Radiance-Field Reinforced Pretraining

• The paper introduces RFRP, employing an asymmetric autoencoder with RF-NeRF decoders to enforce scene-agnostic feature learning.
• It achieves significant localization error reductions (>40% vs non-pretrained, 21% vs supervised) using a fraction of labeled RF data.
• Its physics-based neural rendering and MoE expert-balancing losses enhance robustness, transferability, and latent feature consistency.

Radiance-Field Reinforced Pretraining (RFRP) is a self-supervised pretraining framework designed to scale radio-frequency (RF)-based indoor localization models via large-scale unlabeled signal data. RFRP addresses the persistent challenge of poor cross-scene generalization in deep localization models, which traditionally rely on scene-specific labeled datasets. The approach achieves label-efficient, robust, and transferable feature learning for localization by aligning the inductive bias of physical radiative transport, as encoded by neural radiance fields (NeRFs), with the latent space of a large encoder model on wireless measurements. Experimental results across 100 diverse indoor scenes and four major RF modalities demonstrate significant reductions in localization error—>40% compared to non-pretrained models and 21% versus supervised pretraining—using a fraction of labeled data (Wang et al., 8 Dec 2025).

1. Architectural Overview

RFRP employs an asymmetric autoencoder architecture coupling a shared localization model (LM) encoder with scene-specific RF-NeRF decoders. The LM encoder—LocGPT+—processes one or more spatial RF spectra (Ω) from antenna arrays to produce a latent embedding (z) that encodes geometric (position-relevant) features while suppressing scene-specific artifacts such as multipath clutter. For each environment, a separate NeRF²-instance RF-NeRF decoder utilizes the latent code z and the receiver position $P_{\mathrm{RX}}$ to reconstruct the original measurement $\widetilde\Omega$ through a physically motivated neural rendering process. The use of a common encoder across all decoders strictly enforces the learning of scene-agnostic, robust representations required for successful spectral reconstruction in any target scene. The decoder’s physics-based parameterization acts as an inductive prior, shaping the LM’s feature space towards universal geometric relevance.

2. RF-NeRF Mathematical Formulation

The RF-NeRF decoder is inspired by the volumetric rendering paradigm in visual NeRFs but is parameterized for complex RF propagation phenomena. Each 3D voxel at position $P_x$ holds an attenuation/density $\delta(P_x)\in\mathbb{C}$ and a directionally modulated radiance $S(P_x,\omega)\in\mathbb{C}$. For a receiver located at $P_{\mathrm{RX}}$, a sampled ray in direction $\omega$ is defined as

$$P(r, \omega) = P_{\mathrm{RX}} + r\omega, \quad r \in [0, D].$$

The modeled received signal from this direction is

$$R(\omega) = \int_0^D T(r)\,S(P(r, \omega), -\omega)\,dr$$

with cumulative transmittance along the ray

$$T(r) = \prod_{\tilde{r}=0}^{r} \delta(P(\tilde{r},\omega)) = \exp\left(\int_0^r \ln \delta(P(\tilde{r},\omega))\,d\tilde{r}\right).$$

This formulation generalizes classic NeRF notation to RF by identifying $\sigma \leftrightarrow -\ln \delta$, and $\mathbf{c}\leftrightarrow S$, preserving the correspondence between attenuation, emission, and observable spectrum via learned volumetric scene representations.

3. Pretraining Objective and Loss Functions

RFRP jointly optimizes three core loss components using unlabeled RF data:

• Spectral Reconstruction Loss ($\mathcal{L}_{\mathrm{cons}}$): Enforces accurate reconstruction of the input spectrum using the decoder, formalized as

$$\mathcal{L}_{\mathrm{cons}} = \lambda_{\mathrm{cons}}\,\mathbb{E}_{\Omega\sim\mathcal{D}}[\|\Omega - \widetilde\Omega\|_2^2].$$

• MoE Expert-Balance Loss ($\mathcal{L}_{\mathrm{bal}}$): Regularizes the Mixture-of-Experts (MoE) layers in the LocGPT+ encoder to prevent routing collapse, ensuring balanced utilization of network capacity.
• Latent-Code Regularization ($\mathcal{L}_{\mathrm{lat}}$): Penalizes excessive scaling of the latent code vector z,

$$\mathcal{L}_{\mathrm{lat}} = \lambda_{\mathrm{lat}}\,\|\mathbf{z}\|_2^2.$$

The overall objective function is: $$\mathcal{L} = \mathcal{L}_{\mathrm{cons}} + \mathcal{L}_{\mathrm{bal}} + \mathcal{L}_{\mathrm{lat}}.$$

4. Dataset, Training Protocol, and Implementation

Training leverages a comprehensive dataset of 7,327,321 RF measurements across 100 real-world indoor environments (offices, classrooms, warehouses, restaurants). Four distinct wireless modalities are present: RFID (920 MHz, 1.3M samples), BLE (2.4 GHz, 4.34M), IIoT (1.27/3.44 GHz, 0.45M), and WiFi (2.4 GHz, 1.23M). Pretraining draws from 6.69 million samples over 75 scenes, with 21.3% being labeled. Testing utilizes 0.64 million fully labeled samples from the remaining 25 scenes.

Training specifics are as follows:

Parameter	Value
Optimizer	Adam ($\beta_1=0.9,\, \beta_2=0.999$), weight decay = 0.001
Learning Rate	Warm-up from $3\times10^{-5}$ to $3\times10^{-4}$ (50 epochs), cosine decay
Batch Size	512 spectra (18,000 tokens)
Epochs	500
Loss Weights	$$\lambda_{\mathrm{cons}}=1,\, \lambda_{\mathrm{bal}}=0.01,\, \lambda_{\mathrm{lat}}=0.01$$
Compute	7 × NVIDIA A100 GPUs (~150 hours)

5. Empirical Results and Comparative Analysis

RFRP pretraining demonstrates substantial improvements in localization accuracy across all tested modalities and scenes:

• On four representative test scenes (S1, S10, S20, S25), using 20% of fine-tuning labels, RFRP reduces localization error by 19.6–29.9% relative to training from scratch; with 60% labels, peak improvement reaches 47.0%.
• RFRP outperforms both supervised pretraining (21% error reduction) and symmetric autoencoding alternatives, as measured using RFID, BLE, IIoT, and WiFi data.
• Over 25 held-out test scenes, LocGPT+ models pretrained with RFRP achieve a mean localization error of 39.06 cm, outperforming DLoc (68.45 cm), iArk (81.12 cm), and LocGPT with supervised pretraining (49.95 cm). All differences are statistically significant ($p < 0.01$ under paired t-test of scene errors).

6. Transferability, Robustness, and Downstream Effectiveness

RFRP-pretrained LM encoders demonstrate markedly improved cross-scene transferability. Fine-tuning on sparse labeled data enables strong performance in novel and out-of-distribution environments. The internal MoE structure in the encoder enhances adaptability by routing signals through specialized subnetworks, matching unique environmental characteristics. Masked-autoencoder pretraining, with up to 75% random patch masking, further improves resilience to partial observability or RF interference, supporting reliable operation in the presence of signal dropout.

7. Limitations and Prospects for Future Research

Current RFRP methodology requires training a distinct RF-NeRF per scene, imposing resource and time overheads. This necessity motivates the development of shared, incremental, or otherwise more efficient radiance field representations. The computational burden of volumetric RF-NeRF training is considerable; adapting rendering paradigms such as voxel splatting or diffusion-based approaches offers a pathway to reduction in training costs. RFRP presently does not address dynamic scenes or temporal variability—a direction for subsequent research is to incorporate models that account for mobile agents or environmental changes.

In summary, RFRP integrates physics-informed neural rendering with large-scale self-supervised learning, achieving scalable, label-efficient, and generalizable RF-based indoor localization (Wang et al., 8 Dec 2025).