In this paper, we present a sharper version of the results in the paper Dimension independent bounds for general shallow networks; Neural Networks, \textbf{123} (2020), 142-152. Let $\mathbb{X}$ and $\mathbb{Y}$ be compact metric spaces. We consider approximation of functions of the form $ x\mapsto\int_{\mathbb{Y}} G( x, y)d\tau( y)$, $ x\in\mathbb{X}$, by $G$-networks of the form $ x\mapsto \sum_{k=1}^n a_kG( x, y_k)$, $ y_1,\cdots, y_n\in\mathbb{Y}$, $a_1,\cdots, a_n\in\mathbb{R}$. Defining the dimensions of $\mathbb{X}$ and $\mathbb{Y}$ in terms of covering numbers, we obtain dimension independent bounds on the degree of approximation in terms of $n$, where also the constants involved are all dependent at most polynomially on the dimensions. Applications include approximation by power rectified linear unit networks, zonal function networks, certain radial basis function networks as well as the important problem of function extension to higher dimensional spaces.

Graph Neural Networks (GNNs), despite achieving remarkable performance across different tasks, are theoretically bounded by the 1-Weisfeiler-Lehman test, resulting in limitations in terms of graph expressivity. Even though prior works on topological higher-order GNNs overcome that boundary, these models often depend on assumptions about sub-structures of graphs. Specifically, topological GNNs leverage the prevalence of cliques, cycles, and rings to enhance the message-passing procedure. Our study presents a novel perspective by focusing on simple paths within graphs during the topological message-passing process, thus liberating the model from restrictive inductive biases. We prove that by lifting graphs to path complexes, our model can generalize the existing works on topology while inheriting several theoretical results on simplicial complexes and regular cell complexes. Without making prior assumptions about graph sub-structures, our method outperforms earlier works in other topological domains and achieves state-of-the-art results on various benchmarks.

In the process of training a generative model, it becomes essential to measure the discrepancy between two high-dimensional probability distributions: the generative distribution and the ground-truth distribution of the observed dataset. Recently, there has been growing interest in an approach that involves slicing high-dimensional distributions, with the Cramer-Wold distance emerging as a promising method. However, we have identified that the Cramer-Wold distance primarily focuses on joint distributional learning, whereas understanding marginal distributional patterns is crucial for effective synthetic data generation. In this paper, we introduce a novel measure of dissimilarity, the mixture Cramer-Wold distance. This measure enables us to capture both marginal and joint distributional information simultaneously, as it incorporates a mixture measure with point masses on standard basis vectors. Building upon the mixture Cramer-Wold distance, we propose a new generative model called CWDAE (Cramer-Wold Distributional AutoEncoder), which shows remarkable performance in generating synthetic data when applied to real tabular datasets. Furthermore, our model offers the flexibility to adjust the level of data privacy with ease.

Reinforcement learning (RL) is recognized as lacking generalization and robustness under environmental perturbations, which excessively restricts its application for real-world robotics. Prior work claimed that adding regularization to the value function is equivalent to learning a robust policy with uncertain transitions. Although the regularization-robustness transformation is appealing for its simplicity and efficiency, it is still lacking in continuous control tasks. In this paper, we propose a new regularizer named $\textbf{U}$ncertainty $\textbf{S}$et $\textbf{R}$egularizer (USR), by formulating the uncertainty set on the parameter space of the transition function. In particular, USR is flexible enough to be plugged into any existing RL framework. To deal with unknown uncertainty sets, we further propose a novel adversarial approach to generate them based on the value function. We evaluate USR on the Real-world Reinforcement Learning (RWRL) benchmark, demonstrating improvements in the robust performance for perturbed testing environments.

Unlike most reinforcement learning agents which require an unrealistic amount of environment interactions to learn a new behaviour, humans excel at learning quickly by merely observing and imitating others. This ability highly depends on the fact that humans have a model of their own embodiment that allows them to infer the most likely actions that led to the observed behaviour. In this paper, we propose Action Inference by Maximising Evidence (AIME) to replicate this behaviour using world models. AIME consists of two distinct phases. In the first phase, the agent learns a world model from its past experience to understand its own body by maximising the ELBO. While in the second phase, the agent is given some observation-only demonstrations of an expert performing a novel task and tries to imitate the expert's behaviour. AIME achieves this by defining a policy as an inference model and maximising the evidence of the demonstration under the policy and world model. Our method is "zero-shot" in the sense that it does not require further training for the world model or online interactions with the environment after given the demonstration. We empirically validate the zero-shot imitation performance of our method on the Walker and Cheetah embodiment of the DeepMind Control Suite and find it outperforms the state-of-the-art baselines. Code is available at: https://github.com/argmax-ai/aime.

Reinforcement learning has shown promising results in learning neural network policies for complicated control tasks. However, the lack of formal guarantees about the behavior of such policies remains an impediment to their deployment. We propose a novel method for learning a composition of neural network policies in stochastic environments, along with a formal certificate which guarantees that a specification over the policy's behavior is satisfied with the desired probability. Unlike prior work on verifiable RL, our approach leverages the compositional nature of logical specifications provided in SpectRL, to learn over graphs of probabilistic reach-avoid specifications. The formal guarantees are provided by learning neural network policies together with reach-avoid supermartingales (RASM) for the graph's sub-tasks and then composing them into a global policy. We also derive a tighter lower bound compared to previous work on the probability of reach-avoidance implied by a RASM, which is required to find a compositional policy with an acceptable probabilistic threshold for complex tasks with multiple edge policies. We implement a prototype of our approach and evaluate it on a Stochastic Nine Rooms environment.

Deep learning vulnerability detection tools are increasing in popularity and have been shown to be effective. These tools rely on large volume of high quality training data, which are very hard to get. Most of the currently available datasets provide function-level labels, reporting whether a function is vulnerable or not vulnerable. However, for a vulnerability detection to be useful, we need to also know the lines that are relevant to the vulnerability. This paper makes efforts towards developing systematic tools and proposes. ActiveClean to generate the large volume of line-level vulnerability data from commits. That is, in addition to function-level labels, it also reports which lines in the function are likely responsible for vulnerability detection. In the past, static analysis has been applied to clean commits to generate line-level data. Our approach based on active learning, which is easy to use and scalable, provide a complementary approach to static analysis. We designed semantic and syntactic properties from commit lines and use them to train the model. We evaluated our approach on both Java and C datasets processing more than 4.3K commits and 119K commit lines. AcitveClean achieved an F1 score between 70-74. Further, we also show that active learning is effective by using just 400 training data to reach F1 score of 70.23. Using ActiveClean, we generate the line-level labels for the entire FFMpeg project in the Devign dataset, including 5K functions, and also detected incorrect function-level labels. We demonstrated that using our cleaned data, LineVul, a SOTA line-level vulnerability detection tool, detected 70 more vulnerable lines and 18 more vulnerable functions, and improved Top 10 accuracy from 66% to 73%.

Diffusion probabilistic models (DPMs) have exhibited exceptional proficiency in generating visual media of outstanding quality and realism. Nonetheless, their potential in non-generative domains, such as face recognition, has yet to be thoroughly investigated. Meanwhile, despite the extensive development of multi-modal face recognition methods, their emphasis has predominantly centered on visual modalities. In this context, face recognition through textual description presents a unique and promising solution that not only transcends the limitations from application scenarios but also expands the potential for research in the field of cross-modal face recognition. It is regrettable that this avenue remains unexplored and underutilized, a consequence from the challenges mainly associated with three aspects: 1) the intrinsic imprecision of verbal descriptions; 2) the significant gaps between texts and images; and 3) the immense hurdle posed by insufficient databases.To tackle this problem, we present DiFace, a solution that effectively achieves face recognition via text through a controllable diffusion process, by establishing its theoretical connection with probability transport. Our approach not only unleashes the potential of DPMs across a broader spectrum of tasks but also achieves, to the best of our knowledge, a significant accuracy in text-to-image face recognition for the first time, as demonstrated by our experiments on verification and identification.

We propose an innovative and generic methodology to analyse individual and collective behaviour through individual trajectory data. The work is motivated by the analysis of GPS trajectories of fishing vessels collected from regulatory tracking data in the context of marine biodiversity conservation and ecosystem-based fisheries management. We build a low-dimensional latent representation of trajectories using convolutional neural networks as non-linear mapping. This is done by training a conditional variational auto-encoder taking into account covariates. The posterior distributions of the latent representations can be linked to the characteristics of the actual trajectories. The latent distributions of the trajectories are compared with the Bhattacharyya coefficient, which is well-suited for comparing distributions. Using this coefficient, we analyse the variation of the individual behaviour of each vessel during time. For collective behaviour analysis, we build proximity graphs and use an extension of the stochastic block model for multiple networks. This model results in a clustering of the individuals based on their set of trajectories. The application to French fishing vessels enables us to obtain groups of vessels whose individual and collective behaviours exhibit spatio-temporal patterns over the period 2014-2018.

The current paradigm of large-scale pre-training and fine-tuning Transformer large language models has lead to significant improvements across the board in natural language processing. However, such large models are susceptible to overfitting to their training data, and as a result the models perform poorly when the domain changes. Also, due to the model's scale, the cost of fine-tuning the model to the new domain is large. Nonparametric Variational Information Bottleneck (NVIB) has been proposed as a regulariser for training cross-attention in Transformers, potentially addressing the overfitting problem. We extend the NVIB framework to replace all types of attention functions in Transformers, and show that existing pretrained Transformers can be reinterpreted as Nonparametric Variational (NV) models using a proposed identity initialisation. We then show that changing the initialisation introduces a novel, information-theoretic post-training regularisation in the attention mechanism, which improves out-of-domain generalisation without any training. This success supports the hypothesis that pretrained Transformers are implicitly NV Bayesian models.