Querying knowledge graphs (KGs) using deep learning approaches can naturally leverage the reasoning and generalization ability to learn to infer better answers. Traditional neural complex query answering (CQA) approaches mostly work on entity-centric KGs. However, in the real world, we also need to make logical inferences about events, states, and activities (i.e., eventualities or situations) to push learning systems from System I to System II, as proposed by Yoshua Bengio. Querying logically from an EVentuality-centric KG (EVKG) can naturally provide references to such kind of intuitive and logical inference. Thus, in this paper, we propose a new framework to leverage neural methods to answer complex logical queries based on an EVKG, which can satisfy not only traditional first-order logic constraints but also implicit logical constraints over eventualities concerning their occurrences and orders. For instance, if we know that happens before, then is unlikely to be the cause of due to implicit temporal constraint. To facilitate consistent reasoning on EVKGs, we propose Complex Eventuality Query Answering (CEQA), a more rigorous definition of CQA that considers the implicit logical constraints governing the temporal order and occurrence of eventualities. In this manner, we propose to leverage theorem provers for constructing benchmark datasets to ensure the answers satisfy implicit logical constraints. We also propose a Memory-Enhanced Query Encoding (MEQE) approach to significantly improve the performance of state-of-the-art neural query encoders on the CEQA task.

Recent advancements in Chain of Thought (COT) generation have significantly improved the reasoning capabilities of Large Language Models (LLMs), with reinforcement learning (RL) emerging as an effective post-training approach. Multimodal Large Language Models (MLLMs) inherit this reasoning potential but remain underexplored in tasks requiring both perception and logical reasoning. To address this, we introduce SEED-Bench-R1, a benchmark designed to systematically evaluate post-training methods for MLLMs in video understanding. It includes intricate real-world videos and complex everyday planning tasks in the format of multiple-choice questions, requiring sophisticated perception and reasoning. SEED-Bench-R1 assesses generalization through a three-level hierarchy: in-distribution, cross-environment, and cross-environment-task scenarios, equipped with a large-scale training dataset with easily verifiable ground-truth answers. Using Qwen2-VL-Instruct-7B as a base model, we compare RL with supervised fine-tuning (SFT), demonstrating RL's data efficiency and superior performance on both in-distribution and out-of-distribution tasks, even outperforming SFT on general video understanding benchmarks like LongVideoBench. Our detailed analysis reveals that RL enhances visual perception but often produces less logically coherent reasoning chains. We identify key limitations such as inconsistent reasoning and overlooked visual cues, and suggest future improvements in base model reasoning, reward modeling, and RL robustness against noisy signals.

Neural networks, as currently designed, fall short of achieving true logical intelligence. Modern AI models rely on standard neural computation-inner-product-based transformations and nonlinear activations-to approximate patterns from data. While effective for inductive learning, this architecture lacks the structural guarantees necessary for deductive inference and logical consistency. As a result, deep networks struggle with rule-based reasoning, structured generalization, and interpretability without extensive post-hoc modifications. This position paper argues that standard neural layers must be fundamentally rethought to integrate logical reasoning. We advocate for Logical Neural Units (LNUs)-modular components that embed differentiable approximations of logical operations (e.g., AND, OR, NOT) directly within neural architectures. We critique existing neurosymbolic approaches, highlight the limitations of standard neural computation for logical inference, and present LNUs as a necessary paradigm shift in AI. Finally, we outline a roadmap for implementation, discussing theoretical foundations, architectural integration, and key challenges for future research.

Querying knowledge graphs (KGs) using deep learning approaches can naturally leverage the reasoning and generalization ability to learn to infer better answers. Traditional neural complex query answering (CQA) approaches mostly work on entity-centric KGs. However, in the real world, we also need to make logical inferences about events, states, and activities (i.e., eventualities or situations) to push learning systems from System I to System II, as proposed by Yoshua Bengio. Querying logically from an EVentuality-centric KG (EVKG) can naturally provide references to such kind of intuitive and logical inference. Thus, in this paper, we propose a new framework to leverage neural methods to answer complex logical queries based on an EVKG, which can satisfy not only traditional first-order logic constraints but also implicit logical constraints over eventualities concerning their occurrences and orders. For instance, if we know that Food is bad happens before PersonX adds soy sauce, then PersonX adds soy sauce is unlikely to be the cause of Food is bad due to implicit temporal constraint.

In this paper we propose that a restricted version of logical inference can be implemented with self-attention networks. We are aiming at showing that LLMs (Large Language Models) constructed with transformer networks can make logical inferences. We would reveal the potential of LLMs by analyzing self-attention networks, which are main components of transformer networks. Our approach is not based on semantics of natural languages but operations of logical inference. %point of view. We show that hierarchical constructions of self-attention networks with feed forward networks (FFNs) can implement top-down derivations for a class of logical formulae. We also show bottom-up derivations are also implemented for the same class. We believe that our results show that LLMs implicitly have the power of logical inference.

As LLMs become increasingly prevalent across various applications, it is critical to establish safety guardrails to moderate input/output content of LLMs. Existing guardrail models treat various safety categories independently and fail to explicitly capture the intercorrelations among them. This has led to limitations such as ineffectiveness due to inadequate training on long-tail data from correlated safety categories, susceptibility to jailbreaking attacks, and inflexibility regarding new safety categories. To address these limitations, we propose $R^2$-Guard, a robust reasoning enabled LLM guardrail via knowledge-enhanced logical reasoning. Specifically, $R^2$-Guard comprises two parts: data-driven category-specific learning and reasoning components. The data-driven guardrail models provide unsafety probabilities of moderated content on different safety categories. We then encode safety knowledge among different categories as first-order logical rules and embed them into a probabilistic graphic model (PGM) based reasoning component. The unsafety probabilities of different categories from data-driven guardrail models are sent to the reasoning component for final inference. We employ two types of PGMs: Markov logic networks (MLNs) and probabilistic circuits (PCs), and optimize PCs to achieve precision-efficiency balance via improved graph structure. To further perform stress tests for guardrail models, we employ a pairwise construction method to construct a new safety benchmark TwinSafety, which features principled categories. We demonstrate the effectiveness of $R^2$-Guard by comparisons with eight strong guardrail models on six safety benchmarks, and demonstrate the robustness of $R^2$-Guard against four SOTA jailbreaking attacks. $R^2$-Guard significantly surpasses SOTA method LlamaGuard by 30.2% on ToxicChat and by 59.5% against jailbreaking attacks.

The reasoning performance of Large Language Models (LLMs) on a wide range of problems critically relies on chain-of-thought prompting, which involves providing a few chain of thought demonstrations as exemplars in prompts. Recent work, e.g., Tree of Thoughts, has pointed out the importance of exploration and self-evaluation in reasoning step selection for complex problem solving. In this paper, we present Boosting of Thoughts (BoT), an automated prompting framework for problem solving with LLMs by iteratively exploring and self-evaluating many trees of thoughts in order to acquire an ensemble of trial-and-error reasoning experiences, which will serve as a new form of prompting to solve the complex problem. Starting from a simple prompt without requiring examples, BoT iteratively explores and evaluates a large collection of reasoning steps, and more importantly, uses error analysis obtained from the LLM on them to explicitly revise prompting, which in turn enhances reasoning step generation, until a final answer is attained. Our experiments with GPT-4 and Llama2 across extensive complex mathematical problems demonstrate that BoT consistently achieves higher or comparable problem-solving rates than other advanced prompting approaches.

This paper investigates whether current large language models exhibit biases in logical reasoning, similar to humans. Specifically, we focus on syllogistic reasoning, a well-studied form of inference in the cognitive science of human deduction. To facilitate our analysis, we introduce a dataset called NeuBAROCO, originally designed for psychological experiments that assess human logical abilities in syllogistic reasoning. The dataset consists of syllogistic inferences in both English and Japanese. We examine three types of biases observed in human syllogistic reasoning: belief biases, conversion errors, and atmosphere effects. Our findings demonstrate that current large language models struggle more with problems involving these three types of biases.

Automatic programming has been actively studied for a long time by various approaches including genetic programming. In recent years, automatic programming using neural networks such as GPT-3 has been actively studied and is attracting a lot of attention. However, these methods are illogical inference based on experience by enormous learning, and their thinking process is unclear. Even using the method by logical inference with a clear thinking process, the system that automatically generates any programs has not yet been realized. Especially, the inductive inference generalized by logical inference from one example is an important issue that the artificial intelligence can acquire knowledge by itself. In this study, we propose NP4G: Network Programming for Generalization, which can automatically generate programs by inductive inference. Because the proposed method can realize "sequence", "selection", and "iteration" in programming and can satisfy the conditions of the structured program theorem, it is expected that NP4G is a method automatically acquire any programs by inductive inference. As an example, we automatically construct a bitwise NOT operation program from several training data by generalization using NP4G. Although NP4G only randomly selects and connects nodes, by adjusting the number of nodes and the number of phase of "Phased Learning", we show the bitwise NOT operation programs are acquired in a comparatively short time and at a rate of about 7 in 10 running. The source code of NP4G is available on GitHub as a public repository.

Large language models have been shown to achieve remarkable performance across a variety of natural language tasks using few-shot learning, which drastically reduces the number of task-specific training examples needed to adapt the model to a particular application. To further our understanding of the impact of scale on few-shot learning, we trained a 540-billion parameter, densely activated, Transformer language model, which we call Pathways Language Model PaLM. We trained PaLM on 6144 TPU v4 chips using Pathways, a new ML system which enables highly efficient training across multiple TPU Pods. We demonstrate continued benefits of scaling by achieving state-of-the-art few-shot learning results on hundreds of language understanding and generation benchmarks. On a number of these tasks, PaLM 540B achieves breakthrough performance, outperforming the finetuned state-of-the-art on a suite of multi-step reasoning tasks, and outperforming average human performance on the recently released BIG-bench benchmark. A significant number of BIG-bench tasks showed discontinuous improvements from model scale, meaning that performance steeply increased as we scaled to our largest model. PaLM also has strong capabilities in multilingual tasks and source code generation, which we demonstrate on a wide array of benchmarks. We additionally provide a comprehensive analysis on bias and toxicity, and study the extent of training data memorization with respect to model scale. Finally, we discuss the ethical considerations related to large language models and discuss potential mitigation strategies.