We consider the problem of automatically inferring specifications in the branching-time logic, Computation Tree Logic (CTL), from a given system. Designing functional and usable specifications has always been one of the biggest challenges of formal methods. While in recent years, works have focused on automatically designing specifications in linear-time logics such as Linear Temporal Logic (LTL) and Signal Temporal Logic (STL), little attention has been given to branching-time logics despite its popularity in formal methods. We intend to infer concise (thus, interpretable) CTL formulas from a given finite state model of the system in consideration. However, inferring specification only from the given model (and, in general, from only positive examples) is an ill-posed problem. As a result, we infer a CTL formula that, along with being concise, is also language-minimal, meaning that it is rather specific to the given model. We design a counter-example guided algorithm to infer a concise and language-minimal CTL formula via the generation of undesirable models. In the process, we also develop, for the first time, a passive learning algorithm to infer CTL formulas from a set of desirable and undesirable Kripke structures. The passive learning algorithm involves encoding a popular CTL model-checking procedure in the Boolean Satisfiability problem.
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Natural gradient descent has a remarkable property that in the small learning rate limit, it displays an invariance with respect to network reparameterizations, leading to robust training behavior even for highly covariant network parameterizations. We show that optimization algorithms with this property can be viewed as discrete approximations of natural transformations from the functor determining an optimizer's state space from the diffeomorphism group if its configuration manifold, to the functor determining that state space's tangent bundle from this group. Algorithms with this property enjoy greater efficiency when used to train poorly parameterized networks, as the network evolution they generate is approximately invariant to network reparameterizations. More specifically, the flow generated by these algorithms in the limit as the learning rate vanishes is invariant under smooth reparameterizations, the respective flows of the parameters being determined by equivariant maps. By casting this property a natural transformation, we allow for generalizations beyond equivariance with respect to group actions; this framework can account for non-invertible maps such as projections, creating a framework for the direct comparison of training behavior across non-isomorphic network architectures, and the formal examination of limiting behavior as network size increases by considering inverse limits of these projections, should they exist. We introduce a simple method of introducing this naturality more generally and examine a number of popular machine learning training algorithms, finding that most are unnatural.
The current state of the art on jamming detection relies on link-layer metrics. A few examples are the bit-error-rate (BER), the packet delivery ratio, the throughput, and the increase in the signal-to-noise ratio (SNR). As a result, these techniques can only detect jamming \emph{ex-post}, i.e., once the attack has already taken down the communication link. These solutions are unfit for mobile devices, e.g., drones, which might lose the connection to the remote controller, being unable to predict the attack. Our solution is rooted in the idea that a drone unknowingly flying toward a jammed area is experiencing an increasing effect of the jamming, e.g., in terms of BER and SNR. Therefore, drones might use the above-mentioned phenomenon to detect jamming before the decrease of the BER and the increase of the SNR completely disrupt the communication link. Such an approach would allow drones and their pilots to make informed decisions and maintain complete control of navigation, enhancing security and safety. This paper proposes Bloodhound+, a solution for jamming detection on mobile devices in low-BER regimes. Our approach analyzes raw physical-layer information (I-Q samples) acquired from the wireless channel. We assemble this information into grayscale images and use sparse autoencoders to detect image anomalies caused by jamming attacks. To test our solution against a wide set of configurations, we acquired a large dataset of indoor measurements using multiple hardware, jamming strategies, and communication parameters. Our results indicate that Bloodhound+ can detect indoor jamming up to 20 meters from the jamming source at the minimum available relative jamming power, with a minimum accuracy of 99.7\%. Our solution is also robust to various sampling rates adopted by the jammer and to the type of signal used for jamming.
Recently, optimal time variable learning in deep neural networks (DNNs) was introduced in arXiv:2204.08528. In this manuscript we extend the concept by introducing a regularization term that directly relates to the time horizon in discrete dynamical systems. Furthermore, we propose an adaptive pruning approach for Residual Neural Networks (ResNets), which reduces network complexity without compromising expressiveness, while simultaneously decreasing training time. The results are illustrated by applying the proposed concepts to classification tasks on the well known MNIST and Fashion MNIST data sets. Our PyTorch code is available on //github.com/frederikkoehne/time_variable_learning.
We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability measures that interpolates between a fixed Gaussian measure and the data distribution, followed by learning a vector field on the underlying space of functions that generates this path of measures. Our method does not rely on likelihoods or simulations, making it well-suited to the function space setting. We provide both a theoretical framework for building such models and an empirical evaluation of our techniques. We demonstrate through experiments on several real-world benchmarks that our proposed FFM method outperforms several recently proposed function-space generative models.
While Reinforcement Learning (RL) achieves tremendous success in sequential decision-making problems of many domains, it still faces key challenges of data inefficiency and the lack of interpretability. Interestingly, many researchers have leveraged insights from the causality literature recently, bringing forth flourishing works to unify the merits of causality and address well the challenges from RL. As such, it is of great necessity and significance to collate these Causal Reinforcement Learning (CRL) works, offer a review of CRL methods, and investigate the potential functionality from causality toward RL. In particular, we divide existing CRL approaches into two categories according to whether their causality-based information is given in advance or not. We further analyze each category in terms of the formalization of different models, ranging from the Markov Decision Process (MDP), Partially Observed Markov Decision Process (POMDP), Multi-Arm Bandits (MAB), and Dynamic Treatment Regime (DTR). Moreover, we summarize the evaluation matrices and open sources while we discuss emerging applications, along with promising prospects for the future development of CRL.
Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information from its neighbors using a permutation-invariant aggregation function. Standard well-examined choices such as the mean or sum aggregation functions have limited capabilities, as they are not able to capture interactions among neighbors. In this work, we formalize these interactions using an information-theoretic framework that notably includes synergistic information. Driven by this definition, we introduce the Graph Ordering Attention (GOAT) layer, a novel GNN component that captures interactions between nodes in a neighborhood. This is achieved by learning local node orderings via an attention mechanism and processing the ordered representations using a recurrent neural network aggregator. This design allows us to make use of a permutation-sensitive aggregator while maintaining the permutation-equivariance of the proposed GOAT layer. The GOAT model demonstrates its increased performance in modeling graph metrics that capture complex information, such as the betweenness centrality and the effective size of a node. In practical use-cases, its superior modeling capability is confirmed through its success in several real-world node classification benchmarks.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.
Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.
The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provides a comprehensive survey on works that employ Deep Learning models to solve the task of MOT on single-camera videos. Four main steps in MOT algorithms are identified, and an in-depth review of how Deep Learning was employed in each one of these stages is presented. A complete experimental comparison of the presented works on the three MOTChallenge datasets is also provided, identifying a number of similarities among the top-performing methods and presenting some possible future research directions.
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