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This article explores the theoretical underpinnings of -- and practical results for -- topological and geometric features of data collected by synthetic aperture sonar systems. We prove a strong theoretical guarantee about the structure of the space of echos (the signature space) that is relevant for classification, and that this structure is measurable in laboratory conditions. The guarantee makes minimal assumptions about the sonar platform's trajectory, and establishes that the signature space divides neatly into topological features based upon the number of prominent echos and their placement, and geometric features that capture their corresponding sonar cross section., Comment: 34 pages, 16 figures

While the origin of neutrino masses remains unknown, several key neutrino mass generation models result in a non-unitary three-neutrino mixing matrix. To put such models to test, the deviations of the mixing matrix from unitarity can be measured directly through neutrino oscillation experiments. In this study, we perform a Bayesian analysis of the non-unitary mixing model using the recent public data from atmospheric and reactor neutrino experiments - namely IceCube-DeepCore, Daya Bay, and KamLAND. The novelty of our approach compared to the preceding global fits for non-unitarity is in the detailed treatment of the atmospheric neutrino data, which for the first time includes the relevant flux and detector systematic uncertainties. From the Bayesian posteriors on the individual mixing matrix elements, we derive the non-unitarity constraints in the form of normalisations and closures of the mixing matrix rows and columns. We find comparable constraints for electron and tau row normalisations as other similar studies in literature, and additionally reveal strong correlations between muon and tau row constraints induced by the atmospheric systematic uncertainties. We find that the current data is well described by both unitary and non-unitary mixing models, with a strong preference for the unitary mixing indicated by the Bayes factor. With the upcoming IceCube-Upgrade and JUNO detectors, both featuring superior energy resolution compared to the current atmospheric and reactor neutrino experiments, our constraints on the row normalisations are expected to improve by a factor of 2 (2.5) in the tau (muon) sector and by nearly 25% in the electron sector. In the future, our approach can be expanded to include solar and long-baseline neutrino experiments, with the aim to provide more stringent constraints while keeping track of the nuisance parameters that may be degenerate with non-unitarity., Comment: 46 pages, 26 figures

Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of assumptions on the graphical structure of the model and observational data, represented as a non-causal covariance matrix. In this paper, we give a new sound and complete algorithm for generic identification which runs in polynomial space. By standard simulation results, this algorithm has exponential running time which vastly improves the state-of-the-art double exponential time method using a Gr\"obner basis approach. The paper also presents evidence that parameter identification is computationally hard in general. In particular, we prove, that the task asking whether, for a given feasible correlation matrix, there are exactly one or two or more parameter sets explaining the observed matrix, is hard for $\forall R$, the co-class of the existential theory of the reals. In particular, this problem is $coNP$-hard. To our best knowledge, this is the first hardness result for some notion of identifiability.

Constrained optimization problems, where not all possible variable assignments are feasible solutions, comprise numerous practically relevant optimization problems such as the Traveling Salesman Problem (TSP), or portfolio optimization. Established methods such as quantum annealing or vanilla QAOA usually transform the problem statement into a QUBO (Quadratic Unconstrained Binary Optimization) form, where the constraints are enforced by auxiliary terms in the QUBO objective. Consequently, such approaches fail to utilize the additional structure provided by the constraints. In this paper, we present a method for solving the industry relevant Product Breakdown Structure problem. Our solution is based on constrained QAOA, which by construction never explores the part of the Hilbert space that represents solutions forbidden by the problem constraints. The size of the search space is thereby reduced significantly. We experimentally show that this approach has not only a very favorable scaling behavior, but also appears to suppress the negative effects of Barren Plateaus., Comment: 13 pages

While significant progress has been made on the hardware side of quantum computing, support for high-level quantum programming abstractions remains underdeveloped compared to classical programming languages. In this article, we introduce Qrisp, a framework designed to bridge several gaps between high-level programming paradigms in state-of-the-art software engineering and the physical reality of today's quantum hardware. The framework aims to provide a systematic approach to quantum algorithm development such that they can be effortlessly implemented, maintained and improved. We propose a number of programming abstractions that are inspired by classical paradigms, yet consistently focus on the particular needs of a quantum developer. Unlike many other high-level language approaches, Qrisp's standout feature is its ability to compile programs to the circuit level, making them executable on most existing physical backends. The introduced abstractions enable the Qrisp compiler to leverage algorithm structure for increased compilation efficiency. Finally, we present a set of code examples, including an implementation of Shor's factoring algorithm. For the latter, the resulting circuit shows significantly reduced quantum resource requirements, strongly supporting the claim that systematic quantum algorithm development can give quantitative benefits.

Moral judgement is a complex human reaction that engages cognitive and emotional dimensions. While some of the morality neural correlates are known, it is currently unclear if we can detect moral violation at a single-trial level. In a pilot study, here we explore the feasibility of moral judgement decoding from text stimuli with passive brain-computer interfaces. For effective moral judgement elicitation, we use video-audio affective priming prior to text stimuli presentation and attribute the text to moral agents. Our results show that further efforts are necessary to achieve reliable classification between moral congruency vs. incongruency states. We obtain good accuracy results for neutral vs. morally-charged trials. With this research, we try to pave the way towards neuroadaptive human-computer interaction and more human-compatible large language models (LLMs), Comment: 7 pages, 2 figures, conference

The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving either the probability flow ODE or diffusion SDE wherein a neural network approximates the score function or related quantity, allowing a numerical ODE/SDE solver to be used. However, na\"ive backpropagation techniques are memory intensive, requiring the storage of all intermediate states, and face additional complexity in handling the injected noise from the diffusion term of the diffusion SDE. We propose a novel method based on the stochastic adjoint sensitivity method to calculate the gradientwith respect to the initial noise, conditional information, and model parameters by solving an additional SDE whose solution is the gradient of the diffusion SDE. We exploit the unique construction of diffusion SDEs to further simplify the formulation of the adjoint diffusion SDE and use a change-of-variables to simplify the solution to an exponentially weighted integral. Using this formulation we derive a custom solver for the adjoint SDE as well as the simpler adjoint ODE. The proposed adjoint diffusion solvers can efficiently compute the gradients for both the probability flow ODE and diffusion SDE for latents and parameters of the model. Lastly, we demonstrate the effectiveness of the adjoint diffusion solvers onthe face morphing problem., Comment: Initial pre-print

The framework of Pearl's Causal Hierarchy (PCH) formalizes three types of reasoning: observational, interventional, and counterfactual, that reflect the progressive sophistication of human thought regarding causation. We investigate the computational complexity aspects of reasoning in this framework focusing mainly on satisfiability problems expressed in probabilistic and causal languages across the PCH. That is, given a system of formulas in the standard probabilistic and causal languages, does there exist a model satisfying the formulas? The resulting complexity changes depending on the level of the hierarchy as well as the operators allowed in the formulas (addition, multiplication, or marginalization). We focus on formulas involving marginalization that are widely used in probabilistic and causal inference, but whose complexity issues are still little explored. Our main contribution are the exact computational complexity results showing that linear languages (allowing addition and marginalization) yield NP^PP-, PSPACE-, and NEXP-complete satisfiability problems, depending on the level of the PCH. Moreover, we prove that the problem for the full language (allowing additionally multiplication) is complete for the class succ$\exists$R for languages on the highest, counterfactual level, which extends previous results for the lower levels of the PCH. Finally, we consider constrained models that are restricted to a given Bayesian network, a Directed Acyclic Graph structure, or a small polynomial size. The complexity of languages on the interventional level is increased to the complexity of counterfactual languages without such a constraint, that is, linear languages become NEXP-complete. On the other hand, the complexity on the counterfactual level does not change. The constraint on the size reduces the complexity of the interventional and counterfactual languages to NEXP-complete., Comment: update adds complexity results involving a graph structure; submitted to NIPS

To characterize the computational complexity of satisfiability problems for probabilistic and causal reasoning within the Pearl's Causal Hierarchy, arXiv:2305.09508 [cs.AI] introduce a new natural class, named succ-$\exists$R. This class can be viewed as a succinct variant of the well-studied class $\exists$R based on the Existential Theory of the Reals (ETR). Analogously to $\exists$R, succ-$\exists$R is an intermediate class between NEXP and EXPSPACE, the exponential versions of NP and PSPACE. The main contributions of this work are threefold. Firstly, we characterize the class succ-$\exists$R in terms of nondeterministic real RAM machines and develop structural complexity theoretic results for real RAMs, including translation and hierarchy theorems. Notably, we demonstrate the separation of $\exists$R and succ-$\exists$R. Secondly, we examine the complexity of model checking and satisfiability of fragments of existential second-order logic and probabilistic independence logic. We show succ-$\exists$R- completeness of several of these problems, for which the best-known complexity lower and upper bounds were previously NEXP-hardness and EXPSPACE, respectively. Thirdly, while succ-$\exists$R is characterized in terms of ordinary (non-succinct) ETR instances enriched by exponential sums and a mechanism to index exponentially many variables, in this paper, we prove that when only exponential sums are added, the corresponding class $\exists$R^{\Sigma} is contained in PSPACE. We conjecture that this inclusion is strict, as this class is equivalent to adding a VNP-oracle to a polynomial time nondeterministic real RAM. Conversely, the addition of exponential products to ETR, yields PSPACE. Additionally, we study the satisfiability problem for probabilistic reasoning, with the additional requirement of a small model and prove that this problem is complete for $\exists$R^{\Sigma}.

Face morphing attacks pose an increasing threat to face recognition (FR) systems. A morphed photo contains biometric information from two different subjects to take advantage of vulnerabilities in FRs. These systems are particularly susceptible to attacks when the morphs are subjected to print-scanning to mask the artifacts generated during the morphing process. We investigate the impact of print-scanning on morphing attack detection through a series of evaluations on heterogeneous morphing attack scenarios. Our experiments show that we can increase the Mated Morph Presentation Match Rate (MMPMR) by up to 8.48%. Furthermore, when a Single-image Morphing Attack Detection (S-MAD) algorithm is not trained to detect print-scanned morphs the Morphing Attack Classification Error Rate (MACER) can increase by up to 96.12%, indicating significant vulnerability., Comment: Accepted as a special sessions paper at IJCB 2024

Morphing attacks are an emerging threat to state-of-the-art Face Recognition (FR) systems, which aim to create a single image that contains the biometric information of multiple identities. Diffusion Morphs (DiM) are a recently proposed morphing attack that has achieved state-of-the-art performance for representation-based morphing attacks. However, none of the existing research on DiMs have leveraged the iterative nature of DiMs and left the DiM model as a black box, treating it no differently than one would a Generative Adversarial Network (GAN) or Varational AutoEncoder (VAE). We propose a greedy strategy on the iterative sampling process of DiM models which searches for an optimal step guided by an identity-based heuristic function. We compare our proposed algorithm against ten other state-of-the-art morphing algorithms using the open-source SYN-MAD 2022 competition dataset. We find that our proposed algorithm is unreasonably effective, fooling all of the tested FR systems with an MMPMR of 100%, outperforming all other morphing algorithms compared., Comment: Accepted as a conference paper at IJCB 2024

A standard reconfigurable intelligent surface (RIS) can be configured to reflect signals from an arbitrary impinging direction to an arbitrary outgoing direction. However, if a signal impinges from any other direction, said signal is reflected, with full beamforming gain, to a specific direction, which is easily determined. The goal of this paper is to propose a RIS which \emph{only} reflects signals from the configured impinging direction. This can be accomplished by a RIS architecture that permutes the antenna elements in the sense that a signal is re-radiated from a different antenna than the one receiving the signal. We analytically prove this fact, and also discuss several variants and hardware implementations., Comment: ICC 2024, 6 pages, 4 figures

Language models (LMs) are trained on web text originating from many points in time and, in general, without any explicit temporal grounding. This work investigates the temporal chaos of pretrained LMs and explores various methods to align their internal knowledge to a target time, which we call "temporal alignment." To do this, we first automatically construct a dataset containing 20K time-sensitive questions and their answers for each year from 2000 to 2023. Based on this dataset, we empirically show that pretrained LMs (e.g., LLaMa2), despite having a recent pretraining cutoff (e.g., 2022), mostly answer questions using earlier knowledge (e.g., in 2019). We then develop several methods, from prompting to finetuning, to align LMs to use their most recent knowledge when answering questions, and investigate various factors in this alignment. Our experiments demonstrate that aligning LLaMa2 to the year 2022 can enhance its performance by up to 62% according to that year's answers. This improvement occurs even without explicitly mentioning time information, indicating the possibility of aligning models' internal sense of time after pretraining. Finally, we find that alignment to a historical time is also possible, with up to 2.8$\times$ the performance of the unaligned LM in 2010 if finetuning models to that year. These findings hint at the sophistication of LMs' internal knowledge organization and the necessity of tuning them properly., Comment: Accepted as Findings of ACL 2024. Our code and data is available at https://github.com/yizhongw/llm-temporal-alignment

The quantum backtracking algorithm proposed by Ashley Montanaro raised considerable interest, as it provides a quantum speed-up for a large class of classical optimization algorithms. It does not suffer from Barren-Plateaus and transfers well into the fault-tolerant era, as it requires only a limited number of arbitrary angle gates. Despite its potential, the algorithm has seen limited implementation efforts, presumably due to its abstract formulation. In this work, we provide a detailed instruction on implementing the quantum step operator for arbitrary backtracking instances. For a single controlled diffuser of a binary backtracking tree with depth n, our implementation requires only $6n+14$ CX gates. We detail the process of constructing accept and reject oracles for Sudoku problems using our interface to quantum backtracking. The presented code is written using Qrisp, a high-level quantum programming language, making it executable on most current physical backends and simulators. Subsequently, we perform several simulator based experiments and demonstrate solving 4x4 Sudoku instances with up to 9 empty fields. This is, to the best of our knowledge, the first instance of a compilable implementation of this generality, marking a significant and exciting step forward in quantum software engineering.

As quantum computing technology slowly matures and the number of available qubits on a QPU gradually increases, interest in assessing the capabilities of quantum computing hardware in a scalable manner is growing. One of the key properties for quantum computing is the ability to generate multipartite entangled states. In this paper, aspects of benchmarking entanglement generation capabilities of noisy intermediate-scale quantum (NISQ) devices are discussed based on the preparation of graph states and the verification of entanglement in the prepared states. Thereby, we use entanglement witnesses that are specifically suited for a scalable experiment design. This choice of entanglement witnesses can detect A) bipartite entanglement and B) genuine multipartite entanglement for graph states with constant two measurement settings if the prepared graph state is based on a 2-colorable graph, e.g., a square grid graph or one of its subgraphs. With this, we experimentally verify that a fully bipartite entangled state can be prepared on a 127-qubit IBM Quantum superconducting QPU, and genuine multipartite entanglement can be detected for states of up to 23 qubits with quantum readout error mitigation., Comment: 13 pages

We present the first experimental constraints on models with many additional neutrino species in an analysis of current neutrino data. These types of models are motivated as a solution to the hierarchy problem by lowering the species scale of gravity to TeV. Additionally, they offer a natural mechanism to generate small neutrino masses and provide interesting dark matter candidates. This study analyzes data from DayaBay, KamLAND, MINOS, NOvA and KATRIN. We do not find evidence for the presence of any additional neutrino species, therefore we report lower bounds on the allowed number of neutrino species realized in nature. For the normal/inverted neutrino mass ordering, we can give a lower bound on the number of neutrino species of O(30) and O(100), respectively, over a large range of the parameter space., Comment: 8 pages, 4 figures

Unreliable predictions can occur when using artificial intelligence (AI) systems with negative consequences for downstream applications, particularly when employed for decision-making. Conformal prediction provides a model-agnostic framework for uncertainty quantification that can be applied to any dataset, irrespective of its distribution, post hoc. In contrast to other pixel-level uncertainty quantification methods, conformal prediction operates without requiring access to the underlying model and training dataset, concurrently offering statistically valid and informative prediction regions, all while maintaining computational efficiency. In response to the increased need to report uncertainty alongside point predictions, we bring attention to the promise of conformal prediction within the domain of Earth Observation (EO) applications. To accomplish this, we assess the current state of uncertainty quantification in the EO domain and found that only 20% of the reviewed Google Earth Engine (GEE) datasets incorporated a degree of uncertainty information, with unreliable methods prevalent. Next, we introduce modules that seamlessly integrate into existing GEE predictive modelling workflows and demonstrate the application of these tools for datasets spanning local to global scales, including the Dynamic World and Global Ecosystem Dynamics Investigation (GEDI) datasets. These case studies encompass regression and classification tasks, featuring both traditional and deep learning-based workflows. Subsequently, we discuss the opportunities arising from the use of conformal prediction in EO. We anticipate that the increased availability of easy-to-use implementations of conformal predictors, such as those provided here, will drive wider adoption of rigorous uncertainty quantification in EO, thereby enhancing the reliability of uses such as operational monitoring and decision making.

We revisit the fundamental Boolean Matrix Multiplication (BMM) problem. With the invention of algebraic fast matrix multiplication over 50 years ago, it also became known that BMM can be solved in truly subcubic $O(n^\omega)$ time, where $\omega<3$; much work has gone into bringing $\omega$ closer to $2$. Since then, a parallel line of work has sought comparably fast combinatorial algorithms but with limited success. The naive $O(n^3)$-time algorithm was initially improved by a $\log^2{n}$ factor [Arlazarov et al.; RAS'70], then by $\log^{2.25}{n}$ [Bansal and Williams; FOCS'09], then by $\log^3{n}$ [Chan; SODA'15], and finally by $\log^4{n}$ [Yu; ICALP'15]. We design a combinatorial algorithm for BMM running in time $n^3 / 2^{\Omega(\sqrt[7]{\log n})}$ -- a speed-up over cubic time that is stronger than any poly-log factor. This comes tantalizingly close to refuting the conjecture from the 90s that truly subcubic combinatorial algorithms for BMM are impossible. This popular conjecture is the basis for dozens of fine-grained hardness results. Our main technical contribution is a new regularity decomposition theorem for Boolean matrices (or equivalently, bipartite graphs) under a notion of regularity that was recently introduced and analyzed analytically in the context of communication complexity [Kelley, Lovett, Meka; arXiv'23], and is related to a similar notion from the recent work on $3$-term arithmetic progression free sets [Kelley, Meka; FOCS'23]., Comment: To appear at STOC 2024

Diffusion Morphs (DiM) are a recent state-of-the-art method for creating high quality face morphs; however, they require a high number of network function evaluations (NFE) to create the morphs. We propose a new DiM pipeline, Fast-DiM, which can create morphs of a similar quality but with fewer NFE. We investigate the ODE solvers used to solve the Probability Flow ODE and the impact they have on the the creation of face morphs. Additionally, we employ an alternative method for encoding images into the latent space of the Diffusion model by solving the Probability Flow ODE as time runs forwards. Our experiments show that we can reduce the NFE by upwards of 85% in the encoding process while experiencing only 1.6\% reduction in Mated Morph Presentation Match Rate (MMPMR). Likewise, we showed we could cut NFE, in the sampling process, in half with only a maximal reduction of 0.23% in MMPMR., Comment: Accepted as a paper in IEEE Security and Privacy

This article presents a new tool for the automatic detection of meteors. Fast Meteor Detection Toolbox (FMDT) is able to detect meteor sightings by analyzing videos acquired by cameras onboard weather balloons or within airplane with stabilization. The challenge consists in designing a processing chain composed of simple algorithms, that are robust to the high fluctuation of the videos and that satisfy the constraints on power consumption (10 W) and real-time processing (25 frames per second)., Comment: in French language, Groupe de Recherche et d'{\'E}tudes de Traitement du Signal et des Images (GRETSI), Aug 2023, Grenoble, France

We study the power of randomness in the Number-on-Forehead (NOF) model in communication complexity. We construct an explicit 3-player function $f:[N]^3 \to \{0,1\}$, such that: (i) there exist a randomized NOF protocol computing it that sends a constant number of bits; but (ii) any deterministic or nondeterministic NOF protocol computing it requires sending about $(\log N)^{1/3}$ many bits. This exponentially improves upon the previously best-known such separation. At the core of our proof is an extension of a recent result of the first and third authors on sets of integers without 3-term arithmetic progressions into a non-arithmetic setting.

We present the very first constraints on the number of Standard Model (SM) copies with an additional Dirac right-handed neutrino. From cosmology, we are able to pose strong limits on large regions of the parameter space. Moreover, we show that it is possible to account for the right dark matter density in form of stable particles from the dark sectors.

With increasingly digitalized workplaces, the potential for sophisticated analyses of employee data rises. This increases the relevance of people analytics (PA), which are tools for the behavioral analysis of employees. Despite this potential, the successful usage of PA is hindered by employee concerns. Especially in Europe, where the GDPR or equivalent laws apply, employee consent is required before data can be processed in PA. Therefore, PA can only provide relevant insights if employees are willing to share their data. One potential way of achieving this is the use of appeal strategies. In the design of PA, the core strategy that can be used is the inclusion of data owner benefits, such as automated feedback, that are given to employees in exchange for sharing their own data. In this paper, we examine benefits as an appeal strategy and develop four design principles for the inclusion of benefits in PA. Then, we describe an exemplary set of analyses and benefits, demonstrating how our principles may be put into practice. Based on this exemplary implementation, we describe and discuss the results of a user study ($n = 46$) among employees in the EU and UK. Our study investigates the factors that foster or hinder employees' consent to sharing their data with PA. Then, we introduce our data owner benefits and analyze whether they can positively influence this consent decision. Our introduced data owner benefits were, contrary to our expectations, not suited to motivate our participants to consent to sharing their data. We therefore analyze how participants judge the benefits. Participants generally appreciate having them, confirming the value of including data owner benefits when designing PA. Some of our introduced benefits negatively influenced participants' sharing decision, though, meaning that careful consideration of potential risks is required when conceptualizing them., Comment: Peer-reviewed version accepted for publication in Proceedings of the ACM on Human-Computer Interaction (PACMHCI), EICS issue

We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose instance formulas allow expressing many tasks in probabilistic and causal inference. The main contribution of this work is establishing the exact computational complexity of these satisfiability problems. We introduce a new natural complexity class, named succ$\exists$R, which can be viewed as a succinct variant of the well-studied class $\exists$R, and show that the problems we consider are complete for succ$\exists$R. Our results imply even stronger algorithmic limitations than were proven by Fagin, Halpern, and Megiddo (1990) and Moss\'{e}, Ibeling, and Icard (2022) for some variants of the standard languages used commonly in probabilistic and causal inference., Comment: accepted at IJCAI 23