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Investigating solutions of nonlinear equation systems is challenging in a general framework, especially if the equations contain uncertainties about parameters modeled by probability densities. Such random equations, understood as stationary (non-dynamical) equations with parameters as random variables, have a long history and a broad range of applications. In this work, we study nonlinear random equations by combining them with mixture model parameter random variables in order to investigate the combinatorial complexity of such equations and how this can be utilized practically. We derive a general likelihood function and posterior density of approximate best fit solutions while avoiding significant restrictions about the type of nonlinearity or mixture models, and demonstrate their numerically efficient application for the applied researcher. In the results section we are specifically focusing on example simulations of approximate likelihood/posterior solutions for random linear equation systems, nonlinear systems of random conic section equations, as well as applications to portfolio optimization, stochastic control and random matrix theory in order to show the wide applicability of the presented methodology.

Recent work on discrete speech tokenization has paved the way for models that can seamlessly perform multiple tasks across modalities, e.g., speech recognition, text to speech, speech to speech translation. Moreover, large language models (LLMs) pretrained from vast text corpora contain rich linguistic information that can improve accuracy in a variety of tasks. In this paper, we present a decoder-only Discrete Multimodal Language Model (DMLM), which can be flexibly applied to multiple tasks (ASR, T2S, S2TT, etc.) and modalities (text, speech, vision). We explore several critical aspects of discrete multi-modal models, including the loss function, weight initialization, mixed training supervision, and codebook. Our results show that DMLM benefits significantly, across multiple tasks and datasets, from a combination of supervised and unsupervised training. Moreover, for ASR, it benefits from initializing DMLM from a pretrained LLM, and from a codebook derived from Whisper activations.

Robust estimation of the essential matrix, which encodes the relative position and orientation of two cameras, is a fundamental step in structure from motion pipelines. Recent deep-based methods achieved accurate estimation by using complex network architectures that involve graphs, attention layers, and hard pruning steps. Here, we propose a simpler network architecture based on Deep Sets. Given a collection of point matches extracted from two images, our method identifies outlier point matches and models the displacement noise in inlier matches. A weighted DLT module uses these predictions to regress the essential matrix. Our network achieves accurate recovery that is superior to existing networks with significantly more complex architectures.

The modelling of temporal patterns in dynamic graphs is an important current research issue in the development of time-aware GNNs. Whether or not a specific sequence of events in a temporal graph constitutes a temporal pattern not only depends on the frequency of its occurrence. We consider whether it deviates from what is expected in a temporal graph where timestamps are randomly shuffled. While accounting for such a random baseline is important to model temporal patterns, it has mostly been ignored by current temporal graph neural networks. To address this issue we propose HYPA-DBGNN, a novel two-step approach that combines (i) the inference of anomalous sequential patterns in time series data on graphs based on a statistically principled null model, with (ii) a neural message passing approach that utilizes a higher-order De Bruijn graph whose edges capture overrepresented sequential patterns. Our method leverages hypergeometric graph ensembles to identify anomalous edges within both first- and higher-order De Bruijn graphs, which encode the temporal ordering of events. The model introduces an inductive bias that enhances model interpretability. We evaluate our approach for static node classification using benchmark datasets and a synthetic dataset that showcases its ability to incorporate the observed inductive bias regarding over- and under-represented temporal edges. We demonstrate the framework's effectiveness in detecting similar patterns within empirical datasets, resulting in superior performance compared to baseline methods in node classification tasks. To the best of our knowledge, our work is the first to introduce statistically informed GNNs that leverage temporal and causal sequence anomalies. HYPA-DBGNN represents a path for bridging the gap between statistical graph inference and neural graph representation learning, with potential applications to static GNNs.

Characterizing the minimal communication needed for the quantum channel simulation is a fundamental task in the quantum information theory. In this paper, we show that, in fidelity, the quantum channel simulation can be directly achieved via quantum state splitting without using a technique known as the de~Finetti reduction, and thus provide a pair of tighter one-shot bounds. Using the bounds, we also recover the quantum reverse Shannon theorem in a much simpler way.

Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts due to their inherent quantum behavior. One of the main challenges of such quantum algorithms is up-scaling the system size, which is necessary to achieve meaningful quantum advantage. In this work, we present an approach to improve the scalability of eigenspace filtering for the ground state preparation of a given Hamiltonian. Our method aims to tackle limitations introduced by a small spectral gap and high degeneracy of low energy states. It is based on an adaptive sequence of eigenspace filtering through Quantum Eigenvalue Transformation of Unitary Matrices (QETU) followed by spectrum profiling. By combining our proposed algorithm with state-of-the-art phase estimation methods, we achieved good approximations for the ground state energy with local, two-qubit gate depolarizing probability up to $10^{-4}$. To demonstrate the key results in this work, we ran simulations with the transverse-field Ising Model on classical computers using Qiskit. We compare the performance of our approach with the static implementation of QETU and show that we can consistently achieve three to four orders of magnitude improvement in the absolute error rate.

We formulate discussion graph semantics of first-order logic with equality for reasoning about discussion and argumentation as naturally as we would reason about sentences. While there are a few existing proposals to use a formal logic for reasoning about argumentation, they are constructed bottom-up and specialised to the argumentation model by Dung. There is indeed a conspicuous lack of a formal reasoning framework for handling general discussion and argumentation models. We achieve the generality through a top-down formulation of the semantics of first-order logic (with equality) formulas, addressing the current shortage.

Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft objects are often highly nonlinear and, thus, complex to predict. Data-driven approaches seem promising for modeling those complex dynamics but often neglect basic physical principles, which consequently makes them untrustworthy and limits generalization. To address this problem, we propose a physics-constrained learning method that combines powerful learning tools and reliable physical models. Our method leverages the data collected from observations by sending them into a Gaussian process that is physically constrained by a distributed Port-Hamiltonian model. Based on the Bayesian nature of the Gaussian process, we not only learn the dynamics of the system, but also enable uncertainty quantification. Furthermore, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.

Edge computing has recently emerged as a promising paradigm to boost the performance of distributed learning by leveraging the distributed resources at edge nodes. Architecturally, the introduction of edge nodes adds an additional intermediate layer between the master and workers in the original distributed learning systems, potentially leading to more severe straggler effect. Recently, coding theory-based approaches have been proposed for stragglers mitigation in distributed learning, but the majority focus on the conventional workers-master architecture. In this paper, along a different line, we investigate the problem of mitigating the straggler effect in hierarchical distributed learning systems with an additional layer composed of edge nodes. Technically, we first derive the fundamental trade-off between the computational loads of workers and the stragglers tolerance. Then, we propose a hierarchical gradient coding framework, which provides better stragglers mitigation, to achieve the derived computational trade-off. To further improve the performance of our framework in heterogeneous scenarios, we formulate an optimization problem with the objective of minimizing the expected execution time for each iteration in the learning process. We develop an efficient algorithm to mathematically solve the problem by outputting the optimum strategy. Extensive simulation results demonstrate the superiority of our schemes compared with conventional solutions.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.