A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions are constructed exploiting an accurate knowledge of the underlying model: in real-life applications, this may be a costly assumption. By sampling random $\ell$-step trajectories of an unknown system, we build an abstraction based on the notion of $\ell$-completeness. We newly define the notion of probabilistic behavioural inclusion, and provide probably approximately correct (PAC) guarantees that this abstraction includes all behaviours of the concrete system, for finite and infinite time horizon, leveraging the scenario theory for non convex problems. Our method is then tested on several numerical benchmarks.
Model selection is a strategy aimed at creating accurate and robust models. A key challenge in designing these algorithms is identifying the optimal model for classifying any particular input sample. This paper addresses this challenge and proposes a novel framework for differentiable model selection integrating machine learning and combinatorial optimization. The framework is tailored for ensemble learning, a strategy that combines the outputs of individually pre-trained models, and learns to select appropriate ensemble members for a particular input sample by transforming the ensemble learning task into a differentiable selection program trained end-to-end within the ensemble learning model. Tested on various tasks, the proposed framework demonstrates its versatility and effectiveness, outperforming conventional and advanced consensus rules across a variety of settings and learning tasks.
Humans and animals have a rich and flexible understanding of the physical world, which enables them to infer the underlying dynamical trajectories of objects and events, plausible future states, and use that to plan and anticipate the consequences of actions. However, the neural mechanisms underlying these computations are unclear. We combine a goal-driven modeling approach with dense neurophysiological data and high-throughput human behavioral readouts to directly impinge on this question. Specifically, we construct and evaluate several classes of sensory-cognitive networks to predict the future state of rich, ethologically-relevant environments, ranging from self-supervised end-to-end models with pixel-wise or object-centric objectives, to models that future predict in the latent space of purely static image-based or dynamic video-based pretrained foundation models. We find strong differentiation across these model classes in their ability to predict neural and behavioral data both within and across diverse environments. In particular, we find that neural responses are currently best predicted by models trained to predict the future state of their environment in the latent space of pretrained foundation models optimized for dynamic scenes in a self-supervised manner. Notably, models that future predict in the latent space of video foundation models that are optimized to support a diverse range of sensorimotor tasks, reasonably match both human behavioral error patterns and neural dynamics across all environmental scenarios that we were able to test. Overall, these findings suggest that the neural mechanisms and behaviors of primate mental simulation are thus far most consistent with being optimized to future predict on dynamic, reusable visual representations that are useful for embodied AI more generally.
Software engineering techniques are increasingly relying on deep learning approaches to support many software engineering tasks, from bug triaging to code generation. To assess the efficacy of such techniques researchers typically perform controlled experiments. Conducting these experiments, however, is particularly challenging given the complexity of the space of variables involved, from specialized and intricate architectures and algorithms to a large number of training hyper-parameters and choices of evolving datasets, all compounded by how rapidly the machine learning technology is advancing, and the inherent sources of randomness in the training process. In this work we conduct a mapping study, examining 194 experiments with techniques that rely on deep neural networks appearing in 55 papers published in premier software engineering venues to provide a characterization of the state-of-the-practice, pinpointing experiments common trends and pitfalls. Our study reveals that most of the experiments, including those that have received ACM artifact badges, have fundamental limitations that raise doubts about the reliability of their findings. More specifically, we find: weak analyses to determine that there is a true relationship between independent and dependent variables (87% of the experiments); limited control over the space of DNN relevant variables, which can render a relationship between dependent variables and treatments that may not be causal but rather correlational (100% of the experiments); and lack of specificity in terms of what are the DNN variables and their values utilized in the experiments (86% of the experiments) to define the treatments being applied, which makes it unclear whether the techniques designed are the ones being assessed, or how the sources of extraneous variation are controlled. We provide some practical recommendations to address these limitations.
Several studies have compared the in-distribution (ID) and out-of-distribution (OOD) performance of models in computer vision and NLP. They report a frequent positive correlation and some surprisingly never even observe an inverse correlation indicative of a necessary trade-off. The possibility of inverse patterns is important to determine whether ID performance can serve as a proxy for OOD generalization capabilities. This paper shows with multiple datasets that inverse correlations between ID and OOD performance do happen in real-world data - not only in theoretical worst-case settings. We also explain theoretically how these cases can arise even in a minimal linear setting, and why past studies could miss such cases due to a biased selection of models. Our observations lead to recommendations that contradict those found in much of the current literature. - High OOD performance sometimes requires trading off ID performance. - Focusing on ID performance alone may not lead to optimal OOD performance. It may produce diminishing (eventually negative) returns in OOD performance. - In these cases, studies on OOD generalization that use ID performance for model selection (a common recommended practice) will necessarily miss the best-performing models, making these studies blind to a whole range of phenomena.
Cooperative adaptive cruise control presents an opportunity to improve road transportation through increase in road capacity and reduction in energy use and accidents. Clever design of control algorithms and communication systems is required to ensure that the vehicle platoon is stable and meets desired safety requirements. In this paper, we propose a centralized model predictive controller for a heterogeneous platoon of vehicles to reach a desired platoon velocity and individual inter-vehicle distances with driver-selected headway time. As a novel concept, we allow for interruption from a human driver in the platoon that temporarily takes control of their vehicle with the assumption that the driver will, at minimum, obey legal velocity limits and the physical performance constraints of their vehicle. The finite horizon cost function of our proposed platoon controller is inspired from the infinite horizon design. To the best of our knowledge, this is the first platoon controller that integrates human-driven vehicles. We illustrate the performance of our proposed design with a numerical study, demonstrating that the safety distance, velocity, and actuation constraints are obeyed. Additionally, in simulation we illustrate a key property of string stability where the impact of a disturbance is reduced through the platoon.
This paper is devoted to the study of infinitesimal limit cycles that can bifurcate from zero-Hopf equilibria of differential systems based on the averaging method. We develop an efficient symbolic program using Maple for computing the averaged functions of any order for continuous differential systems in arbitrary dimension. The program allows us to systematically analyze zero-Hopf bifurcations of polynomial differential systems using symbolic computation methods. We show that for the first-order averaging, $\ell\in\{0,1,\ldots,2^{n-3}\}$ limit cycles can bifurcate from the zero-Hopf equilibrium for the general class of perturbed differential systems and up to the second-order averaging, the maximum number of limit cycles can be determined by computing the mixed volume of a polynomial system obtained from the averaged functions. A number of examples are presented to demonstrate the effectiveness of the proposed algorithmic approach.
The generalization error of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature. The feature is obtained by projecting the data on a random line after embedding it into a higher-dimensional space parametrized by monomials of order up to k. More specifically, the extended data is projected n-times and the best classifier among those n, based on its performance on training data, is chosen. We show that this type of classifier is extremely flexible, as it is likely to approximate, to an arbitrary precision, any continuous function on a compact set as well as any boolean function on a compact set that splits the support into measurable subsets. In particular, given full knowledge of the class conditional densities, the error of these low-complexity classifiers would converge to the optimal (Bayes) error as k and n go to infinity. On the other hand, if only a training dataset is given, we show that the classifiers will perfectly classify all the training points as k and n go to infinity. We also bound the generalization error of our random classifiers. In general, our bounds are better than those for any classifier with VC dimension greater than O (ln n) . In particular, our bounds imply that, unless the number of projections n is extremely large, there is a significant advantageous gap between the generalization error of the random projection approach and that of a linear classifier in the extended space. Asymptotically, as the number of samples approaches infinity, the gap persists for any such n. Thus, there is a potentially large gain in generalization properties by selecting parameters at random, rather than optimization.
We study multiclass online prediction where the learner can predict using a list of multiple labels (as opposed to just one label in the traditional setting). We characterize learnability in this model using the $b$-ary Littlestone dimension. This dimension is a variation of the classical Littlestone dimension with the difference that binary mistake trees are replaced with $(k+1)$-ary mistake trees, where $k$ is the number of labels in the list. In the agnostic setting, we explore different scenarios depending on whether the comparator class consists of single-labeled or multi-labeled functions and its tradeoff with the size of the lists the algorithm uses. We find that it is possible to achieve negative regret in some cases and provide a complete characterization of when this is possible. As part of our work, we adapt classical algorithms such as Littlestone's SOA and Rosenblatt's Perceptron to predict using lists of labels. We also establish combinatorial results for list-learnable classes, including an list online version of the Sauer-Shelah-Perles Lemma. We state our results within the framework of pattern classes -- a generalization of hypothesis classes which can represent adaptive hypotheses (i.e. functions with memory), and model data-dependent assumptions such as linear classification with margin.
Integrated visible light positioning and communication (VLPC), capable of combining advantages of visible light communications (VLC) and visible light positioning (VLP), is a promising key technology for the future Internet of Things. In VLPC networks, positioning and communications are inherently coupled, which has not been sufficiently explored in the literature. We propose a robust power allocation scheme for integrated VLPC Networks by exploiting the intrinsic relationship between positioning and communications. Specifically, we derive explicit relationships between random positioning errors, following both a Gaussian distribution and an arbitrary distribution, and channel state information errors. Then, we minimize the Cramer-Rao lower bound (CRLB) of positioning errors, subject to the rate outage constraint and the power constraints, which is a chance-constrained optimization problem and generally computationally intractable. To circumvent the nonconvex challenge, we conservatively transform the chance constraints to deterministic forms by using the Bernstein-type inequality and the conditional value-at-risk for the Gaussian and arbitrary distributed positioning errors, respectively, and then approximate them as convex semidefinite programs. Finally, simulation results verify the robustness and effectiveness of our proposed integrated VLPC design schemes.
Graph-based semi-supervised learning (SSL) is an important learning problem where the goal is to assign labels to initially unlabeled nodes in a graph. Graph Convolutional Networks (GCNs) have recently been shown to be effective for graph-based SSL problems. GCNs inherently assume existence of pairwise relationships in the graph-structured data. However, in many real-world problems, relationships go beyond pairwise connections and hence are more complex. Hypergraphs provide a natural modeling tool to capture such complex relationships. In this work, we explore the use of GCNs for hypergraph-based SSL. In particular, we propose HyperGCN, an SSL method which uses a layer-wise propagation rule for convolutional neural networks operating directly on hypergraphs. To the best of our knowledge, this is the first principled adaptation of GCNs to hypergraphs. HyperGCN is able to encode both the hypergraph structure and hypernode features in an effective manner. Through detailed experimentation, we demonstrate HyperGCN's effectiveness at hypergraph-based SSL.