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We represent 3D shape by structured 2D representations of fixed length making it feasible to apply well investigated 2D convolutional neural networks (CNN) for both discriminative and geometric tasks on 3D shapes. We first provide a general introduction to such structured descriptors, analyze their different forms and show how a simple 2D CNN can be used to achieve good classification result. With a specialized classification network for images and our structured representation, we achieve the classification accuracy of 99.7\% in the ModelNet40 test set - improving the previous state-of-the-art by a large margin. We finally provide a novel framework for performing the geometric task of 3D segmentation using 2D CNNs and the structured representation - concluding the utility of such descriptors for both discriminative and geometric tasks.

Collaborative filtering (CF) is a pivotal technique in modern recommender systems. The learning process of CF models typically consists of three components: interaction encoder, loss function, and negative sampling. Although many existing studies have proposed various CF models to design sophisticated interaction encoders, recent work shows that simply reformulating the loss functions can achieve significant performance gains. This paper delves into analyzing the relationship among existing loss functions. Our mathematical analysis reveals that the previous loss functions can be interpreted as alignment and uniformity functions: (i) the alignment matches user and item representations, and (ii) the uniformity disperses user and item distributions. Inspired by this analysis, we propose a novel loss function that improves the design of alignment and uniformity considering the unique patterns of datasets called Margin-aware Alignment and Weighted Uniformity (MAWU). The key novelty of MAWU is two-fold: (i) margin-aware alignment (MA) mitigates user/item-specific popularity biases, and (ii) weighted uniformity (WU) adjusts the significance between user and item uniformities to reflect the inherent characteristics of datasets. Extensive experimental results show that MF and LightGCN equipped with MAWU are comparable or superior to state-of-the-art CF models with various loss functions on three public datasets.

We present VERF, a collection of two methods (VERF-PnP and VERF-Light) for providing runtime assurance on the correctness of a camera pose estimate of a monocular camera without relying on direct depth measurements. We leverage the ability of NeRF (Neural Radiance Fields) to render novel RGB perspectives of a scene. We only require as input the camera image whose pose is being estimated, an estimate of the camera pose we want to monitor, and a NeRF model containing the scene pictured by the camera. We can then predict if the pose estimate is within a desired distance from the ground truth and justify our prediction with a level of confidence. VERF-Light does this by rendering a viewpoint with NeRF at the estimated pose and estimating its relative offset to the sensor image up to scale. Since scene scale is unknown, the approach renders another auxiliary image and reasons over the consistency of the optical flows across the three images. VERF-PnP takes a different approach by rendering a stereo pair of images with NeRF and utilizing the Perspective-n-Point (PnP) algorithm. We evaluate both methods on the LLFF dataset, on data from a Unitree A1 quadruped robot, and on data collected from Blue Origin's sub-orbital New Shepard rocket to demonstrate the effectiveness of the proposed pose monitoring method across a range of scene scales. We also show monitoring can be completed in under half a second on a 3090 GPU.

In recent years there have been remarkable advancements in autonomous driving. While autonomous vehicles demonstrate high performance in closed-set conditions, they encounter difficulties when confronted with unexpected situations. At the same time, world models emerged in the field of model-based reinforcement learning as a way to enable agents to predict the future depending on potential actions. This led to outstanding results in sparse reward and complex control tasks. This work provides an overview of how world models can be leveraged to perform anomaly detection in the domain of autonomous driving. We provide a characterization of world models and relate individual components to previous works in anomaly detection to facilitate further research in the field.

The Skolem problem is a long-standing open problem in linear dynamical systems: can a linear recurrence sequence (LRS) ever reach 0 from a given initial configuration? Similarly, the positivity problem asks whether the LRS stays positive from an initial configuration. Deciding Skolem (or positivity) has been open for half a century: the best known decidability results are for LRS with special properties (e.g., low order recurrences). But these problems are easier for "uninitialized" variants, where the initial configuration is not fixed but can vary arbitrarily: checking if there is an initial configuration from which the LRS stays positive can be decided in polynomial time (Tiwari in 2004, Braverman in 2006). In this paper, we consider problems that lie between the initialized and uninitialized variant. More precisely, we ask if 0 (resp. negative numbers) can be avoided from every initial configuration in a neighborhood of a given initial configuration. This can be considered as a robust variant of the Skolem (resp. positivity) problem. We show that these problems lie at the frontier of decidability: if the neighbourhood is given as part of the input, then robust Skolem and robust positivity are Diophantine hard, i.e., solving either would entail major breakthrough in Diophantine approximations, as happens for (non-robust) positivity. However, if one asks whether such a neighbourhood exists, then the problems turn out to be decidable with PSPACE complexity. Our techniques also allow us to tackle robustness for ultimate positivity, which asks whether there is a bound on the number of steps after which the LRS remains positive. There are two variants depending on whether we ask for a "uniform" bound on this number of steps. For the non-uniform variant, when the neighbourhood is open, the problem turns out to be tractable, even when the neighbourhood is given as input.

We study a generalization of the classic Spanning Tree problem that allows for a non-uniform failure model. More precisely, edges are either \emph{safe} or \emph{unsafe} and we assume that failures only affect unsafe edges. In Unweighted Flexible Graph Connectivity we are given an undirected graph $G = (V,E)$ in which the edge set $E$ is partitioned into a set $S$ of safe edges and a set $U$ of unsafe edges and the task is to find a set $T$ of at most $k$ edges such that $T - \{u\}$ is connected and spans $V$ for any unsafe edge $u \in T$. Unweighted Flexible Graph Connectivity generalizes both Spanning Tree and Hamiltonian Cycle. We study Unweighted Flexible Graph Connectivity in terms of fixed-parameter tractability (FPT). We show an almost complete dichotomy on which parameters lead to fixed-parameter tractability and which lead to hardness. To this end, we obtain FPT-time algorithms with respect to the vertex deletion distance to cluster graphs and with respect to the treewidth. By exploiting the close relationship to Hamiltonian Cycle, we show that FPT-time algorithms for many smaller parameters are unlikely under standard parameterized complexity assumptions. Regarding problem-specific parameters, we observe that Unweighted Flexible Graph Connectivity} admits an FPT-time algorithm when parameterized by the number of unsafe edges. Furthermore, we investigate a below-upper-bound parameter for the number of edges of a solution. We show that this parameter also leads to an FPT-time algorithm.

Recent advancements in Digital Document Restoration (DDR) have led to significant breakthroughs in analyzing highly damaged written artifacts. Among those, there has been an increasing interest in applying Artificial Intelligence techniques for virtually unwrapping and automatically detecting ink on the Herculaneum papyri collection. This collection consists of carbonized scrolls and fragments of documents, which have been digitized via X-ray tomography to allow the development of ad-hoc deep learning-based DDR solutions. In this work, we propose a modification of the Fast Fourier Convolution operator for volumetric data and apply it in a segmentation architecture for ink detection on the challenging Herculaneum papyri, demonstrating its suitability via deep experimental analysis. To encourage the research on this task and the application of the proposed operator to other tasks involving volumetric data, we will release our implementation (//github.com/aimagelab/vffc)

The advent of large language models marks a revolutionary breakthrough in artificial intelligence. With the unprecedented scale of training and model parameters, the capability of large language models has been dramatically improved, leading to human-like performances in understanding, language synthesizing, and common-sense reasoning, etc. Such a major leap-forward in general AI capacity will change the pattern of how personalization is conducted. For one thing, it will reform the way of interaction between humans and personalization systems. Instead of being a passive medium of information filtering, large language models present the foundation for active user engagement. On top of such a new foundation, user requests can be proactively explored, and user's required information can be delivered in a natural and explainable way. For another thing, it will also considerably expand the scope of personalization, making it grow from the sole function of collecting personalized information to the compound function of providing personalized services. By leveraging large language models as general-purpose interface, the personalization systems may compile user requests into plans, calls the functions of external tools to execute the plans, and integrate the tools' outputs to complete the end-to-end personalization tasks. Today, large language models are still being developed, whereas the application in personalization is largely unexplored. Therefore, we consider it to be the right time to review the challenges in personalization and the opportunities to address them with LLMs. In particular, we dedicate this perspective paper to the discussion of the following aspects: the development and challenges for the existing personalization system, the newly emerged capabilities of large language models, and the potential ways of making use of large language models for personalization.

The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.

Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.