Franz Pernkopf

Christian Toth, Lars Lorch, Christian Knoll et al. · eth-zurich

Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.

Benedikt Mayrhofer, Franz Pernkopf, Philipp Aichinger et al.

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.

Sophie Steger, Rui Li, Sofiane Ennadir et al.

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.

Benedikt Kantz, Clemens Staudinger, Christoph Feilmayr et al.

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.

Johanna Rock, Mate Toth, Elmar Messner et al.

Driver assistance systems as well as autonomous cars have to rely on sensors to perceive their environment. A heterogeneous set of sensors is used to perform this task robustly. Among them, radar sensors are indispensable because of their range resolution and the possibility to directly measure velocity. Since more and more radar sensors are deployed on the streets, mutual interference must be dealt with. In the so far unregulated automotive radar frequency band, a sensor must be capable of detecting, or even mitigating the harmful effects of interference, which include a decreased detection sensitivity. In this paper, we address this issue with Convolutional Neural Networks (CNNs), which are state-of-the-art machine learning tools. We show that the ability of CNNs to find structured information in data while preserving local information enables superior denoising performance. To achieve this, CNN parameters are found using training with simulated data and integrated into the automotive radar signal processing chain. The presented method is compared with the state of the art, highlighting its promising performance. Hence, CNNs can be employed for interference mitigation as an alternative to conventional signal processing methods. Code and pre-trained models are available at https://github.com/johanna-rock/imRICnn.

Christian Toth, Christian Knoll, Franz Pernkopf et al.

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.

Christian Oswald, Mate Toth, Paul Meissner et al.

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.

Sophie Steger, Christian Knoll, Bernhard Klein et al.

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.

Christian Oswald, Mate Toth, Paul Meissner et al.

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.

Bernhard Klein, Falk Selker, Hendrik Borras et al.

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.

Harald Leisenberger, Franz Pernkopf

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.

Harald Leisenberger, Christian Knoll, Franz Pernkopf

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.

Christoph Obermair, Thomas Cartier-Michaud, Andrea Apollonio et al.

The occurrence of vacuum arcs or radio frequency (rf) breakdowns is one of the most prevalent factors limiting the high-gradient performance of normal conducting rf cavities in particle accelerators. In this paper, we search for the existence of previously unrecognized features related to the incidence of rf breakdowns by applying a machine learning strategy to high-gradient cavity data from CERN's test stand for the Compact Linear Collider (CLIC). By interpreting the parameters of the learned models with explainable artificial intelligence (AI), we reverse-engineer physical properties for deriving fast, reliable, and simple rule-based models. Based on 6 months of historical data and dedicated experiments, our models show fractions of data with a high influence on the occurrence of breakdowns. Specifically, it is shown that the field emitted current following an initial breakdown is closely related to the probability of another breakdown occurring shortly thereafter. Results also indicate that the cavity pressure should be monitored with increased temporal resolution in future experiments, to further explore the vacuum activity associated with breakdowns.

Johanna Rock, Wolfgang Roth, Mate Toth et al.

Radar sensors are crucial for environment perception of driver assistance systems as well as autonomous vehicles. With a rising number of radar sensors and the so far unregulated automotive radar frequency band, mutual interference is inevitable and must be dealt with. Algorithms and models operating on radar data are required to run the early processing steps on specialized radar sensor hardware. This specialized hardware typically has strict resource-constraints, i.e. a low memory capacity and low computational power. Convolutional Neural Network (CNN)-based approaches for denoising and interference mitigation yield promising results for radar processing in terms of performance. Regarding resource-constraints, however, CNNs typically exceed the hardware's capacities by far. In this paper we investigate quantization techniques for CNN-based denoising and interference mitigation of radar signals. We analyze the quantization of (i) weights and (ii) activations of different CNN-based model architectures. This quantization results in reduced memory requirements for model storage and during inference. We compare models with fixed and learned bit-widths and contrast two different methodologies for training quantized CNNs, i.e. the straight-through gradient estimator and training distributions over discrete weights. We illustrate the importance of structurally small real-valued base models for quantization and show that learned bit-widths yield the smallest models. We achieve a memory reduction of around 80\% compared to the real-valued baseline. Due to practical reasons, however, we recommend the use of 8 bits for weights and activations, which results in models that require only 0.2 megabytes of memory.

Alexander Fuchs, Christian Knoll, Franz Pernkopf

Deep neural networks rely heavily on normalization methods to improve their performance and learning behavior. Although normalization methods spurred the development of increasingly deep and efficient architectures, they also increase the vulnerability with respect to noise and input corruptions. In most applications, however, noise is ubiquitous and diverse; this can often lead to complete failure of machine learning systems as they fail to cope with mismatches between the input distribution during training- and test-time. The most common normalization method, batch normalization, reduces the distribution shift during training but is agnostic to changes in the input distribution during test time. This makes batch normalization prone to performance degradation whenever noise is present during test-time. Sample-based normalization methods can correct linear transformations of the activation distribution but cannot mitigate changes in the distribution shape; this makes the network vulnerable to distribution changes that cannot be reflected in the normalization parameters. We propose an unsupervised non-parametric distribution correction method that adapts the activation distribution of each layer. This reduces the mismatch between the training and test-time distribution by minimizing the 1-D Wasserstein distance. In our experiments, we empirically show that the proposed method effectively reduces the impact of intense image corruptions and thus improves the classification performance without the need for retraining or fine-tuning the model.

Truc Nguyen, Franz Pernkopf

In this paper, we use pre-trained ResNet models as backbone architectures for classification of adventitious lung sounds and respiratory diseases. The knowledge of the pre-trained model is transferred by using vanilla fine-tuning, co-tuning, stochastic normalization and the combination of the co-tuning and stochastic normalization techniques. Furthermore, data augmentation in both time domain and time-frequency domain is used to account for the class imbalance of the ICBHI and our multi-channel lung sound dataset. Additionally, we apply spectrum correction to consider the variations of the recording device properties on the ICBHI dataset. Empirically, our proposed systems mostly outperform all state-of-the-art lung sound classification systems for the adventitious lung sounds and respiratory diseases of both datasets.

Truc Nguyen, Franz Pernkopf

Large annotated lung sound databases are publicly available and might be used to train algorithms for diagnosis systems. However, it might be a challenge to develop a well-performing algorithm for small non-public data, which have only a few subjects and show differences in recording devices and setup. In this paper, we use transfer learning to tackle the mismatch of the recording setup. This allows us to transfer knowledge from one dataset to another dataset for crackle detection in lung sounds. In particular, a single input convolutional neural network (CNN) model is pre-trained on a source domain using ICBHI 2017, the largest publicly available database of lung sounds. We use log-mel spectrogram features of respiratory cycles of lung sounds. The pre-trained network is used to build a multi-input CNN model, which shares the same network architecture for respiratory cycles and their corresponding respiratory phases. The multi-input model is then fine-tuned on the target domain of our self-collected lung sound database for classifying crackles and normal lung sounds. Our experimental results show significant performance improvements of 9.84% (absolute) in F-score on the target domain using the multi-input CNN model based on transfer learning for crackle detection in adventitious lung sound classification task.

Alexander Fuchs, Johanna Rock, Mate Toth et al.

Autonomous driving highly depends on capable sensors to perceive the environment and to deliver reliable information to the vehicles' control systems. To increase its robustness, a diversified set of sensors is used, including radar sensors. Radar is a vital contribution of sensory information, providing high resolution range as well as velocity measurements. The increased use of radar sensors in road traffic introduces new challenges. As the so far unregulated frequency band becomes increasingly crowded, radar sensors suffer from mutual interference between multiple radar sensors. This interference must be mitigated in order to ensure a high and consistent detection sensitivity. In this paper, we propose the use of Complex-Valued Convolutional Neural Networks (CVCNNs) to address the issue of mutual interference between radar sensors. We extend previously developed methods to the complex domain in order to process radar data according to its physical characteristics. This not only increases data efficiency, but also improves the conservation of phase information during filtering, which is crucial for further processing, such as angle estimation. Our experiments show, that the use of CVCNNs increases data efficiency, speeds up network training and substantially improves the conservation of phase information during interference removal.

David Peter, Wolfgang Roth, Franz Pernkopf

This paper introduces neural architecture search (NAS) for the automatic discovery of end-to-end keyword spotting (KWS) models in limited resource environments. We employ a differentiable NAS approach to optimize the structure of convolutional neural networks (CNNs) operating on raw audio waveforms. After a suitable KWS model is found with NAS, we conduct quantization of weights and activations to reduce the memory footprint. We conduct extensive experiments on the Google speech commands dataset. In particular, we compare our end-to-end approach to mel-frequency cepstral coefficient (MFCC) based systems. For quantization, we compare fixed bit-width quantization and trained bit-width quantization. Using NAS only, we were able to obtain a highly efficient model with an accuracy of 95.55% using 75.7k parameters and 13.6M operations. Using trained bit-width quantization, the same model achieves a test accuracy of 93.76% while using on average only 2.91 bits per activation and 2.51 bits per weight.

Lukas Pfeifenberger, Franz Pernkopf

In this paper, we present the Blind Speech Separation and Dereverberation (BSSD) network, which performs simultaneous speaker separation, dereverberation and speaker identification in a single neural network. Speaker separation is guided by a set of predefined spatial cues. Dereverberation is performed by using neural beamforming, and speaker identification is aided by embedding vectors and triplet mining. We introduce a frequency-domain model which uses complex-valued neural networks, and a time-domain variant which performs beamforming in latent space. Further, we propose a block-online mode to process longer audio recordings, as they occur in meeting scenarios. We evaluate our system in terms of Scale Independent Signal to Distortion Ratio (SI-SDR), Word Error Rate (WER) and Equal Error Rate (EER).

David Peter, Wolfgang Roth, Franz Pernkopf

This paper introduces neural architecture search (NAS) for the automatic discovery of small models for keyword spotting (KWS) in limited resource environments. We employ a differentiable NAS approach to optimize the structure of convolutional neural networks (CNNs) to maximize the classification accuracy while minimizing the number of operations per inference. Using NAS only, we were able to obtain a highly efficient model with 95.4% accuracy on the Google speech commands dataset with 494.8 kB of memory usage and 19.6 million operations. Additionally, weight quantization is used to reduce the memory consumption even further. We show that weight quantization to low bit-widths (e.g. 1 bit) can be used without substantial loss in accuracy. By increasing the number of input features from 10 MFCC to 20 MFCC we were able to increase the accuracy to 96.3% at 340.1 kB of memory usage and 27.1 million operations.

Johanna Rock, Mate Toth, Paul Meissner et al.

Radar sensors are crucial for environment perception of driver assistance systems as well as autonomous cars. Key performance factors are a fine range resolution and the possibility to directly measure velocity. With a rising number of radar sensors and the so far unregulated automotive radar frequency band, mutual interference is inevitable and must be dealt with. Sensors must be capable of detecting, or even mitigating the harmful effects of interference, which include a decreased detection sensitivity. In this paper, we evaluate a Convolutional Neural Network (CNN)-based approach for interference mitigation on real-world radar measurements. We combine real measurements with simulated interference in order to create input-output data suitable for training the model. We analyze the performance to model complexity relation on simulated and measurement data, based on an extensive parameter search. Further, a finite sample size performance comparison shows the effectiveness of the model trained on either simulated or real data as well as for transfer learning. A comparative performance analysis with the state of the art emphasizes the potential of CNN-based models for interference mitigation and denoising of real-world measurements, also considering resource constraints of the hardware.

Johanna Rock, Wolfgang Roth, Paul Meissner et al.

Radar sensors are crucial for environment perception of driver assistance systems as well as autonomous vehicles. Key performance factors are weather resistance and the possibility to directly measure velocity. With a rising number of radar sensors and the so far unregulated automotive radar frequency band, mutual interference is inevitable and must be dealt with. Algorithms and models operating on radar data in early processing stages are required to run directly on specialized hardware, i.e. the radar sensor. This specialized hardware typically has strict resource-constraints, i.e. a low memory capacity and low computational power. Convolutional Neural Network (CNN)-based approaches for denoising and interference mitigation yield promising results for radar processing in terms of performance. However, these models typically contain millions of parameters, stored in hundreds of megabytes of memory, and require additional memory during execution. In this paper we investigate quantization techniques for CNN-based denoising and interference mitigation of radar signals. We analyze the quantization potential of different CNN-based model architectures and sizes by considering (i) quantized weights and (ii) piecewise constant activation functions, which results in reduced memory requirements for model storage and during the inference step respectively.

Wolfgang Roth, Günther Schindler, Holger Fröning et al.

We present two methods to reduce the complexity of Bayesian network (BN) classifiers. First, we introduce quantization-aware training using the straight-through gradient estimator to quantize the parameters of BNs to few bits. Second, we extend a recently proposed differentiable tree-augmented naive Bayes (TAN) structure learning approach by also considering the model size. Both methods are motivated by recent developments in the deep learning community, and they provide effective means to trade off between model size and prediction accuracy, which is demonstrated in extensive experiments. Furthermore, we contrast quantized BN classifiers with quantized deep neural networks (DNNs) for small-scale scenarios which have hardly been investigated in the literature. We show Pareto optimal models with respect to model size, number of operations, and test error and find that both model classes are viable options.

Wolfgang Roth, Franz Pernkopf

Learning the structure of Bayesian networks is a difficult combinatorial optimization problem. In this paper, we consider learning of tree-augmented naive Bayes (TAN) structures for Bayesian network classifiers with discrete input features. Instead of performing a combinatorial optimization over the space of possible graph structures, the proposed method learns a distribution over graph structures. After training, we select the most probable structure of this distribution. This allows for a joint training of the Bayesian network parameters along with its TAN structure using gradient-based optimization. The proposed method is agnostic to the specific loss and only requires that it is differentiable. We perform extensive experiments using a hybrid generative-discriminative loss based on the discriminative probabilistic margin. Our method consistently outperforms random TAN structures and Chow-Liu TAN structures.

Lukas Pfeifenberger, Matthias Zöhrer, Günther Schindler et al.

While machine learning techniques are traditionally resource intensive, we are currently witnessing an increased interest in hardware and energy efficient approaches. This need for resource-efficient machine learning is primarily driven by the demand for embedded systems and their usage in ubiquitous computing and IoT applications. In this article, we provide a resource-efficient approach for multi-channel speech enhancement based on Deep Neural Networks (DNNs). In particular, we use reduced-precision DNNs for estimating a speech mask from noisy, multi-channel microphone observations. This speech mask is used to obtain either the Minimum Variance Distortionless Response (MVDR) or Generalized Eigenvalue (GEV) beamformer. In the extreme case of binary weights and reduced precision activations, a significant reduction of execution time and memory footprint is possible while still obtaining an audio quality almost on par to single-precision DNNs and a slightly larger Word Error Rate (WER) for single speaker scenarios using the WSJ0 speech corpus.

Alexander Fuchs, Franz Pernkopf

Capsule networks offer interesting properties and provide an alternative to today's deep neural network architectures. However, recent approaches have failed to consistently achieve competitive results across different image datasets. We propose a new parameter efficient capsule architecture, that is able to tackle complex tasks by using neural networks trained with an approximate Wasserstein objective to dynamically select capsules throughout the entire architecture. This approach focuses on implementing a robust routing scheme, which can deliver improved results using little overhead. We perform several ablation studies verifying the proposed concepts and show that our network is able to substantially outperform other capsule approaches by over 1.2 % on CIFAR-10, using fewer parameters.

Wolfgang Roth, Günther Schindler, Bernhard Klein et al.

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.

Martin Trapp, Robert Peharz, Franz Pernkopf et al.

Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference is frequently employed, where a prominent class of approximation techniques is based on local GP experts. However, local-expert techniques proposed so far are either not well-principled, come with limited approximation guarantees, or lead to intractable models. In this paper, we introduce deep structured mixtures of GP experts, a stochastic process model which i) allows exact posterior inference, ii) has attractive computational and memory costs, and iii) when used as GP approximation, captures predictive uncertainties consistently better than previous expert-based approximations. In a variety of experiments, we show that deep structured mixtures have a low approximation error and often perform competitive or outperform prior work.

Bernhard K. Aichernig, Roderick Bloem, Masoud Ebrahimi et al.

Models play an essential role in the design process of cyber-physical systems. They form the basis for simulation and analysis and help in identifying design problems as early as possible. However, the construction of models that comprise physical and digital behavior is challenging. Therefore, there is considerable interest in learning such hybrid behavior by means of machine learning which requires sufficient and representative training data covering the behavior of the physical system adequately. In this work, we exploit a combination of automata learning and model-based testing to generate sufficient training data fully automatically. Experimental results on a platooning scenario show that recurrent neural networks learned with this data achieved significantly better results compared to models learned from randomly generated data. In particular, the classification error for crash detection is reduced by a factor of five and a similar F1-score is obtained with up to three orders of magnitude fewer training samples.

Guenther Schindler, Wolfgang Roth, Franz Pernkopf et al.

As a result of the growing size of Deep Neural Networks (DNNs), the gap to hardware capabilities in terms of memory and compute increases. To effectively compress DNNs, quantization and connection pruning are usually considered. However, unconstrained pruning usually leads to unstructured parallelism, which maps poorly to massively parallel processors, and substantially reduces the efficiency of general-purpose processors. Similar applies to quantization, which often requires dedicated hardware. We propose Parameterized Structured Pruning (PSP), a novel method to dynamically learn the shape of DNNs through structured sparsity. PSP parameterizes structures (e.g. channel- or layer-wise) in a weight tensor and leverages weight decay to learn a clear distinction between important and unimportant structures. As a result, PSP maintains prediction performance, creates a substantial amount of sparsity that is structured and, thus, easy and efficient to map to a variety of massively parallel processors, which are mandatory for utmost compute power and energy efficiency. PSP is experimentally validated on the popular CIFAR10/100 and ILSVRC2012 datasets using ResNet and DenseNet architectures, respectively.

Martin Trapp, Robert Peharz, Hong Ge et al.

Sum-product networks (SPNs) are flexible density estimators and have received significant attention due to their attractive inference properties. While parameter learning in SPNs is well developed, structure learning leaves something to be desired: Even though there is a plethora of SPN structure learners, most of them are somewhat ad-hoc and based on intuition rather than a clear learning principle. In this paper, we introduce a well-principled Bayesian framework for SPN structure learning. First, we decompose the problem into i) laying out a computational graph, and ii) learning the so-called scope function over the graph. The first is rather unproblematic and akin to neural network architecture validation. The second represents the effective structure of the SPN and needs to respect the usual structural constraints in SPN, i.e. completeness and decomposability. While representing and learning the scope function is somewhat involved in general, in this paper, we propose a natural parametrisation for an important and widely used special case of SPNs. These structural parameters are incorporated into a Bayesian model, such that simultaneous structure and parameter learning is cast into monolithic Bayesian posterior inference. In various experiments, our Bayesian SPNs often improve test likelihoods over greedy SPN learners. Further, since the Bayesian framework protects against overfitting, we can evaluate hyper-parameters directly on the Bayesian model score, waiving the need for a separate validation set, which is especially beneficial in low data regimes. Bayesian SPNs can be applied to heterogeneous domains and can easily be extended to nonparametric formulations. Moreover, our Bayesian approach is the first, which consistently and robustly learns SPN structures under missing data.

Martin Trapp, Robert Peharz, Franz Pernkopf

It seems to be a pearl of conventional wisdom that parameter learning in deep sum-product networks is surprisingly fast compared to shallow mixture models. This paper examines the effects of overparameterization in sum-product networks on the speed of parameter optimisation. Using theoretical analysis and empirical experiments, we show that deep sum-product networks exhibit an implicit acceleration compared to their shallow counterpart. In fact, gradient-based optimisation in deep tree-structured sum-product networks is equal to gradient ascend with adaptive and time-varying learning rates and additional momentum terms.

Franz Pernkopf, Wolfgang Roth, Matthias Zoehrer et al.

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 require a carefully chosen trade-off between performance and resource consumption in terms of computation and energy. On top of this, it is crucial to treat uncertainty in a consistent manner in all but the simplest applications of machine learning systems. In particular, a desideratum for any real-world system is to be robust in the presence of outliers and corrupted data, as well as being `aware' of its limits, i.e.\ the system should maintain and provide an uncertainty estimate over its own predictions. These complex demands are among the major challenges in current machine learning research and key to ensure a smooth transition of machine learning technology into every day'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. First we provide a comprehensive review of resource-efficiency in deep neural networks with focus on techniques for model size reduction, compression and reduced precision. These techniques can be applied during training or as post-processing and are widely used to reduce both computational complexity and memory footprint. As most (practical) neural networks are limited in their ways to treat uncertainty, we contrast them with probabilistic graphical models, which readily serve these desiderata by means of probabilistic inference. In that way, we provide an extensive overview of the current state-of-the-art of robust and efficient machine learning for real-world systems.

Christian Knoll, Adrian Weller, Franz Pernkopf

Belief propagation (BP) is a popular method for performing probabilistic inference on graphical models. In this work, we enhance BP and propose self-guided belief propagation (SBP) that incorporates the pairwise potentials only gradually. This homotopy continuation method converges to a unique solution and increases the accuracy without increasing the computational burden. We provide a formal analysis to demonstrate that SBP finds the global optimum of the Bethe approximation for attractive models where all variables favor the same state. Moreover, we apply SBP to various graphs with random potentials and empirically show that: (i) SBP is superior in terms of accuracy whenever BP converges, and (ii) SBP obtains a unique, stable, and accurate solution whenever BP does not converge.

Robert Harb, Franz Pernkopf

In this paper, we present a gated convolutional recurrent neural network based approach to solve task 4, large-scale weakly labelled semi-supervised sound event detection in domestic environments, of the DCASE 2018 challenge. Gated linear units and a temporal attention layer are used to predict the onset and offset of sound events in 10s long audio clips. Whereby for training only weakly-labelled data is used. Virtual adversarial training is used for regularization, utilizing both labelled and unlabeled data. Furthermore, we introduce self-adaptive label refinement, a method which allows unsupervised adaption of our trained system to refine the accuracy of frame-level class predictions. The proposed system reaches an overall macro averaged event-based F-score of 34.6%, resulting in a relative improvement of 20.5% over the baseline system.

Martin Trapp, Robert Peharz, Carl E. Rasmussen et al.

While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive way to tackle these problems, by incorporating GPs in sum-product networks (SPNs), a recently proposed tractable probabilistic model allowing exact and efficient inference. In particular, by using GPs as leaves of an SPN we obtain a novel flexible prior over functions, which implicitly represents an exponentially large mixture of local GPs. Exact and efficient posterior inference in this model can be done in a natural interplay of the inference mechanisms in GPs and SPNs. Thereby, each GP is -- similarly as in a mixture of experts approach -- responsible only for a subset of data points, which effectively reduces inference cost in a divide and conquer fashion. We show that integrating GPs into the SPN framework leads to a promising probabilistic regression model which is: (1) computational and memory efficient, (2) allows efficient and exact posterior inference, (3) is flexible enough to mix different kernel functions, and (4) naturally accounts for non-stationarities in time series. In a variate of experiments, we show that the SPN-GP model can learn input dependent parameters and hyper-parameters and is on par with or outperforms the traditional GPs as well as state of the art approximations on real-world data.

Martin Ratajczak, Sebastian Tschiatschek, Franz Pernkopf

We consider higher-order linear-chain conditional random fields (HO-LC-CRFs) for sequence modelling, and use sum-product networks (SPNs) for representing higher-order input- and output-dependent factors. SPNs are a recently introduced class of deep models for which exact and efficient inference can be performed. By combining HO-LC-CRFs with SPNs, expressive models over both the output labels and the hidden variables are instantiated while still enabling efficient exact inference. Furthermore, the use of higher-order factors allows us to capture relations of multiple input segments and multiple output labels as often present in real-world data. These relations can not be modelled by the commonly used first-order models and higher-order models with local factors including only a single output label. We demonstrate the effectiveness of our proposed models for sequence labeling. In extensive experiments, we outperform other state-of-the-art methods in optical character recognition and achieve competitive results in phone classification.

Tobias Schrank, Franz Pernkopf

Abstraction is a fundamental part when learning behavioral models of systems. Usually the process of abstraction is manually defined by domain experts. This paper presents a method to perform automatic abstraction for network protocols. In particular a weakly supervised clustering algorithm is used to build an abstraction with a small vocabulary size for the widely used TLS protocol. To show the effectiveness of the proposed method we compare the resultant abstract messages to a manually constructed (reference) abstraction. With a small amount of side-information in the form of a few labeled examples this method finds an abstraction that matches the reference abstraction perfectly.

Martin Trapp, Tamas Madl, Robert Peharz et al.

In several domains obtaining class annotations is expensive while at the same time unlabelled data are abundant. While most semi-supervised approaches enforce restrictive assumptions on the data distribution, recent work has managed to learn semi-supervised models in a non-restrictive regime. However, so far such approaches have only been proposed for linear models. In this work, we introduce semi-supervised parameter learning for Sum-Product Networks (SPNs). SPNs are deep probabilistic models admitting inference in linear time in number of network edges. Our approach has several advantages, as it (1) allows generative and discriminative semi-supervised learning, (2) guarantees that adding unlabelled data can increase, but not degrade, the performance (safe), and (3) is computationally efficient and does not enforce restrictive assumptions on the data distribution. We show on a variety of data sets that safe semi-supervised learning with SPNs is competitive compared to state-of-the-art and can lead to a better generative and discriminative objective value than a purely supervised approach.

Christian Knoll, Franz Pernkopf, Dhagash Mehta et al.

Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the model. To understand this dependence it is interesting to find \emph{all} fixed points. In this work, we formulate a set of polynomial equations, the solutions of which correspond to BP fixed points. To solve such a nonlinear system we present the numerical polynomial-homotopy-continuation (NPHC) method. Experiments on binary Ising models and on error-correcting codes show how our method is capable of obtaining all BP fixed points. On Ising models with fixed parameters we show how the structure influences both the number of fixed points and the convergence properties. We further asses the accuracy of the marginals and weighted combinations thereof. Weighting marginals with their respective partition function increases the accuracy in all experiments. Contrary to the conjecture that uniqueness of BP fixed points implies convergence, we find graphs for which BP fails to converge, even though a unique fixed point exists. Moreover, we show that this fixed point gives a good approximation, and the NPHC method is able to obtain this fixed point.

Robert Peharz, Robert Gens, Franz Pernkopf et al.

One of the central themes in Sum-Product networks (SPNs) is the interpretation of sum nodes as marginalized latent variables (LVs). This interpretation yields an increased syntactic or semantic structure, allows the application of the EM algorithm and to efficiently perform MPE inference. In literature, the LV interpretation was justified by explicitly introducing the indicator variables corresponding to the LVs' states. However, as pointed out in this paper, this approach is in conflict with the completeness condition in SPNs and does not fully specify the probabilistic model. We propose a remedy for this problem by modifying the original approach for introducing the LVs, which we call SPN augmentation. We discuss conditional independencies in augmented SPNs, formally establish the probabilistic interpretation of the sum-weights and give an interpretation of augmented SPNs as Bayesian networks. Based on these results, we find a sound derivation of the EM algorithm for SPNs. Furthermore, the Viterbi-style algorithm for MPE proposed in literature was never proven to be correct. We show that this is indeed a correct algorithm, when applied to selective SPNs, and in particular when applied to augmented SPNs. Our theoretical results are confirmed in experiments on synthetic data and 103 real-world datasets.

Robert Peharz, Franz Pernkopf

Recently, there has been much interest in finding globally optimal Bayesian network structures. These techniques were developed for generative scores and can not be directly extended to discriminative scores, as desired for classification. In this paper, we propose an exact method for finding network structures maximizing the probabilistic soft margin, a successfully applied discriminative score. Our method is based on branch-and-bound techniques within a linear programming framework and maintains an any-time solution, together with worst-case sub-optimality bounds. We apply a set of order constraints for enforcing the network structure to be acyclic, which allows a compact problem representation and the use of general-purpose optimization techniques. In classification experiments, our methods clearly outperform generatively trained network structures and compete with support vector machines.