Dspy-based Neural-Symbolic Pipeline to Enhance Spatial Reasoning in LLMs

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks, yet they often struggle with spatial reasoning. This paper presents a novel neural-symbolic framework that enhances LLMs' spatial reasoning abilities through iterative feedback between LLMs and Answer Set Programming (ASP). We evaluate our approach on two benchmark datasets: StepGame and SparQA, implementing three distinct strategies: (1) direct prompting baseline, (2) Facts+Rules prompting, and (3) DSPy-based LLM+ASP pipeline with iterative refinement. Our experimental results demonstrate that the LLM+ASP pipeline significantly outperforms baseline methods, achieving an average 82% accuracy on StepGame and 69% on SparQA, marking improvements of 40-50% and 8-15% respectively over direct prompting. The success stems from three key innovations: (1) effective separation of semantic parsing and logical reasoning through a modular pipeline, (2) iterative feedback mechanism between LLMs and ASP solvers that improves program rate, and (3) robust error handling that addresses parsing, grounding, and solving failures. Additionally, we propose Facts+Rules as a lightweight alternative that achieves comparable performance on complex SparQA dataset, while reducing computational overhead.Our analysis across different LLM architectures (Deepseek, Llama3-70B, GPT-4.0 mini) demonstrates the framework's generalizability and provides insights into the trade-offs between implementation complexity and reasoning capability, contributing to the development of more interpretable and reliable AI systems.

A Pipeline of Neural-Symbolic Integration to Enhance Spatial Reasoning in Large Language Models

Large Language Models (LLMs) have demonstrated impressive capabilities across various tasks. However, LLMs often struggle with spatial reasoning which is one essential part of reasoning and inference and requires understanding complex relationships between objects in space. This paper proposes a novel neural-symbolic framework that enhances LLMs' spatial reasoning abilities. We evaluate our approach on two benchmark datasets: StepGame and SparQA, implementing three distinct strategies: (1) ASP (Answer Set Programming)-based symbolic reasoning, (2) LLM + ASP pipeline using DSPy, and (3) Fact + Logical rules. Our experiments demonstrate significant improvements over the baseline prompting methods, with accuracy increases of 40-50% on StepGame} dataset and 3-13% on the more complex SparQA dataset. The "LLM + ASP" pipeline achieves particularly strong results on the tasks of Finding Relations (FR) and Finding Block (FB) questions, though performance varies across different question types. The impressive results suggest that while neural-symbolic approaches offer promising directions for enhancing spatial reasoning in LLMs, their effectiveness depends heavily on the specific task characteristics and implementation strategies. We propose an integrated, simple yet effective set of strategies using a neural-symbolic pipeline to boost spatial reasoning abilities in LLMs. This pipeline and its strategies demonstrate strong and broader applicability to other reasoning domains in LLMs, such as temporal reasoning, deductive inference etc.

Fast Semi-supervised Learning on Large Graphs: An Improved Green-function Method

In the graph-based semi-supervised learning, the Green-function method is a classical method that works by computing the Green's function in the graph space. However, when applied to large graphs, especially those sparse ones, this method performs unstably and unsatisfactorily. We make a detailed analysis on it and propose a novel method from the perspective of optimization. On fully connected graphs, the method is equivalent to the Green-function method and can be seen as another interpretation with physical meanings, while on non-fully connected graphs, it helps to explain why the Green-function method causes a mess on large sparse graphs. To solve this dilemma, we propose a workable approach to improve our proposed method. Unlike the original method, our improved method can also apply two accelerating techniques, Gaussian Elimination, and Anchored Graphs to become more efficient on large graphs. Finally, the extensive experiments prove our conclusions and the efficiency, accuracy, and stability of our improved Green's function method.

Clustering Based on Density Propagation and Subcluster Merging

We propose the DPSM method, a density-based node clustering approach that automatically determines the number of clusters and can be applied in both data space and graph space. Unlike traditional density-based clustering methods, which necessitate calculating the distance between any two nodes, our proposed technique determines density through a propagation process, thereby making it suitable for a graph space. In DPSM, nodes are partitioned into small clusters based on propagated density. The partitioning technique has been proved to be sound and complete. We then extend the concept of spectral clustering from individual nodes to these small clusters, while introducing the CluCut measure to guide cluster merging. This measure is modified in various ways to account for cluster properties, thus provides guidance on when to terminate the merging process. Various experiments have validated the effectiveness of DOSM and the accuracy of these conclusions.

The Roles of Contextual Semantic Relevance Metrics in Human Visual Processing

Semantic relevance metrics can capture both the inherent semantics of individual objects and their relationships to other elements within a visual scene. Numerous previous research has demonstrated that these metrics can influence human visual processing. However, these studies often did not fully account for contextual information or employ the recent deep learning models for more accurate computation. This study investigates human visual perception and processing by introducing the metrics of contextual semantic relevance. We evaluate semantic relationships between target objects and their surroundings from both vision-based and language-based perspectives. Testing a large eye-movement dataset from visual comprehension, we employ state-of-the-art deep learning techniques to compute these metrics and analyze their impacts on fixation measures on human visual processing through advanced statistical models. These metrics could also simulate top-down and bottom-up processing in visual perception. This study further integrates vision-based and language-based metrics into a novel combined metric, addressing a critical gap in previous research that often treated visual and semantic similarities separately. Results indicate that all metrics could precisely predict fixation measures in visual perception and processing, but with distinct roles in prediction. The combined metric outperforms other metrics, supporting theories that emphasize the interaction between semantic and visual information in shaping visual perception/processing. This finding aligns with growing recognition of the importance of multi-modal information processing in human cognition. These insights enhance our understanding of cognitive mechanisms underlying visual processing and have implications for developing more accurate computational models in fields such as cognitive science and human-computer interaction.

FAST-LIVO2: Fast, Direct LiDAR-Inertial-Visual Odometry

This paper proposes FAST-LIVO2: a fast, direct LiDAR-inertial-visual odometry framework to achieve accurate and robust state estimation in SLAM tasks and provide great potential in real-time, onboard robotic applications. FAST-LIVO2 fuses the IMU, LiDAR and image measurements efficiently through an ESIKF. To address the dimension mismatch between the heterogeneous LiDAR and image measurements, we use a sequential update strategy in the Kalman filter. To enhance the efficiency, we use direct methods for both the visual and LiDAR fusion, where the LiDAR module registers raw points without extracting edge or plane features and the visual module minimizes direct photometric errors without extracting ORB or FAST corner features. The fusion of both visual and LiDAR measurements is based on a single unified voxel map where the LiDAR module constructs the geometric structure for registering new LiDAR scans and the visual module attaches image patches to the LiDAR points. To enhance the accuracy of image alignment, we use plane priors from the LiDAR points in the voxel map (and even refine the plane prior) and update the reference patch dynamically after new images are aligned. Furthermore, to enhance the robustness of image alignment, FAST-LIVO2 employs an on-demanding raycast operation and estimates the image exposure time in real time. Lastly, we detail three applications of FAST-LIVO2: UAV onboard navigation demonstrating the system's computation efficiency for real-time onboard navigation, airborne mapping showcasing the system's mapping accuracy, and 3D model rendering (mesh-based and NeRF-based) underscoring the suitability of our reconstructed dense map for subsequent rendering tasks. We open source our code, dataset and application on GitHub to benefit the robotics community.

Multi-Task Curriculum Graph Contrastive Learning with Clustering Entropy Guidance

Recent advances in unsupervised deep graph clustering have been significantly promoted by contrastive learning. Despite the strides, most graph contrastive learning models face challenges: 1) graph augmentation is used to improve learning diversity, but commonly used random augmentation methods may destroy inherent semantics and cause noise; 2) the fixed positive and negative sample selection strategy is limited to deal with complex real data, thereby impeding the model's capability to capture fine-grained patterns and relationships. To reduce these problems, we propose the Clustering-guided Curriculum Graph contrastive Learning (CCGL) framework. CCGL uses clustering entropy as the guidance of the following graph augmentation and contrastive learning. Specifically, according to the clustering entropy, the intra-class edges and important features are emphasized in augmentation. Then, a multi-task curriculum learning scheme is proposed, which employs the clustering guidance to shift the focus from the discrimination task to the clustering task. In this way, the sample selection strategy of contrastive learning can be adjusted adaptively from early to late stage, which enhances the model's flexibility for complex data structure. Experimental results demonstrate that CCGL has achieved excellent performance compared to state-of-the-art competitors.

Doubly Stochastic Adaptive Neighbors Clustering via the Marcus Mapping

Clustering is a fundamental task in machine learning and data science, and similarity graph-based clustering is an important approach within this domain. Doubly stochastic symmetric similarity graphs provide numerous benefits for clustering problems and downstream tasks, yet learning such graphs remains a significant challenge. Marcus theorem states that a strictly positive symmetric matrix can be transformed into a doubly stochastic symmetric matrix by diagonal matrices. However, in clustering, learning sparse matrices is crucial for computational efficiency. We extend Marcus theorem by proposing the Marcus mapping, which indicates that certain sparse matrices can also be transformed into doubly stochastic symmetric matrices via diagonal matrices. Additionally, we introduce rank constraints into the clustering problem and propose the Doubly Stochastic Adaptive Neighbors Clustering algorithm based on the Marcus Mapping (ANCMM). This ensures that the learned graph naturally divides into the desired number of clusters. We validate the effectiveness of our algorithm through extensive comparisons with state-of-the-art algorithms. Finally, we explore the relationship between the Marcus mapping and optimal transport. We prove that the Marcus mapping solves a specific type of optimal transport problem and demonstrate that solving this problem through Marcus mapping is more efficient than directly applying optimal transport methods.

Achieving More with Less: A Tensor-Optimization-Powered Ensemble Method

Ensemble learning is a method that leverages weak learners to produce a strong learner. However, obtaining a large number of base learners requires substantial time and computational resources. Therefore, it is meaningful to study how to achieve the performance typically obtained with many base learners using only a few. We argue that to achieve this, it is essential to enhance both classification performance and generalization ability during the ensemble process. To increase model accuracy, each weak base learner needs to be more efficiently integrated. It is observed that different base learners exhibit varying levels of accuracy in predicting different classes. To capitalize on this, we introduce confidence tensors $\tilde{\mathbf{\Theta}}$ and $\tilde{\mathbf{\Theta}}_{rst}$ signifies that the $t$-th base classifier assigns the sample to class $r$ while it actually belongs to class $s$. To the best of our knowledge, this is the first time an evaluation of the performance of base classifiers across different classes has been proposed. The proposed confidence tensor compensates for the strengths and weaknesses of each base classifier in different classes, enabling the method to achieve superior results with a smaller number of base learners. To enhance generalization performance, we design a smooth and convex objective function that leverages the concept of margin, making the strong learner more discriminative. Furthermore, it is proved that in gradient matrix of the loss function, the sum of each column's elements is zero, allowing us to solve a constrained optimization problem using gradient-based methods. We then compare our algorithm with random forests of ten times the size and other classical methods across numerous datasets, demonstrating the superiority of our approach.

A Novel Dependency Framework for Enhancing Discourse Data Analysis

The development of different theories of discourse structure has led to the establishment of discourse corpora based on these theories. However, the existence of discourse corpora established on different theoretical bases creates challenges when it comes to exploring them in a consistent and cohesive way. This study has as its primary focus the conversion of PDTB annotations into dependency structures. It employs refined BERT-based discourse parsers to test the validity of the dependency data derived from the PDTB-style corpora in English, Chinese, and several other languages. By converting both PDTB and RST annotations for the same texts into dependencies, this study also applies ``dependency distance'' metrics to examine the correlation between RST dependencies and PDTB dependencies in English. The results show that the PDTB dependency data is valid and that there is a strong correlation between the two types of dependency distance. This study presents a comprehensive approach for analyzing and evaluating discourse corpora by employing discourse dependencies to achieve unified analysis. By applying dependency representations, we can extract data from PDTB, RST, and SDRT corpora in a coherent and unified manner. Moreover, the cross-linguistic validation establishes the framework's generalizability beyond English. The establishment of this comprehensive dependency framework overcomes limitations of existing discourse corpora, supporting a diverse range of algorithms and facilitating further studies in computational discourse analysis and language sciences.