However, such "black-box" policies lack interpretability and reliability, and often,

We present a novel framework for training large language models with continuously adjustable internal representations that span the full spectrum from localist (interpretable, rule-based) to distributed (generalizable, efficient) encodings. The key innovation is a locality dial, a tunable parameter that dynamically controls the degree of localization during both training and inference without requiring model retraining. This is achieved through group sparsity penalties on attention mechanisms, information-theoretic anchor design, and dynamic rule injection. We provide rigorous mathematical proofs establishing explicit threshold conditions under which attention provably concentrates on semantically relevant blocks, with exponential bounds on attention entropy and pointer fidelity. Specifically, we prove that when group sparsity penalties exceed certain threshold values, the model's attention mechanisms concentrate on semantically relevant blocks, achieving low entropy and high fidelity with negligible error. This framework enables practitioners to continuously interpolate between interpretable and high-performance modes, supporting applications in regulated domains requiring both transparency and capability.

SOAR, a classic symbol-based cognitive architecture, has been fostering the development of general, human-like intelligent agents. Nevertheless, its practical adoption is hindered by the laborious manual rule coding. Emerging Large Language Models (LLMs) present the immense potential for efficient rules generation. However, there is a critical gap that current research predominantly focuses on conceptual frameworks and lacks robust experimental validation. To bridge this gap, we propose \textit{N}atural \textit{L}anguage to \textit{Gen}erative \textit{Sym}bolic Rules (NL2GenSym), a novel framework that integrates LLMs with SOAR to autonomously produce generative symbolic rules from natural language. Specifically, our framework introduces a novel Execution-Grounded Generator-Critic mechanism. The LLM-based Generator, guided by a Retrieval-Augmented Generation-accessed self-evolving domain knowledge base, proposes rules from natural language. Subsequently, these rules are immediately executed within the SOAR environment to rigorously validate their correctness. Based on this execution-grounded feedback, a reflective LLM-based Critic drives the iterative refinement of these rules. Experiments on our specialized Water Jug Problem (WJP) dataset, utilizing both Gemini and Qwen series models, validate the efficacy of our framework. It achieves a success rate over 86\% in generating rules from natural language. Crucially, the framework also generates novel heuristic rules, reducing average decision cycles for solving the WJP to 1.98 times the optimal solution and 1/1000 of baseline methods. Additionally, our initial experiments show that NL2GenSym enables smaller-parameter models to achieve better performance than larger counterparts.

Recent advances in spectral learning and graph signal processing have enabled powerful techniques for analyzing data defined on irregular domains such as social networks, transportation systems, biological interaction graphs, and linguistic structures [4, 9]. Central to these developments is the use of the graph Laplacian operator, whose eigensystem defines a Fourier-like basis for signals on graphs. This has laid the foundation for spectral filtering, multiscale decomposition, and efficient data representation on non-Euclidean domains. While spectral graph methods have traditionally been explored in a fixed, analytic setting, recent years have seen a resurgence in their application as components of deep learning architectures--such as graph convolutional networks (GCNs) [10], graph attention networks (GATs) [11], and graph transformers [12]. These models often rely on parametric transformations over graph Laplacian eigenspaces or message-passing mechanisms inspired by spectral filters. However, they remain computationally intensive, opaque, and data-hungry--posing challenges in interpretability, robustness, and deployment on low-resource devices.

Recent advancements have highlighted that Large Language Models (LLMs) are prone to hallucinations when solving complex reasoning problems, leading to erroneous results. To tackle this issue, researchers incorporate Knowledge Graphs (KGs) to improve the reasoning ability of LLMs. However, existing methods face two limitations: 1) they typically assume that all answers to the questions are contained in KGs, neglecting the incompleteness issue of KGs, and 2) they treat the KG as a static repository and overlook the implicit logical reasoning structures inherent in KGs. In this paper, we introduce SymAgent, an innovative neural-symbolic agent framework that achieves collaborative augmentation between KGs and LLMs. We conceptualize KGs as dynamic environments and transform complex reasoning tasks into a multi-step interactive process, enabling KGs to participate deeply in the reasoning process. SymAgent consists of two modules: Agent-Planner and Agent-Executor. The Agent-Planner leverages LLM's inductive reasoning capability to extract symbolic rules from KGs, guiding efficient question decomposition. The Agent-Executor autonomously invokes predefined action tools to integrate information from KGs and external documents, addressing the issues of KG incompleteness. Furthermore, we design a self-learning framework comprising online exploration and offline iterative policy updating phases, enabling the agent to automatically synthesize reasoning trajectories and improve performance. Experimental results demonstrate that SymAgent with weak LLM backbones (i.e., 7B series) yields better or comparable performance compared to various strong baselines. Further analysis reveals that our agent can identify missing triples, facilitating automatic KG updates.

Recent advancements in Large Language Models (LLMs) have paved the way for Large Code Models (LCMs), enabling automation in complex software engineering tasks, such as code generation, software testing, and program comprehension, among others. Tools like GitHub Copilot and ChatGPT have shown substantial benefits in supporting developers across various practices. However, the ambition to scale these models to trillion-parameter sizes, exemplified by GPT-4, poses significant challenges that limit the usage of Artificial Intelligence (AI)-based systems powered by large Deep Learning (DL) models. These include rising computational demands for training and deployment and issues related to trustworthiness, bias, and interpretability. Such factors can make managing these models impractical for many organizations, while their "black-box'' nature undermines key aspects, including transparency and accountability. In this paper, we question the prevailing assumption that increasing model parameters is always the optimal path forward, provided there is sufficient new data to learn additional patterns. In particular, we advocate for a Neurosymbolic research direction that combines the strengths of existing DL techniques (e.g., LLMs) with traditional symbolic methods--renowned for their reliability, speed, and determinism. To this end, we outline the core features and present preliminary results for our envisioned approach, aimed at establishing the first Neurosymbolic Program Comprehension (NsPC) framework to aid in identifying defective code components.

Travel demand prediction is crucial for optimizing transportation planning, resource allocation, and infrastructure development, ensuring efficient mobility and economic sustainability. This study introduces a Neurosymbolic Artificial Intelligence (Neurosymbolic AI) framework that integrates decision tree (DT)-based symbolic rules with neural networks (NNs) to predict travel demand, leveraging the interpretability of symbolic reasoning and the predictive power of neural learning. The framework utilizes data from diverse sources, including geospatial, economic, and mobility datasets, to build a comprehensive feature set. DTs are employed to extract interpretable if-then rules that capture key patterns, which are then incorporated as additional features into a NN to enhance its predictive capabilities. Experimental results show that the combined dataset, enriched with symbolic rules, consistently outperforms standalone datasets across multiple evaluation metrics, including Mean Absolute Error (MAE), \(R^2\), and Common Part of Commuters (CPC). Rules selected at finer variance thresholds (e.g., 0.0001) demonstrate superior effectiveness in capturing nuanced relationships, reducing prediction errors, and aligning with observed commuter patterns. By merging symbolic and neural learning paradigms, this Neurosymbolic approach achieves both interpretability and accuracy.

Vision-Language Models (VLM) can support clinicians by analyzing medical images and engaging in natural language interactions to assist in diagnostic and treatment tasks. However, VLMs often exhibit "hallucinogenic" behavior, generating textual outputs not grounded in contextual multimodal information. This challenge is particularly pronounced in the medical domain, where we do not only require VLM outputs to be accurate in single interactions but also to be consistent with clinical reasoning and diagnostic pathways throughout multi-turn conversations. For this purpose, we propose a new alignment algorithm that uses symbolic representations of clinical reasoning to ground VLMs in medical knowledge. These representations are utilized to (i) generate GPT-4-guided visual instruction tuning data at scale, simulating clinician-VLM conversations with demonstrations of clinical reasoning, and (ii) create an automatic reward function that evaluates the clinical validity of VLM generations throughout clinician-VLM interactions. Our algorithm eliminates the need for human involvement in training data generation or reward model construction, reducing costs compared to standard reinforcement learning with human feedback (RLHF). We apply our alignment algorithm to develop Dr-LLaVA, a conversational VLM finetuned for analyzing bone marrow pathology slides, demonstrating strong performance in multi-turn medical conversations.

To improve the explainability of leading Transformer networks used in NLP, it is important to tease apart genuine symbolic rules from merely associative input-output patterns. However, we identify several inconsistencies in how ``symbolicity'' has been construed in recent NLP literature. To mitigate this problem, we propose two criteria to be the most relevant, one pertaining to a system's internal architecture and the other to the dissociation between abstract rules and specific input identities. From this perspective, we critically examine prior work on the symbolic capacities of Transformers, and deem the results to be fundamentally inconclusive for reasons inherent in experiment design. We further maintain that there is no simple fix to this problem, since it arises -- to an extent -- in all end-to-end settings. Nonetheless, we emphasize the need for more robust evaluation of whether non-symbolic explanations exist for success in seemingly symbolic tasks. To facilitate this, we experiment on four sequence modelling tasks on the T5 Transformer in two experiment settings: zero-shot generalization, and generalization across class-specific vocabularies flipped between the training and test set. We observe that T5's generalization is markedly stronger in sequence-to-sequence tasks than in comparable classification tasks. Based on this, we propose a thus far overlooked analysis, where the Transformer itself does not need to be symbolic to be part of a symbolic architecture as the processor, operating on the input and output as external memory components.