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We design an additive approximation scheme for estimating the cost of the min-weight bipartite matching problem: given a bipartite graph with non-negative edge costs and $\varepsilon > 0$, our algorithm estimates the cost of matching all but $O(\varepsilon)$-fraction of the vertices in truly subquadratic time $O(n^{2-\delta(\varepsilon)})$. Our algorithm has a natural interpretation for computing the Earth Mover's Distance (EMD), up to a $\varepsilon$-additive approximation. Notably, we make no assumptions about the underlying metric (more generally, the costs do not have to satisfy triangle inequality). Note that compared to the size of the instance (an arbitrary $n \times n$ cost matrix), our algorithm runs in {\em sublinear} time. Our algorithm can approximate a slightly more general problem: max-cardinality bipartite matching with a knapsack constraint, where the goal is to maximize the number of vertices that can be matched up to a total cost $B$.

Parameterized convex minorant (PCM) method is proposed for the approximation of the objective function in amortized optimization. In the proposed method, the objective function approximator is expressed by the sum of a PCM and a nonnegative gap function, where the objective function approximator is bounded from below by the PCM convex in the optimization variable. The proposed objective function approximator is a universal approximator for continuous functions, and the global minimizer of the PCM attains the global minimum of the objective function approximator. Therefore, the global minimizer of the objective function approximator can be obtained by a single convex optimization. As a realization of the proposed method, extended parameterized log-sum-exp network is proposed by utilizing a parameterized log-sum-exp network as the PCM. Numerical simulation is performed for parameterized non-convex objective function approximation and for learning-based nonlinear model predictive control to demonstrate the performance and characteristics of the proposed method. The simulation results support that the proposed method can be used to learn objective functions and to find a global minimizer reliably and quickly by using convex optimization algorithms.

Graph-based kNN algorithms have garnered widespread popularity for machine learning tasks due to their simplicity and effectiveness. However, as factual data often inherit complex distributions, the conventional kNN graph's reliance on a unified k-value can hinder its performance. A crucial factor behind this challenge is the presence of ambiguous samples along decision boundaries that are inevitably more prone to incorrect classifications. To address the situation, we propose the Distribution-Informed adaptive kNN Graph (DaNNG), which combines adaptive kNN with distribution-aware graph construction. By incorporating an approximation of the distribution with customized k-adaption criteria, DaNNG can significantly improve performance on ambiguous samples, and hence enhance overall accuracy and generalization capability. Through rigorous evaluations on diverse benchmark datasets, DaNNG outperforms state-of-the-art algorithms, showcasing its adaptability and efficacy across various real-world scenarios.

Registering clothes from 4D scans with vertex-accurate correspondence is challenging, yet important for dynamic appearance modeling and physics parameter estimation from real-world data. However, previous methods either rely on texture information, which is not always reliable, or achieve only coarse-level alignment. In this work, we present a novel approach to enabling accurate surface registration of texture-less clothes with large deformation. Our key idea is to effectively leverage a shape prior learned from pre-captured clothing using diffusion models. We also propose a multi-stage guidance scheme based on learned functional maps, which stabilizes registration for large-scale deformation even when they vary significantly from training data. Using high-fidelity real captured clothes, our experiments show that the proposed approach based on diffusion models generalizes better than surface registration with VAE or PCA-based priors, outperforming both optimization-based and learning-based non-rigid registration methods for both interpolation and extrapolation tests.

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors in high-dimensional spaces. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler. This is distinct from existing methods that rely on additional discriminator networks and unstable adversarial objectives. Furthermore, we present a new sampler architecture that, for the first time, enables implicit distributions over tens of millions of latent variables, addressing computational concerns by using differentiable numerical approximations. We empirically show that our method is capable of recovering correlations across layers in large Bayesian neural networks, a property that is crucial for a network's performance but notoriously challenging to achieve. To the best of our knowledge, no other method has been shown to accomplish this task for such large models. Through experiments in downstream tasks, we demonstrate that our expressive posteriors outperform state-of-the-art uncertainty quantification methods, validating the effectiveness of our training algorithm and the quality of the learned implicit approximation.

This paper integrates manifold learning techniques within a \emph{Gaussian process upper confidence bound} algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means of two devices: 'reachability rules' and 'structural refinement'. Regarding the former device, we introduce reachability rules as special logical rules parameterized with formal grammars (viz. types of semi-Thue systems) that operate by propagating formulae and/or checking if data exists along certain paths within a nested sequent, where paths are encoded as strings generated by a parameterizing grammar. Regarding the latter device, structural refinement is a relatively new methodology used to extract nested sequent systems from labeled systems (which are ultimately obtained from a semantics) by means of eliminating structural/relational rules, introducing reachability rules, and then carrying out a notational translation. We therefore demonstrate how this method can be extended to the setting of first-order modal logics, and expose how reachability rules naturally arise from applying this method.

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the literature with widely varying performance, and the problem of selecting suitable encodings for a given problem instance is not trivial. We explore the problem of selecting encodings for pseudo-Boolean and linear constraints using a supervised machine learning approach. We show that it is possible to select encodings effectively using a standard set of features for constraint problems; however we obtain better performance with a new set of features specifically designed for the pseudo-Boolean and linear constraints. In fact, we achieve good results when selecting encodings for unseen problem classes. Our results compare favourably to AutoFolio when using the same feature set. We discuss the relative importance of instance features to the task of selecting the best encodings, and compare several variations of the machine learning method.

Deep reinforcement learning algorithms can perform poorly in real-world tasks due to the discrepancy between source and target environments. This discrepancy is commonly viewed as the disturbance in transition dynamics. Many existing algorithms learn robust policies by modeling the disturbance and applying it to source environments during training, which usually requires prior knowledge about the disturbance and control of simulators. However, these algorithms can fail in scenarios where the disturbance from target environments is unknown or is intractable to model in simulators. To tackle this problem, we propose a novel model-free actor-critic algorithm -- namely, state-conservative policy optimization (SCPO) -- to learn robust policies without modeling the disturbance in advance. Specifically, SCPO reduces the disturbance in transition dynamics to that in state space and then approximates it by a simple gradient-based regularizer. The appealing features of SCPO include that it is simple to implement and does not require additional knowledge about the disturbance or specially designed simulators. Experiments in several robot control tasks demonstrate that SCPO learns robust policies against the disturbance in transition dynamics.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.