predictions.Source: Figure 1 · p. 1, §I · p. 2, Figure 2 · p. 2

II. RELATED WORK

  • Prior RME work includes physics-based models and supervised image-to-image methods, but these approaches can generalize poorly across layouts or require costly labels and task-specific training.The related-work passage describes supervised methods using CNN or ViT encoder-decoder architectures, customized losses, feature fusion, and data augmentation.Source: §I · p. 1, §II · p. 2

III. PROBLEM FORMULATION

  • In the collaborative formulation, clients use frozen LAVMs and private demonstrations to predict the same query, while the server aggregates local maps under privacy and context-length constraints.Weighted aggregation assigns client weights according to the relevance of their demonstrations to the query.Source: §III · p. 3

IV. METHODOLOGY

POLY-RIPPLE has each client construct a query-specific prompt, tokenize its visual inputs, and predict radio-map tokens autoregressively in an outward ripple order. The server then aggregates the clients’ local predictions.

A. Client-Side In-Context Learning

  • Each client selects at most K demonstrations by pairing the nearest transmitter-location example with spatially diverse cluster representatives.If the nearest-location anchor is not among the cluster representatives, it replaces the representative from its cluster.Source: A. Client-Side In-Context Learning · p. 3
  • A pretrained VQ-GAN maps the selected demonstrations and query inputs into discrete token grids for causal sequence modeling.The tokenizer uses a fixed codebook, and the decoder reconstructs a local radio map from generated output tokens.Source: A. Client-Side In-Context Learning · pp. 3–4
  • Ripple ordering arranges tokens by increasing radial distance from the transmitter, so autoregressive prediction proceeds from nearby regions to farther ones.Within each layer, input and output tokens at the same position are interleaved; layers are concatenated in ascending radial order.Source: A. Client-Side In-Context Learning · pp. 3–4
  • A fixed-parameter causal transformer predicts each client’s output tokens from the prompt, query input, and previously generated tokens, which are decoded into a local radio map.Only the local radio-map prediction is transmitted; private demonstrations and intermediate token sequences stay local.Source: A. Client-Side In-Context Learning · p. 4, Figure 3 · p. 4

B. Server-Side Importance-Aware Aggregation

The server combines clients’ local radio-map predictions using weights based on each client’s relevance to the query. Similarity scores can guide those weights while the original scenes remain private.

B. Server-Side Importance-Aware Aggregation

  • The server uses a weighted aggregator to combine local predictions, assigning client importance according to relevance to the query.The framework also allows confidence-based or hybrid relevance measures.Source: B. Server-Side Importance-Aware… · p. 4
  • Cosine similarity between a representative client scene and the query scene measures structural relevance and is converted into aggregation weights by a temperature-scaled softmax.The scene embedding or similarity score is computed locally and transmitted to the server, while the original scene remains private.Source: B. Server-Side Importance-Aware… · p. 4

V. THEORETICAL ANALYSIS

The theoretical analysis models contextual adaptation as a one-step implicit update on each client and examines its estimation error under stated assumptions. The assumptions capture shared propagation structure, client-specific fluctuations, and signal variability ordered by distance from the transmitter.

A. Estimation Error Analysis

  • The analysis represents each client’s contextual adaptation as one implicit update using its K demonstrations, then studies expected squared estimation error.The bound is stated for an output coordinate and a subset of input coordinates.Source: A. Estimation Error Analysis · pp. 4–5
  • The model assumes shared propagation coefficients with client-specific fluctuations, standardized inputs, and signal variability that decreases with distance from the transmitter.Client initialization mismatch is represented separately to isolate the effect of estimation order.Source: A. Estimation Error Analysis · pp. 4–5

B. Optimal Estimation Order Analysis

The analysis finds that estimating higher-variability coordinates earlier minimizes the order-dependent error term. Under the stated outward-decreasing variability assumption, this optimal order corresponds to ripple ordering from the transmitter outward.

B. Optimal Estimation Order Analysis

  • The optimal estimation order sorts coordinates by nonincreasing signal variability, which under the assumed outward decrease is the ripple order from the transmitter.The analysis attributes this ordering to minimizing the order-dependent term in the total error bound.Source: B. Optimal Estimation Order Analysis · p. 5
  • Estimating high-variability near-transmitter regions first provides context for predicting more stable far-field regions.The optimal-order bound applies under Assumptions 1–4 and allows client heterogeneity through the initialization mismatch term.Source: B. Optimal Estimation Order Analysis · p. 5

C. Aggregation Analysis

The aggregation analysis derives bounds for uniform and weighted averaging across clients, then uses the weighted bound to motivate importance-aware weights. The resulting inverse-risk principle favors clients with smaller mismatch, while practical weighting uses scene relevance because the server cannot observe client mismatch directly.

C. Aggregation Analysis

  • When client errors are comparable and uncorrelated, uniform averaging yields an effective 1/M error gain.The theorem’s uniform-aggregation result assumes Assumptions 1–5 and each client’s optimal ripple estimation order.Source: C. Aggregation Analysis · pp. 5–6
  • The weighted error bound assigns each client’s ripple-order error a coefficient α_m^2, so the aggregate depends on client quality and the weight distribution.The bound also includes shared coordinate-specific signal variability and client-specific mismatch.Source: C. Aggregation Analysis · p. 6
  • The theoretical bound motivates nonuniform importance-aware aggregation, with the objective’s closed-form solution yielding an inverse-risk allocation rule.The client-dependent estimation error proxy defines the risk used to derive the weighting strategy.Source: C. Aggregation Analysis · p. 6
  • The optimal aggregation weight scales inversely with the client-specific risk proxy, giving larger weights to clients with smaller mismatch.The proxy differs across clients through the mismatch term; the server cannot directly observe that mismatch because prompts and intermediate token sequences remain private.Source: C. Aggregation Analysis · p. 6

VI. EXPERIMENTS

The experiments examine POLY-RIPPLE’s performance against ICL baselines, the effects of key parameters, and whether empirical results support the theoretical analysis.

VI. EXPERIMENTS

  • The experiments ask how POLY-RIPPLE compares with ICL baselines in quantitative and qualitative performance.This is the first of three experimental questions.Source: §VI · p. 6
  • The experiments examine how key parameters affect POLY-RIPPLE’s performance.This is the second experimental question.Source: §VI · p. 6
  • The experiments ask whether empirical results support the theoretical analysis.This is the third experimental question.Source: §VI · p. 6

A. Experimental Setup

Experiments on unseen building layouts show that POLY-RIPPLE achieves the lowest RMSE among the compared methods on all five layouts, with performance gains tied to client relevance and collaborative context. The evaluation also examines prompt construction and the effects of client count and aggregation temperature.

A. Experimental Setup

  • The evaluation uses 27,750 radio-map samples across 25 building layouts, three frequency bands, and five antenna patterns, with 20 client layouts and five unseen target layouts.Queries use K = 3 paired demonstrations per client; the reported metric is mean RMSE and standard deviation over five runs.Source: A. Experimental Setup · pp. 6–7, B. Results and Analysis · p. 7

B. Results and Analysis

  • Each client selects a Tx-location anchor closest to the query and K −1 spatially diverse demonstrations, balancing query relevance and contextual diversity within the LAVM context limit.The anchor provides geometrically aligned propagation context, while the remaining demonstrations contribute patterns from other Tx locations.Source: B. Results and Analysis · p. 7, Figure 4 · p. 7, Figure 7 · p. 7
  • More relevant client layouts provide more useful contextual information, while uniform aggregation assigns equal importance despite differences in relevance and local prediction quality.This observed client-dependent mismatch is consistent with the paper’s theoretical analysis.Source: B. Results and Analysis · p. 7
  • POLY-RIPPLE achieves the lowest RMSE on all five unseen layouts, C21 to C25, outperforming local ICL and collaborative ICL with uniform aggregation.Uniform aggregation generally outperforms local ICL; importance-aware aggregation further improves estimation by emphasizing more relevant clients while retaining complementary information.Source: Figure 8 · p. 7, B. Results and Analysis · pp. 7–8
  • POLY-RIPPLE’s example predictions more closely match target radio maps and preserve dominant attenuation patterns extending outward from the Tx than uniform aggregation.The comparison attributes larger deviations under uniform aggregation to equal weighting of predictions from less relevant and better-aligned clients.Source: Figure 9 · p. 8, B. Results and Analysis · p. 8

C. Impact of Key Parameters

  • Average RMSE generally decreases as participating clients increase from 5 to 20, with larger gains at smaller client counts and diminishing marginal improvement.The passage attributes the trend to complementary distributed context and notes that additional clients may contribute redundant or less relevant information.Source: C. Impact of Key Parameters · p. 8, Figure 10 · p. 8
  • Across a moderate range, aggregation temperature τ has relatively limited effect on RMSE, so extensive tuning is not required for a new building layout.Smaller τ concentrates weight on the most relevant clients, while larger τ allows more clients to contribute.Source: C. Impact of Key Parameters · p. 8, Figure 11 · p. 8

D. Discussion of Theory vs. Practice

The discussion connects ripple ordering and client aggregation to theoretical error analysis, and reports that experiments support these design choices. The conclusion reports that POLY-RIPPLE outperforms representative ICL baselines on a public RME benchmark.

D. Discussion of Theory vs. Practice

  • Under Assumption 3, ordering coordinates by decreasing signal dynamic range corresponds to predicting locations outward from the Tx, matching ripple order; Fig. 9 shows dominant outward attenuation patterns.Theorem 1 gives later-predicted coordinates larger error coefficients, while Proposition 1 identifies the optimal order by signal dynamic range.Source: D. Discussion of Theory vs. Practice · p. 8
  • With uncorrelated client errors under Assumption 5, uniform averaging reduces estimation error; for comparable client errors, the theoretical gain scales with 1/M.Fig. 8 shows collaborative ICL generally outperforming local ICL, and Fig. 10 shows average RMSE decreasing as clients participate, with smaller marginal gains at larger M.Source: D. Discussion of Theory vs. Practice · p. 8
  • Theorem 3 and Proposition 2 favor larger weights for lower-risk clients; layout similarity proxies unobservable client-query relevance, and POLY-RIPPLE has lower RMSE than uniform aggregation.Fig. 5 illustrates differing layout relevance, Fig. 6 the resulting nonuniform weights, and Fig. 9 maps that more closely match targets.Source: D. Discussion of Theory vs. Practice · pp. 8–9
  • Temperature τ controls the concentration of relevance-based weights, while RMSE remains relatively stable over a moderate range.The discussion attributes the main performance gains to multi-client collaboration and nonuniform weighting by client relevance.Source: D. Discussion of Theory vs. Practice · p. 9

VII. CONCLUSION

  • POLY-RIPPLE consistently outperforms representative ICL baselines on a public RME benchmark, with empirical results supporting the theoretical analysis.Source: §VII · p. 9

B. Proof of Theorem 1

The proof of Theorem 1 applies Lemma 1 across the autoregressive sequence and sums the resulting stepwise bounds. The proof of Theorem 2 uses uncorrelated client residuals to derive the bound for aggregated predictions.

B. Proof of Theorem 1

  • Theorem 1's proof applies Lemma 1 at each step to coordinate o(t) and subset S(t), then sums the stepwise bounds using finite-sum identities.Source: B. Proof of Theorem 1 · p. 9

C. Proof of Theorem 2

  • Theorem 2's proof uses Assumption 5 to eliminate cross terms between distinct clients' residuals, then sums the stepwise bounds from Corollary 1 to obtain (15).Source: C. Proof of Theorem 2 · p. 9

D. Proof of Theorem 3

Theorem 3's proof derives the weighted-aggregation bound using uncorrelated client residuals. Proposition 2's proof identifies the minimizing weights in terms of client risks.

D. Proof of Theorem 3

  • Theorem 3's proof uses Assumption 5 to eliminate cross terms between distinct clients' residuals, then sums stepwise bounds to obtain (16).Source: D. Proof of Theorem 3 · p. 9

E. Proof of Proposition 2

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