Logistic regression, the Support Vector Machine (SVM), and least squares are well-studied methods in the statistical and computer science community, with various practical applications. High-dimensional data arriving on a real-time basis makes the design of online learning algorithms that produce sparse solutions essential. The seminal work of \hyperlink{cite.langford2009sparse}{Langford, Li, and Zhang (2009)} developed a method to obtain sparsity via truncated gradient descent, showing a near-optimal online regret bound. Based on this method, we develop a quantum sparse online learning algorithm for logistic regression, the SVM, and least squares. Given efficient quantum access to the inputs, we show that a quadratic speedup in the time complexity with respect to the dimension of the problem is achievable, while maintaining a regret of $O(1/\sqrt{T})$, where $T$ is the number of iterations.
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Extracting time-varying latent variables from computational cognitive models is a key step in model-based neural analysis, which aims to understand the neural correlates of cognitive processes. However, existing methods only allow researchers to infer latent variables that explain subjects' behavior in a relatively small class of cognitive models. For example, a broad class of relevant cognitive models with analytically intractable likelihood is currently out of reach from standard techniques, based on Maximum a Posteriori parameter estimation. Here, we present an approach that extends neural Bayes estimation to learn a direct mapping between experimental data and the targeted latent variable space using recurrent neural networks and simulated datasets. We show that our approach achieves competitive performance in inferring latent variable sequences in both tractable and intractable models. Furthermore, the approach is generalizable across different computational models and is adaptable for both continuous and discrete latent spaces. We then demonstrate its applicability in real world datasets. Our work underscores that combining recurrent neural networks and simulation-based inference to identify latent variable sequences can enable researchers to access a wider class of cognitive models for model-based neural analyses, and thus test a broader set of theories.
The geometric dimension of a Vector Addition System with States (VASS), emerged in Leroux and Schmitz (2019) and formalized by Fu, Yang, and Zheng (2024), quantifies the dimension of the vector space spanned by cycle effects in the system. This paper explores the VASS reachability problem through the lens of geometric dimension, revealing key differences from the traditional dimensional parameterization. Notably, we establish that the reachability problem for both geometrically 1-dimensional and 2-dimensional VASS is PSPACE-complete, achieved by extending the pumping technique originally proposed by Czerwi\'nski et al. (2019).
Concurrent computation and communication (C3) is a pervasive paradigm in ML and other domains, making its performance optimization crucial. In this paper, we carefully characterize C3 in ML on GPUs, which are most widely deployed for ML training and inference. We observe that while C3 leads to performance uplifts, the uplifts are far lower than ideal speedups (serial computation and communication versus maximum of computation or communication; all times from isolated executions). C3 on average achieves only 21% of ideal speedup, this is due to known challenges of compute and memory interference between concurrent GPU kernels (that is, sharing of GPU's compute units, caches and HBM). To attain better performance for C3, first, we evaluate dual strategies of schedule prioritization and careful resource partitioning of compute units on GPUs to push performance attained with C3 (on average 42% of ideal speedup). We also provide heuristics that can guide a runtime while employing these strategies. To further enhance C3 performance, we propose to mitigate C3 interference by offloading communication tasks to the GPU's DMA engines. To this end, we build Concurrent Communication CoLlectives (ConCCL) proof-of-concepts that harness DMA engines for communication. We show how ConCCL considerably closes the gap between realized and ideal speedup for C3 (on average 72% of ideal speedup is realized, up to 1.67x speedup). Overall, our work makes a strong case for GPU DMA engine advancements to better support C3 on GPUs.
The Church Problem asks for the construction of a procedure which, given a logical specification A(I,O) between input omega-strings I and output omega-strings O, determines whether there exists an operator F that implements the specification in the sense that A(I, F(I)) holds for all inputs I. Buchi and Landweber provided a procedure to solve the Church problem for MSO specifications and operators computable by finite-state automata. We investigate a generalization of the Church synthesis problem to the continuous time domain of the non-negative reals. We show that in the continuous time domain there are phenomena which are very different from the canonical discrete time domain of the natural numbers.
The emergence of Large Language Models (LLMs), has opened exciting possibilities for constructing computational simulations designed to replicate human behavior accurately. Current research suggests that LLM-based agents become increasingly human-like in their performance, sparking interest in using these AI agents as substitutes for human participants in behavioral studies. However, LLMs are complex statistical learners without straightforward deductive rules, making them prone to unexpected behaviors. Hence, it is crucial to study and pinpoint the key behavioral distinctions between humans and LLM-based agents. In this study, we highlight the limitations of LLMs in simulating human interactions, particularly focusing on LLMs' ability to simulate political debates on topics that are important aspects of people's day-to-day lives and decision-making processes. Our findings indicate a tendency for LLM agents to conform to the model's inherent social biases despite being directed to debate from certain political perspectives. This tendency results in behavioral patterns that seem to deviate from well-established social dynamics among humans. We reinforce these observations using an automatic self-fine-tuning method, which enables us to manipulate the biases within the LLM and demonstrate that agents subsequently align with the altered biases. These results underscore the need for further research to develop methods that help agents overcome these biases, a critical step toward creating more realistic simulations.
Recent advancements in quantum computing (QC) and machine learning (ML) have garnered significant attention, leading to substantial efforts toward the development of quantum machine learning (QML) algorithms to address a variety of complex challenges. The design of high-performance QML models, however, requires expert-level knowledge, posing a significant barrier to the widespread adoption of QML. Key challenges include the design of data encoding mechanisms and parameterized quantum circuits, both of which critically impact the generalization capabilities of QML models. We propose a novel method that encodes quantum circuit architecture information to enable the evolution of quantum circuit designs. In this approach, the fitness function is based on the effective dimension, allowing for the optimization of quantum circuits towards higher model capacity. Through numerical simulations, we demonstrate that the proposed method is capable of discovering variational quantum circuit architectures that offer improved learning capabilities, thereby enhancing the overall performance of QML models for complex tasks.
Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.
Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.
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