arXiv subjects

Franz Pernkopf

Publications and source records attributed to Franz Pernkopf.

At least 19 recordsLinked to original sources

arXiv2026

On the Fractional Fourier Transform for FMCW Radar Interference Mitigation

In this paper, we extend our method [1] for FMCW radar mutual interference mitigation (IM) based on the discrete fractional Fourier transform (DFrFT). Firstly, we propose a radar signal processing chain including our DFrFT-based IM for real-valued receivers, which we compare to reference algorithms on a synthetic data set. We then reduce computational complexity by reformulating DFrFT-based IM in terms of sparse update signals, which enables mitigation of multiple interferences simultaneously. Finally, we conduct a case study on measurement data and show that our method is compatible with real-world environments.

eess.SP↗

arXiv2026

Stochasticity in Tokenisation Improves Robustness

The widespread adoption of large language models (LLMs) has increased concerns about their robustness. Vulnerabilities in perturbations of tokenisation of the input indicate that models trained with a deterministic canonical tokenisation can be brittle to adversarial attacks. Recent studies suggest that stochastic tokenisation can deliver internal representations that are less sensitive to perturbations. In this paper, we analyse how stochastic tokenisations affect robustness to adversarial attacks and random perturbations. We systematically study this over a range of learning regimes (pre-training, supervised fine-tuning, and in-context learning), data sets, and model architectures. We show that pre-training and fine-tuning with uniformly sampled stochastic tokenisations improve robustness to random and adversarial perturbations. Evaluating on uniformly sampled non-canonical tokenisations reduces the accuracy of a canonically trained Llama-1b model by 29.8%. We find that training with stochastic tokenisation preserves accuracy without increasing inference cost.

cs.CL↗

arXiv2026

Lightweight and perceptually-guided voice conversion for electro-laryngeal speech

Electro-laryngeal (EL) speech is characterized by constant pitch, limited prosody, and mechanical noise, reducing naturalness and intelligibility. We propose a lightweight adaptation of the state-of-the-art StreamVC framework to this setting by removing pitch and energy modules and combining self-supervised pretraining with supervised fine-tuning on parallel EL and healthy (HE) speech data, guided by perceptual and intelligibility losses. Objective and subjective evaluations across different loss configurations confirm their influence: the best model variant, based on WavLM features and human-feedback predictions (+WavLM+HF), drastically reduces character error rate (CER) of EL inputs, raises naturalness mean opinion score (nMOS) from 1.1 to 3.3, and consistently narrows the gap to HE ground-truth speech in all evaluated metrics. These findings demonstrate the feasibility of adapting lightweight voice conversion architectures to EL voice rehabilitation while also identifying prosody generation and intelligibility improvements as the main remaining bottlenecks.

cs.SD↗

arXiv2025

Accelerated Execution of Bayesian Neural Networks using a Single Probabilistic Forward Pass and Code Generation

Machine learning models perform well across domains such as diagnostics, weather forecasting, NLP, and autonomous driving, but their limited uncertainty handling restricts use in safety-critical settings. Traditional neural networks often fail to detect out-of-domain (OOD) data and may output confident yet incorrect predictions. Bayesian neural networks (BNNs) address this by providing probabilistic estimates, but incur high computational cost because predictions require sampling weight distributions and multiple forward passes. The Probabilistic Forward Pass (PFP) offers a highly efficient approximation to Stochastic Variational Inference (SVI) by assuming Gaussian-distributed weights and activations, enabling fully analytic uncertainty propagation and replacing sampling with a single deterministic forward pass. We present an end-to-end pipeline for training, compiling, optimizing, and deploying PFP-based BNNs on embedded ARM CPUs. Using the TVM deep learning compiler, we implement a dedicated library of Gaussian-propagating operators for multilayer perceptrons and convolutional neural networks, combined with manual and automated tuning strategies. Ablation studies show that PFP consistently outperforms SVI in computational efficiency, achieving speedups of up to 4200x for small mini-batches. PFP-BNNs match SVI-BNNs on Dirty-MNIST in accuracy, uncertainty estimation, and OOD detection while greatly reducing compute cost. These results highlight the potential of combining Bayesian approximations with code generation to enable efficient BNN deployment on resource-constrained systems.

cs.LG↗

arXiv2025

On Multiangle Discrete Fractional Periodic Transforms

The efficient multiangle centered discrete fractional Fourier transform (MA-CDFRFT) [1] has proven to be a useful tool for time-frequency analysis; in this paper, we generalize the MA-CDFRFT to general M -periodic transforms, which, among others, include the standard discrete Fourier, discrete sine, discrete cosine, Hadamard and discrete Hartley transform. Furthermore, we exploit the symmetries inherent to the MA-CDFRFT and our novel multiangle standard discrete fractional Fourier transform (MA-DFRFT) to halve the number of FFTs needed to compute these transforms, which paves the way for applications in resource-constrained environments.

eess.SP↗

arXiv2025

FMCW Radar Interference Mitigation based on the Fractional Fourier Transform

In this paper, we propose a novel method for frequency modulated continuous wave (FMCW) radar mutual interference mitigation (IM) based on the discrete fractional Fourier transform (DFrFT). Interference chirps are detected and mitigated by compression and zeroing in the fractional domain. We provide an efficient implementation that can deal with multiple interferers, where we perform consecutive DFrFTs utilizing its angle-additivity property. For that purpose, we generalize and reduce the computational complexity of the multi-angle centered discrete fractional Fourier transform [1]. Our algorithm is designed to be simple and fast such that it can be implemented in hardware. We evaluate our algorithm on a synthetic I/Q-modulated dataset and outperform reference methods in terms of the mean squared error, signal-to-interference-plus-noise ratio, error vector magnitude, true positive rate, false alarm rate and F1-score.

eess.SP↗

arXiv2025

Adaptive Variational Inference in Probabilistic Graphical Models: Beyond Bethe, Tree-Reweighted, and Convex Free Energies

Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types of convex free energies. These approximations are efficient but can fail if the model is complex and highly interactive. In this work, we analyze two classes of approximations that include the above methods as special cases: first, if the model parameters are changed; and second, if the entropy approximation is changed. We discuss benefits and drawbacks of either approach, and deduce from this analysis how a free energy approximation should ideally be constructed. Based on our observations, we propose approximations that automatically adapt to a given model and demonstrate their effectiveness for a range of difficult problems.

stat.ML↗

arXiv2024

Function Space Diversity for Uncertainty Prediction via Repulsive Last-Layer Ensembles

Bayesian inference in function space has gained attention due to its robustness against overparameterization in neural networks. However, approximating the infinite-dimensional function space introduces several challenges. In this work, we discuss function space inference via particle optimization and present practical modifications that improve uncertainty estimation and, most importantly, make it applicable for large and pretrained networks. First, we demonstrate that the input samples, where particle predictions are enforced to be diverse, are detrimental to the model performance. While diversity on training data itself can lead to underfitting, the use of label-destroying data augmentation, or unlabeled out-of-distribution data can improve prediction diversity and uncertainty estimates. Furthermore, we take advantage of the function space formulation, which imposes no restrictions on network parameterization other than sufficient flexibility. Instead of using full deep ensembles to represent particles, we propose a single multi-headed network that introduces a minimal increase in parameters and computation. This allows seamless integration to pretrained networks, where this repulsive last-layer ensemble can be used for uncertainty aware fine-tuning at minimal additional cost. We achieve competitive results in disentangling aleatoric and epistemic uncertainty for active learning, detecting out-of-domain data, and providing calibrated uncertainty estimates under distribution shifts with minimal compute and memory.

cs.LG↗

arXiv2024

Robustness of Explainable Artificial Intelligence in Industrial Process Modelling

eXplainable Artificial Intelligence (XAI) aims at providing understandable explanations of black box models. In this paper, we evaluate current XAI methods by scoring them based on ground truth simulations and sensitivity analysis. To this end, we used an Electric Arc Furnace (EAF) model to better understand the limits and robustness characteristics of XAI methods such as SHapley Additive exPlanations (SHAP), Local Interpretable Model-agnostic Explanations (LIME), as well as Averaged Local Effects (ALE) or Smooth Gradients (SG) in a highly topical setting. These XAI methods were applied to various types of black-box models and then scored based on their correctness compared to the ground-truth sensitivity of the data-generating processes using a novel scoring evaluation methodology over a range of simulated additive noise. The resulting evaluation shows that the capability of the Machine Learning (ML) models to capture the process accurately is, indeed, coupled with the correctness of the explainability of the underlying data-generating process. We furthermore show the differences between XAI methods in their ability to correctly predict the true sensitivity of the modeled industrial process.

cs.LG↗

arXiv2024

On the Convexity and Reliability of the Bethe Free Energy Approximation

The Bethe free energy approximation provides an effective way for relaxing NP-hard problems of probabilistic inference. However, its accuracy depends on the model parameters and particularly degrades if a phase transition in the model occurs. In this work, we analyze when the Bethe approximation is reliable and how this can be verified. We argue and show by experiment that it is mostly accurate if it is convex on a submanifold of its domain, the 'Bethe box'. For verifying its convexity, we derive two sufficient conditions that are based on the definiteness properties of the Bethe Hessian matrix: the first uses the concept of diagonal dominance, and the second decomposes the Bethe Hessian matrix into a sum of sparse matrices and characterizes the definiteness properties of the individual matrices in that sum. These theoretical results provide a simple way to estimate the critical phase transition temperature of a model. As a practical contribution we propose $\texttt{BETHE-MIN}$, a projected quasi-Newton method to efficiently find a minimum of the Bethe free energy.

stat.ML↗

arXiv2024

Resource-Efficient Neural Networks for Embedded Systems

While machine learning is traditionally a resource intensive task, embedded systems, autonomous navigation, and the vision of the Internet of Things fuel the interest in resource-efficient approaches. These approaches aim for a carefully chosen trade-off between performance and resource consumption in terms of computation and energy. The development of such approaches is among the major challenges in current machine learning research and key to ensure a smooth transition of machine learning technology from a scientific environment with virtually unlimited computing resources into everyday's applications. In this article, we provide an overview of the current state of the art of machine learning techniques facilitating these real-world requirements. In particular, we focus on resource-efficient inference based on deep neural networks (DNNs), the predominant machine learning models of the past decade. We give a comprehensive overview of the vast literature that can be mainly split into three non-mutually exclusive categories: (i) quantized neural networks, (ii) network pruning, and (iii) structural efficiency. These techniques can be applied during training or as post-processing, and they are widely used to reduce the computational demands in terms of memory footprint, inference speed, and energy efficiency. We also briefly discuss different concepts of embedded hardware for DNNs and their compatibility with machine learning techniques as well as potential for energy and latency reduction. We substantiate our discussion with experiments on well-known benchmark data sets using compression techniques (quantization, pruning) for a set of resource-constrained embedded systems, such as CPUs, GPUs and FPGAs. The obtained results highlight the difficulty of finding good trade-offs between resource efficiency and prediction quality.

stat.ML↗

arXiv2024

Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders

The traditional two-stage approach to causal inference first identifies a single causal model (or equivalence class of models), which is then used to answer causal queries. However, this neglects any epistemic model uncertainty. In contrast, Bayesian causal inference does incorporate epistemic uncertainty into query estimates via Bayesian marginalisation (posterior averaging) over all causal models. While principled, this marginalisation over entire causal models, i.e., both causal structures (graphs) and mechanisms, poses a tremendous computational challenge. In this work, we address this challenge by decomposing structure marginalisation into the marginalisation over (i) causal orders and (ii) directed acyclic graphs (DAGs) given an order. We can marginalise the latter in closed form by limiting the number of parents per variable and utilising Gaussian processes to model mechanisms. To marginalise over orders, we use a sampling-based approximation, for which we devise a novel auto-regressive distribution over causal orders (ARCO). Our method outperforms state-of-the-art in structure learning on simulated non-linear additive noise benchmarks, and yields competitive results on real-world data. Furthermore, we can accurately infer interventional distributions and average causal effects.

cs.LG↗

arXiv2023

Angle-Equivariant Convolutional Neural Networks for Interference Mitigation in Automotive Radar

In automotive applications, frequency modulated continuous wave (FMCW) radar is an established technology to determine the distance, velocity and angle of objects in the vicinity of the vehicle. The quality of predictions might be seriously impaired if mutual interference between radar sensors occurs. Previous work processes data from the entire receiver array in parallel to increase interference mitigation quality using neural networks (NNs). However, these architectures do not generalize well across different angles of arrival (AoAs) of interferences and objects. In this paper we introduce fully convolutional neural network (CNN) with rank-three convolutions which is able to transfer learned patterns between different AoAs. Our proposed architecture outperforms previous work while having higher robustness and a lower number of trainable parameters. We evaluate our network on a diverse data set and demonstrate its angle equivariance.

eess.SP↗

arXiv2023

End-to-End Training of Neural Networks for Automotive Radar Interference Mitigation

In this paper we propose a new method for training neural networks (NNs) for frequency modulated continuous wave (FMCW) radar mutual interference mitigation. Instead of training NNs to regress from interfered to clean radar signals as in previous work, we train NNs directly on object detection maps. We do so by performing a continuous relaxation of the cell-averaging constant false alarm rate (CA-CFAR) peak detector, which is a well-established algorithm for object detection using radar. With this new training objective we are able to increase object detection performance by a large margin. Furthermore, we introduce separable convolution kernels to strongly reduce the number of parameters and computational complexity of convolutional NN architectures for radar applications. We validate our contributions with experiments on real-world measurement data and compare them against signal processing interference mitigation methods.

cs.LG↗

arXiv2023

"UWBCarGraz" Dataset for Car Occupancy Detection using Ultra-Wideband Radar

We present a data-driven car occupancy detection algorithm using ultra-wideband radar based on the ResNet architecture. The algorithm is trained on a dataset of channel impulse responses obtained from measurements at three different activity levels of the occupants (i.e. breathing, talking, moving). We compare the presented algorithm against a state-of-the-art car occupancy detection algorithm based on variational message passing (VMP). Our presented ResNet architecture is able to outperform the VMP algorithm in terms of the area under the receiver operating curve (AUC) at low signal-to-noise ratios (SNRs) for all three activity levels of the target. Specifically, for an SNR of -20 dB the VMP detector achieves an AUC of 0.87 while the ResNet architecture achieves an AUC of 0.91 if the target is sitting still and breathing naturally. The difference in performance for the other activities is similar. To facilitate the implementation in the onboard computer of a car we perform an ablation study to optimize the tradeoff between performance and computational complexity for several ResNet architectures. The dataset used to train and evaluate the algorithm is openly accessible. This facilitates an easy comparison in future works.

eess.SP↗

arXiv2023

Fast Variational Block-Sparse Bayesian Learning

We propose a variational Bayesian (VB) implementation of block-sparse Bayesian learning (BSBL) to compute proxy probability density functions (PDFs) that approximate the posterior PDFs of the weights and associated hyperparameters in a block-sparse linear model, resulting in an iterative algorithm coined variational BSBL (VA-BSBL). The priors of the hyperparameters are selected to belong to the family of generalized inverse Gaussian distributions. This family contains as special cases commonly used hyperpriors. Inspired by previous work on classical sparse Bayesian learning (SBL), we investigate the update stage in which the proxy PDFs of a single block of weights and of its associated hyperparameter are successively updated, while keeping the proxy PDFs of the other parameters fixed. This stage defines a nonlinear first-order recurrence relation for the mean of the proxy PDF of the hyperparameter. By iterating this relation "ad infinitum" we obtain a criterion that determines whether the so-generated sequence of hyperparameter means converges or diverges. Incorporating this criterion into the VA-BSBL algorithm yields a fast implementation, coined fast-BSBL (F-BSBL), which achieves a two-order-of-magnitude runtime improvement. We further identify the range of the parameters of the generalized inverse Gaussian distribution which result in an inherent pruning procedure that switches off "weak" components in the model, which is necessary to obtain sparse results. Lastly, we show that expectation-maximization (EM)-based and VB-based implementations of BSBL are identical methods. Thus, we extend a well-known result from classical SBL to BSBL. Consequently, F-BSBL and BSBL using coordinate ascent to maximize the marginal likelihood coincide. These results provide a unified framework for interpreting existing BSBL methods.

eess.SP↗

arXiv2023

Self-attention for Enhanced OAMP Detection in MIMO Systems

Multiple-Input Multiple-Output (MIMO) systems are essential for wireless communications. Sinceclassical algorithms for symbol detection in MIMO setups require large computational resourcesor provide poor results, data-driven algorithms are becoming more popular. Most of the proposedalgorithms, however, introduce approximations leading to degraded performance for realistic MIMOsystems. In this paper, we introduce a neural-enhanced hybrid model, augmenting the analyticbackbone algorithm with state-of-the-art neural network components. In particular, we introduce aself-attention model for the enhancement of the iterative Orthogonal Approximate Message Passing(OAMP)-based decoding algorithm. In our experiments, we show that the proposed model canoutperform existing data-driven approaches for OAMP while having improved generalization to otherSNR values at limited computational overhead.

cs.IT↗

arXiv2023

Variational Inference of Structured Line Spectra Exploiting Group-Sparsity

In this paper, we present a variational inference algorithm that decomposes a signal into multiple groups of related spectral lines. The spectral lines in each group are associated with a group parameter common to all spectral lines within the group. The proposed algorithm jointly estimates the group parameters, the number of spetral lines within a group, and the number of groups exploiting a Bernoulli-Gamma-Gaussian hierarchical prior model which promotes sparse solutions. Aiming to maximize the evidence lower bound (ELBO), variational inference provides analytic approximations of the posterior probability density functions (PDFs) and also gives estimates of the additional model parameters such as the measurement noise variance. While the activation variables of the groups and the associated group parameters (such as fundamental frequencies and the corresponding higher order harmonics) are estimated as point estimates, the remaining parameters such as the complex amplitudes of the spectral lines and their precision parameters are estimated as approximate posterior PDFs. We demonstrate the versatility and performance of the proposed algorithm on three different inference problems. In particular, the proposed algorithm is applied to the multi-pitch estimation problem, the radar signal-based extended object estimation problem, and variational mode decomposition (VMD) using synthetic measurements and to real multi-pitch estimation problem using the Bach-10 dataset. The results show that the proposed algorithm outperforms state-of-the-art model-based and pre-trained algorithms on all three inference problems.

eess.SP↗