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In this work, we consider an online robust Markov Decision Process (MDP) where we have the information of finitely many prototypes of the underlying transition kernel. We consider an adaptively updated ambiguity set of the prototypes and propose an algorithm that efficiently identifies the true underlying transition kernel while guaranteeing the performance of the corresponding robust policy. To be more specific, we provide a sublinear regret of the subsequent optimal robust policy. We also provide an early stopping mechanism and a worst-case performance bound of the value function. In numerical experiments, we demonstrate that our method outperforms existing approaches, particularly in the early stage with limited data. This work contributes to robust MDPs by considering possible prior information about the underlying transition probability and online learning, offering both theoretical insights and practical algorithms for improved decision-making under uncertainty.

This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of self-map, compound mapping, totality, one-to-oneness, non-primeness, ontoness, bijectivity, default value, (null-)reflexivity, irreflexivity, (null-)symmetry, asymmetry, (null-)idempotency, anti-idempotency, (null-)equivalence, acyclicity, (null-)representative system mapping, the properties that relate them, and the corresponding corollaries on the coherence and minimality of sets made of such mapping properties viewed as database constraints. Its main contribution is the pseudocode algorithm used by MatBase, our intelligent database management system prototype based on both (E)MDM, the relational, and the entity-relationship data models, for enforcing self-map, atomic, and compound mapping constraint sets. We prove that this algorithm guarantees the satisfiability, coherence, and minimality of such sets, while being very fast, solid, complete, and minimal. In the sequel, we also presented the relevant MatBase user interface as well as the tables of its metacatalog used by this algorithm.

Traditional greedy tokenization methods have been a critical step in Natural Language Processing (NLP), influencing how text is converted into tokens and directly impacting model performance. While subword tokenizers like Byte-Pair Encoding (BPE) are widely used, questions remain about their optimality across model scales and languages. In this work, we demonstrate through extensive experiments that an optimal BPE configuration significantly reduces token count compared to greedy segmentation, yielding improvements in token-saving percentages and performance benefits, particularly for smaller models. We evaluate tokenization performance across various intrinsic and extrinsic tasks, including generation and classification. Our findings suggest that compression-optimized tokenization strategies could provide substantial advantages for multilingual and low-resource language applications, highlighting a promising direction for further research and inclusive NLP.

This paper presents the Text Encoding Diffusion Model (TEncDM), a novel approach to diffusion modeling that operates in the space of pre-trained language model encodings. In contrast to traditionally used embeddings, encodings integrate contextual information. In our approach, we also employ a transformer-based decoder, specifically designed to incorporate context in the token prediction process. We conduct a comprehensive examination of the influence of the encoder, decoder, noise scheduler, and self-conditioning on zero-shot generation. Furthermore, we compare TEncDM with previous approaches on three conditional text generation tasks: QQP, XSum, and Wiki-Auto. The results show that TEncDM exhibits superior performance compared to existing non-autoregressive diffusion models. Our code is available at //github.com/M0RJIQUE/tencdm.

In this study, we define and tackle zero shot "real" classification by description, a novel task that evaluates the ability of Vision-Language Models (VLMs) like CLIP to classify objects based solely on descriptive attributes, excluding object class names. This approach highlights the current limitations of VLMs in understanding intricate object descriptions, pushing these models beyond mere object recognition. To facilitate this exploration, we introduce a new challenge and release description data for six popular fine-grained benchmarks, which omit object names to encourage genuine zero-shot learning within the research community. Additionally, we propose a method to enhance CLIP's attribute detection capabilities through targeted training using ImageNet21k's diverse object categories, paired with rich attribute descriptions generated by large language models. Furthermore, we introduce a modified CLIP architecture that leverages multiple resolutions to improve the detection of fine-grained part attributes. Through these efforts, we broaden the understanding of part-attribute recognition in CLIP, improving its performance in fine-grained classification tasks across six popular benchmarks, as well as in the PACO dataset, a widely used benchmark for object-attribute recognition. Code is available at: //github.com/ethanbar11/grounding_ge_public.

In this paper, we focus on the challenging task of reliably estimating factual knowledge that is embedded inside large language models (LLMs). To avoid reliability concerns with prior approaches, we propose to eliminate prompt engineering when probing LLMs for factual knowledge. Our approach, called Zero-Prompt Latent Knowledge Estimator (ZP-LKE), leverages the in-context learning ability of LLMs to communicate both the factual knowledge question as well as the expected answer format. Our knowledge estimator is both conceptually simpler (i.e., doesn't depend on meta-linguistic judgments of LLMs) and easier to apply (i.e., is not LLM-specific), and we demonstrate that it can surface more of the latent knowledge embedded in LLMs. We also investigate how different design choices affect the performance of ZP-LKE. Using the proposed estimator, we perform a large-scale evaluation of the factual knowledge of a variety of open-source LLMs, like OPT, Pythia, Llama(2), Mistral, Gemma, etc. over a large set of relations and facts from the Wikidata knowledge base. We observe differences in the factual knowledge between different model families and models of different sizes, that some relations are consistently better known than others but that models differ in the precise facts they know, and differences in the knowledge of base models and their finetuned counterparts. Code available at: //github.com/QinyuanWu0710/ZeroPrompt_LKE

Evaluating the performance of Grammatical Error Correction (GEC) models has become increasingly challenging, as large language model (LLM)-based GEC systems often produce corrections that diverge from provided gold references. This discrepancy undermines the reliability of traditional reference-based evaluation metrics. In this study, we propose a novel evaluation framework for GEC models, DSGram, integrating Semantic Coherence, Edit Level, and Fluency, and utilizing a dynamic weighting mechanism. Our framework employs the Analytic Hierarchy Process (AHP) in conjunction with large language models to ascertain the relative importance of various evaluation criteria. Additionally, we develop a dataset incorporating human annotations and LLM-simulated sentences to validate our algorithms and fine-tune more cost-effective models. Experimental results indicate that our proposed approach enhances the effectiveness of GEC model evaluations.

In this paper we explain how to use the Fast Fourier Transform (FFT) to solve partial differential equations (PDEs). We start by defining appropriate discrete domains in coordinate and frequency domains. Then describe the main limitation of the method arising from the Sampling Theorem, which defines the critical Nyquist frequency and the aliasing effect. We then define the Fourier Transform (FT) and the FFT in a way that can be implemented in one and more dimensions. Finally, we show how to apply the FFT in the solution of PDEs related to problems involving two spatial dimensions, specifically the Poisson equation, the diffusion equation and the wave equation for elliptic, parabolic and hyperbolic cases respectively.

Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.

Machine learning techniques have deeply rooted in our everyday life. However, since it is knowledge- and labor-intensive to pursue good learning performance, human experts are heavily involved in every aspect of machine learning. In order to make machine learning techniques easier to apply and reduce the demand for experienced human experts, automated machine learning (AutoML) has emerged as a hot topic with both industrial and academic interest. In this paper, we provide an up to date survey on AutoML. First, we introduce and define the AutoML problem, with inspiration from both realms of automation and machine learning. Then, we propose a general AutoML framework that not only covers most existing approaches to date but also can guide the design for new methods. Subsequently, we categorize and review the existing works from two aspects, i.e., the problem setup and the employed techniques. Finally, we provide a detailed analysis of AutoML approaches and explain the reasons underneath their successful applications. We hope this survey can serve as not only an insightful guideline for AutoML beginners but also an inspiration for future research.