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The rising interest in Bayesian deep learning (BDL) has led to a plethora of methods for estimating the posterior distribution. However, efficient computation of inferences, such as predictions, has been largely overlooked with Monte Carlo integration remaining the standard. In this work we examine streamlining prediction in BDL through a single forward pass without sampling. For this we use local linearisation on activation functions and local Gaussian approximations at linear layers. Thus allowing us to analytically compute an approximation to the posterior predictive distribution. We showcase our approach for both MLP and transformers, such as ViT and GPT-2, and assess its performance on regression and classification tasks.

Polycyclic Aromatic Hydrocarbons (PAHs) have been detected throughout the universe where they play essential roles in the evolution of their environments. For example, they are believed to affect atmospheric loss rates of close-in planets and might contribute to the pre-biotic chemistry and emergence of life. Despite their importance, the study of PAHs in exoplanet atmospheres has been limited. We aim to evaluate the possibility of detecting PAHs on exoplanets considering future observations using JWST's NIRSpec PRISM mode. The hot Saturn WASP-6 b shows properties that are consistent with a potential PAH presence and is thus used as a case study for this work. Here, we compare the likelihoods of various synthetic haze species and their combinations with the influence of PAHs on the transmission spectrum of WASP-6 b. This is possible by applying the atmospheric retrieval code petitRADTRANS to a collection of data from previous observations. Subsequently, by exploring synthetic, single transit JWST spectra of this planet that include PAHs, we assess if these molecules can be detected in the near future. Previous observations support the presence of cloud/haze species in the spectrum of WASP-6 b. While this may include PAHs, the current data do not confirm their existence unambiguously. Our research suggests that utilizing the JWST for future observations could lead to a notable advancement in the study of PAHs. Employing this telescope, we find that a PAH abundance of approximately 0.1 per cent of the ISM value could be robustly detectable., Comment: 15 pages,11 figures, accepted for publication in MNRAS

The examination of the musculoskeletal system in dogs is a challenging task in veterinary practice. In this work, a novel method has been developed that enables efficient documentation of a dog's condition through a visual representation. However, since the visual documentation is new, there is no existing training data. The objective of this work is therefore to mitigate the impact of data scarcity in order to develop an AI-based diagnostic support system. To this end, the potential of synthetic data that mimics realistic visual documentations of diseases for pre-training AI models is investigated. We propose a method for generating synthetic image data that mimics realistic visual documentations. Initially, a basic dataset containing three distinct classes is generated, followed by the creation of a more sophisticated dataset containing 36 different classes. Both datasets are used for the pre-training of an AI model. Subsequently, an evaluation dataset is created, consisting of 250 manually created visual documentations for five different diseases. This dataset, along with a subset containing 25 examples. The obtained results on the evaluation dataset containing 25 examples demonstrate a significant enhancement of approximately 10% in diagnosis accuracy when utilizing generated synthetic images that mimic real-world visual documentations. However, these results do not hold true for the larger evaluation dataset containing 250 examples, indicating that the advantages of using synthetic data for pre-training an AI model emerge primarily when dealing with few examples of visual documentations for a given disease. Overall, this work provides valuable insights into mitigating the limitations imposed by limited training data through the strategic use of generated synthetic data, presenting an approach applicable beyond the canine musculoskeletal assessment domain.

Consider a stationary Poisson process $\eta$ in a $d$-dimensional hyperbolic space of constant curvature $-\varkappa$ and let the points of $\eta$ together with a fixed origin $o$ be the vertices of a graph. Connect each point $x\in\eta$ with its radial nearest neighbour, which is the hyperbolically nearest vertex to $x$ that is closer to $o$ than $x$. This construction gives rise to the hyperbolic radial spanning tree, whose geometric properties are in the focus of this paper. In particular, the degree of the origin is studied. For increasing balls around $o$ as observation windows, expectation and variance asymptotics as well as a quantitative central limit theorem for a class of edge-length functionals are derived. The results are contrasted with those for the Euclidean radial spanning tree.

A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC computes the probability mass (or density) function (PMF or PDF) of the distribution. We consider PCs instead computing the cumulative distribution function (CDF). We show that for distributions over binary random variables these representations (PMF and CDF) are essentially equivalent, in the sense that one can be transformed to the other in polynomial time. We then show how a similar equivalence holds for distributions over finite discrete variables using a modification of the standard encoding with binary variables that aligns with the CDF semantics. Finally we show that for continuous variables, smooth, decomposable PCs computing PDFs and CDFs can be efficiently transformed to each other by modifying only the leaves of the circuit.

This paper proposes a data-driven supervised machine learning (ML) for online thermal modeling of electrically excited synchronous motors (EESMs). EESMs are desired for EVs due to their high performance, efficiency, and durability at a relatively low cost. Therefore, obtaining precise EESM temperature estimations are significantly important, because online accurate temperature estimation can lead to EESM performance improvement and guaranteeing its safety and reliability. In this study, in addition to the default inputs' data, EESM losses data is leveraged to improve the performance of the proposed ML approach for thermal modeling. Exponentially weighted moving averages and standard deviations of the inputs are also incorporated in the learning process to consider the memory effect for modeling a dynamical thermal model. Using the experimental data of an EESM prototype, the performance of ordinary least squares (OLS) method is evaluated through a complete training, testing and cross-validation process. Finally, simulation results will provide the key performance metrics of OLS for EESM thermal modeling.

In various technical applications, assessing the impact of non-Gaussian processes on responses of dynamic systems is crucial. While simulating time-domain realizations offers an efficient solution for linear dynamic systems, this method proves time-consuming for finite element (FE) models, which may contain thousands to millions of degrees-of-freedom (DOF). Given the central role of kurtosis in describing non-Gaussianity - owing to its concise, parametric-free and easily interpretable nature - this paper introduces a highly efficient approach for deriving response kurtosis and other related statistical descriptions. This approach makes use of the modal solution of dynamic systems, which allows to reduce DOFs and responses analysis to a minimum number in the modal domain. This computational advantage enables fast assessments of non-Gaussian effects for entire FE models. Our approach is illustrated using a simple FE model that has found regular use in the field of random vibration fatigue.

Probabilistic circuits (PCs) offer a promising avenue to perform embedded reasoning under uncertainty. They support efficient and exact computation of various probabilistic inference tasks by design. Hence, hardware-efficient computation of PCs is highly interesting for edge computing applications. As computations in PCs are based on arithmetic with probability values, they are typically performed in the log domain to avoid underflow. Unfortunately, performing the log operation on hardware is costly. Hence, prior work has focused on computations in the linear domain, resulting in high resolution and energy requirements. This work proposes the first dedicated approximate computing framework for PCs that allows for low-resolution logarithm computations. We leverage Addition As Int, resulting in linear PC computation with simple hardware elements. Further, we provide a theoretical approximation error analysis and present an error compensation mechanism. Empirically, our method obtains up to 357x and 649x energy reduction on custom hardware for evidence and MAP queries respectively with little or no computational error.

Indistinguishable single photons in the telecom-bandwidth of optical fibers are indispensable for long-distance quantum communication. Solid-state single photon emitters have achieved excellent performance in key benchmarks, however, the demonstration of indistinguishability at room-temperature remains a major challenge. Here, we report room-temperature photon indistinguishability at telecom wavelengths from individual nanotube defects in a fiber-based microcavity operated in the regime of incoherent good cavity-coupling. The efficiency of the coupled system outperforms spectral or temporal filtering, and the photon indistinguishability is increased by more than two orders of magnitude compared to the free-space limit. Our results highlight a promising strategy to attain optimized non-classical light sources.

Excursion sets of Poisson shot noise processes are a prominent class of random sets. We consider a specific class of Poisson shot noise processes whose excursion sets within compact convex observation windows are almost surely polyconvex. This class contains, for example, the Boolean model. In this paper, we analyse the behaviour of geometric functionals such as the intrinsic volumes of these excursion sets for growing observation windows. In particular, we study the asymptotics of the expectation and the variance, derive a lower variance bound and show a central limit theorem.

Fueling star formation in large, discy galaxies requires a continuous supply of gas accreting into star-forming regions. Previously, we characterized this accretion in 4 Milky Way mass galaxies ($M_{\rm halo}\sim10^{12}M_{\odot}$) in the FIRE-2 cosmological zoom-in simulations. At $z\sim0$, we found that gas within the inner circumgalactic medium (iCGM) approaches the disc with comparable angular momentum (AM) to the disc edge, joining in the outer half of the gaseous disc. Within the disc, gas moves inward at velocities of $\sim$1-5~km~s$^{-1}$ while fully rotationally supported. In this study, we analyze the torques that drive these flows. In all cases studied, we find that the torques in discs enable gas accreted near the disc edge to transport inwards and fuel star formation in the central few kpc. The primary sources of torque come from gravity, hydrodynamical forces, and the sub-grid $P dV$ work done by supernova (SNe) remnants interacting with gas on $\lesssim$10 pc scales. These SNe remnant interactions induce negative torques within the inner disc and positive torques in the outer disc. The gas-gas gravitational, hydro, and "feedback" torques transfer AM outward to where accreting gas joins the disc, playing an important role in driving inflows and regulating disc structure. Gravitational torques from stars and dark matter provide an AM sink within the innermost regions of the disc and iCGM, respectively. Feedback torques are dominant within the disc, while gravitational and hydrodynamical torques have similar significance depending on the system/region. Torques from viscous shearing, magnetic forces, stellar winds, and radiative transfer are less significant., Comment: 20 pages, 18 figures. Accepted for publication in MNRAS. Added 1 figure to Appendix B, modified text

Deployment of deep neural networks in real-world settings typically requires adaptation to new tasks with few examples. Few-shot classification (FSC) provides a solution to this problem by leveraging pre-trained backbones for fast adaptation to new classes. Surprisingly, most efforts have only focused on developing architectures for easing the adaptation to the target domain without considering the importance of backbone training for good generalisation. We show that flatness-aware backbone training with vanilla fine-tuning results in a simpler yet competitive baseline compared to the state-of-the-art. Our results indicate that for in- and cross-domain FSC, backbone training is crucial to achieving good generalisation across different adaptation methods. We advocate more care should be taken when training these models.

Moir\'e materials provide a unique platform for studies of correlated many-body physics of the Fermi-Hubbard model on triangular spin-charge lattices. Bilayer Hubbard models are of particular significance with regard to the physics of Mott insulating states and their relation to unconventional superconductivity, yet their experimental implementation in moir\'e systems has so far remained elusive. Here, we demonstrate the realization of a staggered bilayer triangular lattice of electrons in an antiparallel MoSe$_{2}$/WS$_{2}$ heterostructure. The bilayer lattice emerges due to strong electron confinement in the moir\'e potential minima and the near-resonant alignment of conduction band edges in MoSe$_{2}$ and WS$_{2}$. As a result, charge filling proceeds layer-by-layer, with the first and second electron per moir\'e cell consecutively occupying first the MoSe$_{2}$ and then the WS$_{2}$ layer. We describe the observed charging sequence by an electrostatic model and provide experimental evidence of spin correlations on the vertically offset and laterally staggered bilayer lattice, yielding absolute exciton Land\'e factors as high as $600$ at lowest temperatures. The bilayer character of the implemented spin-charge lattice allows for electrostatic tunability of Ruderman-Kittel-Kasuya-Yosida magnetism, and establishes antiparallel MoSe$_{2}$/WS$_{2}$ heterostructures as a viable platform for studies of bilayer Hubbard model physics with exotic magnetic phases on frustrated lattices.

Generative AI is increasingly important in software engineering, including safety engineering, where its use ensures that software does not cause harm to people. This also leads to high quality requirements for generative AI. Therefore, the simplistic use of Large Language Models (LLMs) alone will not meet these quality demands. It is crucial to develop more advanced and sophisticated approaches that can effectively address the complexities and safety concerns of software systems. Ultimately, humans must understand and take responsibility for the suggestions provided by generative AI to ensure system safety. To this end, we present an efficient, hybrid strategy to leverage LLMs for safety analysis and Human-AI codesign. In particular, we develop a customized LLM agent that uses elements of prompt engineering, heuristic reasoning, and retrieval-augmented generation to solve tasks associated with predefined safety concepts, in interaction with a system model graph. The reasoning is guided by a cascade of micro-decisions that help preserve structured information. We further suggest a graph verbalization which acts as an intermediate representation of the system model to facilitate LLM-graph interactions. Selected pairs of prompts and responses relevant for safety analytics illustrate our method for the use case of a simplified automated driving system., Comment: 5 pages

We explicitly construct a sequence of hyperbolic links $\{ L_{4n} \}$ where the number of symmetries of each $\mathbb{S}^{3} \setminus L_{4n}$ that are not induced by symmetries of the pair $(\mathbb{S}^{3}, L_{4n})$ grows linearly with n. Specifically, $[Sym(\mathbb{S}^{3} \setminus L_{4n}) : Sym(\mathbb{S}^{3}, L_{4n})] =8n \rightarrow \infty$ as $n \rightarrow \infty$. For this construction, we start with a family of minimally twisted chain links, $\{ C_{4n} \}$, where $Sym(\mathbb{S}^{3}, C_{4n})$ and $Sym(\mathbb{S}^{3} \setminus C_{4n})$ coincide and grow linearly with $n$. We then perform a particular type of homeomorphism on $\mathbb{S}^{3} \setminus C_{4n}$ to produce another link complement $\mathbb{S}^{3} \setminus L_{4n}$ where we can uniformly bound $|Sym(\mathbb{S}^{3}, L_{4n})|$ using a combinatorial condition based on linking number. A more general result highlighting how to control symmetry groups of hyperbolic links is provided, which has potential for further application., Comment: 12 pages, 3 figures

Already since the 1950s TRIZ shows that patents and the technical contradictions they solve are an important source of inspiration for the development of innovative products. However, TRIZ is a heuristic based on a historic patent analysis and does not make use of the ever-increasing number of latest technological solutions in current patents. Because of the huge number of patents, their length, and, last but not least, their complexity there is a need for modern patent retrieval and patent analysis to go beyond keyword-oriented methods. Recent advances in patent retrieval and analysis mainly focus on dense vectors based on neural AI Transformer language models like Google BERT. They are, for example, used for dense retrieval, question answering or summarization and key concept extraction. A research focus within the methods for patent summarization and key concept extraction are generic inventive concepts respectively TRIZ concepts like problems, solutions, advantage of invention, parameters, and contradictions. Succeeding rule-based approaches, finetuned BERT-like language models for sentence-wise classification represent the state-of-the-art of inventive concept extraction. While they work comparatively well for basic concepts like problems or solutions, contradictions - as a more complex abstraction - remain a challenge for these models. This paper goes one step further, as it presents a method to extract TRIZ contradictions from patent texts based on Prompt Engineering using a generative Large Language Model (LLM), namely OpenAI's GPT-4. Contradiction detection, sentence extraction, contradiction summarization, parameter extraction and assignment to the 39 abstract TRIZ engineering parameters are all performed in a single prompt using the LangChain framework. Our results show that "off-the-shelf" GPT-4 is a serious alternative to existing approaches., Comment: 10 pages, 2 tables

As intelligent systems become increasingly important in our daily lives, new ways of interaction are needed. Classical user interfaces pose issues for the physically impaired and are partially not practical or convenient. Gesture recognition is an alternative, but often not reactive enough when conventional cameras are used. This work proposes a Spiking Convolutional Neural Network, processing event- and depth data for gesture recognition. The network is simulated using the open-source neuromorphic computing framework LAVA for offline training and evaluation on an embedded system. For the evaluation three open source data sets are used. Since these do not represent the applied bi-modality, a new data set with synchronized event- and depth data was recorded. The results show the viability of temporal encoding on depth information and modality fusion, even on differently encoded data, to be beneficial to network performance and generalization capabilities., Comment: Accepted to IEEE International Conference on Robotics and Automation (ICRA 2024)

The lack of anomaly detection methods during mechanized tunnelling can cause financial loss and deficits in drilling time. On-site excavation requires hard obstacles to be recognized prior to drilling in order to avoid damaging the tunnel boring machine and to adjust the propagation velocity. The efficiency of the structural anomaly detection can be increased with intelligent optimization techniques and machine learning. In this research, the anomaly in a simple structure is detected by comparing the experimental measurements of the structural vibrations with numerical simulations using parameter estimation methods.

Recent years have witnessed a surge in the popularity of Machine Learning (ML), applied across diverse domains. However, progress is impeded by the scarcity of training data due to expensive acquisition and privacy legislation. Synthetic data emerges as a solution, but the abundance of released models and limited overview literature pose challenges for decision-making. This work surveys 417 Synthetic Data Generation (SDG) models over the last decade, providing a comprehensive overview of model types, functionality, and improvements. Common attributes are identified, leading to a classification and trend analysis. The findings reveal increased model performance and complexity, with neural network-based approaches prevailing, except for privacy-preserving data generation. Computer vision dominates, with GANs as primary generative models, while diffusion models, transformers, and RNNs compete. Implications from our performance evaluation highlight the scarcity of common metrics and datasets, making comparisons challenging. Additionally, the neglect of training and computational costs in literature necessitates attention in future research. This work serves as a guide for SDG model selection and identifies crucial areas for future exploration., Comment: Fixed bug in Figure 44

In many real-world scenarios, it is crucial to be able to reliably and efficiently reason under uncertainty while capturing complex relationships in data. Probabilistic circuits (PCs), a prominent family of tractable probabilistic models, offer a remedy to this challenge by composing simple, tractable distributions into a high-dimensional probability distribution. However, learning PCs on heterogeneous data is challenging and densities of some parametric distributions are not available in closed form, limiting their potential use. We introduce characteristic circuits (CCs), a family of tractable probabilistic models providing a unified formalization of distributions over heterogeneous data in the spectral domain. The one-to-one relationship between characteristic functions and probability measures enables us to learn high-dimensional distributions on heterogeneous data domains and facilitates efficient probabilistic inference even when no closed-form density function is available. We show that the structure and parameters of CCs can be learned efficiently from the data and find that CCs outperform state-of-the-art density estimators for heterogeneous data domains on common benchmark data sets., Comment: Published at NeurIPS 2023

Given two orientable, cusped hyperbolic 3-manifolds containing certain thrice-punctured spheres, Adams gave a diagrammatic definition for a third such manifold, their belted sum. Fully augmented links, or FALs, are hyperbolic links constructed by augmenting a link diagram. This work considers belted sum decompositions in which all manifolds involved are FAL complements. To do so, we provide explicit classifications of thrice punctured spheres in FAL complements, making them easily recognizable. These classifications are used to characterize belted sum prime FALs geometrically, combinatorially and diagrammatically. Finally we prove that, in the context of belted sums, every FAL complement canonically decomposes into FALs which are either prime or two-fold covers of the Whitehead link.

The United States has introduced a special humanitarian parole process for Ukrainian citizens in response to Russia 2022 invasion of Ukraine. To qualify for parole, Ukrainian applicants must have a sponsor in the United States. In collaboration with HIAS, a refugee resettlement agency involved in the parole process, we deployed RUTH (Refugees Uniting Through HIAS), a novel algorithmic matching system that is driven by the relocation preferences of refugees and the priorities of US sponsors. RUTH adapts Thakral Multiple-Waitlist Procedure (MWP) that combines the main FIFO queue with location-specific FIFO queues to effectively manage the preferences of refugees and the supply of community sponsors. RUTH also incorporates various feasibility considerations, such as community capacity religious, and medical needs. The adapted mechanism is envy-free, efficient, and strategy-proof for refugees. Our analysis shows diverse refugee location preferences, not fully explained by observables, highlighting the challenge of predicting preferences directly from them. We use our data for two counterfactual simulations. First, we consider the effects of increased waiting times for refugees on the quality of their matches. We find that with a periodic Top Trading Cycles algorithm, increasing period length from 24 days to 80 days improves the average rank of a refugees match from 3.20 to 2.44. Second, we estimate the arrival rates of sponsors in each location that would be consistent with a long-run steady state. We find that more desirable locations (regarding refugee preferences) require the highest arrival rates, suggesting that preferences might be a useful indicator for investments in sponsorship capacity. Our study highlights the potential for preference-based algorithms such as RUTH to improve the efficiency and fairness of other rapidly deployed humanitarian parole processes., Comment: In Equity and Access in Algorithms, Mechanisms, and Optimization (EAAMO23), October 30-November 1, 2023, Boston, MA, USA. 34 pages, including an appendix

Mixture models are traditionally represented and learned by adding several distributions as components. Allowing mixtures to subtract probability mass or density can drastically reduce the number of components needed to model complex distributions. However, learning such subtractive mixtures while ensuring they still encode a non-negative function is challenging. We investigate how to learn and perform inference on deep subtractive mixtures by squaring them. We do this in the framework of probabilistic circuits, which enable us to represent tensorized mixtures and generalize several other subtractive models. We theoretically prove that the class of squared circuits allowing subtractions can be exponentially more expressive than traditional additive mixtures; and, we empirically show this increased expressiveness on a series of real-world distribution estimation tasks.

This paper outlines the winning solutions employed in addressing the MUAD uncertainty quantification challenge held at ICCV 2023. The challenge was centered around semantic segmentation in urban environments, with a particular focus on natural adversarial scenarios. The report presents the results of 19 submitted entries, with numerous techniques drawing inspiration from cutting-edge uncertainty quantification methodologies presented at prominent conferences in the fields of computer vision and machine learning and journals over the past few years. Within this document, the challenge is introduced, shedding light on its purpose and objectives, which primarily revolved around enhancing the robustness of semantic segmentation in urban scenes under varying natural adversarial conditions. The report then delves into the top-performing solutions. Moreover, the document aims to provide a comprehensive overview of the diverse solutions deployed by all participants. By doing so, it seeks to offer readers a deeper insight into the array of strategies that can be leveraged to effectively handle the inherent uncertainties associated with autonomous driving and semantic segmentation, especially within urban environments., Comment: 11 pages, 4 figures, accepted at ICCV 2023 UNCV workshop

In this article the cyclic cutwidth of the $n$-dimensional cube is explored. It has been conjectured by Dr. Chavez and Dr. Trapp that the cyclic cutwidth of $Q_n$ is minimized with the Graycode numbering. Several results have been found toward the proof of this conjecture., Comment: 8 pages, 3 figures. Summer Research Experiences for Undergraduates report from August 2003, with some typos fixed