arXiv subjects

Yifan Hu

Publications and source records attributed to Yifan Hu.

At least 91 records · Page 5Linked to original sources

arXiv2024

The finitary partitions with $n$ non-singleton blocks of a set

A partition is finitary if all its blocks are finite. For a cardinal $\mathfrak{a}$ and a natural number $n$, let $\mathrm{fin}(\mathfrak{a})$ and $\mathscr{B}_{n}(\mathfrak{a})$ be the cardinalities of the set of finite subsets and the set of finitary partitions with exactly $n$ non-singleton blocks of a set which is of cardinality $\mathfrak{a}$, respectively. In this paper, we prove in $\mathsf{ZF}$ (without the axiom of choice) that for all infinite cardinals $\mathfrak{a}$ and all non-zero natural numbers $n$, \[ (2^{\mathscr{B}_{n}(\mathfrak{a})})^{\aleph_0}=2^{\mathscr{B}_{n}(\mathfrak{a})} \] and \[ 2^{\mathrm{fin}(\mathfrak{a})^n}=2^{\mathscr{B}_{2^n-1}(\mathfrak{a})}. \] It is also proved consistent with $\mathsf{ZF}$ that there exists an infinite cardinal $\mathfrak{a}$ such that \[ 2^{\mathscr{B}_{1}(\mathfrak{a})}<2^{\mathscr{B}_{2}(\mathfrak{a})}<2^{\mathscr{B}_{3}(\mathfrak{a})}<\cdots<2^{\mathrm{fin}(\mathrm{fin}(\mathfrak{a}))}. \]

math.LO↗

arXiv2024

Stochastic Optimization under Hidden Convexity

In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from optimal control, revenue and inventory management, to convex reinforcement learning all admit such a hidden convex structure. Unfortunately, in the majority of applications considered, the map $c(\cdot)$ is unavailable or implicit; therefore, directly solving the convex reformulation is not possible. On the other hand, the stochastic gradients with respect to the original variable are often easy to obtain. Motivated by these observations, we examine the basic projected stochastic (sub-) gradient methods for solving such problems under hidden convexity. We provide the first sample complexity guarantees for global convergence in smooth and non-smooth settings. Additionally, in the smooth setting, we improve our results to the last iterate convergence in terms of function value gap using the momentum variant of projected stochastic gradient descent.

math.OC↗

arXiv2024

Emphasis Rendering for Conversational Text-to-Speech with Multi-modal Multi-scale Context Modeling

Conversational Text-to-Speech (CTTS) aims to accurately express an utterance with the appropriate style within a conversational setting, which attracts more attention nowadays. While recognizing the significance of the CTTS task, prior studies have not thoroughly investigated speech emphasis expression, which is essential for conveying the underlying intention and attitude in human-machine interaction scenarios, due to the scarcity of conversational emphasis datasets and the difficulty in context understanding. In this paper, we propose a novel Emphasis Rendering scheme for the CTTS model, termed ER-CTTS, that includes two main components: 1) we simultaneously take into account textual and acoustic contexts, with both global and local semantic modeling to understand the conversation context comprehensively; 2) we deeply integrate multi-modal and multi-scale context to learn the influence of context on the emphasis expression of the current utterance. Finally, the inferred emphasis feature is fed into the neural speech synthesizer to generate conversational speech. To address data scarcity, we create emphasis intensity annotations on the existing conversational dataset (DailyTalk). Both objective and subjective evaluations suggest that our model outperforms the baseline models in emphasis rendering within a conversational setting. The code and audio samples are available at https://github.com/CodeStoreTTS/ER-CTTS.

cs.CL↗

arXiv2024

Multi-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oracles

We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization paradigms, such as conditional stochastic optimization, distributionally robust optimization, shortfall risk optimization, and machine learning paradigms, such as contrastive learning. We examine a family of multi-level Monte Carlo (MLMC) gradient methods that exploit a delicate tradeoff among bias, variance, and oracle cost. We systematically study their total sample and computational complexities for strongly convex, convex, and nonconvex objectives and demonstrate their superiority over the widely used biased stochastic gradient method. When combined with the variance reduction techniques like SPIDER, these MLMC gradient methods can further reduce the complexity in the nonconvex regime. Our results imply that a series of stochastic optimization problems with biased oracles, previously considered to be more challenging, is fundamentally no harder than the classical stochastic optimization with unbiased oracles. We also delineate the boundary conditions under which these problems become more difficult. Moreover, MLMC gradient methods significantly improve the best-known complexities in the literature for conditional stochastic optimization and shortfall risk optimization. Our extensive numerical experiments on distributionally robust optimization, pricing and staffing scheduling problems, and contrastive learning demonstrate the superior performance of MLMC gradient methods.

math.OC↗

arXiv2024

Generative Expressive Conversational Speech Synthesis

Conversational Speech Synthesis (CSS) aims to express a target utterance with the proper speaking style in a user-agent conversation setting. Existing CSS methods employ effective multi-modal context modeling techniques to achieve empathy understanding and expression. However, they often need to design complex network architectures and meticulously optimize the modules within them. In addition, due to the limitations of small-scale datasets containing scripted recording styles, they often fail to simulate real natural conversational styles. To address the above issues, we propose a novel generative expressive CSS system, termed GPT-Talker.We transform the multimodal information of the multi-turn dialogue history into discrete token sequences and seamlessly integrate them to form a comprehensive user-agent dialogue context. Leveraging the power of GPT, we predict the token sequence, that includes both semantic and style knowledge, of response for the agent. After that, the expressive conversational speech is synthesized by the conversation-enriched VITS to deliver feedback to the user.Furthermore, we propose a large-scale Natural CSS Dataset called NCSSD, that includes both naturally recorded conversational speech in improvised styles and dialogues extracted from TV shows. It encompasses both Chinese and English languages, with a total duration of 236 hours.We conducted comprehensive experiments on the reliability of the NCSSD and the effectiveness of our GPT-Talker. Both subjective and objective evaluations demonstrate that our model outperforms other state-of-the-art CSS systems significantly in terms of naturalness and expressiveness. The Code, Dataset, and Pre-trained Model are available at: https://github.com/AI-S2-Lab/GPT-Talker.

cs.CL↗

arXiv2024

Efficient Algorithms for A Class of Stochastic Hidden Convex Optimization and Its Applications in Network Revenue Management

We study a class of stochastic nonconvex optimization in the form of $\min_{x\in\mathcal{X}} F(x):=\mathbb{E}_ξ[f(ϕ(x,ξ))]$, i.e., $F$ is a composition of a convex function $f$ and a random function $ϕ$. Leveraging an (implicit) convex reformulation via a variable transformation $u=\mathbb{E}[ϕ(x,ξ)]$, we develop stochastic gradient-based algorithms and establish their sample and gradient complexities for achieving an $ε$-global optimal solution. Interestingly, our proposed Mirror Stochastic Gradient (MSG) method operates only in the original $x$-space using gradient estimators of the original nonconvex objective $F$ and achieves $\tilde{\mathcal{O}}(ε^{-2})$ complexities, which matches the lower bounds for solving stochastic convex optimization problems. Under booking limits control, we formulate the air-cargo network revenue management (NRM) problem with random two-dimensional capacity, random consumption, and routing flexibility as a special case of the stochastic nonconvex optimization, where the random function $ϕ(x,ξ)=x\wedgeξ$, i.e., the random demand $ξ$ truncates the booking limit decision $x$. Extensive numerical experiments demonstrate the superior performance of our proposed MSG algorithm for booking limit control with higher revenue and lower computation cost than state-of-the-art bid-price-based control policies, especially when the variance of random capacity is large. KEYWORDS: stochastic nonconvex optimization, hidden convexity, gradient methods, passenger network revenue management, air-cargo network revenue management

math.OC↗

arXiv2024

Long-Term Prediction Accuracy Improvement of Data-Driven Medium-Range Global Weather Forecast

Long-term stability stands as a crucial requirement in data-driven medium-range global weather forecasting. Spectral bias is recognized as the primary contributor to instabilities, as data-driven methods difficult to learn small-scale dynamics. In this paper, we reveal that the universal mechanism for these instabilities is not only related to spectral bias but also to distortions brought by processing spherical data using conventional convolution. These distortions lead to a rapid amplification of errors over successive long-term iterations, resulting in a significant decline in forecast accuracy. To address this issue, a universal neural operator called the Spherical Harmonic Neural Operator (SHNO) is introduced to improve long-term iterative forecasts. SHNO uses the spherical harmonic basis to mitigate distortions for spherical data and uses gated residual spectral attention (GRSA) to correct spectral bias caused by spurious correlations across different scales. The effectiveness and merit of the proposed method have been validated through its application for spherical Shallow Water Equations (SWEs) and medium-range global weather forecasting. Our findings highlight the benefits and potential of SHNO to improve the accuracy of long-term prediction.

cs.LG↗

arXiv2024

Beyond Individual Facts: Investigating Categorical Knowledge Locality of Taxonomy and Meronomy Concepts in GPT Models

The location of knowledge within Generative Pre-trained Transformer (GPT)-like models has seen extensive recent investigation. However, much of the work is focused towards determining locations of individual facts, with the end goal being the editing of facts that are outdated, erroneous, or otherwise harmful, without the time and expense of retraining the entire model. In this work, we investigate a broader view of knowledge location, that of concepts or clusters of related information, instead of disparate individual facts. To do this, we first curate a novel dataset, called DARC, that includes a total of 34 concepts of ~120K factual statements divided into two types of hierarchical categories, namely taxonomy and meronomy. Next, we utilize existing causal mediation analysis methods developed for determining regions of importance for individual facts and apply them to a series of related categories to provide detailed investigation into whether concepts are associated with distinct regions within these models. We find that related categories exhibit similar areas of importance in contrast to less similar categories. However, fine-grained localization of individual category subsets to specific regions is not apparent.

cs.LG↗

arXiv2024

Biased Stochastic First-Order Methods for Conditional Stochastic Optimization and Applications in Meta Learning

Conditional stochastic optimization covers a variety of applications ranging from invariant learning and causal inference to meta-learning. However, constructing unbiased gradient estimators for such problems is challenging due to the composition structure. As an alternative, we propose a biased stochastic gradient descent (BSGD) algorithm and study the bias-variance tradeoff under different structural assumptions. We establish the sample complexities of BSGD for strongly convex, convex, and weakly convex objectives under smooth and non-smooth conditions. Our lower bound analysis shows that the sample complexities of BSGD cannot be improved for general convex objectives and nonconvex objectives except for smooth nonconvex objectives with Lipschitz continuous gradient estimator. For this special setting, we propose an accelerated algorithm called biased SpiderBoost (BSpiderBoost) that matches the lower bound complexity. We further conduct numerical experiments on invariant logistic regression and model-agnostic meta-learning to illustrate the performance of BSGD and BSpiderBoost.

math.OC↗

arXiv2024

Group Robust Preference Optimization in Reward-free RLHF

Adapting large language models (LLMs) for specific tasks usually involves fine-tuning through reinforcement learning with human feedback (RLHF) on preference data. While these data often come from diverse labelers' groups (e.g., different demographics, ethnicities, company teams, etc.), traditional RLHF approaches adopt a "one-size-fits-all" approach, i.e., they indiscriminately assume and optimize a single preference model, thus not being robust to unique characteristics and needs of the various groups. To address this limitation, we propose a novel Group Robust Preference Optimization (GRPO) method to align LLMs to individual groups' preferences robustly. Our approach builds upon reward-free direct preference optimization methods, but unlike previous approaches, it seeks a robust policy which maximizes the worst-case group performance. To achieve this, GRPO adaptively and sequentially weights the importance of different groups, prioritizing groups with worse cumulative loss. We theoretically study the feasibility of GRPO and analyze its convergence for the log-linear policy class. By fine-tuning LLMs with GRPO using diverse group-based global opinion data, we significantly improved performance for the worst-performing groups, reduced loss imbalances across groups, and improved probability accuracies compared to non-robust baselines.

cs.CL↗

arXiv2024

Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Data

We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require matrix inversions nor mini-batches and provides a fully online approach for performing instrumental variable regression with streaming data. When the true model is linear, we derive rates of convergence in expectation, that are of order $\mathcal{O}(\log T/T)$ and $\mathcal{O}(1/T^{1-ι})$ for any $ι>0$, respectively under the availability of two-sample and one-sample oracles, respectively, where $T$ is the number of iterations. Importantly, under the availability of the two-sample oracle, our procedure avoids explicitly modeling and estimating the relationship between confounder and the instrumental variables, demonstrating the benefit of the proposed approach over recent works based on reformulating the problem as minimax optimization problems. Numerical experiments are provided to corroborate the theoretical results.

stat.ML↗

arXiv2023

Emotion Rendering for Conversational Speech Synthesis with Heterogeneous Graph-Based Context Modeling

Conversational Speech Synthesis (CSS) aims to accurately express an utterance with the appropriate prosody and emotional inflection within a conversational setting. While recognising the significance of CSS task, the prior studies have not thoroughly investigated the emotional expressiveness problems due to the scarcity of emotional conversational datasets and the difficulty of stateful emotion modeling. In this paper, we propose a novel emotional CSS model, termed ECSS, that includes two main components: 1) to enhance emotion understanding, we introduce a heterogeneous graph-based emotional context modeling mechanism, which takes the multi-source dialogue history as input to model the dialogue context and learn the emotion cues from the context; 2) to achieve emotion rendering, we employ a contrastive learning-based emotion renderer module to infer the accurate emotion style for the target utterance. To address the issue of data scarcity, we meticulously create emotional labels in terms of category and intensity, and annotate additional emotional information on the existing conversational dataset (DailyTalk). Both objective and subjective evaluations suggest that our model outperforms the baseline models in understanding and rendering emotions. These evaluations also underscore the importance of comprehensive emotional annotations. Code and audio samples can be found at: https://github.com/walker-hyf/ECSS.

cs.CL↗

arXiv2023

Contextual Stochastic Bilevel Optimization

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This framework extends classical stochastic bilevel optimization when the lower-level decision maker responds optimally not only to the decision of the upper-level decision maker but also to some side information and when there are multiple or even infinite many followers. It captures important applications such as meta-learning, personalized federated learning, end-to-end learning, and Wasserstein distributionally robust optimization with side information (WDRO-SI). Due to the presence of contextual information, existing single-loop methods for classical stochastic bilevel optimization are unable to converge. To overcome this challenge, we introduce an efficient double-loop gradient method based on the Multilevel Monte-Carlo (MLMC) technique and establish its sample and computational complexities. When specialized to stochastic nonconvex optimization, our method matches existing lower bounds. For meta-learning, the complexity of our method does not depend on the number of tasks. Numerical experiments further validate our theoretical results.

math.OC↗

arXiv2023

Distributionally Robust Model-based Reinforcement Learning with Large State Spaces

Three major challenges in reinforcement learning are the complex dynamical systems with large state spaces, the costly data acquisition processes, and the deviation of real-world dynamics from the training environment deployment. To overcome these issues, we study distributionally robust Markov decision processes with continuous state spaces under the widely used Kullback-Leibler, chi-square, and total variation uncertainty sets. We propose a model-based approach that utilizes Gaussian Processes and the maximum variance reduction algorithm to efficiently learn multi-output nominal transition dynamics, leveraging access to a generative model (i.e., simulator). We further demonstrate the statistical sample complexity of the proposed method for different uncertainty sets. These complexity bounds are independent of the number of states and extend beyond linear dynamics, ensuring the effectiveness of our approach in identifying near-optimal distributionally-robust policies. The proposed method can be further combined with other model-free distributionally robust reinforcement learning methods to obtain a near-optimal robust policy. Experimental results demonstrate the robustness of our algorithm to distributional shifts and its superior performance in terms of the number of samples needed.

cs.LG↗

arXiv2023

SmartGD: A GAN-Based Graph Drawing Framework for Diverse Aesthetic Goals

While a multitude of studies have been conducted on graph drawing, many existing methods only focus on optimizing a single aesthetic aspect of graph layouts, which can lead to sub-optimal results. There are a few existing methods that have attempted to develop a flexible solution for optimizing different aesthetic aspects measured by different aesthetic criteria. Furthermore, thanks to the significant advance in deep learning techniques, several deep learning-based layout methods were proposed recently. These methods have demonstrated the advantages of deep learning approaches for graph drawing. However, none of these existing methods can be directly applied to optimizing non-differentiable criteria without special accommodation. In this work, we propose a novel Generative Adversarial Network (GAN) based deep learning framework for graph drawing, called SmartGD, which can optimize different quantitative aesthetic goals, regardless of their differentiability. To demonstrate the effectiveness and efficiency of SmartGD, we conducted experiments on minimizing stress, minimizing edge crossing, maximizing crossing angle, maximizing shape-based metrics, and a combination of multiple aesthetics. Compared with several popular graph drawing algorithms, the experimental results show that SmartGD achieves good performance both quantitatively and qualitatively.

cs.LG↗

arXiv2023

Deep Directly-Trained Spiking Neural Networks for Object Detection

Spiking neural networks (SNNs) are brain-inspired energy-efficient models that encode information in spatiotemporal dynamics. Recently, deep SNNs trained directly have shown great success in achieving high performance on classification tasks with very few time steps. However, how to design a directly-trained SNN for the regression task of object detection still remains a challenging problem. To address this problem, we propose EMS-YOLO, a novel directly-trained SNN framework for object detection, which is the first trial to train a deep SNN with surrogate gradients for object detection rather than ANN-SNN conversion strategies. Specifically, we design a full-spike residual block, EMS-ResNet, which can effectively extend the depth of the directly-trained SNN with low power consumption. Furthermore, we theoretically analyze and prove the EMS-ResNet could avoid gradient vanishing or exploding. The results demonstrate that our approach outperforms the state-of-the-art ANN-SNN conversion methods (at least 500 time steps) in extremely fewer time steps (only 4 time steps). It is shown that our model could achieve comparable performance to the ANN with the same architecture while consuming 5.83 times less energy on the frame-based COCO Dataset and the event-based Gen1 Dataset.

cs.CV↗

arXiv2023

Improvement of Memory Characteristics of Charge-Trapping Memory Device by Using HfO$_2$/Al$_2$O$_3$ Laminate

Current portable memory device relies heavily on flash memory technology for its implementation. New generation of non-volatile memory is likely to replace floating gates, charge-trapping memory currently still suffering from inadequate retention performance and slow programming speeds as well as small memory window. In contrast, the use of HfO$_2$/Al$_2$O$_3$ stacked high-k materials has substantially increased the memory window of memory devices, with a 63% increase relative to pure HfO$_2$ materials. The current goal of up to 80% retention characteristics over a ten-year period has been achieved by adjusting the deposition ratio or dopant material. Process conditions can continue to be investigated in the future to reduce charge loss while maintaining the increased memory window.

physics.app-ph↗

arXiv2023

Advancing Spiking Neural Networks towards Deep Residual Learning

Despite the rapid progress of neuromorphic computing, inadequate capacity and insufficient representation power of spiking neural networks (SNNs) severely restrict their application scope in practice. Residual learning and shortcuts have been evidenced as an important approach for training deep neural networks, but rarely did previous work assess their applicability to the characteristics of spike-based communication and spatiotemporal dynamics. In this paper, we first identify that this negligence leads to impeded information flow and the accompanying degradation problem in previous residual SNNs. To address this issue, we propose a novel SNN-oriented residual architecture termed MS-ResNet, which establishes membrane-based shortcut pathways, and further prove that the gradient norm equality can be achieved in MS-ResNet by introducing block dynamical isometry theory, which ensures the network can be well-behaved in a depth-insensitive way. Thus we are able to significantly extend the depth of directly trained SNNs, e.g., up to 482 layers on CIFAR-10 and 104 layers on ImageNet, without observing any slight degradation problem. To validate the effectiveness of MS-ResNet, experiments on both frame-based and neuromorphic datasets are conducted. MS-ResNet104 achieves a superior result of 76.02% accuracy on ImageNet, which is the highest to our best knowledge in the domain of directly trained SNNs. Great energy efficiency is also observed, with an average of only one spike per neuron needed to classify an input sample. We believe our powerful and scalable models will provide a strong support for further exploration of SNNs.

cs.NE↗