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Almost all problems in applied mathematics, including the analysis of dynamical systems, deal with spaces of real-valued functions on Euclidean domains in their formulation and solution. In this paper, we describe the the tool Ariadne, which provides a rigorous calculus for working with Euclidean functions. We first introduce the Ariadne framework, which is based on a clean separation of objects as providing exact, effective, validated and approximate information. We then discuss the function calculus as implemented in \Ariadne, including polynomial function models which are the fundamental class for concrete computations. We then consider solution of some core problems of functional analysis, namely solution of algebraic equations and differential equations, and briefly discuss their use for the analysis of hybrid systems. We will give examples of C++ and Python code for performing the various calculations. Finally, we will discuss progress on extensions, including improvements to the function calculus and extensions to more complicated classes of system.

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Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent strides have been taken to apply this computational framework in tackling and resolving various issues related to text processing. The resultant solutions demonstrate marked advantages over their classical counterparts. This study employs quantum computation to efficaciously surmount text processing challenges, particularly those involving string comparison. The focus is on the alignment of fixed-length substrings within two input strings. Specifically, given two input strings, $x$ and $y$, both of length $n$, and a value $d \leq n$, we want to verify the following conditions: the existence of a common prefix of length $d$, the presence of a common substring of length $d$ beginning at position $j$ (with $0 \leq j < n$) and, the presence of any common substring of length $d$ beginning in both strings at the same position. Such problems find applications as sub-procedures in a variety of problems concerning text processing and sequence analysis. Notably, our approach furnishes polylogarithmic solutions, a stark contrast to the linear complexity inherent in the best classical alternatives.

We consider the problem of evaluating distinct multivariate polynomials over several massive datasets in a distributed computing system with a single master node and multiple worker nodes. We focus on the general case when each multivariate polynomial is evaluated over its corresponding dataset and propose a generalization of the Lagrange Coded Computing framework (Yu et al. 2019) to perform all computations simultaneously while providing robustness against stragglers who do not respond in time, adversarial workers who respond with wrong computation and information-theoretic security of dataset against colluding workers. Our scheme introduces a small computation overhead which results in a reduction in download cost and also offers comparable resistance to stragglers over existing solutions. On top of it, we also propose two verification schemes to detect the presence of adversaries, which leads to incorrect results, without involving additional nodes.

Measures of algorithmic fairness are usually discussed in the context of binary decisions. We extend the approach to continuous scores. So far, ROC-based measures have mainly been suggested for this purpose. Other existing methods depend heavily on the distribution of scores, are unsuitable for ranking tasks, or their effect sizes are not interpretable. Here, we propose a distributionally invariant version of fairness measures for continuous scores with a reasonable interpretation based on the Wasserstein distance. Our measures are easily computable and well suited for quantifying and interpreting the strength of group disparities as well as for comparing biases across different models, datasets, or time points. We derive a link between the different families of existing fairness measures for scores and show that the proposed distributionally invariant fairness measures outperform ROC-based fairness measures because they are more explicit and can quantify significant biases that ROC-based fairness measures miss. Finally, we demonstrate their effectiveness through experiments on the most commonly used fairness benchmark datasets.

Popularity bias is a widespread problem in the field of recommender systems, where popular items tend to dominate recommendation results. In this work, we propose 'Test Time Embedding Normalization' as a simple yet effective strategy for mitigating popularity bias, which surpasses the performance of the previous mitigation approaches by a significant margin. Our approach utilizes the normalized item embedding during the inference stage to control the influence of embedding magnitude, which is highly correlated with item popularity. Through extensive experiments, we show that our method combined with the sampled softmax loss effectively reduces popularity bias compare to previous approaches for bias mitigation. We further investigate the relationship between user and item embeddings and find that the angular similarity between embeddings distinguishes preferable and non-preferable items regardless of their popularity. The analysis explains the mechanism behind the success of our approach in eliminating the impact of popularity bias. Our code is available at //github.com/ml-postech/TTEN.

It is desirable to have accurate uncertainty estimation from a single deterministic forward-pass model, as traditional methods for uncertainty quantification are computationally expensive. However, this is difficult because single forward-pass models do not sample weights during inference and often make assumptions about the target distribution, such as assuming it is Gaussian. This can be restrictive in regression tasks, where the mean and standard deviation are inadequate to model the target distribution accurately. This paper proposes a deep Bayesian quantile regression model that can estimate the quantiles of a continuous target distribution without the Gaussian assumption. The proposed method is based on evidential learning, which allows the model to capture aleatoric and epistemic uncertainty with a single deterministic forward-pass model. This makes the method efficient and scalable to large models and datasets. We demonstrate that the proposed method achieves calibrated uncertainties on non-Gaussian distributions, disentanglement of aleatoric and epistemic uncertainty, and robustness to out-of-distribution samples.

We analysis performance of semantic segmentation models wrt. adversarial attacks, and observe that the adversarial examples generated from a source model fail to attack the target models. i.e The conventional attack methods, such as PGD and FGSM, do not transfer well to target models, making it necessary to study the transferable attacks, especially transferable attacks for semantic segmentation. We find two main factors to achieve transferable attack. Firstly, the attack should come with effective data augmentation and translation-invariant features to deal with unseen models. Secondly, stabilized optimization strategies are needed to find the optimal attack direction. Based on the above observations, we propose an ensemble attack for semantic segmentation to achieve more effective attacks with higher transferability. The source code and experimental results are publicly available via our project page: //github.com/anucvers/TASS.

Currently, most speaker recognition backends, such as cosine, linear discriminant analysis (LDA), or probabilistic linear discriminant analysis (PLDA), make decisions by calculating similarity or distance between enrollment and test embeddings which are already extracted from neural networks. However, for each embedding, the local structure of itself and its neighbor embeddings in the low-dimensional space is different, which may be helpful for the recognition but is often ignored. In order to take advantage of it, we propose a graph neural network (GNN) backend to mine latent relationships among embeddings for classification. We assume all the embeddings as nodes on a graph, and their edges are computed based on some similarity function, such as cosine, LDA+cosine, or LDA+PLDA. We study different graph settings and explore variants of GNN to find a better message passing and aggregation way to accomplish the recognition task. Experimental results on NIST SRE14 i-vector challenging, VoxCeleb1-O, VoxCeleb1-E, and VoxCeleb1-H datasets demonstrate that our proposed GNN backends significantly outperform current mainstream methods.

We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By carefully combining a focalized variant of call-by-push-value, bidirectional typing, and our novel technique of value-determined indexes, our system generates solvable SMT constraints without existential (unification) variables. We design a polarized subtyping relation allowing us to prove our logically focused typing algorithm is sound, complete, and decidable. We prove type soundness of our declarative system with respect to an elementary domain-theoretic denotational semantics. Type soundness implies, relatively simply, the total correctness and logical consistency of our system. The relative ease with which we obtain both algorithmic and semantic results ultimately stems from the proof-theoretic technique of focalization.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.

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