With the widespread adoption of large language models (LLMs) in numerous applications, the challenge of factuality and the propensity for hallucinations raises significant concerns. To address this issue, particularly in retrieval-augmented in-context learning, we introduce the hierarchical graph of thoughts (HGOT), a structured, multi-layered graph approach designed to enhance the retrieval of pertinent passages during in-context learning. The framework utilizes the emergent planning capabilities of LLMs, employing the divide-and-conquer strategy to break down complex queries into manageable sub-queries. It refines self-consistency majority voting for answer selection, which incorporates the recently proposed citation recall and precision metrics to assess the quality of thoughts, linking an answer's credibility intrinsically to the thought's quality. This methodology introduces a weighted system in majority voting, prioritizing answers based on the citation quality of their thoughts. Additionally, we propose a scoring mechanism for evaluating retrieved passages, considering factors such as citation frequency and quality, self-consistency confidence, and the retrieval module's ranking. Experiments reveal that HGOT outperforms other retrieval-augmented in-context learning methods, including Demonstrate-Search-Predict (DSP), ReAct, Self-Ask, and Retrieve-then-Read on different datasets by as much as $7\%$, demonstrating its efficacy in enhancing the factuality of LLMs.

Open intent detection, a crucial aspect of natural language understanding, involves the identification of previously unseen intents in user-generated text. Despite the progress made in this field, challenges persist in handling new combinations of language components, which is essential for compositional generalization. In this paper, we present a case study exploring the use of ChatGPT as a data augmentation technique to enhance compositional generalization in open intent detection tasks. We begin by discussing the limitations of existing benchmarks in evaluating this problem, highlighting the need for constructing datasets for addressing compositional generalization in open intent detection tasks. By incorporating synthetic data generated by ChatGPT into the training process, we demonstrate that our approach can effectively improve model performance. Rigorous evaluation of multiple benchmarks reveals that our method outperforms existing techniques and significantly enhances open intent detection capabilities. Our findings underscore the potential of large language models like ChatGPT for data augmentation in natural language understanding tasks.

We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an equivariant embedding from the manifold to its image in the Euclidean space. Moreover, intrinsic deep neural networks (iDNNs) incorporate the underlying intrinsic geometry of manifolds via exponential and log maps with respect to a Riemannian structure. Consequently, we prove that the empirical risk of the empirical risk minimizers (ERM) of eDNNs and iDNNs converge in optimal rates. Overall, The eDNNs framework is simple and easy to compute, while the iDNNs framework is accurate and fast converging. To demonstrate the utilities of our framework, various simulation studies, and real data analyses are presented with eDNNs and iDNNs.

We propose an extrinsic Bayesian optimization (eBO) framework for general optimization problems on manifolds. Bayesian optimization algorithms build a surrogate of the objective function by employing Gaussian processes and quantify the uncertainty in that surrogate by deriving an acquisition function. This acquisition function represents the probability of improvement based on the kernel of the Gaussian process, which guides the search in the optimization process. The critical challenge for designing Bayesian optimization algorithms on manifolds lies in the difficulty of constructing valid covariance kernels for Gaussian processes on general manifolds. Our approach is to employ extrinsic Gaussian processes by first embedding the manifold onto some higher dimensional Euclidean space via equivariant embeddings and then constructing a valid covariance kernel on the image manifold after the embedding. This leads to efficient and scalable algorithms for optimization over complex manifolds. Simulation study and real data analysis are carried out to demonstrate the utilities of our eBO framework by applying the eBO to various optimization problems over manifolds such as the sphere, the Grassmannian, and the manifold of positive definite matrices.

The invention of transformer-based models such as BERT, GPT, and RoBERTa has enabled researchers and financial companies to finetune these powerful models and use them in different downstream tasks to achieve state-of-the-art performance. Recently, a lightweight alternative (approximately 0.1% - 3% of the original model parameters) to fine-tuning, known as prefix tuning has been introduced. This method freezes the model parameters and only updates the prefix to achieve performance comparable to full fine-tuning. Prefix tuning enables researchers and financial practitioners to achieve similar results with much fewer parameters. In this paper, we explore the robustness of prefix tuning when facing noisy data. Our experiments demonstrate that fine-tuning is more robust to noise than prefix tuning -- the latter method faces a significant decrease in performance on most corrupted data sets with increasing noise levels. Furthermore, prefix tuning has high variances in the F1 scores compared to fine-tuning in many corruption methods. We strongly advocate that caution should be carefully taken when applying the state-of-the-art prefix tuning method to noisy data.

In this work, we propose to employ information-geometric tools to optimize a graph neural network architecture such as the graph convolutional networks. More specifically, we develop optimization algorithms for the graph-based semi-supervised learning by employing the natural gradient information in the optimization process. This allows us to efficiently exploit the geometry of the underlying statistical model or parameter space for optimization and inference. To the best of our knowledge, this is the first work that has utilized the natural gradient for the optimization of graph neural networks that can be extended to other semi-supervised problems. Efficient computations algorithms are developed and extensive numerical studies are conducted to demonstrate the superior performance of our algorithms over existing algorithms such as ADAM and SGD.