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Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-quality text or computer code. For many professions, LLMs represent an invaluable tool that can speed up and improve the quality of work. In this note, we discuss to what extent they can aid professional mathematicians. We first provide a mathematical description of the transformer model used in all modern language models. Based on recent studies, we then outline best practices and potential issues and report on the mathematical abilities of language models. Finally, we shed light on the potential of LMMs to change how mathematicians work.

As language models (LMs) advance, interest is growing in applying them to high-stakes societal decisions, such as determining financing or housing eligibility. However, their potential for discrimination in such contexts raises ethical concerns, motivating the need for better methods to evaluate these risks. We present a method for proactively evaluating the potential discriminatory impact of LMs in a wide range of use cases, including hypothetical use cases where they have not yet been deployed. Specifically, we use an LM to generate a wide array of potential prompts that decision-makers may input into an LM, spanning 70 diverse decision scenarios across society, and systematically vary the demographic information in each prompt. Applying this methodology reveals patterns of both positive and negative discrimination in the Claude 2.0 model in select settings when no interventions are applied. While we do not endorse or permit the use of language models to make automated decisions for the high-risk use cases we study, we demonstrate techniques to significantly decrease both positive and negative discrimination through careful prompt engineering, providing pathways toward safer deployment in use cases where they may be appropriate. Our work enables developers and policymakers to anticipate, measure, and address discrimination as language model capabilities and applications continue to expand. We release our dataset and prompts at //huggingface.co/datasets/Anthropic/discrim-eval

Reasoning is a fundamental capability of AI agents. Recently, large language models (LLMs) have shown remarkable abilities to perform reasoning tasks. However, numerous evaluations of the reasoning capabilities of LLMs have also showed some limitations. An outstanding limitation is length generalization, meaning that when trained on reasoning problems of smaller lengths or sizes, the resulting models struggle with problems of larger sizes or lengths. This potentially indicates some theoretical limitations of generalization in learning reasoning skills. These evaluations and their observations motivated us to perform a theoretical study of the length generalization problem. This work focuses on reasoning tasks that can be formulated as Markov dynamic processes (MDPs) and/or directed acyclic graphs (DAGs). It identifies and proves conditions that decide whether the length generalization problem can be solved or not for a reasoning task in a particular representation. Experiments are also conducted to verify the theoretical results.

While large language models (LLMs) have demonstrated impressive performance on a range of decision-making tasks, they rely on simple acting processes and fall short of broad deployment as autonomous agents. We introduce LATS (Language Agent Tree Search), a general framework that synergizes the capabilities of LLMs in planning, acting, and reasoning. Drawing inspiration from Monte Carlo tree search in model-based reinforcement learning, LATS employs LLMs as agents, value functions, and optimizers, repurposing their latent strengths for enhanced decision-making. What is crucial in this method is the use of an environment for external feedback, which offers a more deliberate and adaptive problem-solving mechanism that moves beyond the limitations of existing techniques. Our experimental evaluation across diverse domains, such as programming, HotPotQA, and WebShop, illustrates the applicability of LATS for both reasoning and acting. In particular, LATS achieves 94.4% for programming on HumanEval with GPT-4 and an average score of 75.9 for web browsing on WebShop with GPT-3.5, demonstrating the effectiveness and generality of our method.

The ability to generate SQL queries from natural language has significant implications for making data accessible to non-specialists. This paper presents a novel approach to fine-tuning open-source large language models (LLMs) for the task of transforming natural language into SQL queries within the retail domain. We introduce models specialized in generating SQL queries, trained on synthetic datasets tailored to the Snowflake SQL and GoogleSQL dialects. Our methodology involves generating a context-specific dataset using GPT-4, then fine-tuning three open-source LLMs(Starcoder Plus, Code-Llama, and Mistral) employing the LoRa technique to optimize for resource constraints. The fine-tuned models demonstrate superior performance in zero-shot settings compared to the baseline GPT-4, with Code-Llama achieving the highest accuracy rates, at 81.58% for Snowflake SQL and 82.66% for GoogleSQL. These results underscore the effectiveness of fine-tuning LLMs on domain-specific tasks and suggest a promising direction for enhancing the accessibility of relational databases through natural language interfaces.

Large language models (LLMs) have demonstrated impressive capabilities in natural language processing. However, their internal mechanisms are still unclear and this lack of transparency poses unwanted risks for downstream applications. Therefore, understanding and explaining these models is crucial for elucidating their behaviors, limitations, and social impacts. In this paper, we introduce a taxonomy of explainability techniques and provide a structured overview of methods for explaining Transformer-based language models. We categorize techniques based on the training paradigms of LLMs: traditional fine-tuning-based paradigm and prompting-based paradigm. For each paradigm, we summarize the goals and dominant approaches for generating local explanations of individual predictions and global explanations of overall model knowledge. We also discuss metrics for evaluating generated explanations, and discuss how explanations can be leveraged to debug models and improve performance. Lastly, we examine key challenges and emerging opportunities for explanation techniques in the era of LLMs in comparison to conventional machine learning models.

The emergence of large language models (LLMs) has substantially influenced natural language processing, demonstrating exceptional results across various tasks. In this study, we employ ``Introspective Tips" to facilitate LLMs in self-optimizing their decision-making. By introspectively examining trajectories, LLM refines its policy by generating succinct and valuable tips. Our method enhances the agent's performance in both few-shot and zero-shot learning situations by considering three essential scenarios: learning from the agent's past experiences, integrating expert demonstrations, and generalizing across diverse games. Importantly, we accomplish these improvements without fine-tuning the LLM parameters; rather, we adjust the prompt to generalize insights from the three aforementioned situations. Our framework not only supports but also emphasizes the advantage of employing LLM in in-contxt decision-making. Experiments involving over 100 games in TextWorld illustrate the superior performance of our approach.

Transformer-based pretrained language models (T-PTLMs) have achieved great success in almost every NLP task. The evolution of these models started with GPT and BERT. These models are built on the top of transformers, self-supervised learning and transfer learning. Transformed-based PTLMs learn universal language representations from large volumes of text data using self-supervised learning and transfer this knowledge to downstream tasks. These models provide good background knowledge to downstream tasks which avoids training of downstream models from scratch. In this comprehensive survey paper, we initially give a brief overview of self-supervised learning. Next, we explain various core concepts like pretraining, pretraining methods, pretraining tasks, embeddings and downstream adaptation methods. Next, we present a new taxonomy of T-PTLMs and then give brief overview of various benchmarks including both intrinsic and extrinsic. We present a summary of various useful libraries to work with T-PTLMs. Finally, we highlight some of the future research directions which will further improve these models. We strongly believe that this comprehensive survey paper will serve as a good reference to learn the core concepts as well as to stay updated with the recent happenings in T-PTLMs.

External knowledge is often useful for natural language understanding tasks. We introduce a contextual text representation model called Conceptual-Contextual (CC) embeddings, which incorporates structured knowledge into text representations. Unlike entity embedding methods, our approach encodes a knowledge graph into a context model. CC embeddings can be easily reused for a wide range of tasks just like pre-trained language models. Our model effectively encodes the huge UMLS database by leveraging semantic generalizability. Experiments on electronic health records (EHRs) and medical text processing benchmarks showed our model gives a major boost to the performance of supervised medical NLP tasks.

External knowledge is often useful for natural language understanding tasks. We introduce a contextual text representation model called Conceptual-Contextual (CC) embeddings, which incorporates structured knowledge into text representations. Unlike entity embedding methods, our approach encodes a knowledge graph into a context model. CC embeddings can be easily reused for a wide range of tasks just like pre-trained language models. Our model effectively encodes the huge UMLS database by leveraging semantic generalizability. Experiments on electronic health records (EHRs) and medical text processing benchmarks showed our model gives a major boost to the performance of supervised medical NLP tasks.