Language Models can be Logical Solvers

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

ALLURE: Auditing and Improving LLM-based Evaluation of Text using Iterative In-Context-Learning

From grading papers to summarizing medical documents, large language models (LLMs) are evermore used for evaluation of text generated by humans and AI alike. However, despite their extensive utility, LLMs exhibit distinct failure modes, necessitating a thorough audit and improvement of their text evaluation capabilities. Here we introduce ALLURE, a systematic approach to Auditing Large Language Models Understanding and Reasoning Errors. ALLURE involves comparing LLM-generated evaluations with annotated data, and iteratively incorporating instances of significant deviation into the evaluator, which leverages in-context learning (ICL) to enhance and improve robust evaluation of text by LLMs. Through this iterative process, we refine the performance of the evaluator LLM, ultimately reducing reliance on human annotators in the evaluation process. We anticipate ALLURE to serve diverse applications of LLMs in various domains related to evaluation of textual data, such as medical summarization, education, and and productivity.

Evaluating Cognitive Maps and Planning in Large Language Models with CogEval

Recently an influx of studies claim emergent cognitive abilities in large language models (LLMs). Yet, most rely on anecdotes, overlook contamination of training sets, or lack systematic Evaluation involving multiple tasks, control conditions, multiple iterations, and statistical robustness tests. Here we make two major contributions. First, we propose CogEval, a cognitive science-inspired protocol for the systematic evaluation of cognitive capacities in Large Language Models. The CogEval protocol can be followed for the evaluation of various abilities. Second, here we follow CogEval to systematically evaluate cognitive maps and planning ability across eight LLMs (OpenAI GPT-4, GPT-3.5-turbo-175B, davinci-003-175B, Google Bard, Cohere-xlarge-52.4B, Anthropic Claude-1-52B, LLaMA-13B, and Alpaca-7B). We base our task prompts on human experiments, which offer both established construct validity for evaluating planning, and are absent from LLM training sets. We find that, while LLMs show apparent competence in a few planning tasks with simpler structures, systematic evaluation reveals striking failure modes in planning tasks, including hallucinations of invalid trajectories and getting trapped in loops. These findings do not support the idea of emergent out-of-the-box planning ability in LLMs. This could be because LLMs do not understand the latent relational structures underlying planning problems, known as cognitive maps, and fail at unrolling goal-directed trajectories based on the underlying structure. Implications for application and future directions are discussed.

Fine-Tuning Language Models with Advantage-Induced Policy Alignment

Reinforcement learning from human feedback (RLHF) has emerged as a reliable approach to aligning large language models (LLMs) to human preferences. Among the plethora of RLHF techniques, proximal policy optimization (PPO) is of the most widely used methods. Despite its popularity, however, PPO may suffer from mode collapse, instability, and poor sample efficiency. We show that these issues can be alleviated by a novel algorithm that we refer to as Advantage-Induced Policy Alignment (APA), which leverages a squared error loss function based on the estimated advantages. We demonstrate empirically that APA consistently outperforms PPO in language tasks by a large margin, when a separate reward model is employed as the evaluator. In addition, compared with PPO, APA offers a more stable form of control over the deviation from the model's initial policy, ensuring that the model improves its performance without collapsing to deterministic output. In addition to empirical results, we also provide a theoretical justification supporting the design of our loss function.

Randomized Policy Learning for Continuous State and Action MDPs

Deep reinforcement learning methods have achieved state-of-the-art results in a variety of challenging, high-dimensional domains ranging from video games to locomotion. The key to success has been the use of deep neural networks used to approximate the policy and value function. Yet, substantial tuning of weights is required for good results. We instead use randomized function approximation. Such networks are not only cheaper than training fully connected networks but also improve the numerical performance. We present \texttt{RANDPOL}, a generalized policy iteration algorithm for MDPs with continuous state and action spaces. Both the policy and value functions are represented with randomized networks. We also give finite time guarantees on the performance of the algorithm. Then we show the numerical performance on challenging environments and compare them with deep neural network based algorithms.

Model-free Reinforcement Learning in Infinite-horizon Average-reward Markov Decision Processes

Model-free reinforcement learning is known to be memory and computation efficient and more amendable to large scale problems. In this paper, two model-free algorithms are introduced for learning infinite-horizon average-reward Markov Decision Processes (MDPs). The first algorithm reduces the problem to the discounted-reward version and achieves $\mathcal{O}(T^{2/3})$ regret after $T$ steps, under the minimal assumption of weakly communicating MDPs. The second algorithm makes use of recent advances in adaptive algorithms for adversarial multi-armed bandits and improves the regret to $\mathcal{O}(\sqrt{T})$, albeit with a stronger ergodic assumption. To the best of our knowledge, these are the first model-free algorithms with sub-linear regret (that is polynomial in all parameters) in the infinite-horizon average-reward setting.