arXiv subjects

Peter Jung

Publications and source records attributed to Peter Jung.

At least 19 recordsLinked to original sources

arXiv2026

On the Estimation of Chernoff Information

Chernoff information is a fundamental divergence measure characterizing the optimal error exponent in Bayesian binary hypothesis testing, with applications in information fusion, time-series analysis, and statistical learning theory. However, closed-form expressions exist only for simple parametric families, and nonparametric estimation remains difficult because the quantity is defined as an optimization of the unnormalized R\'enyi divergence over its order. We reformulate this optimization via a derivative condition, whose zero locates the optimal mixture parameter, and estimate the derivative directly using a $k$-nearest-neighbor method. We prove the $L_2$-consistency of the derivative estimator under mild regularity conditions on the densities and their domain. Coupled with a bisection procedure that locates the optimal parameter up to arbitrary precision, this yields an estimator for Chernoff information.

cs.IT↗

arXiv2026

A Hybrid Physics-Informed Neural Network Framework for Subcritical and Supercritical Dynamics in Multi-Species Chemotaxis

We study a two-species chemotaxis system that exhibits two qualitatively different regimes: subcritical dynamics, in which solutions remain smooth, and supercritical dynamics, in which strong aggregation may lead to finite-time blow-up. In the subcritical regime, we use a standard continuous-time physics-informed neural network (PINN) with alternating training for the coupled fields and show that it provides accurate and efficient approximations. In the supercritical regime, however, this formulation is not sufficiently robust to resolve the highly localized structures and steep gradients associated with blow-up. To address this limitation, we introduce a discrete-time PINN based on backward Euler time stepping, combined with a logarithmic transformation to stabilize large solution values and a residual-adaptive collocation strategy that concentrates training points near regions of high activity. This hybrid framework allows us to use a simple and computationally inexpensive PINN when the solution is smooth, while switching to a more robust discrete formulation when singular dynamics emerge. Numerical experiments confirm that the continuous-time formulation accurately resolves subcritical dynamics, while the discrete-time formulation reliably captures singular aggregation and finite-time blow-up in the supercritical regime.

math.NA↗

arXiv2026

Parallel Noising in Neural Markov Logic Networks

Neural Markov Logic Networks (NMLNs) are a flexible neurosymbolic relational model. Previous work has shown that, although NMLNs achieve strong performance as generative models for small relational structures, they underperform diffusion-based generative graph models on larger structures. In this paper, we strengthen NMLNs along two main dimensions: (i) we increase the expressive capacity of their potential functions using graph neural networks, and (ii) we develop a new training and inference algorithm inspired by parallel-tempering Markov chain Monte Carlo methods, which we name parallel noising. Together, these enhancements enable NMLNs to attain strong performance in graph generation relative to general diffusion-based generative graph models. Furthermore, they allow NMLNs to match the performance of specialized text-based recurrent models when generating small molecular structures.

cs.LG↗

arXiv2026

Physics-constrained neural networks for surrogate modeling of lossless periodic structures

We introduce a physics-constrained neural network for the rapid prediction of rigorous coupled-wave analysis outputs in the form of Jones matrices. Starting from energy conservation in lossless layered periodic structures, we use the fact that the scattering outputs lie on a Stiefel manifold. This energy constraint is enforced as a hard condition by projecting onto the manifold using differentiable symmetric orthogonalization. The resulting surrogate enforces energy conservation by construction while preserving differentiability for gradient-based inverse design. The performance and generality of the proposed approach are demonstrated through the inverse design of a diffractive waveguide combiner for augmented reality glasses.

physics.optics↗

arXiv2026

Implicit Hypothesis Testing and Divergence Preservation in Neural Network Representations

We study the training dynamics of neural classifiers through the lens of binary hypothesis testing. We re-formalize classification as a collection of binary tests between class-conditional distributions induced by learned representations and show empirically that, along training trajectories, well-generalizing networks progressively approach Neyman-Pearson optimal decision rules, as measured by monotonic growth in the KL divergence retained by learned representations. We provide sufficient conditions for exact optimality, discuss its implications for training regularization, and define an informational plane, (so-called Evidence-Error plane) where convergence can be assessed methodically across network architecture.

cs.LG↗

arXiv2025

Robustness of Covariance Estimators with Application in Activity Detection

The first part of this work considers a general class of covariance estimators. Each estimator of that class is generated by a real-valued function $g$ and a set of model covariance matrices $H$. If $\bf{W}$ is a potentially perturbed observation of a searched covariance matrix, then the estimator is the minimizer of the sum of $g$ applied to each eigenvalue of $\bf{W}^\frac{1}{2}\bf{Z}^{-1}\bf{W}^\frac{1}{2}$ under the constraint that $\bf{Z}$ is from $H$. It is shown that under mild conditions on $g$ and $H$ such estimators are robust, meaning the estimation error can be made arbitrarily small if the perturbation of $\bf{W}$ gets small enough. \par In the second part of this work the previous results are applied to activity detection in random access with multiple receive antennas. In activity detection recovering the large scale fading coefficients is a sparse recovery problem which can be reduced to a structured covariance estimation problem. The recovery can be done with a non-negative least squares estimator or with a relaxed maximum likelihood estimator. It is shown that under suitable assumptions on the distributions of the noise and the channel coefficients, the relaxed maximum likelihood estimator is from the general class of covariance estimators considered in the first part of this work. Then, codebooks based upon a signed kernel condition are proposed. It is shown that with the proposed codebooks both estimators can recover the large-scale fading coefficients if the number of receive antennas is high enough and $S\leq\left\lceil\frac{1}{2}M^2\right\rceil-1$ where $S$ is the number of active users and $M$ is number of pilot symbols per user.

cs.IT↗

arXiv2024

A Deep Unfolding-Based Scalarization Approach for Power Control in D2D Networks

Optimizing network utility in device-to-device networks is typically formulated as a non-convex optimization problem. This paper addresses the scenario where the optimization variables are from a bounded but continuous set, allowing each device to perform power control. The power at each link is optimized to maximize a desired network utility. Specifically, we consider the weighted-sum-rate. The state of the art benchmark for this problem is fractional programming with quadratic transform, known as FPLinQ. We propose a scalarization approach to transform the weighted-sum-rate, developing an iterative algorithm that depends on step sizes, a reference, and a direction vector. By employing the deep unfolding approach, we optimize these parameters by presenting the iterative algorithm as a finite sequence of steps, enabling it to be trained as a deep neural network. Numerical experiments demonstrate that the unfolded algorithm performs comparably to the benchmark in most cases while exhibiting lower complexity. Furthermore, the unfolded algorithm shows strong generalizability in terms of varying the number of users, the signal-to-noise ratio and arbitrary weights. The weighted-sum-rate maximizer can be integrated into a low-complexity fairness scheduler, updating priority weights via virtual queues and Lyapunov Drift Plus Penalty. This is demonstrated through experiments using proportional and max-min fairness.

cs.IT↗

arXiv2024

Non-negative Sparse Recovery at Minimal Sampling Rate

It is known that sparse recovery is possible if the number of measurements is in the order of the sparsity, but the corresponding decoders either lack polynomial decoding time or robustness to noise. Commonly, decoders that rely on a null space property are being used. These achieve polynomial time decoding and are robust to additive noise but pay the price by requiring more measurements. The non-negative least residual has been established as such a decoder for non-negative recovery. A new equivalent condition for uniform, robust recovery of non-negative sparse vectors with the non-negative least residual that is not based on null space properties is introduced. It is shown that the number of measurements for this equivalent condition only needs to be in the order of the sparsity. Further, it is explained why the robustness to additive noise is similar, but not equal, to the robustness of decoders based on null space properties.

cs.IT↗

arXiv2024

Performance of Slotted ALOHA in User-Centric Cell-Free Massive MIMO

To efficiently utilize the scarce wireless resource, the random access scheme has been attaining renewed interest primarily in supporting the sporadic traffic of a large number of devices encountered in the Internet of Things (IoT). In this paper we investigate the performance of slotted ALOHA -- a simple and practical random access scheme -- in connection with the grant-free random access protocol applied for user-centric cell-free massive MIMO. More specifically, we provide the expression of the sum-throughput under the assumptions of the capture capability owned by the centralized detector in the uplink. Further, a comparative study of user-centric cell-free massive MIMO with other types of networks is provided, which allows us to identify its potential and possible limitation. Our numerical simulations show that the user-centric cell-free massive MIMO has a good trade-off between performance and fronthaul load, especially at low activation probability regime.

cs.IT↗

arXiv2024

Onboard Out-of-Calibration Detection of Deep Learning Models using Conformal Prediction

The black box nature of deep learning models complicate their usage in critical applications such as remote sensing. Conformal prediction is a method to ensure trust in such scenarios. Subject to data exchangeability, conformal prediction provides finite sample coverage guarantees in the form of a prediction set that is guaranteed to contain the true class within a user defined error rate. In this letter we show that conformal prediction algorithms are related to the uncertainty of the deep learning model and that this relation can be used to detect if the deep learning model is out-of-calibration. Popular classification models like Resnet50, Densenet161, InceptionV3, and MobileNetV2 are applied on remote sensing datasets such as the EuroSAT to demonstrate how under noisy scenarios the model outputs become untrustworthy. Furthermore an out-of-calibration detection procedure relating the model uncertainty and the average size of the conformal prediction set is presented.

cs.LG↗

arXiv2024

Fundamentals of Delay-Doppler Communications: Practical Implementation and Extensions to OTFS

The recently proposed orthogonal time frequency space (OTFS) modulation, which is a typical Delay-Doppler (DD) communication scheme, has attracted significant attention thanks to its appealing performance over doubly-selective channels. In this paper, we present the fundamentals of general DD communications from the viewpoint of the Zak transform. We start our study by constructing DD domain basis functions aligning with the time-frequency (TF)-consistency condition, which are globally quasi-periodic and locally twisted-shifted. We unveil that these features are translated to unique signal structures in both time and frequency, which are beneficial for communication purposes. Then, we focus on the practical implementations of DD Nyquist communications, where we show that rectangular windows achieve perfect DD orthogonality, while truncated periodic signals can obtain sufficient DD orthogonality. Particularly, smoothed rectangular window with excess bandwidth can result in a slightly worse orthogonality but better pulse localization in the DD domain. Furthermore, we present a practical pulse shaping framework for general DD communications and derive the corresponding input-output relation under various shaping pulses. Our numerical results agree with our derivations and also demonstrate advantages of DD communications over conventional orthogonal frequency-division multiplexing (OFDM).

cs.IT↗

arXiv2023

HyperLISTA-ABT: An Ultra-light Unfolded Network for Accurate Multi-component Differential Tomographic SAR Inversion

Deep neural networks based on unrolled iterative algorithms have achieved remarkable success in sparse reconstruction applications, such as synthetic aperture radar (SAR) tomographic inversion (TomoSAR). However, the currently available deep learning-based TomoSAR algorithms are limited to three-dimensional (3D) reconstruction. The extension of deep learning-based algorithms to four-dimensional (4D) imaging, i.e., differential TomoSAR (D-TomoSAR) applications, is impeded mainly due to the high-dimensional weight matrices required by the network designed for D-TomoSAR inversion, which typically contain millions of freely trainable parameters. Learning such huge number of weights requires an enormous number of training samples, resulting in a large memory burden and excessive time consumption. To tackle this issue, we propose an efficient and accurate algorithm called HyperLISTA-ABT. The weights in HyperLISTA-ABT are determined in an analytical way according to a minimum coherence criterion, trimming the model down to an ultra-light one with only three hyperparameters. Additionally, HyperLISTA-ABT improves the global thresholding by utilizing an adaptive blockwise thresholding scheme, which applies block-coordinate techniques and conducts thresholding in local blocks, so that weak expressions and local features can be retained in the shrinkage step layer by layer. Simulations were performed and demonstrated the effectiveness of our approach, showing that HyperLISTA-ABT achieves superior computational efficiency and with no significant performance degradation compared to state-of-the-art methods. Real data experiments showed that a high-quality 4D point cloud could be reconstructed over a large area by the proposed HyperLISTA-ABT with affordable computational resources and in a fast time.

eess.SP↗

arXiv2023

Multi-static Parameter Estimation in the Near/Far Field Beam Space for Integrated Sensing and Communication Applications

This work proposes a maximum likelihood (ML)-based parameter estimation framework for a millimeter wave (mmWave) integrated sensing and communication (ISAC) system in a multi-static configuration using energy-efficient hybrid digital-analog arrays. Due to the typically large arrays deployed in the higher frequency bands to mitigate isotropic path loss, such arrays may operate in the near-field regime. The proposed parameter estimation in this work consists of a two-stage estimation process, where the first stage is based on far-field assumptions, and is used to obtain a first estimate of the target parameters. In cases where the target is determined to be in the near-field of the arrays, a second estimation based on near-field assumptions is carried out to obtain more accurate estimates. In particular, we select beamfocusing array weights designed to achieve a constant gain over an extended spatial region and re-estimate the target parameters at the receivers. We evaluate the effectiveness of the proposed framework in numerous scenarios through numerical simulations and demonstrate the impact of the custom-designed flat-gain beamfocusing codewords in increasing the communication performance of the system.

eess.SP↗

arXiv2023

Extended Target Parameter Estimation and Tracking with an HDA Setup for ISAC Applications

We investigate radar parameter estimation and beam tracking with a hybrid digital-analog (HDA) architecture in a multi-block measurement framework using an extended target model. In the considered setup, the backscattered data signal is utilized to predict the user position in the next time slots. Specifically, a simplified maximum likelihood framework is adopted for parameter estimation, based on which a simple tracking scheme is also developed. Furthermore, the proposed framework supports adaptive transmitter beamwidth selection, whose effects on the communication performance are also studied. Finally, we verify the effectiveness of the proposed framework via numerical simulations over complex motion patterns that emulate a realistic integrated sensing and communication (ISAC) scenario.

eess.SP↗

arXiv2023

Integrated Sensing and Communication with MOCZ Waveform

In this work, we propose a waveform based on Modulation on Conjugate-reciprocal Zeros (MOCZ) originally proposed for short-packet communications in [1], as a new Integrated Sensing and Communication (ISAC) waveform. Having previously established the key advantages of MOCZ for noncoherent and sporadic communication, here we leverage the optimal auto-correlation property of Binary MOCZ (BMOCZ) for sensing applications. Due to this property, which eliminates the need for separate communication and radar-centric waveforms, we propose a new frame structure for ISAC, where pilot sequences and preambles become obsolete and are completely removed from the frame. As a result, the data rate can be significantly improved. Aimed at (hardware-) cost-effective radar-sensing applications, we consider a Hybrid Digital-Analog (HDA) beamforming architecture for data transmission and radar sensing. We demonstrate via extensive simulations, that a communication data rate, significantly higher than existing standards can be achieved, while simultaneously achieving sensing performance comparable to state-of-the-art sensing systems.

cs.IT↗

arXiv2023

Basis Pursuit Denoising via Recurrent Neural Network Applied to Super-resolving SAR Tomography

Finding sparse solutions of underdetermined linear systems commonly requires the solving of L1 regularized least squares minimization problem, which is also known as the basis pursuit denoising (BPDN). They are computationally expensive since they cannot be solved analytically. An emerging technique known as deep unrolling provided a good combination of the descriptive ability of neural networks, explainable, and computational efficiency for BPDN. Many unrolled neural networks for BPDN, e.g. learned iterative shrinkage thresholding algorithm and its variants, employ shrinkage functions to prune elements with small magnitude. Through experiments on synthetic aperture radar tomography (TomoSAR), we discover the shrinkage step leads to unavoidable information loss in the dynamics of networks and degrades the performance of the model. We propose a recurrent neural network (RNN) with novel sparse minimal gated units (SMGUs) to solve the information loss issue. The proposed RNN architecture with SMGUs benefits from incorporating historical information into optimization, and thus effectively preserves full information in the final output. Taking TomoSAR inversion as an example, extensive simulations demonstrated that the proposed RNN outperforms the state-of-the-art deep learning-based algorithm in terms of super-resolution power as well as generalization ability. It achieved a 10% to 20% higher double scatterers detection rate and is less sensitive to phase and amplitude ratio differences between scatterers. Test on real TerraSAR-X spotlight images also shows a high-quality 3-D reconstruction of the test site.

eess.SP↗

arXiv2023

A physics-informed neural network framework for modeling obstacle-related equations

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g., TensorFlow or PyTorch. Physics-informed neural networks (PINNs) are an attractive tool for solving partial differential equations based on sparse and noisy data. Here extend PINNs to solve obstacle-related PDEs which present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of the solution that lies above a given obstacle. The performance of the proposed PINNs is demonstrated in multiple scenarios for linear and nonlinear PDEs subject to regular and irregular obstacles.

cs.LG↗

arXiv2023

On Discovering Interesting Combinatorial Integer Sequences

We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial objects, e.g., undirected graphs, permutations, matchings etc. In the second step, we use algorithms for lifted first-order model counting to generate integer sequences that count the objects encoded by the first-order logic formulas generated in the first step. For instance, if the first-order sentence defines permutations then the generated integer sequence is the sequence of factorial numbers $n!$. We demonstrate that our approach is able to generate interesting new sequences by showing that a non-negligible fraction of the automatically generated sequences can actually be found in the Online Encyclopaedia of Integer Sequences (OEIS) while generating many other similar sequences which are not present in OEIS and which are potentially interesting. A key technical contribution of our work is the method for generation of first-order logic sentences which is able to drastically prune the space of sentences by discarding large fraction of sentences which would lead to redundant integer sequences.

cs.LO↗