Diffusion probabilistic models (DPMs) have recently shown great potential for denoising tasks. Despite their practical utility, there is a notable gap in their theoretical understanding. This paper contributes novel theoretical insights by rigorously proving the asymptotic convergence of a specific DPM denoising strategy to the mean square error (MSE)-optimal conditional mean estimator (CME) over a large number of diffusion steps. The studied DPM-based denoiser shares the training procedure of DPMs but distinguishes itself by forwarding only the conditional mean during the reverse inference process after training. We highlight the unique perspective that DPMs are composed of an asymptotically optimal denoiser while simultaneously inheriting a powerful generator by switching re-sampling in the reverse process on and off. The theoretical findings are validated by numerical results.
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Large language models (LLMs) demonstrate substantial capabilities in solving math problems. However, they tend to produce hallucinations when given questions containing unreasonable errors. In this paper, we study the behavior of LLMs when faced with unreasonable math problems and further explore their potential to address these problems. We construct the Unreasonable Math Problem (UMP) benchmark to examine the error detection ability of LLMs. Experiments show that LLMs are able to detect unreasonable errors, but still fail in generating non-hallucinatory content. In order to improve their ability of error detection and correction, we further design a strategic prompt template called Critical Calculation and Conclusion(CCC). With CCC, LLMs can better self-evaluate and detect unreasonable errors in math questions, making them more reliable and safe in practical application scenarios.
Large-scale Pretrained Language Models (LLMs), such as ChatGPT and GPT4, have shown strong abilities in multilingual translations, without being explicitly trained on parallel corpora. It is interesting how the LLMs obtain their ability to carry out translation instructions for different languages. In this paper, we present a detailed analysis by finetuning a multilingual pretrained language model, XGLM-7B, to perform multilingual translation following given instructions. Firstly, we show that multilingual LLMs have stronger translation abilities than previously demonstrated. For a certain language, the performance depends on its similarity to English and the amount of data used in the pretraining phase. Secondly, we find that LLMs' ability to carry out translation instructions relies on the understanding of translation instructions and the alignment among different languages. With multilingual finetuning, LLMs could learn to perform the translation task well even for those language pairs unseen during the instruction tuning phase.
Transformer language models (LMs) are fundamental to NLP research methodologies and applications in various languages. However, developing such models specifically for the Russian language has received little attention. This paper introduces a collection of 13 Russian Transformer LMs, which spans encoder (ruBERT, ruRoBERTa, ruELECTRA), decoder (ruGPT-3), and encoder-decoder (ruT5, FRED-T5) architectures. We provide a report on the model architecture design and pretraining, and the results of evaluating their generalization abilities on Russian language understanding and generation datasets and benchmarks. By pretraining and releasing these specialized Transformer LMs, we aim to broaden the scope of the NLP research directions and enable the development of industrial solutions for the Russian language.
Metadata play a crucial role in ensuring the findability, accessibility, interoperability, and reusability of datasets. This paper investigates the potential of large language models (LLMs), specifically GPT-4, to improve adherence to metadata standards. We conducted experiments on 200 random data records describing human samples relating to lung cancer from the NCBI BioSample repository, evaluating GPT-4's ability to suggest edits for adherence to metadata standards. We computed the adherence accuracy of field name-field value pairs through a peer review process, and we observed a marginal average improvement in adherence to the standard data dictionary from 79% to 80% (p<0.01). We then prompted GPT-4 with domain information in the form of the textual descriptions of CEDAR templates and recorded a significant improvement to 97% from 79% (p<0.01). These results indicate that, while LLMs may not be able to correct legacy metadata to ensure satisfactory adherence to standards when unaided, they do show promise for use in automated metadata curation when integrated with a structured knowledge base.
Generating proofs of unsatisfiability is a valuable capability of most SAT solvers, and is an active area of research for SMT solvers. This paper introduces the first method to efficiently generate proofs of unsatisfiability specifically for an important subset of SMT: SAT Modulo Monotonic Theories (SMMT), which includes many useful finite-domain theories (e.g., bit vectors and many graph-theoretic properties) and is used in production at Amazon Web Services. Our method uses propositional definitions of the theory predicates, from which it generates compact Horn approximations of the definitions, which lead to efficient DRAT proofs, leveraging the large investment the SAT community has made in DRAT. In experiments on practical SMMT problems, our proof generation overhead is minimal (7.41% geometric mean slowdown, 28.8% worst-case), and we can generate and check proofs for many problems that were previously intractable.
We present a new challenge to examine whether large language models understand social norms. In contrast to existing datasets, our dataset requires a fundamental understanding of social norms to solve. Our dataset features the largest set of social norm skills, consisting of 402 skills and 12,383 questions covering a wide set of social norms ranging from opinions and arguments to culture and laws. We design our dataset according to the K-12 curriculum. This enables the direct comparison of the social understanding of large language models to humans, more specifically, elementary students. While prior work generates nearly random accuracy on our benchmark, recent large language models such as GPT3.5-Turbo and LLaMA2-Chat are able to improve the performance significantly, only slightly below human performance. We then propose a multi-agent framework based on large language models to improve the models' ability to understand social norms. This method further improves large language models to be on par with humans. Given the increasing adoption of large language models in real-world applications, our finding is particularly important and presents a unique direction for future improvements.
The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as a discounting parameter. When the discounting parameter is modeled as random, the normalized power prior is recommended. Bayesian hierarchical modeling is a widely used method for synthesizing information from different sources, including historical data. In this work, we examine the analytical relationship between the normalized power prior (NPP) and Bayesian hierarchical models (BHM) for \emph{i.i.d.} normal data. We establish a direct relationship between the prior for the discounting parameter of the NPP and the prior for the variance parameter of the BHM. Such a relationship is first established for the case of a single historical dataset, and then extended to the case with multiple historical datasets with dataset-specific discounting parameters. For multiple historical datasets, we develop and establish theory for the BHM-matching NPP (BNPP) which establishes dependence between the dataset-specific discounting parameters leading to inferences that are identical to the BHM. Establishing this relationship not only justifies the NPP from the perspective of hierarchical modeling, but also provides insight on prior elicitation for the NPP. We present strategies on inducing priors on the discounting parameter based on hierarchical models, and investigate the borrowing properties of the BNPP.
We investigated whether large language models (LLMs) can develop data validation tests. We considered 96 conditions each for both GPT-3.5 and GPT-4, examining different prompt scenarios, learning modes, temperature settings, and roles. The prompt scenarios were: 1) Asking for expectations, 2) Asking for expectations with a given context, 3) Asking for expectations after requesting a data simulation, and 4) Asking for expectations with a provided data sample. The learning modes were: 1) zero-shot, 2) one-shot, and 3) few-shot learning. We also tested four temperature settings: 0, 0.4, 0.6, and 1. And the two distinct roles were: 1) helpful assistant, 2) expert data scientist. To gauge consistency, every setup was tested five times. The LLM-generated responses were benchmarked against a gold standard data validation suite, created by an experienced data scientist knowledgeable about the data in question. We find there are considerable returns to the use of few-shot learning, and that the more explicit the data setting can be the better, to a point. The best LLM configurations complement, rather than substitute, the gold standard results. This study underscores the value LLMs can bring to the data cleaning and preparation stages of the data science workflow, but highlights that they need considerable evaluation by experienced analysts.
In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.
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.
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