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Model counting is a fundamental problem in many practical applications, including query evaluation in probabilistic databases and failure-probability estimation of networks. In this work, we focus on a variant of this problem where the underlying formula is expressed in the Disjunctive Normal Form (DNF), also known as #DNF. This problem has been shown to be #P-complete, making it often intractable to solve exactly. Much research has therefore focused on obtaining approximate solutions, particularly in the form of $(\varepsilon, \delta)$ approximations. The primary contribution of this paper is a new approach, called pepin, an approximate #DNF counter that significantly outperforms prior state-of-the-art approaches. Our work is based on the recent breakthrough in the context of the union of sets in the streaming model. We demonstrate the effectiveness of our approach through extensive experiments and show that it provides an affirmative answer to the challenge of efficiently computing #DNF.

The classification problem for countable finitely bounded homogeneous structures is notoriously difficult, with only a handful of published partial classification results, e.g., for directed graphs. We prove the Inside-Out correspondence, which states that the classification problem, viewed as a computational decision problem, is polynomial-time equivalent to the problem of testing the containment between finitely bounded amalgamation classes up to taking reducts to a given subset of their signatures. The correspondence enables polynomial-time reductions from various decision problems that can be represented within such containment, e.g., the double-exponential square tiling problem. This leads to a new lower bound for the complexity of the classification problem: $\textsf{2NEXPTIME}$-hardness. On the other hand, it also follows from the correspondence that the classification (decision) problem is effectively reducible to the (search) problem of finding a finitely bounded Ramsey expansion of a finitely bounded strong amalgamation class. We subsequently prove that the closely related problem of homogenizability is already undecidable.

Developing text-based robot trajectory generation models is made particularly difficult by the small dataset size, high dimensionality of the trajectory space, and the inherent complexity of the text-conditional motion distribution. Recent manifold learning-based methods have partially addressed the dimensionality and dataset size issues, but struggle with the complex text-conditional distribution. In this paper we propose a text-based trajectory generation model that attempts to address all three challenges while relying on only a handful of demonstration trajectory data. Our key idea is to leverage recent flow-based models capable of capturing complex conditional distributions, not directly in the high-dimensional trajectory space, but rather in the low-dimensional latent coordinate space of the motion manifold, with deliberately designed regularization terms to ensure smoothness of motions and robustness to text variations. We show that our {\it Motion Manifold Flow Primitive (MMFP)} framework can accurately generate qualitatively distinct motions for a wide range of text inputs, significantly outperforming existing methods.

This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the posterior probability of a certain ellipsoidal solution given the data. We establish a more robust correlation between these points based on the predictive distribution within the Bayesian framework. We incorporate a uniform prior distribution to constrain the search for primitive parameters within an ellipsoidal domain, ensuring ellipsoid-specific results regardless of inputs. We then establish the connection between measurement point and model data via Bayes' rule to enhance the method's robustness against noise. Due to independent of spatial dimensions, the proposed method not only delivers high-quality fittings to challenging elongated ellipsoids but also generalizes well to multidimensional spaces. To address outlier disturbances, often overlooked by previous approaches, we further introduce a uniform distribution on top of the predictive distribution to significantly enhance the algorithm's robustness against outliers. We introduce an {\epsilon}-accelerated technique to expedite the convergence of EM considerably. To the best of our knowledge, this is the first comprehensive method capable of performing multidimensional ellipsoid specific fitting within the Bayesian optimization paradigm under diverse disturbances. We evaluate it across lower and higher dimensional spaces in the presence of heavy noise, outliers, and substantial variations in axis ratios. Also, we apply it to a wide range of practical applications such as microscopy cell counting, 3D reconstruction, geometric shape approximation, and magnetometer calibration tasks.

We propose a hybrid model predictive control algorithm, consensus complementarity control (C3), for systems that make and break contact with their environment. Many state-of-the-art controllers for tasks which require initiating contact with the environment, such as locomotion and manipulation, require a priori mode schedules or are too computationally complex to run at real-time rates. We present a method based on the alternating direction method of multipliers (ADMM) that is capable of high-speed reasoning over potential contact events. Via a consensus formulation, our approach enables parallelization of the contact scheduling problem. We validate our results on five numerical examples, including four high-dimensional frictional contact problems, and a physical experimentation on an underactuated multi-contact system. We further demonstrate the effectiveness of our method on a physical experiment accomplishing a high-dimensional, multi-contact manipulation task with a robot arm.

Multi-objective optimization problems can be found in many real-world applications, where the objectives often conflict each other and cannot be optimized by a single solution. In the past few decades, numerous methods have been proposed to find Pareto solutions that represent optimal trade-offs among the objectives for a given problem. However, these existing methods could have high computational complexity or may not have good theoretical properties for solving a general differentiable multi-objective optimization problem. In this work, by leveraging the smooth optimization technique, we propose a lightweight and efficient smooth Tchebycheff scalarization approach for gradient-based multi-objective optimization. It has good theoretical properties for finding all Pareto solutions with valid trade-off preferences, while enjoying significantly lower computational complexity compared to other methods. Experimental results on various real-world application problems fully demonstrate the effectiveness of our proposed method.

Nominal algebra includes $\alpha$-equality and freshness constraints on nominal terms endowed with a nominal set semantics that facilitates reasoning about languages with binders. Nominal unification is decidable and unitary, however, its extension with equational axioms such as Commutativity (which is finitary) is no longer finitary unless permutation fixed-point constraints are used. In this paper, we extend the notion of nominal algebra by introducing fixed-point constraints and provide a sound semantics using strong nominal sets. We show, by providing a counter-example, that the class of nominal sets is not a sound denotation for this extended nominal algebra. To recover soundness we propose two different formulations of nominal algebra, one obtained by restricting to a class of fixed-point contexts that are in direct correspondence with freshness contexts and another obtained by using a different set of derivation rules.

Hand gesture recognition allows humans to interact with machines non-verbally, which has a huge application in underwater exploration using autonomous underwater vehicles. Recently, a new gesture-based language called CADDIAN has been devised for divers, and supervised learning methods have been applied to recognize the gestures with high accuracy. However, such methods fail when they encounter unseen gestures in real time. In this work, we advocate the need for zero-shot underwater gesture recognition (ZSUGR), where the objective is to train a model with visual samples of gestures from a few ``seen'' classes only and transfer the gained knowledge at test time to recognize semantically-similar unseen gesture classes as well. After discussing the problem and dataset-specific challenges, we propose new seen-unseen splits for gesture classes in CADDY dataset. Then, we present a two-stage framework, where a novel transformer learns strong visual gesture cues and feeds them to a conditional generative adversarial network that learns to mimic feature distribution. We use the trained generator as a feature synthesizer for unseen classes, enabling zero-shot learning. Extensive experiments demonstrate that our method outperforms the existing zero-shot techniques. We conclude by providing useful insights into our framework and suggesting directions for future research.

Learning latent representations of nodes in graphs is an important and ubiquitous task with widespread applications such as link prediction, node classification, and graph visualization. Previous methods on graph representation learning mainly focus on static graphs, however, many real-world graphs are dynamic and evolve over time. In this paper, we present Dynamic Self-Attention Network (DySAT), a novel neural architecture that operates on dynamic graphs and learns node representations that capture both structural properties and temporal evolutionary patterns. Specifically, DySAT computes node representations by jointly employing self-attention layers along two dimensions: structural neighborhood and temporal dynamics. We conduct link prediction experiments on two classes of graphs: communication networks and bipartite rating networks. Our experimental results show that DySAT has a significant performance gain over several different state-of-the-art graph embedding baselines.

It is always well believed that modeling relationships between objects would be helpful for representing and eventually describing an image. Nevertheless, there has not been evidence in support of the idea on image description generation. In this paper, we introduce a new design to explore the connections between objects for image captioning under the umbrella of attention-based encoder-decoder framework. Specifically, we present Graph Convolutional Networks plus Long Short-Term Memory (dubbed as GCN-LSTM) architecture that novelly integrates both semantic and spatial object relationships into image encoder. Technically, we build graphs over the detected objects in an image based on their spatial and semantic connections. The representations of each region proposed on objects are then refined by leveraging graph structure through GCN. With the learnt region-level features, our GCN-LSTM capitalizes on LSTM-based captioning framework with attention mechanism for sentence generation. Extensive experiments are conducted on COCO image captioning dataset, and superior results are reported when comparing to state-of-the-art approaches. More remarkably, GCN-LSTM increases CIDEr-D performance from 120.1% to 128.7% on COCO testing set.