Inferring causal structure from data is a challenging task of fundamental importance in science. Observational data are often insufficient to identify a system's causal structure uniquely. While conducting interventions (i.e., experiments) can improve the identifiability, such samples are usually challenging and expensive to obtain. Hence, experimental design approaches for causal discovery aim to minimize the number of interventions by estimating the most informative intervention target. In this work, we propose a novel Gradient-based Intervention Targeting method, abbreviated GIT, that 'trusts' the gradient estimator of a gradient-based causal discovery framework to provide signals for the intervention acquisition function. We provide extensive experiments in simulated and real-world datasets and demonstrate that GIT performs on par with competitive baselines, surpassing them in the low-data regime.
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We address the task of deriving fixpoint equations from modal logics characterizing behavioural equivalences and metrics (summarized under the term conformances). We rely on earlier work that obtains Hennessy-Milner theorems as corollaries to a fixpoint preservation property along Galois connections between suitable lattices. We instantiate this to the setting of coalgebras, in which we spell out the compatibility property ensuring that we can derive a behaviour function whose greatest fixpoint coincides with the logical conformance. We then concentrate on the linear-time case, for which we study coalgebras based on the machine functor living in Eilenberg-Moore categories, a scenario for which we obtain a particularly simple logic and fixpoint equation. The theory is instantiated to concrete examples, both in the branching-time case (bisimilarity and behavioural metrics) and in the linear-time case (trace equivalences and trace distances).
In 2021, Casares, Colcombet and Fijalkow introduced the Alternating Cycle Decomposition (ACD), a structure used to define optimal transformations of Muller into parity automata and to obtain theoretical results about the possibility of relabelling automata with different acceptance conditions. In this work, we study the complexity of computing the ACD and its DAG-version, proving that this can be done in polynomial time for suitable representations of the acceptance condition of the Muller automaton. As corollaries, we obtain that we can decide typeness of Muller automata in polynomial time, as well as the parity index of the languages they recognise. Furthermore, we show that we can minimise in polynomial time the number of colours (resp. Rabin pairs) defining a Muller (resp. Rabin) acceptance condition, but that these problems become NP-complete when taking into account the structure of an automaton using such a condition.
Nowadays, most 3D model quality assessment (3DQA) methods have been aimed at improving performance. However, little attention has been paid to the computational cost and inference time required for practical applications. Model-based 3DQA methods extract features directly from the 3D models, which are characterized by their high degree of complexity. As a result, many researchers are inclined towards utilizing projection-based 3DQA methods. Nevertheless, previous projection-based 3DQA methods directly extract features from multi-projections to ensure quality prediction accuracy, which calls for more resource consumption and inevitably leads to inefficiency. Thus in this paper, we address this challenge by proposing a no-reference (NR) projection-based \textit{\underline{G}rid \underline{M}ini-patch \underline{S}ampling \underline{3D} Model \underline{Q}uality \underline{A}ssessment (GMS-3DQA)} method. The projection images are rendered from six perpendicular viewpoints of the 3D model to cover sufficient quality information. To reduce redundancy and inference resources, we propose a multi-projection grid mini-patch sampling strategy (MP-GMS), which samples grid mini-patches from the multi-projections and forms the sampled grid mini-patches into one quality mini-patch map (QMM). The Swin-Transformer tiny backbone is then used to extract quality-aware features from the QMMs. The experimental results show that the proposed GMS-3DQA outperforms existing state-of-the-art NR-3DQA methods on the point cloud quality assessment databases. The efficiency analysis reveals that the proposed GMS-3DQA requires far less computational resources and inference time than other 3DQA competitors. The code will be available at //github.com/zzc-1998/GMS-3DQA.
Answering complex logical queries on incomplete knowledge graphs (KGs) is a fundamental and challenging task in multi-hop reasoning. Recent work defines this task as an end-to-end optimization problem, which significantly reduces the training cost and enhances the generalization of the model by a pretrained link predictors for query answering. However, most existing proposals ignore the critical semantic knowledge inherently available in KGs, such as type information, which could help answer complex logical queries. To this end, we propose TypE-based Neural Link Prediction Adapter (TENLPA), a novel model that constructs type-based entity-relation graphs to discover the latent relationships between entities and relations by leveraging type information in KGs. Meanwhile, in order to effectively combine type information with complex logical queries, an adaptive learning mechanism is introduced, which is trained by back-propagating during the complex query answering process to achieve adaptive adjustment of neural link predictors. Experiments on 3 standard datasets show that TENLPA model achieves state-of-the-art performance on complex query answering with good generalization and robustness.
Deep neural network approximation of nonlinear operators, commonly referred to as DeepONet, has proven capable of approximating PDE backstepping designs in which a single Goursat-form PDE governs a single feedback gain function. In boundary control of coupled PDEs, coupled Goursat-form PDEs govern two or more gain kernels -- a PDE structure unaddressed thus far with DeepONet. In this note, we open the subject of approximating systems of gain kernel PDEs for hyperbolic PDE plants by considering a simple counter-convecting $2\times 2$ coupled system in whose control a $2\times 2$ kernel PDE systems in Goursat form arises. Applications include oil drilling, Saint-Venant model of shallow water waves, and Aw-Rascle-Zhang model of stop-and-go instability in congested traffic flow. In this paper we establish the continuity of the mapping from (a total of five) plant PDE functional coefficients to the kernel PDE solutions, prove the existence of an arbitrarily close DeepONet approximation to the kernel PDEs, and establish that the DeepONet-approximated gains guarantee stabilization when replacing the exact backstepping gain kernels. Taking into account anti-collocated boundary actuation and sensing, our $L^2$\emph{-Globally-exponentially} stabilizing (GES) approximate gain kernel-based output feedback design implies the deep learning of both the controller's and the observer's gains. Moreover, the encoding of the output-feedback law into DeepONet ensures \emph{semi-global practical exponential stability (SG-PES).} The DeepONet operator speeds up the computation of the controller gains by multiple orders of magnitude. Its theoretically proven stabilizing capability is demonstrated through simulations.
Evolutionary algorithms have been successful in solving multi-objective optimization problems (MOPs). However, as a class of population-based search methodology, evolutionary algorithms require a large number of evaluations of the objective functions, preventing them from being applied to a wide range of expensive MOPs. To tackle the above challenge, this work proposes for the first time a diffusion model that can learn to perform evolutionary multi-objective search, called EmoDM. This is achieved by treating the reversed convergence process of evolutionary search as the forward diffusion and learn the noise distributions from previously solved evolutionary optimization tasks. The pre-trained EmoDM can then generate a set of non-dominated solutions for a new MOP by means of its reverse diffusion without further evolutionary search, thereby significantly reducing the required function evaluations. To enhance the scalability of EmoDM, a mutual entropy-based attention mechanism is introduced to capture the decision variables that are most important for the objectives. Experimental results demonstrate the competitiveness of EmoDM in terms of both the search performance and computational efficiency compared with state-of-the-art evolutionary algorithms in solving MOPs having up to 5000 decision variables. The pre-trained EmoDM is shown to generalize well to unseen problems, revealing its strong potential as a general and efficient MOP solver.
Value decomposition is widely used in cooperative multi-agent reinforcement learning, however, its implicit credit assignment mechanism is not yet fully understood due to black-box networks. In this work, we study an interpretable value decomposition framework via the family of generalized additive models. We present a novel method, named Neural Attention Additive Q-learning (N$\text{A}^\text{2}$Q), providing inherent intelligibility of collaboration behavior. N$\text{A}^\text{2}$Q can explicitly factorize the optimal joint policy induced by enriching shape functions to model all possible coalitions of agents into individual policies. Moreover, we construct identity semantics to promote estimating credits together with the global state and individual value functions, where local semantic masks help us diagnose whether each agent captures relevant-task information. Extensive experiments show that N$\text{A}^\text{2}$Q consistently achieves superior performance compared to different state-of-the-art methods on all challenging tasks, while yielding human-like interpretability.
Adversarial training has been proposed to hedge against adversarial attacks in machine learning and statistical models. This paper focuses on adversarial training under $\ell_\infty$-perturbation, which has recently attracted much research attention. The asymptotic behavior of the adversarial training estimator is investigated in the generalized linear model. The results imply that the limiting distribution of the adversarial training estimator under $\ell_\infty$-perturbation could put a positive probability mass at $0$ when the true parameter is $0$, providing a theoretical guarantee of the associated sparsity-recovery ability. Alternatively, a two-step procedure is proposed -- adaptive adversarial training, which could further improve the performance of adversarial training under $\ell_\infty$-perturbation. Specifically, the proposed procedure could achieve asymptotic unbiasedness and variable-selection consistency. Numerical experiments are conducted to show the sparsity-recovery ability of adversarial training under $\ell_\infty$-perturbation and to compare the empirical performance between classic adversarial training and adaptive adversarial training.
Uplift modeling is a technique used to predict the effect of a treatment (e.g., discounts) on an individual's response. Although several methods have been proposed for multi-valued treatment, they are extended from binary treatment methods. There are still some limitations. Firstly, existing methods calculate uplift based on predicted responses, which may not guarantee a consistent uplift distribution between treatment and control groups. Moreover, this may cause cumulative errors for multi-valued treatment. Secondly, the model parameters become numerous with many prediction heads, leading to reduced efficiency. To address these issues, we propose a novel \underline{M}ulti-gate \underline{M}ixture-of-Experts based \underline{M}ulti-valued \underline{T}reatment \underline{N}etwork (M$^3$TN). M$^3$TN consists of two components: 1) a feature representation module with Multi-gate Mixture-of-Experts to improve the efficiency; 2) a reparameterization module by modeling uplift explicitly to improve the effectiveness. We also conduct extensive experiments to demonstrate the effectiveness and efficiency of our M$^3$TN.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
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