Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier inclusion, outlier trimming, and post hoc outlier identification methods, with the former two often requiring pre-specification of the number of outliers. The fact that sample squared Mahalanobis distance is beta-distributed is used to derive an approximate distribution for the log-likelihoods of subset finite Gaussian mixture models. An algorithm is then proposed that removes the least plausible points according to the subset log-likelihoods, which are deemed outliers, until the subset log-likelihoods adhere to the reference distribution. This results in a trimming method, called OCLUST, that inherently estimates the number of outliers.
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Various robotic tool manipulation methods have been developed so far. However, to our knowledge, none of them have taken into account the fact that the grasping state such as grasping position and tool angle can change at any time during the tool manipulation. In addition, there are few studies that can handle deformable tools. In this study, we develop a method for estimating the position of a tool-tip, controlling the tool-tip, and handling online adaptation to changes in the relationship between the body and the tool, using a neural network including parametric bias. We demonstrate the effectiveness of our method for online change in grasping state and for deformable tools, in experiments using two different types of robots: axis-driven robot PR2 and tendon-driven robot MusashiLarm.
Previous work has demonstrated that MLPs within ReLU Transformers exhibit high levels of sparsity, with many of their activations equal to zero for any given token. We build on that work to more deeply explore how token-level sparsity evolves over the course of training, and how it connects to broader sparsity patterns over the course of a sequence or batch, demonstrating that the different layers within small transformers exhibit distinctly layer-specific patterns on both of these fronts. In particular, we demonstrate that the first and last layer of the network have distinctive and in many ways inverted relationships to sparsity, and explore implications for the structure of feature representations being learned at different depths of the model. We additionally explore the phenomenon of ReLU dimensions "turning off", and show evidence suggesting that "neuron death" is being primarily driven by the dynamics of training, rather than simply occurring randomly or accidentally as a result of outliers.
In developing efficient optimization algorithms, it is crucial to account for communication constraints -- a significant challenge in modern federated learning settings. The best-known communication complexity among non-accelerated algorithms is achieved by DANE, a distributed proximal-point algorithm that solves local subproblems in each iteration and that can exploit second-order similarity among individual functions. However, to achieve such communication efficiency, the accuracy requirement for solving the local subproblems is slightly sub-optimal. Inspired by the hybrid projection-proximal point method, in this work, we i) propose a novel distributed algorithm S-DANE. This method adopts a more stabilized prox-center in the proximal step compared with DANE, and matches its deterministic communication complexity. Moreover, the accuracy condition of the subproblem is milder, leading to enhanced local computation efficiency. Furthermore, it supports partial client participation and arbitrary stochastic local solvers, making it more attractive in practice. We further ii) accelerate S-DANE, and show that the resulting algorithm achieves the best-known communication complexity among all existing methods for distributed convex optimization, with the same improved local computation efficiency as S-DANE.
This paper provides an NP procedure that decides whether a linear-exponential system of constraints has an integer solution. Linear-exponential systems extend standard integer linear programs with exponential terms $2^x$ and remainder terms ${(x \bmod 2^y)}$. Our result implies that the existential theory of the structure $(\mathbb{N},0,1,+,2^{(\cdot)},V_2(\cdot,\cdot),\leq)$ has an NP-complete satisfiability problem, thus improving upon a recent EXPSPACE upper bound. This theory extends the existential fragment of Presburger arithmetic with the exponentiation function $x \mapsto 2^x$ and the binary predicate $V_2(x,y)$ that is true whenever $y \geq 1$ is the largest power of $2$ dividing $x$. Our procedure for solving linear-exponential systems uses the method of quantifier elimination. As a by-product, we modify the classical Gaussian variable elimination into a non-deterministic polynomial-time procedure for integer linear programming (or: existential Presburger arithmetic).
Lensless imaging has emerged as a promising field within inverse imaging, offering compact, cost-effective solutions with the potential to revolutionize the computational camera market. By circumventing traditional optical components like lenses and mirrors, novel approaches like mask-based lensless imaging eliminate the need for conventional hardware. However, advancements in lensless image reconstruction, particularly those leveraging Generative Adversarial Networks (GANs), are hindered by the reliance on data-driven training processes, resulting in network specificity to the Point Spread Function (PSF) of the imaging system. This necessitates a complete retraining for minor PSF changes, limiting adaptability and generalizability across diverse imaging scenarios. In this paper, we introduce a novel approach to multi-PSF lensless imaging, employing a dual discriminator cyclic adversarial framework. We propose a unique generator architecture with a sparse convolutional PSF-aware auxiliary branch, coupled with a forward model integrated into the training loop to facilitate physics-informed learning to handle the substantial domain gap between lensless and lensed images. Comprehensive performance evaluation and ablation studies underscore the effectiveness of our model, offering robust and adaptable lensless image reconstruction capabilities. Our method achieves comparable performance to existing PSF-agnostic generative methods for single PSF cases and demonstrates resilience to PSF changes without the need for retraining.
Many datasets have been developed to train and evaluate document-level relation extraction (RE) models. Most of these are constructed using real-world data. It has been shown that RE models trained on real-world data suffer from factual biases. To evaluate and address this issue, we present CovEReD, a counterfactual data generation approach for document-level relation extraction datasets using entity replacement. We first demonstrate that models trained on factual data exhibit inconsistent behavior: while they accurately extract triples from factual data, they fail to extract the same triples after counterfactual modification. This inconsistency suggests that models trained on factual data rely on spurious signals such as specific entities and external knowledge $\unicode{x2013}$ rather than on the input context $\unicode{x2013}$ to extract triples. We show that by generating document-level counterfactual data with CovEReD and training models on them, consistency is maintained with minimal impact on RE performance. We release our CovEReD pipeline as well as Re-DocRED-CF, a dataset of counterfactual RE documents, to assist in evaluating and addressing inconsistency in document-level RE.
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.
Social relations are often used to improve recommendation quality when user-item interaction data is sparse in recommender systems. Most existing social recommendation models exploit pairwise relations to mine potential user preferences. However, real-life interactions among users are very complicated and user relations can be high-order. Hypergraph provides a natural way to model complex high-order relations, while its potentials for improving social recommendation are under-explored. In this paper, we fill this gap and propose a multi-channel hypergraph convolutional network to enhance social recommendation by leveraging high-order user relations. Technically, each channel in the network encodes a hypergraph that depicts a common high-order user relation pattern via hypergraph convolution. By aggregating the embeddings learned through multiple channels, we obtain comprehensive user representations to generate recommendation results. However, the aggregation operation might also obscure the inherent characteristics of different types of high-order connectivity information. To compensate for the aggregating loss, we innovatively integrate self-supervised learning into the training of the hypergraph convolutional network to regain the connectivity information with hierarchical mutual information maximization. The experimental results on multiple real-world datasets show that the proposed model outperforms the SOTA methods, and the ablation study verifies the effectiveness of the multi-channel setting and the self-supervised task. The implementation of our model is available via //github.com/Coder-Yu/RecQ.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
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.
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