Rule-based models ofer interpretability but struggle with complex data, while deep neural networks excel in performance yet lack transparency. This work investigates RL-Net, a neuro-symbolic architecture that learns interpretable rule lists through neural optimization, applied for the first time to radar-based hand gesture recognition (HGR). We benchmark RL-Net against a fully transparent rule-based system (MIRA) and an explainable black-box model (XentricAI), evaluating accuracy, interpretability, and user adaptability via transfer learning. Our results show that RL-Net achieves a favorable trade-of, maintaining strong performance ( 93% F1) while significantly reducing rule complexity. We identify optimization challenges specific to rule pruning and hierarchy bias and propose stability-enhancing modifications. Compared to MIRA and XentricAI, RL-Net emerges as a practical middle ground between transparency and performance. This study highlights the real-world feasibility of neuro-symbolic models for interpretable HGR and ofers insights for extending explainable AI to edge-deployable sensing systems.
Hand gestures ofer a natural modality for human–computer interaction, with applications in automotive
safety, healthcare, and augmented reality [
Despite recent success of deep learning for radar-based HGR [
Fully transparent, rule-based models provide interpretability but fail to generalize in complex
highdimensional settings. Neuro-symbolic artificial intelligence (AI) ofers a promising middle ground
by integrating symbolic logic with neural architectures [
In this work, we explore the RL-Net architecture [
Our main contributions are: 1. First application of RL-Net to radar-based HGR: We demonstrate the first real-world deployment of a neuro-symbolic model on FMCW radar gesture data. 2. Training stabilization and architectural improvements: We enhance RL-Net with batch normalization and validation-time regularization to improve robustness and reduce rule complexity. 3. Personalized transfer learning: We apply user-specific fine-tuning to RL-Net, improving accuracy while simplifying learned rule sets. 4. Comparative evaluation: We benchmark RL-Net against MIRA (white-box) and XentricAI (black-box), assessing accuracy, interpretability, and adaptability. 5. Limitations and future work: We identify structural training issues in RL-Net’s fixed rule hierarchy and outline lightweight improvements to support scalable, interpretable deployment.
Transparent models like decision trees, logistic regression, and rule-based systems are essential for
high-stakes applications due to their interpretability [
A rule comprises multiple feature-based conditions leading to a prediction, e.g., "IF (x1 > 0.5 AND x2 ≤ 3.0) THEN class = 1". This clarity supports traceability and user trust.
MIRA [
Deep Neural Networks (NN) (convolutional NNs [
Recent work such as XentricAI [
Neuro-symbolic AI bridges rule-based interpretability and neural flexibility [
DR-Net [
RL-Net [
Figure 1 summarizes model trade-ofs between interpretability and performance, positioning RL-Net between black-box deep models and fully symbolic approaches.
y t i l i b a t e r p r e t n I l e d o M
White-Box Model
DR-Net RL-Net ...
Gray-Box Model
RNN CNN ...
Ideal Black-Box Model Model Performance
To date, neuro-symbolic models have not been applied to real-world FMCW radar gesture data. Their adaptability via Transfer learning (TL) also remains underexplored. This work fills that gap by evaluating RL-Net in comparison to MIRA and XentricAI, analyzing the performance–interpretability trade-of and exploring its potential for user-specific gesture adaptation.
We apply RL-Net [
Raw Data Collection
Signal Prepocessing chirps samples
Feature Extraction NeuTraraliNneintgwork
Binarized Rule Layer Hierarchy Features Layer
A B ReLu C ReLu D ReLu
Rule-Based
Prediction Output Layer
IF A and C and not D THEN 1 0 1 ELSE IF not B and not C THEN 2 2
ELSE 0
Input & Rule Layers. The input layer receives binarized features ∈ {0, 1}. Each rule neuron
functions as a logical AND, with ternary weights W encoding positive, negative, or excluded feature
use. To enable diferentiable training, these weights are reparameterized as W = W ∘ W , where
W ∈ [
A neuron activates only when all conditions are satisfied: = ∑︁ − ∑︁ + 1 >0 where ∈ W and the step function () = 1 if = 1, else 0, binarizes the output.
To improve training stability, we add batch normalization.
Hierarchy & Output Layers. A fixed hierarchy enforces ordered rule evaluation: a rule activates only if all previous rules are inactive. The final neuron acts as a default rule. Only one rule fires per sample, and a softmax assigns its associated class label.
Loss Function. The regularization loss is defined as ℒsparse = ∑︀, ︁( loc−− )︁ , where loc are the logits controlling the binary mask sampling, and , are stretch parameters controlling the thresholding behavior. This penalty encourages many weights to converge to zero and thus shortens the learned rules. The training optimizes the loss based on the cross-entropy loss, the sparsity and L2 regularization terms:
ℒ = ℒCE + 1ℒsparse + 2‖Wout‖22
We compare RL-Net to MIRA [
A summary of capabilities is shown in Table 1.
The gesture dataset used in this study was collected using Infineon Technologies’ XENSIV ™ BGT60LTR13C 60 GHz FMCW radar operating in indoor environments. Twelve users performed ifve predefined hand gestures ( SwipeLeft, SwipeRight, SwipeUp, SwipeDown, and Push) across six diferent room types. A Background class was added to represent the absence of gestures. Each participant completed 1,000 samples, totaling 31,000 gesture recordings.
Recordings were captured over 100 frames per gesture using three receive antennas, with dimensions
[100 × 3 × 32 × 64] representing frames, antennas, chirps, and fast-time samples, respectively. The
dataset is publicly available via IEEE Dataport [
Following the method in [
We applied a lightweight, real-time-capable preprocessing pipeline based on [
From this processing, we extract five features per frame: radial distance (range), radial velocity (Doppler), azimuth angle, elevation angle, and signal magnitude. These were averaged over the ten gesture frames to construct the input to the models.
To evaluate both the generalization capabilities and adaptability of RL-Net, we conducted two main experiments: (i) optimized training of a user-agnostic pretrained model, and (ii) user-specific TL. Gesture data from twelve users (12,000 samples) was used in total. Data from six users (6,000 samples) was used to train and validate the base model, while data from the remaining six users was reserved for TL and evaluation.
Dataset Split. Six users (6,000 gestures) were used to pretrain all models; six diferent users (6,000 gestures) were held out for TL and testing.
Training Protocol. An extensive hyperparameter search was performed using Grid Search, selecting values based on prior work and empirical stability. We used the Adam optimizer with a learning rate of 0.01 and batch size of 40. Training was run for 200 epochs with early stopping on validation loss. A batch normalization layer was added after the rule layer for improved stability. Sparsity was controlled via a regularization weight ( 1,train = 0.025), while a higher weight ( 1,val = 0.3) was applied during validation to promote simpler models. L2 regularization was disabled. Hard concrete parameters were = − 0.1, = 1.1, and = 23 .
Custom Early Stopping Strategy. Standard early stopping based on validation cross-entropy often favored overly complex models with minimal gains in accuracy. On the other hand, strong regularization led to premature convergence and vanishing gradients. To balance interpretability and performance, we introduced a custom early stopping criterion using an increased validation-time regularization weight ( 1,val = 0.3). This steered model selection toward sparser rule sets without compromising predictive accuracy.
Transfer Learning. For user adaptation, pretrained weights were partially frozen: rule masks and output weights were updated while base rule weights were fixed. Each user had 1,000 samples (20% test, 64% train, 16% val).
Evaluation Metrics. We report accuracy and F1 score, along with rule complexity measured by the number of active rules and total rule conditions. These metrics are tracked before and after fine-tuning.
Baselines. RL-Net was compared to MIRA [
While we initially experimented with DR-Net by training independent rule sets for each gesture class, the resulting rules were not mutually exclusive, making them unsuitable for robust multi-class classification. As a result, we focused exclusively on RL-Net, which provides a hierarchical rule list enabling consistent multi-class predictions.
We evaluate the model’s robustness and interpretability across three architectural variants: the original RL-Net, RL-Net with batch normalization, and RL-Net with both batch normalization and a modified validation loss incorporating regularization weight 1,val. Results, averaged over four runs per configuration with consistent seeding, are summarized in Table 2.
Introducing batch normalization significantly improved both performance stability and model simplicity. Further incorporating validation-time regularization reduced model complexity even more, with only a slight trade-of in F1 score. The reduction in standard deviation across runs also indicates improved training consistency.
Optimization Bottleneck from Rule Ordering and Vanishing Gradients. While training improves overall sparsity (Figure 3, Panel A), we observed a persistent structural issue: RL-Net’s fixed hierarchy layer causes early rules to being suppressed and pruned. As shown in Panel B, this results in only high-index rules remaining active, often with long, complex conditions, compromising rule diversity and interpretability. This bottleneck stems from the fixed top-down rule evaluation, which prioritizes later rules during optimization. Addressing this may require adaptive or learnable rule ordering, ideally without increasing model complexity to maintain suitability for edge deployment.
Comparison with Baselines. As a reference, the white-box model MIRA achieves an F1 score of 79.7%, while the GRU-based classification backbone of XentricAI reaches 85%. RL-Net demonstrates a compelling trade-of: It achives strong performance ( ∼ 90%) while maintaining interpretable, compact rule lists. This positions RL-Net efectively between the extremes of full transparency and pure black-box modeling.
For these experiments, we initialized the model using a randomly selected baseline model consisting of seven rules and 36 total conditions.
Table 3 summarizes the classification performance and rule complexity before and after TL. All results are reported for the best-performing epoch on the validation set, using accuracy and F1-score as primary metrics, and the number of rules and total rule conditions as proxies for interpretability.
Across all users, TL consistently improved model performance, with F1-score increases ranging from modest (+0.71% for user3) to substantial (+9.08% for user1). Importantly, these gains were accompanied by a consistent reduction in rule complexity. All adapted models converged to five rules, and in several cases, the total number of rule conditions decreased significantly, highlighting the dual benefit of enhanced personalization and improved interpretability. Comparison with Baselines. RL-Net achieved an average user-specific performance of 93.05%, surpassing the fine-tuned XentricAI model, which reached 90.2%. However, it is important to note that XentricAI includes a Background class and performs both gesture detection and classification at the frame level, an extended functionality that goes beyond RL-Net’s current scope. MIRA achieved the highest average accuracy of 94.9% after user-specific calibration. While deterministic, MIRA relies on handcrafted rule tuning and lacks the learning flexibility of neural approaches.
Overall, RL-Net strikes a favorable balance between interpretability and performance, ofering greater modeling flexibility than MIRA and better classification accuracy than XentricAI. That said, one limitation may lie in the fixed thresholds used for binarizing continuous features, which could constrain the model’s adaptability to subtle user-specific variations. Future research should explore adaptive thresholding or learnable binarization strategies to further improve generalization and personalization.
RL-Net inherits optimization challenges from DR-Net, notably vanishing gradients caused by multiplicative logical activations. This leads to early-rule pruning and dominance of later, often longer rules, limiting generalization. Fixed rule ordering further amplifies this by prioritizing high-indexed neurons and suppressing earlier ones.
While batch normalization improved stability, training remains inconsistent across runs. Attempts
like L2 regularization worsened gradient flow and performance. Though more advanced techniques (e.g.,
HyperLogic [
Future work should explore gradient-stable activations, adaptive thresholding for input binarization, and learnable rule hierarchies. Physics-informed constraints tailored to gesture kinematics may further improve robustness without added complexity. These insights extend beyond HGR, pointing to broader improvements in neuro-symbolic learning.
This work presents the first real-world application of RL-Net, a neuro-symbolic model, to radar-based HGR. RL-Net achieves a strong balance between interpretability and performance, outperforming fully transparent models and approaching the accuracy of black-box methods.
Through optimized training and TL, we demonstrate RL-Net’s potential for user-adaptive, explainable gesture sensing. However, challenges in optimization and rule hierarchy remain. Addressing these without increasing model complexity is key to advancing interpretable AI for edge deployment and beyond.
The author has not employed any Generative AI tools.