Human emotion is expressed in many communication modalities and media formats and so their computational study is equally diversified into natural language processing, audio signal analysis, computer vision, etc. Similarly, the large variety of representation formats used in previous research to describe emotions (polarity scales, basic emotion categories, dimensional approaches, appraisal theory, etc.) have led to an ever proliferating diversity of datasets, predictive models, and software tools for emotion analysis. Because of these two distinct types of heterogeneity, at the expressional and representational level, there is a dire need to unify previous work on increasingly diverging data and label types. This article presents such a unifying computational model. We propose a training procedure that learns a shared latent representation for emotions, so-called emotion embeddings, independent of different natural languages, communication modalities, media or representation label formats, and even disparate model architectures. Experiments on a wide range of heterogeneous affective datasets indicate that this approach yields the desired interoperability for the sake of reusability, interpretability and flexibility, without penalizing prediction quality. Code and data are archived under //doi.org/10.5281/zenodo.7405327 .
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Recent methods in text-to-3D leverage powerful pretrained diffusion models to optimize NeRF. Notably, these methods are able to produce high-quality 3D scenes without training on 3D data. Due to the open-ended nature of the task, most studies evaluate their results with subjective case studies and user experiments, thereby presenting a challenge in quantitatively addressing the question: How has current progress in Text-to-3D gone so far? In this paper, we introduce T$^3$Bench, the first comprehensive text-to-3D benchmark containing diverse text prompts of three increasing complexity levels that are specially designed for 3D generation. To assess both the subjective quality and the text alignment, we propose two automatic metrics based on multi-view images produced by the 3D contents. The quality metric combines multi-view text-image scores and regional convolution to detect quality and view inconsistency. The alignment metric uses multi-view captioning and Large Language Model (LLM) evaluation to measure text-3D consistency. Both metrics closely correlate with different dimensions of human judgments, providing a paradigm for efficiently evaluating text-to-3D models. The benchmarking results, shown in Fig. 1, reveal performance differences among six prevalent text-to-3D methods. Our analysis further highlights the common struggles for current methods on generating surroundings and multi-object scenes, as well as the bottleneck of leveraging 2D guidance for 3D generation. Our project page is available at: //t3bench.com.
Based on the theory of homogeneous spaces we derive \textit{geometrically optimal edge attributes} to be used within the flexible message passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions $\mathbb{R}^3$, position and orientations $\mathbb{R}^3 {\times} S^2$, and the group SE$(3)$ itself. Among these, $\mathbb{R}^3 {\times} S^2$ is an optimal choice due to the ability to represent directional information, which $\mathbb{R}^3$ methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE$(3)$ group. We empirically support this claim by reaching state-of-the-art results -- in accuracy and speed -- on three different benchmarks: interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.
Knowledge bases are widely used for information management, enabling high-impact applications such as web search, question answering, and natural language processing. They also serve as the backbone for automatic decision systems, e.g., for medical diagnostics and credit scoring. As stakeholders affected by these decisions would like to understand their situation and verify how fair the decisions are, a number of explanation approaches have been proposed. An intrinsically transparent way to do classification is by using concepts in description logics. However, these concepts can become long and difficult to fathom for non-experts, even when verbalized. One solution is to employ counterfactuals to answer the question, ``How must feature values be changed to obtain a different classification?'' By focusing on the minimal feature changes, the explanations are short, human-friendly, and provide a clear path of action regarding the change in prediction. While previous work investigated counterfactuals for tabular data, in this paper, we transfer the notion of counterfactuals to knowledge bases and the description logic $\mathcal{ELH}$. Our approach starts by generating counterfactual candidates from concepts, followed by selecting the candidates requiring the fewest feature changes as counterfactuals. When multiple counterfactuals exist, we rank them based on the likeliness of their feature combinations. We evaluate our method by conducting a user survey to determine which counterfactual candidates participants prefer for explanation.
Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an explicit constant factor that holds true for the entire function class. Furthermore, in the stochastic setting, only a modified version of AdaGrad, different from the one commonly used in practice, in which the latest gradient is not used to update the stepsize, has been analyzed. Our paper aims at bridging these gaps and developing a deeper understanding of AdaGrad and its variants in the standard setting of smooth convex functions as well as the more general setting of quasar convex functions. First, we demonstrate new techniques to explicitly bound the convergence rate of the vanilla AdaGrad for unconstrained problems in both deterministic and stochastic settings. Second, we propose a variant of AdaGrad for which we can show the convergence of the last iterate, instead of the average iterate. Finally, we give new accelerated adaptive algorithms and their convergence guarantee in the deterministic setting with explicit dependency on the problem parameters, improving upon the asymptotic rate shown in previous works.
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo theories), an alphabet is represented by an effective Boolean algebra, supported by a decision procedure for satisfiability. Regular languages over infinite words (so called $\omega$-regular languages) have a rich history paralleling that of regular languages over finite words, with well known applications to model checking via B\"uchi automata and temporal logics. We generalize symbolic automata to support $\omega$-regular languages via symbolic transition terms and symbolic derivatives, bringing together a variety of classic automata and logics in a unified framework that provides all the necessary ingredients to support symbolic model checking modulo $A$, $NBW_A$. In particular, we define: (1) alternating B\"uchi automata modulo $A$, $ABW_A$ as well (non-alternating) non-deterministic B\"uchi automata modulo $A$, $NBW_A$; (2) an alternation elimination algorithm that incrementally constructs an $NBW_A$ from an $ABW_A$, and can also be used for constructing the product of two $NBW_A$'s; (3) a definition of linear temporal logic (LTL) modulo $A$ that generalizes Vardi's construction of alternating B\"uchi automata from LTL, using (2) to go from LTL modulo $A$ to $NBW_A$ via $ABW_A$. Finally, we present a combination of LTL modulo $A$ with extended regular expressions modulo $A$ that generalizes the Property Specification Language (PSL). Our combination allows regex complement, that is not supported in PSL but can be supported naturally by using symbolic transition terms.
Simplicial complexes are a convenient semantic primitive to reason about processes (agents) communicating with each other in synchronous and asynchronous computation. Impure simplicial complexes distinguish active processes from crashed ones, in other words, agents that are alive from agents that are dead. In order to rule out that dead agents reason about themselves and about other agents, three-valued epistemic semantics have been proposed where, in addition to the usual values true and false, the third value stands for undefined: the knowledge of dead agents is undefined and so are the propositional variables describing their local state. Other semantics for impure complexes are two-valued where a dead agent knows everything. Different choices in designing a semantics produce different three-valued semantics, and also different two-valued semantics. In this work, we categorize the available choices by discounting the bad ones, identifying the equivalent ones, and connecting the non-equivalent ones via a translation. The main result of the paper is identifying the main relevant distinction to be the number of truth values and bridging this difference by means of a novel embedding from three- into two-valued semantics. This translation also enables us to highlight quite fundamental modeling differences underpinning various two- and three-valued approaches in this area of combinatorial topology. In particular, pure complexes can be defined as those invariant under the translation.
The learning with errors problem (LWE) is one of the most important building blocks for post-quantum cryptography. To better understand the quantum hardness of LWE, it is crucial to explore quantum variants of LWE, show quantum algorithms for those variants, or prove they are as hard as standard LWE. To this end, Chen, Liu, and Zhandry [Eurocrypt 2022] define the $\sf{S|LWE\rangle}$ problem, which encodes the error of LWE samples into quantum amplitudes. They then show efficient quantum algorithms for $\sf{S|LWE\rangle}$ with a few interesting amplitudes. However, the hardness of the most interesting amplitude, Gaussian, was not addressed by Chen et al., or only known for some restricted settings (for example, when the number of $\sf{S|LWE\rangle}$ samples is very small, it is well known that $\sf{S|LWE\rangle}$ is as hard as standard LWE). In this paper, we show new hardness and algorithms for $\sf{S|LWE\rangle}$ with Gaussian and other amplitudes. Our main results are 1. There exist quantum reductions from standard LWE or worst-case GapSVP to $\sf{S|LWE\rangle}$ with Gaussian amplitude with unknown phase, and arbitrarily many $\sf{S|LWE\rangle}$ samples. 2. There is a $2^{\widetilde{O}(\sqrt{n})}$-time algorithm for $\sf{S|LWE\rangle}$ with Gaussian amplitude with known phase, given $2^{\widetilde{O}(\sqrt{n})}$ many quantum samples. The algorithm is modified from Kuperberg's sieve, and in fact works for more general amplitudes as long as the amplitudes and phases are completely known. One way of interpreting our result is: to show a sub-exponential time quantum algorithm for standard LWE, all we need is to handle phases in $\sf{S|LWE\rangle}$ amplitudes better, either in the algorithm or the reduction.
Omnidirectional camera is a cost-effective and information-rich sensor highly suitable for many marine applications and the ocean scientific community, encompassing several domains such as augmented reality, mapping, motion estimation, visual surveillance, and simultaneous localization and mapping. However, designing and constructing such a high-quality 360$^{\circ}$ real-time streaming camera system for underwater applications is a challenging problem due to the technical complexity in several aspects including sensor resolution, wide field of view, power supply, optical design, system calibration, and overheating management. This paper presents a novel and comprehensive system that addresses the complexities associated with the design, construction, and implementation of a fully functional 360$^{\circ}$ real-time streaming camera system specifically tailored for underwater environments. Our proposed system, UWA360CAM, can stream video in real time, operate in 24/7, and capture 360$^{\circ}$ underwater panorama images. Notably, our work is the pioneering effort in providing a detailed and replicable account of this system. The experiments provide a comprehensive analysis of our proposed system.
In an era where scientific experimentation is often costly, multi-fidelity emulation provides a powerful tool for predictive scientific computing. While there has been notable work on multi-fidelity modeling, existing models do not incorporate an important "conglomerate" property of multi-fidelity simulators, where the accuracies of different simulator components are controlled by different fidelity parameters. Such conglomerate simulators are widely encountered in complex nuclear physics and astrophysics applications. We thus propose a new CONglomerate multi-FIdelity Gaussian process (CONFIG) model, which embeds this conglomerate structure within a novel non-stationary covariance function. We show that the proposed CONFIG model can capture prior knowledge on the numerical convergence of conglomerate simulators, which allows for cost-efficient emulation of multi-fidelity systems. We demonstrate the improved predictive performance of CONFIG over state-of-the-art models in a suite of numerical experiments and two applications, the first for emulation of cantilever beam deflection and the second for emulating the evolution of the quark-gluon plasma, which was theorized to have filled the Universe shortly after the Big Bang.
Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.
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