NMINE: Normalized Mutual Information Neural Estimation

Mutual information is a general measure of statistical dependence that captures both linear and nonlinear relationships between random variables. For continuous and multidimensional variables For continuous multidimensional variables, mutual information must be estimated from samples. Because mutual information is unbounded, its values are not directly comparable across datasets, dimensions, or applications. Normalized mutual information addresses this limitation by converting mutual information into a normalized dependency score. Recent work has demonstrated the practical value of normalized mutual information in applications such as molecular dynamics {arXiv:2405.04980} and interpretable machine learning {arXiv:2409.16768}, but existing estimators remain sensitive to dimensionality and numerical stability {arXiv:2410.07642}. In this paper, we propose a fully neural normalized mutual information estimator for continuous variables. The proposed approach combines a MINE-based neural mutual information estimator {arXiv:1801.04062} with MI-NEE-inspired neural marginal entropy estimators {arXiv:1905.12957}. Mutual information is estimated using the Donsker--Varadhan representation, while marginal entropies are estimated by learning the divergence between each marginal distribution and a uniform reference distribution, from which entropy is recovered. The resulting estimator provides a neural alternative to k-nearest-neighbor-based normalized mutual information estimation {arXiv:2405.04980}. Experiments on Gaussian data from one to eight dimensions show that the proposed estimator improves accuracy over a KSG-based normalized mutual information baseline. These results indicate that neural estimation is a promising direction for normalized dependency measurement in continuous multidimensional settings.

Targeted Fine-Tuning of DNN-Based Receivers via Influence Functions

We present the first use of influence functions for deep learning-based wireless receivers. Applied to DeepRx, a fully convolutional receiver, influence analysis reveals which training samples drive bit predictions, enabling targeted fine-tuning of poorly performing cases. We show that loss-relative influence with capacity-like binary cross-entropy loss and first-order updates on beneficial samples most consistently improves bit error rate toward genie-aided performance, outperforming random fine-tuning in single-target scenarios. Multi-target adaptation proved less effective, underscoring open challenges. Beyond experiments, we connect influence to self-influence corrections and propose a second-order, influence-aligned update strategy. Our results establish influence functions as both an interpretability tool and a basis for efficient receiver adaptation.

Refining Neural Activation Patterns for Layer-Level Concept Discovery in Neural Network-Based Receivers

Concept discovery in neural networks often targets individual neurons or human-interpretable features, overlooking distributed layer-wide patterns. We study the Neural Activation Pattern (NAP) methodology, which clusters full-layer activation distributions to identify such layer-level concepts. Applied to visual object recognition and radio receiver models, we propose improved normalization, distribution estimation, distance metrics, and varied cluster selection. In the radio receiver model, distinct concepts did not emerge; instead, a continuous activation manifold shaped by Signal-to-Noise Ratio (SNR) was observed -- highlighting SNR as a key learned factor, consistent with classical receiver behavior and supporting physical plausibility. Our enhancements to NAP improved in-distribution vs. out-of-distribution separation, suggesting better generalization and indirectly validating clustering quality. These results underscore the importance of clustering design and activation manifolds in interpreting and troubleshooting neural network behavior.

Improving Numerical Stability of Normalized Mutual Information Estimator on High Dimensions

Mutual information provides a powerful, general-purpose metric for quantifying the amount of shared information between variables. Estimating normalized mutual information using a k-Nearest Neighbor (k-NN) based approach involves the calculation of the scaling-invariant k-NN radius. Calculation of the radius suffers from numerical overflow when the joint dimensionality of the data becomes high, typically in the range of several hundred dimensions. To address this issue, we propose a logarithmic transformation technique that improves the numerical stability of the radius calculation in high-dimensional spaces. By applying the proposed transformation during the calculation of the radius, numerical overflow is avoided, and precision is maintained. Proposed transformation is validated through both theoretical analysis and empirical evaluation, demonstrating its ability to stabilize the calculation without compromizing the precision of the results.

Interpreting Deep Neural Network-Based Receiver Under Varying Signal-To-Noise Ratios

We propose a novel method for interpreting neural networks, focusing on convolutional neural network-based receiver model. The method identifies which unit or units of the model contain most (or least) information about the channel parameter(s) of the interest, providing insights at both global and local levels -- with global explanations aggregating local ones. Experiments on link-level simulations demonstrate the method's effectiveness in identifying units that contribute most (and least) to signal-to-noise ratio processing. Although we focus on a radio receiver model, the method generalizes to other neural network architectures and applications, offering robust estimation even in high-dimensional settings.