In this pioneering research paper, we present a groundbreaking exploration into the synergistic fusion of classical and quantum computing paradigms within the realm of Generative Adversarial Networks (GANs). Our objective is to seamlessly integrate quantum computational elements into the conventional GAN architecture, thereby unlocking novel pathways for enhanced training processes. Drawing inspiration from the inherent capabilities of quantum bits (qubits), we delve into the incorporation of quantum data representation methodologies within the GAN framework. By capitalizing on the unique quantum features, we aim to accelerate the training process of GANs, offering a fresh perspective on the optimization of generative models. Our investigation deals with theoretical considerations and evaluates the potential quantum advantages that may manifest in terms of training efficiency and generative quality. We confront the challenges inherent in the quantum-classical amalgamation, addressing issues related to quantum hardware constraints, error correction mechanisms, and scalability considerations. This research is positioned at the forefront of quantum-enhanced machine learning, presenting a critical stride towards harnessing the computational power of quantum systems to expedite the training of Generative Adversarial Networks. Through our comprehensive examination of the interface between classical and quantum realms, we aim to uncover transformative insights that will propel the field forward, fostering innovation and advancing the frontier of quantum machine learning.
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In this work, we introduce a novel evaluation paradigm for Large Language Models, one that challenges them to engage in meta-reasoning. This approach addresses critical shortcomings in existing math problem-solving benchmarks, traditionally used to evaluate the cognitive capabilities of agents. Our paradigm shifts the focus from result-oriented assessments, which often overlook the reasoning process, to a more holistic evaluation that effectively differentiates the cognitive capabilities among models. For example, in our benchmark, GPT-4 demonstrates a performance five times better than GPT3-5. The significance of this new paradigm lies in its ability to reveal potential cognitive deficiencies in LLMs that current benchmarks, such as GSM8K, fail to uncover due to their saturation and lack of effective differentiation among varying reasoning abilities. Our comprehensive analysis includes several state-of-the-art math models from both open-source and closed-source communities, uncovering fundamental deficiencies in their training and evaluation approaches. This paper not only advocates for a paradigm shift in the assessment of LLMs but also contributes to the ongoing discourse on the trajectory towards Artificial General Intelligence (AGI). By promoting the adoption of meta-reasoning evaluation methods similar to ours, we aim to facilitate a more accurate assessment of the true cognitive abilities of LLMs.
In this paper we adopt a representation-centric perspective on exploration in reinforcement learning, viewing exploration fundamentally as a density estimation problem. We investigate the effectiveness of clustering representations for exploration in 3-D environments, based on the observation that the importance of pixel changes between transitions is less pronounced in 3-D environments compared to 2-D environments, where pixel changes between transitions are typically distinct and significant. We propose a method that performs episodic and global clustering on random representations and on pre-trained DINO representations to count states, i.e, estimate pseudo-counts. Surprisingly, even random features can be clustered effectively to count states in 3-D environments, however when these become visually more complex, pre-trained DINO representations are more effective thanks to the pre-trained inductive biases in the representations. Overall, this presents a pathway for integrating pre-trained biases into exploration. We evaluate our approach on the VizDoom and Habitat environments, demonstrating that our method surpasses other well-known exploration methods in these settings.
In this paper, we investigate the negative effect of activation functions on forward and backward propagation and how to counteract this effect. First, We examine how activation functions affect the forward and backward propagation of neural networks and derive a general form for gradient variance that extends the previous work in this area. We try to use mini-batch statistics to dynamically update the normalization factor to ensure the normalization property throughout the training process, rather than only accounting for the state of the neural network after weight initialization. Second, we propose ANAct, a method that normalizes activation functions to maintain consistent gradient variance across layers and demonstrate its effectiveness through experiments. We observe that the convergence rate is roughly related to the normalization property. We compare ANAct with several common activation functions on CNNs and residual networks and show that ANAct consistently improves their performance. For instance, normalized Swish achieves 1.4\% higher top-1 accuracy than vanilla Swish on ResNet50 with the Tiny ImageNet dataset and more than 1.2\% higher with CIFAR-100.
In this paper, we study the stochastic collocation (SC) methods for uncertainty quantification (UQ) in hyperbolic systems of nonlinear partial differential equations (PDEs). In these methods, the underlying PDEs are numerically solved at a set of collocation points in random space. A standard SC approach is based on a generalized polynomial chaos (gPC) expansion, which relies on choosing the collocation points based on the prescribed probability distribution and approximating the computed solution by a linear combination of orthogonal polynomials in the random variable. We demonstrate that this approach struggles to accurately capture discontinuous solutions, often leading to oscillations (Gibbs phenomenon) that deviate significantly from the physical solutions. We explore alternative SC methods, in which one can choose an arbitrary set of collocation points and employ shape-preserving splines to interpolate the solution in a random space. Our study demonstrates the effectiveness of spline-based collocation in accurately capturing and assessing uncertainties while suppressing oscillations. We illustrate the superiority of the spline-based collocation on two numerical examples, including the inviscid Burgers and shallow water equations.
In this paper, we introduce a multi-label lazy learning approach to deal with automatic semantic indexing in large document collections in the presence of complex and structured label vocabularies with high inter-label correlation. The proposed method is an evolution of the traditional k-Nearest Neighbors algorithm which uses a large autoencoder trained to map the large label space to a reduced size latent space and to regenerate the predicted labels from this latent space. We have evaluated our proposal in a large portion of the MEDLINE biomedical document collection which uses the Medical Subject Headings (MeSH) thesaurus as a controlled vocabulary. In our experiments we propose and evaluate several document representation approaches and different label autoencoder configurations.
Based on SGD, previous works have proposed many algorithms that have improved convergence speed and generalization in stochastic optimization, such as SGDm, AdaGrad, Adam, etc. However, their convergence analysis under non-convex conditions is challenging. In this work, we propose a unified framework to address this issue. For any first-order methods, we interpret the updated direction $g_t$ as the sum of the stochastic subgradient $\nabla f_t(x_t)$ and an additional acceleration term $\frac{2|\langle v_t, \nabla f_t(x_t) \rangle|}{\|v_t\|_2^2} v_t$, thus we can discuss the convergence by analyzing $\langle v_t, \nabla f_t(x_t) \rangle$. Through our framework, we have discovered two plug-and-play acceleration methods: \textbf{Reject Accelerating} and \textbf{Random Vector Accelerating}, we theoretically demonstrate that these two methods can directly lead to an improvement in convergence rate.
To address the communication bottleneck challenge in distributed learning, our work introduces a novel two-stage quantization strategy designed to enhance the communication efficiency of distributed Stochastic Gradient Descent (SGD). The proposed method initially employs truncation to mitigate the impact of long-tail noise, followed by a non-uniform quantization of the post-truncation gradients based on their statistical characteristics. We provide a comprehensive convergence analysis of the quantized distributed SGD, establishing theoretical guarantees for its performance. Furthermore, by minimizing the convergence error, we derive optimal closed-form solutions for the truncation threshold and non-uniform quantization levels under given communication constraints. Both theoretical insights and extensive experimental evaluations demonstrate that our proposed algorithm outperforms existing quantization schemes, striking a superior balance between communication efficiency and convergence performance.
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks with state-of-the-art performance. The data is generally represented in the Euclidean space in these domains. Various other domains conform to non-Euclidean space, for which graph is an ideal representation. Graphs are suitable for representing the dependencies and interrelationships between various entities. Traditionally, handcrafted features for graphs are incapable of providing the necessary inference for various tasks from this complex data representation. Recently, there is an emergence of employing various advances in deep learning to graph data-based tasks. This article provides a comprehensive survey of graph neural networks (GNNs) in each learning setting: supervised, unsupervised, semi-supervised, and self-supervised learning. Taxonomy of each graph based learning setting is provided with logical divisions of methods falling in the given learning setting. The approaches for each learning task are analyzed from both theoretical as well as empirical standpoints. Further, we provide general architecture guidelines for building GNNs. Various applications and benchmark datasets are also provided, along with open challenges still plaguing the general applicability of GNNs.
Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive capacity and effective model complexity. We review the existing studies on those two categories along four important factors, including model framework, model size, optimization process and data complexity. We also discuss the applications of deep learning model complexity including understanding model generalization capability, model optimization, and model selection and design. We conclude by proposing several interesting future directions.
In this paper, we present a comprehensive review of the imbalance problems in object detection. To analyze the problems in a systematic manner, we introduce a problem-based taxonomy. Following this taxonomy, we discuss each problem in depth and present a unifying yet critical perspective on the solutions in the literature. In addition, we identify major open issues regarding the existing imbalance problems as well as imbalance problems that have not been discussed before. Moreover, in order to keep our review up to date, we provide an accompanying webpage which catalogs papers addressing imbalance problems, according to our problem-based taxonomy. Researchers can track newer studies on this webpage available at: //github.com/kemaloksuz/ObjectDetectionImbalance .
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