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We introduce two new extensions to the beam search algorithm based on conformal predictions (CP) to produce sets of sequences with theoretical coverage guarantees. The first method is very simple and proposes dynamically-sized subsets of beam search results but, unlike typical CP procedures, has an upper bound on the achievable guarantee depending on a post-hoc calibration measure. Our second algorithm introduces the conformal set prediction procedure as part of the decoding process, producing a variable beam width which adapts to the current uncertainty. While more complex, this procedure can achieve coverage guarantees selected a priori. We provide marginal coverage bounds for each method, and evaluate them empirically on a selection of tasks drawing from natural language processing and chemistry.

We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We present a sparsity characterization for distributions of random graphs (that are allowed to contain high-degree nodes), based on which we study fundamental trade-offs between the number of measurements, the complexity of the graph class, and the probability of error. We first derive a necessary condition on the number of measurements. Then, by considering a three-stage recovery scheme, we give a sufficient condition for recovery. Furthermore, assuming the measurements are Gaussian IID, we prove upper and lower bounds on the (worst-case) sample complexity for both noisy and noiseless recovery. In the special cases of the uniform distribution on trees with n nodes and the Erdos-Renyi (n,p) class, the fundamental trade-offs are tight up to multiplicative factors with noiseless measurements. In addition, for practical applications, we design and implement a polynomial-time (in n) algorithm based on the three-stage recovery scheme. Experiments show that the heuristic algorithm outperforms basis pursuit on star graphs. We apply the heuristic algorithm to learn admittance matrices in electric grids. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness and robustness of the proposed algorithm for parameter reconstruction.

In multimodal-aware recommendation, the extraction of meaningful multimodal features is at the basis of high-quality recommendations. Generally, each recommendation framework implements its multimodal extraction procedures with specific strategies and tools. This is limiting for two reasons: (i) different extraction strategies do not ease the interdependence among multimodal recommendation frameworks; thus, they cannot be efficiently and fairly compared; (ii) given the large plethora of pre-trained deep learning models made available by different open source tools, model designers do not have access to shared interfaces to extract features. Motivated by the outlined aspects, we propose \framework, a unified framework for the extraction of multimodal features in recommendation. By integrating three widely-adopted deep learning libraries as backends, namely, TensorFlow, PyTorch, and Transformers, we provide a shared interface to extract and process features where each backend's specific methods are abstracted to the end user. Noteworthy, the extraction pipeline is easily configurable with a YAML-based file where the user can specify, for each modality, the list of models (and their specific backends/parameters) to perform the extraction. Finally, to make \framework accessible to the community, we build a public Docker image equipped with a ready-to-use CUDA environment and propose three demos to test its functionalities for different scenarios and tasks. The GitHub repository and the documentation are accessible at this link: //github.com/sisinflab/Ducho.

We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language equivalence (under the standard language valuation) for Kleene algebra terms, this coincidence is broken if we extend the terms with complements. In this paper, we prove the decidability of some fragments of the equational theory: the universality problem is coNP-complete, and the inequational theory t <= s is coNP-complete when t does not contain Kleene-star. To this end, we introduce words-to-letters valuations; they are sufficient valuations for the equational theory and ease us in investigating the equational theory w.r.t. languages. Additionally, we prove that for words with variable complements, the equational theory coincides with the word equivalence.

In this paper, we explore the role of matrix scaling on a matrix of counts when building a topic model using non-negative matrix factorization. We present a scaling inspired by the normalized Laplacian (NL) for graphs that can greatly improve the quality of a non-negative matrix factorization. The results parallel those in the spectral graph clustering work of \cite{Priebe:2019}, where the authors proved adjacency spectral embedding (ASE) spectral clustering was more likely to discover core-periphery partitions and Laplacian Spectral Embedding (LSE) was more likely to discover affinity partitions. In text analysis non-negative matrix factorization (NMF) is typically used on a matrix of co-occurrence ``contexts'' and ``terms" counts. The matrix scaling inspired by LSE gives significant improvement for text topic models in a variety of datasets. We illustrate the dramatic difference a matrix scalings in NMF can greatly improve the quality of a topic model on three datasets where human annotation is available. Using the adjusted Rand index (ARI), a measure cluster similarity we see an increase of 50\% for Twitter data and over 200\% for a newsgroup dataset versus using counts, which is the analogue of ASE. For clean data, such as those from the Document Understanding Conference, NL gives over 40\% improvement over ASE. We conclude with some analysis of this phenomenon and some connections of this scaling with other matrix scaling methods.

We investigate the complexity of several manipulation and control problems under numerous prevalent approval-based multiwinner voting rules. Particularly, the rules we study include approval voting (AV), satisfaction approval voting (SAV), net-satisfaction approval voting (NSAV), proportional approval voting (PAV), approval-based Chamberlin-Courant voting (ABCCV), minimax approval voting (MAV), etc. We show that these rules generally resist the strategic types scrutinized in the paper, with only a few exceptions. In addition, we also obtain many fixed-parameter tractability results for these problems with respect to several natural parameters, and derive polynomial-time algorithms for certain special cases.

The objective of topic inference in research proposals aims to obtain the most suitable disciplinary division from the discipline system defined by a funding agency. The agency will subsequently find appropriate peer review experts from their database based on this division. Automated topic inference can reduce human errors caused by manual topic filling, bridge the knowledge gap between funding agencies and project applicants, and improve system efficiency. Existing methods focus on modeling this as a hierarchical multi-label classification problem, using generative models to iteratively infer the most appropriate topic information. However, these methods overlook the gap in scale between interdisciplinary research proposals and non-interdisciplinary ones, leading to an unjust phenomenon where the automated inference system categorizes interdisciplinary proposals as non-interdisciplinary, causing unfairness during the expert assignment. How can we address this data imbalance issue under a complex discipline system and hence resolve this unfairness? In this paper, we implement a topic label inference system based on a Transformer encoder-decoder architecture. Furthermore, we utilize interpolation techniques to create a series of pseudo-interdisciplinary proposals from non-interdisciplinary ones during training based on non-parametric indicators such as cross-topic probabilities and topic occurrence probabilities. This approach aims to reduce the bias of the system during model training. Finally, we conduct extensive experiments on a real-world dataset to verify the effectiveness of the proposed method. The experimental results demonstrate that our training strategy can significantly mitigate the unfairness generated in the topic inference task.

Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on heuristics, e.g., the solution operators of partial differential equations (PDE), such as the Laplace or biharmonic equation. Especially the latter, which shows good numerical performance for large displacements, is expensive. Moreover, from a continuous perspective, choosing the mesh motion technique is to a certain extent arbitrary and has no influence on the physically relevant quantities. Therefore, we consider approaches inspired by machine learning. We present a hybrid PDE-NN approach, where the neural network (NN) serves as parameterization of a coefficient in a second order nonlinear PDE. We ensure existence of solutions for the nonlinear PDE by the choice of the neural network architecture. Moreover, we present an approach where a neural network corrects the harmonic extension such that the boundary displacement is not changed. In order to avoid technical difficulties in coupling finite element and machine learning software, we work with a splitting of the monolithic FSI system into three smaller subsystems. This allows to solve the mesh motion equation in a separate step. We assess the quality of the learned mesh motion technique by applying it to a FSI benchmark problem.

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.

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.