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Monotonic Differentiable Sorting Networks [article]

Felix Petersen, Christian Borgelt, Hilde Kuehne, Oliver Deussen
2022 arXiv   pre-print
REPRODUCIBILITY STATEMENT We made the source code and experiments of this work publicly available at to foster future research in this direction.  ...  The source code of this work is publicly available at  ...  Petersen et al. [10] also proposed a general method for continuously relaxing algorithms via logistic distributions.  ... 
arXiv:2203.09630v1 fatcat:c3aopk3erzhlpbcivwucryrwwm

GenDR: A Generalized Differentiable Renderer [article]

Felix Petersen, Bastian Goldluecke, Christian Borgelt, Oliver Deussen
2022 arXiv   pre-print
Here, λ = 10 −1.5 ≈ 0.03 1 The source code will be available at performs best in almost all cases.  ...  [3] model it with the square root of a logistic distribution, Petersen et al. [14] use a logistic distribution, and Chen et al. [6] use the exponential distribution.  ... 
arXiv:2204.13845v1 fatcat:66ggp2ozrzbkjeg5f6i6jf3cny

Towards Formula Translation using Recursive Neural Networks [article]

Felix Petersen, Moritz Schubotz, Bela Gipp
2018 arXiv   pre-print
While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural networks because mathematical formulae inherently include a structural encoding. In our implementation, we developed new techniques and topologies for recursive tree-to-tree
more » ... l networks based on multi-variate multi-valued Long Short-Term Memory cells. We propose a novel approach for mini-batch training that utilizes clustering and tree traversal. We evaluate our translator and analyze the behavior of our proposed topologies and techniques based on a translation from generic LaTeX to the semantic LaTeX notation. We use the semantic LaTeX notation from the Digital Library for Mathematical Formulae and the Digital Repository for Mathematical Formulae at the National Institute for Standards and Technology. We find that a simple heuristics-based clustering algorithm outperforms the conventional clustering algorithms on the task of clustering binary trees of mathematical formulae with respect to their topology. Furthermore, we find a mask for the loss function, which can prevent the neural network from finding a local minimum of the loss function. Given our preliminary results, a complete translation from formula to formula is not yet possible. However, we achieved a prediction accuracy of 47.05% for predicting symbols at the correct position and an accuracy of 92.3% when ignoring the predicted position. Concluding, our work advances the field of recursive neural networks by improving the training speed and quality of training. In the future, we will work towards a complete translation allowing a machine-interpretation of LaTeX formulae.
arXiv:1811.04234v1 fatcat:wphz4fmxprbthmgxqnqh67bjiq

Approximation in L^p(μ) with deep ReLU neural networks [article]

Felix Voigtlaender, Philipp Petersen
2019 arXiv   pre-print
We discuss the expressive power of neural networks which use the non-smooth ReLU activation function ϱ(x) = {0,x} by analyzing the approximation theoretic properties of such networks. The existing results mainly fall into two categories: approximation using ReLU networks with a fixed depth, or using ReLU networks whose depth increases with the approximation accuracy. After reviewing these findings, we show that the results concerning networks with fixed depth--- which up to now only consider
more » ... roximation in L^p(λ) for the Lebesgue measure λ--- can be generalized to approximation in L^p(μ), for any finite Borel measure μ. In particular, the generalized results apply in the usual setting of statistical learning theory, where one is interested in approximation in L^2(P), with the probability measure P describing the distribution of the data.
arXiv:1904.04789v1 fatcat:o5avt63wf5a37pbfuxtdjiobbe

Style Agnostic 3D Reconstruction via Adversarial Style Transfer [article]

Felix Petersen, Bastian Goldluecke, Oliver Deussen, Hilde Kuehne
2021 arXiv   pre-print
all results based on mean 3D IoU averaged over 3 runs for 13 object classes as well as the mean over all classes. 1 Our implementation as well as our new data sets are openly available at  ... 
arXiv:2110.10784v1 fatcat:q3uk3p2mwncfdofitbqc3j472y

AlgoNet: C^∞ Smooth Algorithmic Neural Networks [article]

Felix Petersen, Christian Borgelt, Oliver Deussen
2019 arXiv   pre-print
Artificial neural networks revolutionized many areas of computer science in recent years since they provide solutions to a number of previously unsolved problems. On the other hand, for many problems, classic algorithms exist, which typically exceed the accuracy and stability of neural networks. To combine these two concepts, we present a new kind of neural networks-algorithmic neural networks (AlgoNets). These networks integrate smooth versions of classic algorithms into the topology of neural
more » ... networks. A forward AlgoNet includes algorithmic layers into existing architectures while a backward AlgoNet can solve inverse problems without or with only weak supervision. In addition, we present the algonet package, a PyTorch based library that includes, inter alia, a smoothly evaluated programming language, a smooth 3D mesh renderer, and smooth sorting algorithms.
arXiv:1905.06886v2 fatcat:6ncun2neorfq3c2y65h2n2wa7u

Domain Adaptation meets Individual Fairness. And they get along [article]

Debarghya Mukherjee, Felix Petersen, Mikhail Yurochkin, Yuekai Sun
2022 arXiv   pre-print
For example, Petersen et al.  ...  [18] , and Petersen et al. [7] used the graph Laplacian regularizer to post-process ML models so that they are individually fair.  ... 
arXiv:2205.00504v1 fatcat:gnusztq6ubgc3pbzz3qwu5zdim

24x7: Digital Preservation of the NLM Digital Collections

Doron Shalvi, John Doyle, John Rees, Ben Petersen, Felix Kong
2015 Zenodo  
This presentation will cover the topic of digital preservation with respect to the National Library of Medicine (NLM) Digital Repository. The presentation will describe our overall preservation goals and requirements, the aspects of preservation satisfied by our current system, and where we plan to enhance our system in the future to further meet these preservation goals. We will describe the architecture of our system and the detail of components that provide preservation services, and how
more » ... are implemented. Specific topics to be reviewed include the current and potential implementation of services for identification, fixity, auditing, replication, and interface to other systems. We will relate these services to our current Fedora 3-based system and how these functions could be implemented in a Fedora 4-based system. The presentation should serve as a useful example to other organizations with systems of similar size and complexity that are looking to implement preservation services within their systems.
doi:10.5281/zenodo.6570934 fatcat:7wotflrihbethl5pdixm25n7cm

Sensory Assessment of Regional Analgesia in Humans

Michele Curatolo, Steen Petersen-Felix, Lars Arendt-Nielsen
2000 Anesthesiology  
doi:10.1097/00000542-200012000-00025 pmid:11149448 fatcat:whlni46me5e7rl27c63sfawjsa

Learning with Algorithmic Supervision via Continuous Relaxations [article]

Felix Petersen, Christian Borgelt, Hilde Kuehne, Oliver Deussen
2021 arXiv   pre-print
The integration of algorithmic components into neural architectures has gained increased attention recently, as it allows training neural networks with new forms of supervision such as ordering constraints or silhouettes instead of using ground truth labels. Many approaches in the field focus on the continuous relaxation of a specific task and show promising results in this context. But the focus on single tasks also limits the applicability of the proposed concepts to a narrow range of
more » ... ions. In this work, we build on those ideas to propose an approach that allows to integrate algorithms into end-to-end trainable neural network architectures based on a general approximation of discrete conditions. To this end, we relax these conditions in control structures such as conditional statements, loops, and indexing, so that resulting algorithms are smoothly differentiable. To obtain meaningful gradients, each relevant variable is perturbed via logistic distributions and the expectation value under this perturbation is approximated. We evaluate the proposed continuous relaxation model on four challenging tasks and show that it can keep up with relaxations specifically designed for each individual task.
arXiv:2110.05651v2 fatcat:3qlvl4vl2rcixdcuxnoy7nfg7y

Robustly Removing Deep Sea Lighting Effects for Visual Mapping of Abyssal Plains [article]

Kevin Köser, Yifan Song, Lasse Petersen, Emanuel Wenzlaff, Felix Woelk
2021 arXiv   pre-print
The majority of Earth's surface lies deep in the oceans, where no surface light reaches. Robots diving down to great depths must bring light sources that create moving illumination patterns in the darkness, such that the same 3D point appears with different color in each image. On top, scattering and attenuation of light in the water makes images appear foggy and typically blueish, the degradation depending on each pixel's distance to its observed seafloor patch, on the local composition of the
more » ... water and the relative poses and cones of the light sources. Consequently, visual mapping, including image matching and surface albedo estimation, severely suffers from the effects that co-moving light sources produce, and larger mosaic maps from photos are often dominated by lighting effects that obscure the actual seafloor structure. In this contribution a practical approach to estimating and compensating these lighting effects on predominantly homogeneous, flat seafloor regions, as can be found in the Abyssal plains of our oceans, is presented. The method is essentially parameter-free and intended as a preprocessing step to facilitate visual mapping, but already produces convincing lighting artefact compensation up to a global white balance factor. It does not require to be trained beforehand on huge sets of annotated images, which are not available for the deep sea. Rather, we motivate our work by physical models of light propagation, perform robust statistics-based estimates of additive and multiplicative nuisances that avoid explicit parameters for light, camera, water or scene, discuss the breakdown point of the algorithms and show results on imagery captured by robots in several kilometer water depth.
arXiv:2110.00480v1 fatcat:eq4xqdq4c5bgdeyn3lpb6rd3fq


1993 British Journal of Anaesthesia  
Sir,-Thank you for inviting us to reply to the interesting letter from Drs Petersen-Felix and Zbinden.  ...  PETERSEN-FELIX A. M. ZBINDEN University of Berne Switzerland 1. Thornton C, Creagh-Barry P, Jordan C, LuffNP, Dore CJ, Henley M, Newton DEF.  ... 
doi:10.1093/bja/70.6.704-b pmid:8329276 fatcat:mreoe4jutjetnbpjzbjlnlrvlq

Temporal summation during extradural anaesthesia

M Curatolo, S Petersen-Felix, L Arendt-Nielsen, M Fischer, A M Zbinden
1995 British Journal of Anaesthesia  
We have investigated in 10 patients the effect of extradural anaesthesia on temporal summation by comparing pain thresholds to single and repeated (five impulses at 2 Hz) electrical stimuli and compared these tests with pinprick and cold stimulation. Bupivacaine 0.5 % (20 ml) was injected at L2-3. After extradural anaesthesia the threshold to repeated stimuli was significantly lower than the threshold to single stimuli (P : 0.0007). Nine patients lost cold sensation and 10 patients pinprick
more » ... ation. Pain to single electrical stimulation disappeared in six patients and pain to repeated electrical stimulation in one. Pain may be evoked by temporal summation of repeated electrical stimuli even when pinprick sensation, cold sensation and pain to single electrical stimuli are inhibited. Thus temporal summation should be taken into consideration when extradural analgesia is assessed. (Br. J. Anaesth. 1995; 75: 634-635)
doi:10.1093/bja/75.5.634 pmid:7577294 fatcat:e4gnhjohtfgz7pet5bp3pahvxi

Neuroplasticity--an important factor in acute and chronic pain

Steen Petersen-Felix, Michele Curatolo
2002 Swiss Medical Weekly  
Steen Petersen-Felix Leitender Arzt Anästhesie Frauenklinik Institut für Anästhesiologie Inselspital CH-3010 Berne E-Mail: S W I S S M E D W K LY 2 0 0 2 ; 1 3 2 : 2 7 3 -2  ... 
pmid:12362284 fatcat:hdsicxdkcrd4xmaj2nszm5yrxq

Spinal anaesthesia inhibits central temporal summation

M Curatolo, S Petersen-Felix, L Arendt-Nielsen, A M Zbinden
1997 British Journal of Anaesthesia  
In a previous investigation we found that extradural anaesthesia did not adequately inhibit temporal summation of repeated electrical stimuli: pain to repeated stimuli was blocked in only one of 10 patients, and pain thresholds to repeated stimuli were significantly lower than pain thresholds to a single stimulus. In this study we have investigated in 10 patients the effect of spinal anaesthesia on temporal summation, assessed by repeated electrical stimulation of the sural nerve. Plain 0.5%
more » ... ivacaine 18 mg was injected at L2-3. The pain threshold to a single electrical stimulus, summation threshold (increase in perception during repeated electrical stimuli with five impulses of the same intensity at 2 Hz), pinprick and cold sensation were assessed. After spinal anaesthesia, pain to both single and repeated stimulation, and pinprick and cold sensation, disappeared in all patients. We conclude that spinal anaesthesia inhibits temporal summation elicited by repeated electrical stimulation. (Br.
doi:10.1093/bja/78.1.88 pmid:9059212 fatcat:iymgleh7lfgqbp2ovwipkjzmxe
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