Large language models (LLMs) have achieved significant performance in various natural language reasoning tasks. However, they still struggle with performing first-order logic reasoning over formal logical theories expressed in natural language. This is because the previous LLMs-based reasoning systems have the theoretical incompleteness issue. As a result, it can only address a limited set of simple reasoning problems, which significantly decreases their generalization ability. To address this issue, we propose a novel framework, named Generalizable and Faithful Reasoner (GFaiR), which introduces the paradigm of resolution refutation. Resolution refutation has the capability to solve all first-order logic reasoning problems by extending reasoning rules and employing the principle of proof by contradiction, so our system's completeness can be improved by introducing resolution refutation. Experimental results demonstrate that our system outperforms previous works by achieving state-of-the-art performances in complex scenarios while maintaining performances in simple scenarios. Besides, we observe that GFaiR is faithful to its reasoning process.

Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for large language models (LLMs), even though they have demonstrated promising performance in other reasoning tasks. Within this context, some recent studies use programming languages (e.g., Python) to express the necessary logic for solving a given instance/question (e.g., Program-of-Thought) as inspired by their strict and precise syntaxes. However, it is non-trivial to write an executable code that expresses the correct logic on the fly within a single inference call. Also, the code generated specifically for an instance cannot be reused for others, even if they are from the same task and might require identical logic to solve. This paper presents Think-and-Execute, a novel framework that decomposes the reasoning process of language models into two steps. (1) In Think, we discover a task-level logic that is shared across all instances for solving a given task and then express the logic with pseudocode; (2) In Execute, we further tailor the generated pseudocode to each instance and simulate the execution of the code. With extensive experiments on seven algorithmic reasoning tasks, we demonstrate the effectiveness of Think-and-Execute. Our approach better improves LMs' reasoning compared to several strong baselines performing instance-specific reasoning (e.g., CoT and PoT), suggesting the helpfulness of discovering task-level logic. Also, we show that compared to natural language, pseudocode can better guide the reasoning of LMs, even though they are trained to follow natural language instructions.

Language models are rarely shown fruitful mistakes while training. They then struggle to look beyond the next token, suffering from a snowballing of errors and struggling to predict the consequence of their actions several steps ahead. In this paper, we show how language models can be taught to search by representing the process of search in language, as a flattened string -- a stream of search (SoS). We propose a unified language for search that captures an array of different symbolic search strategies. We demonstrate our approach using the simple yet difficult game of Countdown, where the goal is to combine input numbers with arithmetic operations to reach a target number. We pretrain a transformer-based language model from scratch on a dataset of streams of search generated by heuristic solvers. We find that SoS pretraining increases search accuracy by 25% over models trained to predict only the optimal search trajectory. We further finetune this model with two policy improvement methods: Advantage-Induced Policy Alignment (APA) and Self-Taught Reasoner (STaR). The finetuned SoS models solve 36% of previously unsolved problems, including problems that cannot be solved by any of the heuristic solvers. Our results indicate that language models can learn to solve problems via search, self-improve to flexibly use different search strategies, and potentially discover new ones.

Length generalization (LG) is a challenging problem in learning to reason. It refers to the phenomenon that when trained on reasoning problems of smaller lengths or sizes, the resulting model struggles with problems of larger sizes or lengths. Although LG has been studied by many researchers, the challenge remains. This paper proposes a theoretical study of LG for problems whose reasoning processes can be modeled as DAGs (directed acyclic graphs). The paper first identifies and proves the conditions under which LG can be achieved in learning to reason. It then designs problem representations based on the theory to learn to solve challenging reasoning problems like parity, addition, and multiplication, using a Transformer to achieve perfect LG.

With the increasing use of robots in tasks involving humans in the perception-action loop, understanding the reasons behind failures in both planning and execution is a significant challenge for enhancing the reliability, adaptability, and safety of autonomous systems. Robots need to comprehend why and when failures occur and devise appropriate solutions based on the current situation. To achieve this, robots should be equipped with robust planning, perception, and reasoning capabilities enabling them to analyze failures and propose recovery strategies in real time. The standard approaches to autonomous robots are typically model-based or policy-based [3]. Model-based approaches can involve offline planning, where the robot considers the current state and utilizes its model to predict the next state and potential rewards, enabling it to plan a sequence of actions expected to maximize reward. In online model-based planning instead, the robot continuously re-plans based on the current state, adjusting its actions in response to changes in the environment. Policy-based approaches usually entail either open-loop policy, where the robot predicts a sequence of actions based on the initial state and goal, or closed-loop policy, where the robot predicts individual actions at each moment based on the current state and goal.

Conceptual reasoning, the ability to reason in abstract and high-level perspectives, is key to generalization in human cognition. However, limited study has been done on large language models' capability to perform conceptual reasoning. In this work, we bridge this gap and propose a novel conceptualization framework that forces models to perform conceptual reasoning on abstract questions and generate solutions in a verifiable symbolic space. Using this framework as an analytical tool, we show that existing large language models fall short on conceptual reasoning, dropping 9% to 28% on various benchmarks compared to direct inference methods. We then discuss how models can improve since high-level abstract reasoning is key to unbiased and generalizable decision-making. We propose two techniques to add trustworthy induction signals by generating familiar questions with similar underlying reasoning paths and asking models to perform self-refinement. Experiments show that our proposed techniques improve models' conceptual reasoning performance by 8% to 11%, achieving a more robust reasoning system that relies less on inductive biases.

Large language models (LLMs) have demonstrated outstanding performance across various tasks, yet they still exhibit limitations such as hallucination, unfaithful reasoning, and toxic content. One potential approach to mitigate these issues is learning from human or external feedback (e.g. tools). In this paper, we introduce an intrinsic self-correct reasoning framework for LLMs that eliminates the need for human feedback, external tools, and handcraft prompts. The proposed framework, based on a multi-step reasoning paradigm \textbf{Le}arning from \textbf{Co}rrectness (\textsc{LeCo}), improves reasoning performance without needing to learn from errors. This paradigm prioritizes learning from correct reasoning steps, and a unique method to measure confidence for each reasoning step based on generation logits. Experimental results across various multi-step reasoning tasks demonstrate the effectiveness of the framework in improving reasoning performance with reduced token consumption.

Autonomous systems are soon to be ubiquitous, from manufacturing autonomy to agricultural field robots, and from health care assistants to the entertainment industry. The majority of these systems are developed with modular sub-components for decision-making, planning, and control that may be hand-engineered or learning-based. While these existing approaches have been shown to perform well under the situations they were specifically designed for, they can perform especially poorly in rare, out-of-distribution scenarios that will undoubtedly arise at test-time. The rise of foundation models trained on multiple tasks with impressively large datasets from a variety of fields has led researchers to believe that these models may provide common sense reasoning that existing planners are missing. Researchers posit that this common sense reasoning will bridge the gap between algorithm development and deployment to out-of-distribution tasks, like how humans adapt to unexpected scenarios. Large language models have already penetrated the robotics and autonomous systems domains as researchers are scrambling to showcase their potential use cases in deployment. While this application direction is very promising empirically, foundation models are known to hallucinate and generate decisions that may sound reasonable, but are in fact poor. We argue there is a need to step back and simultaneously design systems that can quantify the certainty of a model's decision, and detect when it may be hallucinating. In this work, we discuss the current use cases of foundation models for decision-making tasks, provide a general definition for hallucinations with examples, discuss existing approaches to hallucination detection and mitigation with a focus on decision problems, and explore areas for further research in this exciting field.

Recently, a simple but powerful language for expressing and learning general policies and problem decompositions (sketches) has been introduced in terms of rules defined over a set of Boolean and numerical features. In this work, we consider three extensions of this language aimed at making policies and sketches more flexible and reusable: internal memory states, as in finite state controllers; indexical features, whose values are a function of the state and a number of internal registers that can be loaded with objects; and modules that wrap up policies and sketches and allow them to call each other by passing parameters. In addition, unlike general policies that select state transitions rather than ground actions, the new language allows for the selection of such actions. The expressive power of the resulting language for policies and sketches is illustrated through a number of examples.

We consider the question of what properties a Machine Ethics system should have. This question is complicated by the existence of ethical dilemmas with no agreed upon solution. We provide an example to motivate why we do not believe falling back on the elicitation of values from stakeholders is sufficient to guarantee correctness of such systems. We go on to define two broad categories of ethical property that have arisen in our own work and present a challenge to the community to approach this question in a more systematic way.