Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought. To elicit their reasoning abilities, a prevalent paradigm has been the chainof-thought reasoning approach (Nye et al., 2021; Wei et al., 2022b; Kojima et al., 2022). Under this paradigm, models are trained or prompted to articulate intermediate steps before producing the final answer. Although this approach aligns with human problem-solving strategies, it might not fully leverage the computational potential of these language models. Consider the transformer architecture (Vaswani et al., 2017), which can manifest computation both "horizontally" by generating words in sequence and "vertically" by processing through its many layers of internal hidden states. With models like GPT-3 having as many as 96 layers (Brown et al., 2020), one might wonder: Why not let these models reason internally, "vertically" through their layers, and present the solution without necessarily articulating every intermediate step? Such an approach would not only save the significant time cost of autoregressively generating the chain-of-thought: it may also allow models to develop more efficient, if less human-interpretable, methods of reasoning, unconstrained by human conventions.

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This begs the question: Are these errors incidental, or do they signal more substantial limitations? In an attempt to demystify transformer LLMs, we investigate the limits of these models across three representative compositional tasks -- multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. We formulate compositional tasks as computation graphs to systematically quantify the level of complexity, and break down reasoning steps into intermediate sub-procedures. Our empirical findings suggest that transformer LLMs solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching, without necessarily developing systematic problem-solving skills. To round off our empirical study, we provide theoretical arguments on abstract multi-step reasoning problems that highlight how autoregressive generations' performance can rapidly decay with\,increased\,task\,complexity.

Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs help to tighten relaxations and improve dual bounds. However, running the CGLPs at the nodes of the branch-and-bound tree is computationally cumbersome due to the large number of node candidates and the lack of a priori knowledge on which nodes admit useful cutting planes. As a result, CGLPs are often avoided at default settings of branch-and-cut algorithms despite their potential impact on improving dual bounds. In this paper, we propose a novel framework based on machine learning to approximate the optimal value of a CGLP class that determines whether a cutting plane can be generated at a node of the branch-and-bound tree. Translating the CGLP as an indicator function of the objective function vector, we show that it can be approximated through conventional data classification techniques. We provide a systematic procedure to efficiently generate training data sets for the corresponding classification problem based on the CGLP structure. We conduct computational experiments on benchmark instances using classification methods such as logistic regression. These results suggest that the approximate CGLP obtained from classification can improve the solution time compared to that of conventional cutting plane methods. Our proposed framework can be efficiently applied to a large number of nodes in the branch-and-bound tree to identify the best candidates for adding a cut.

Abstract reasoning is a key ability for an intelligent system. Large language models (LMs) achieve above-chance performance on abstract reasoning tasks, but exhibit many imperfections. However, human abstract reasoning is also imperfect. For example, human reasoning is affected by our real-world knowledge and beliefs, and shows notable "content effects"; humans reason more reliably when the semantic content of a problem supports the correct logical inferences. These content-entangled reasoning patterns play a central role in debates about the fundamental nature of human intelligence. Here, we investigate whether language models $\unicode{x2014}$ whose prior expectations capture some aspects of human knowledge $\unicode{x2014}$ similarly mix content into their answers to logical problems. We explored this question across three logical reasoning tasks: natural language inference, judging the logical validity of syllogisms, and the Wason selection task. We evaluate state of the art large language models, as well as humans, and find that the language models reflect many of the same patterns observed in humans across these tasks $\unicode{x2014}$ like humans, models answer more accurately when the semantic content of a task supports the logical inferences. These parallels are reflected both in answer patterns, and in lower-level features like the relationship between model answer distributions and human response times. Our findings have implications for understanding both these cognitive effects in humans, and the factors that contribute to language model performance.

A key aspect of human intelligence is the ability to imagine -- composing learned concepts in novel ways -- to make sense of new scenarios. Such capacity is not yet attained for machine learning systems. In this work, in the context of visual reasoning, we show how modularity can be leveraged to derive a compositional data augmentation framework inspired by imagination. Our method, denoted Object-centric Compositional Neural Module Network (OC-NMN), decomposes visual generative reasoning tasks into a series of primitives applied to objects without using a domain-specific language. We show that our modular architectural choices can be used to generate new training tasks that lead to better out-of-distribution generalization. We compare our model to existing and new baselines in proposed visual reasoning benchmark that consists of applying arithmetic operations to MNIST digits.

Recent advances in LLMs have revolutionized the landscape of reasoning tasks. To enhance the capabilities of LLMs to emulate human reasoning, prior works focus on modeling reasoning steps using specific thought structures like chains, trees, or graphs. However, LLM-based reasoning continues to encounter three challenges: 1) Selecting appropriate reasoning structures for various tasks; 2) Exploiting known conditions sufficiently and efficiently to deduce new insights; 3) Considering the impact of historical reasoning experience. To address these challenges, we propose DetermLR, a novel reasoning framework that formulates the reasoning process as a transformational journey from indeterminate premises to determinate ones. This process is marked by the incremental accumulation of determinate premises, making the conclusion progressively closer to clarity. DetermLR includes three essential components: 1) Premise identification: We categorize premises into two distinct types: determinate and indeterminate. This empowers LLMs to customize reasoning structures to match the specific task complexities. 2) Premise prioritization and exploration: We leverage quantitative measurements to assess the relevance of each premise to the target, prioritizing more relevant premises for exploring new insights. 3) Iterative process with reasoning memory: We introduce a reasoning memory module to automate storage and extraction of available premises and reasoning paths, preserving historical reasoning details for more accurate premise prioritization. Comprehensive experimental results show that DetermLR outperforms all baselines on four challenging logical reasoning tasks: LogiQA, ProofWriter, FOLIO, and LogicalDeduction. DetermLR can achieve better reasoning performance while requiring fewer visited states, highlighting its superior efficiency and effectiveness in tackling logical reasoning tasks.

Despite rapid progress in Visual question answering (VQA), existing datasets and models mainly focus on testing reasoning in 2D. However, it is important that VQA models also understand the 3D structure of visual scenes, for example to support tasks like navigation or manipulation. This includes an understanding of the 3D object pose, their parts and occlusions. In this work, we introduce the task of 3D-aware VQA, which focuses on challenging questions that require a compositional reasoning over the 3D structure of visual scenes. We address 3D-aware VQA from both the dataset and the model perspective. First, we introduce Super-CLEVR-3D, a compositional reasoning dataset that contains questions about object parts, their 3D poses, and occlusions. Second, we propose PO3D-VQA, a 3D-aware VQA model that marries two powerful ideas: probabilistic neural symbolic program execution for reasoning and deep neural networks with 3D generative representations of objects for robust visual recognition. Our experimental results show our model PO3D-VQA outperforms existing methods significantly, but we still observe a significant performance gap compared to 2D VQA benchmarks, indicating that 3D-aware VQA remains an important open research area.

Robots performing human-scale manipulation tasks require an extensive amount of knowledge about their surroundings in order to perform their actions competently and human-like. In this work, we investigate the use of virtual reality technology as an implementation for robot environment modeling, and present a technique for translating scene graphs into knowledge bases. To this end, we take advantage of the Universal Scene Description (USD) format which is an emerging standard for the authoring, visualization and simulation of complex environments. We investigate the conversion of USD-based environment models into Knowledge Graph (KG) representations that facilitate semantic querying and integration with additional knowledge sources.

Open-ended Commonsense Reasoning is defined as solving a commonsense question without providing 1) a short list of answer candidates and 2) a pre-defined answer scope. Conventional ways of formulating the commonsense question into a question-answering form or utilizing external knowledge to learn retrieval-based methods are less applicable in the open-ended setting due to an inherent challenge. Without pre-defining an answer scope or a few candidates, open-ended commonsense reasoning entails predicting answers by searching over an extremely large searching space. Moreover, most questions require implicit multi-hop reasoning, which presents even more challenges to our problem. In this work, we leverage pre-trained language models to iteratively retrieve reasoning paths on the external knowledge base, which does not require task-specific supervision. The reasoning paths can help to identify the most precise answer to the commonsense question. We conduct experiments on two commonsense benchmark datasets. Compared to other approaches, our proposed method achieves better performance both quantitatively and qualitatively.