Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in Artificial Intelligence. State of the art Machine Learning (ML) approaches are mostly based on gradient descent optimisation in continuous spaces, while learning logic is framed in the discrete syntactic space of formulae. Using continuous optimisation to learn logic properties is a challenging problem, requiring to embed formulae in a continuous space in a meaningful way, i.e. preserving the semantics. Approaches like [BGKN22] are able to construct effective semantic-preserving embeddings via kernel methods (for linear temporal logic), but the map they define is not invertible. In this work we address this problem, learning how to invert such an embedding leveraging deep architectures based on the Graph Variational Autoencoder framework. We propose a novel model specifically designed for this setting, justifying our design choices through an extensive experimental evaluation. Reported results in the context of propositional logic are promising, and several challenges regarding learning invertible embeddings of formulae are highlighted and addressed.

An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable, while in linear regression, the direction of effect cannot be identified. For such linear models, non-Gaussianity of the (latent) variables has been shown to provide identifiability. In the case of factor analysis, this leads to independent component analysis, while in the case of the direction of effect, non-Gaussian versions of structural equation modelling solve the problem. More recently, we have shown how even general nonparametric nonlinear versions of such models can be estimated. Non-Gaussianity is not enough in this case, but assuming we have time series, or that the distributions are suitably modulated by some observed auxiliary variables, the models are identifiable. This paper reviews the identifiability theory for the linear and nonlinear cases, considering both factor analytic models and structural equation models.

This paper provide several mathematical analyses of the diffusion model in machine learning. The drift term of the backwards sampling process is represented as a conditional expectation involving the data distribution and the forward diffusion. The training process aims to find such a drift function by minimizing the mean-squared residue related to the conditional expectation. Using small-time approximations of the Green's function of the forward diffusion, we show that the analytical mean drift function in DDPM and the score function in SGM asymptotically blow up in the final stages of the sampling process for singular data distributions such as those concentrated on lower-dimensional manifolds, and is therefore difficult to approximate by a network. To overcome this difficulty, we derive a new target function and associated loss, which remains bounded even for singular data distributions. We illustrate the theoretical findings with several numerical examples.

Object recognition and instance segmentation are fundamental skills in any robotic or autonomous system. Existing state-of-the-art methods are often unable to capture meaningful uncertainty in challenging or ambiguous scenes, and as such can cause critical errors in high-performance applications. In this paper, we explore a class of distributional instance segmentation models using latent codes that can model uncertainty over plausible hypotheses of object masks. For robotic picking applications, we propose a confidence mask method to achieve the high precision necessary in industrial use cases. We show that our method can significantly reduce critical errors in robotic systems, including our newly released dataset of ambiguous scenes in a robotic application. On a real-world apparel-picking robot, our method significantly reduces double pick errors while maintaining high performance.

Differentiable particle filters are an emerging class of particle filtering methods that use neural networks to construct and learn parametric state-space models. In real-world applications, both the state dynamics and measurements can switch between a set of candidate models. For instance, in target tracking, vehicles can idle, move through traffic, or cruise on motorways, and measurements are collected in different geographical or weather conditions. This paper proposes a new differentiable particle filter for regime-switching state-space models. The method can learn a set of unknown candidate dynamic and measurement models and track the state posteriors. We evaluate the performance of the novel algorithm in relevant models, showing its great performance compared to other competitive algorithms.

Strategic classification studies learning in settings where users can modify their features to obtain favorable predictions. Most current works focus on simple classifiers that trigger independent user responses. Here we examine the implications of learning with more elaborate models that break the independence assumption. Motivated by the idea that applications of strategic classification are often social in nature, we focus on graph neural networks, which make use of social relations between users to improve predictions. Using a graph for learning introduces inter-user dependencies in prediction; our key point is that strategic users can exploit these to promote their own goals. As we show through analysis and simulation, this can work either against the system--or for it. Based on this, we propose a differentiable framework for strategically-robust learning of graph-based classifiers. Experiments on several real networked datasets demonstrate the utility of our approach. Machine learning is increasingly being used to inform decisions about humans. But when users of a system stand to gain from certain predictive outcomes, they may be prone to "game" the system by strategically modifying their features (at some cost). The literature on strategic classification (Brückner & Scheffer, 2011; Hardt et al., 2016) studies learning in this setting, with emphasis on how to learn classifiers that are robust to strategic user behavior. The idea that users may respond to a decision rule applies broadly and across many domains, from hiring, admissions, and scholarships to loan approval, insurance, welfare benefits, and medical eligibility (McCrary, 2008; Almond et al., 2010; Camacho & Conover, 2011; Lee & Lemieux, 2010). But despite these advances, most works in strategic classification remain to follow the original problem formulation in assuming independence across users responses. From a technical perspective, this assumption greatly simplifies the learning task, as it allows the classifier to consider each user's response in isolation: user behavior is modeled via a response mapping Intuitively, a user will modify her features if this'moves' her across the decision boundary, as long as this is worthwhile (i.e., gains from prediction exceed modification costs).

Conventional supervised learning methods typically assume i.i.d samples and are found to be sensitive to out-of-distribution (OOD) data. We propose Generative Causal Representation Learning (GCRL) which leverages causality to facilitate knowledge transfer under distribution shifts. While we evaluate the effectiveness of our proposed method in human trajectory prediction models, GCRL can be applied to other domains as well. First, we propose a novel causal model that explains the generative factors in motion forecasting datasets using features that are common across all environments and with features that are specific to each environment. Selection variables are used to determine which parts of the model can be directly transferred to a new environment without fine-tuning. Second, we propose an end-to-end variational learning paradigm to learn the causal mechanisms that generate observations from features. GCRL is supported by strong theoretical results that imply identifiability of the causal model under certain assumptions. Experimental results on synthetic and real-world motion forecasting datasets show the robustness and effectiveness of our proposed method for knowledge transfer under zero-shot and low-shot settings by substantially outperforming the prior motion forecasting models on out-of-distribution prediction. Our code is available at https://github.com/sshirahmad/GCRL.

Recent advances have extended the scope of Bayesian optimization (BO) to expensive-to-evaluate black-box functions with dozens of dimensions, aspiring to unlock impactful applications, for example, in the life sciences, neural architecture search, and robotics. However, a closer examination reveals that the state-of-the-art methods for high-dimensional Bayesian optimization (HDBO) suffer from degrading performance as the number of dimensions increases or even risk failure if certain unverifiable assumptions are not met. This paper proposes BAxUS that leverages a novel family of nested random subspaces to adapt the space it optimizes over to the problem. This ensures high performance while removing the risk of failure, which we assert via theoretical guarantees. A comprehensive evaluation demonstrates that BAxUS achieves better results than the state-of-the-art methods for a broad set of applications.

Vertical federated learning (VFL) is a cloud-edge collaboration paradigm that enables edge nodes, comprising resource-constrained Internet of Things (IoT) devices, to cooperatively train artificial intelligence (AI) models while retaining their data locally. This paradigm facilitates improved privacy and security for edges and IoT devices, making VFL an essential component of Artificial Intelligence of Things (AIoT) systems. Nevertheless, the partitioned structure of VFL can be exploited by adversaries to inject a backdoor, enabling them to manipulate the VFL predictions. In this paper, we aim to investigate the vulnerability of VFL in the context of binary classification tasks. To this end, we define a threat model for backdoor attacks in VFL and introduce a universal adversarial backdoor (UAB) attack to poison the predictions of VFL. The UAB attack, consisting of universal trigger generation and clean-label backdoor injection, is incorporated during the VFL training at specific iterations. This is achieved by alternately optimizing the universal trigger and model parameters of VFL sub-problems. Our work distinguishes itself from existing studies on designing backdoor attacks for VFL, as those require the knowledge of auxiliary information not accessible within the split VFL architecture. In contrast, our approach does not necessitate any additional data to execute the attack. On the LendingClub and Zhongyuan datasets, our approach surpasses existing state-of-the-art methods, achieving up to 100\% backdoor task performance while maintaining the main task performance. Our results in this paper make a major advance to revealing the hidden backdoor risks of VFL, hence paving the way for the future development of secure AIoT.

Diffusion models currently achieve state-of-the-art performance for both conditional and unconditional image generation. However, so far, image diffusion models do not support tasks required for 3D understanding, such as view-consistent 3D generation or single-view object reconstruction. In this paper, we present RenderDiffusion, the first diffusion model for 3D generation and inference, trained using only monocular 2D supervision. Central to our method is a novel image denoising architecture that generates and renders an intermediate three-dimensional representation of a scene in each denoising step. This enforces a strong inductive structure within the diffusion process, providing a 3D consistent representation while only requiring 2D supervision. The resulting 3D representation can be rendered from any view. We evaluate RenderDiffusion on FFHQ, AFHQ, ShapeNet and CLEVR datasets, showing competitive performance for generation of 3D scenes and inference of 3D scenes from 2D images. Additionally, our diffusion-based approach allows us to use 2D inpainting to edit 3D scenes.