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Mathematical reasoning demands two critical, complementary skills: constructing rigorous proofs for true statements and discovering counterexamples that disprove false ones. However, current AI efforts in mathematics focus almost…

Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…

We propose a method to teach multiple large language models (LLM) to collaborate by interleaving their generations at the token level. We model the decision of which LLM generates the next token as a latent variable. By optimizing the…

Retrieving and extracting knowledge from extensive research documents and large databases presents significant challenges for researchers, students, and professionals in today's information-rich era. Existing retrieval systems, which rely…

Recent works have shown that Large Language Models (LLMs) could empower traditional neuro-symbolic models via programming capabilities to translate language into module descriptions, thus achieving strong visual reasoning results while…

As one of their many applications, large language models (LLMs) have recently shown promise in automating register transfer level (RTL) code generation. However, conventional LLM decoding strategies, originally designed for natural…

Large language models (LLMs) struggle with formal domains that require rigorous logical deduction and symbolic reasoning, such as mathematical proof generation. We propose a neuro-symbolic approach that combines LLMs' generative strengths…

Reflection is widely recognized as a cornerstone of student development, fostering critical thinking, self-regulation, and deep conceptual understanding. Traditionally, reflective skills have been cultivated through structured feedback,…

Large language models (LLMs) excel at processing and generating both text and code. However, LLMs have had limited applicability in grounded task-oriented dialogue as they are difficult to steer toward task objectives and fail to handle…

The rapid expansion of English technical terminology presents a significant challenge to traditional expert-based standardization, particularly in rapidly developing areas such as artificial intelligence and quantum computing. Manual…

Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…

The integration of visual inputs with large language models (LLMs) has led to remarkable advancements in multi-modal capabilities, giving rise to visual large language models (VLLMs). However, effectively harnessing VLLMs for intricate…

Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic…

Generative cross-modal retrieval, which treats retrieval as a generation task, has emerged as a promising direction with the rise of Multimodal Large Language Models (MLLMs). In this setting, the model responds to a text query by generating…

Knowledge retrieval with multi-modal queries plays a crucial role in supporting knowledge-intensive multi-modal applications. However, existing methods face challenges in terms of their effectiveness and training efficiency, especially when…

Large decoder-only language models (LLMs) have achieved remarkable success in generation and reasoning tasks, where they generate text responses given instructions. However, many applications, e.g., retrieval augmented generation (RAG),…

Large Language Models (LLMs) for complex reasoning is often hindered by high computational costs and latency, while resource-efficient Small Language Models (SLMs) typically lack the necessary reasoning capacity. Existing collaborative…

Linguistic steganography provides convenient implementation to hide messages, particularly with the emergence of AI generation technology. The potential abuse of this technology raises security concerns within societies, calling for…

Large language models (LLMs) are introducing a paradigm shift in molecular discovery by enabling text-guided interaction with chemical spaces through natural language, symbolic notations, with emerging extensions to incorporate multi-modal…

Scientific software relies on high-precision computation, yet finite floating-point representations can introduce precision errors that propagate in safety-critical domains. Despite the growing use of large language models (LLMs) in…