The rapid development of artificial intelligence (AI), marked by breakthroughs like 'AlphaEvolve' and 'Gemini Deep Think', is beginning to offer powerful new tools that have the potential to significantly alter the research practice in many areas of mathematics. This paper explores the current landscape of publicly accessible large language models (LLMs) in a mathematical research context, based on developments up to August 2, 2025. Our analysis of recent benchmarks, such as MathArena and the Open Proof Corpus (Balunović et al., 2025; Dekoninck et al., 2025), reveals a complex duality: while state-of-the-art models demonstrate strong abilities in solving problems and evaluating proofs, they also exhibit systematic flaws, including a lack of self-critique and a model depending discrepancy between final-answer accuracy and full-proof validity. Based on these findings, we propose a durable framework for integrating AI into the research workflow, centered on the principle of the augmented mathematician. In this model, the AI functions as a copilot under the critical guidance of the human researcher, an approach distilled into five guiding principles for effective and responsible use. We then systematically explore seven fundamental ways AI can be applied across the research lifecycle, from creativity and ideation to the final writing process, demonstrating how these principles translate into concrete practice. We conclude that the primary role of AI is currently augmentation rather than automation. This requires a new skill set focused on strategic prompting, critical verification, and methodological rigor in order to effectively use these powerful tools.

Retrieval-Augmented Generation (RAG) enhances large language models by incorporating external knowledge, yet suffers from critical limitations in high-stakes domains -- namely, sensitivity to noisy or contradictory evidence and opaque, stochastic decision-making. We propose ArgRAG, an explainable, and contestable alternative that replaces black-box reasoning with structured inference using a Quantitative Bipolar Argumentation Framework (QBAF). ArgRAG constructs a QBAF from retrieved documents and performs deterministic reasoning under gradual semantics. This allows faithfully explaining and contesting decisions. Evaluated on two fact verification benchmarks, PubHealth and RAGuard, ArgRAG achieves strong accuracy while significantly improving transparency.

Spiking Neural Networks (SNNs), inspired by the sparse event-driven neural processing and energy-efficient information transmission in the brain, offer a promising alternative for achieving low-power computing. Integrating the event-driven efficiency of spiking neurons with the advanced capabilities of LLMs represents a promising direction for power-efficient LLMs. This work specifically delves into the design of compressed spiking LLMs. Here, we revisit spatial and temporal pruning from the perspective of SNNs and propose a novel spatio-temporal pruning framework for Spiking LLMs to optimize computational efficiency while preserving high performance. Our spatial pruning technique reduces the number of active neurons and attention heads, effectively lowering the computational complexity of the model. Meanwhile, temporal pruning minimizes inference latency by dynamically adjusting the number of timesteps required for different layers. By combining these approaches with other compression techniques, we present the first work in the domain of Spiking LLMs to jointly explore spatial pruning, temporal pruning, extreme quantization and knowledge distillation strategies. Extensive experimental evaluation of our proposed framework for SpikingBERT on the large-scale GLUE benchmark demonstrates the efficacy of our approach in terms of computational operations and inference latency. Our approach offers a compelling solution for real-time, low-power natural language processing applications, making Spiking LLMs more practical for deployment on edge devices and in power-constrained settings.

Generalizing to unseen graph tasks without task-pecific supervision remains challenging. Graph Neural Networks (GNNs) are limited by fixed label spaces, while Large Language Models (LLMs) lack structural inductive biases. Recent advances in Large Reasoning Models (LRMs) provide a zero-shot alternative via explicit, long chain-of-thought reasoning. Inspired by this, we propose a GNN-free approach that reformulates graph tasks--node classification, link prediction, and graph classification--as textual reasoning problems solved by LRMs. We introduce the first datasets with detailed reasoning traces for these tasks and develop Graph-R1, a reinforcement learning framework that leverages task-specific rethink templates to guide reasoning over linearized graphs. Experiments demonstrate that Graph-R1 outperforms state-of-the-art baselines in zero-shot settings, producing interpretable and effective predictions. Our work highlights the promise of explicit reasoning for graph learning and provides new resources for future research.

We present an Audio-Visual Language Model (AVLM) for expressive speech generation by integrating full-face visual cues into a pre-trained expressive speech model. We explore multiple visual encoders and multimodal fusion strategies during pre-training to identify the most effective integration approach. Subsequent fine-tuning on emotion recognition and expressive dialogue tasks yields substantial gains over speech-only baselines (e.g., +5 F1 in emotion recognition). AVLM highlights the value of expressive visual information in guiding speech generation and offers a foundation for end-to-end multimodal conversational systems.

Federated learning (FL) in multi-service provider (SP) ecosystems is fundamentally hampered by non-cooperative dynamics, where privacy constraints and competing interests preclude the centralized optimization of multi-SP communication and computation resources. In this paper, we introduce PAC-MCoFL, a game-theoretic multi-agent reinforcement learning (MARL) framework where SPs act as agents to jointly optimize client assignment, adaptive quantization, and resource allocation. Within the framework, we integrate Pareto Actor-Critic (PAC) principles with expectile regression, enabling agents to conjecture optimal joint policies to achieve Pareto-optimal equilibria while modeling heterogeneous risk profiles. To manage the high-dimensional action space, we devise a ternary Cartesian decomposition (TCAD) mechanism that facilitates fine-grained control. Further, we develop PAC-MCoFL-p, a scalable variant featuring a parameterized conjecture generator that substantially reduces computational complexity with a provably bounded error. Alongside theoretical convergence guarantees, our framework's superiority is validated through extensive simulations -- PAC-MCoFL achieves approximately 5.8% and 4.2% improvements in total reward and hypervolume indicator (HVI), respectively, over the latest MARL solutions. The results also demonstrate that our method can more effectively balance individual SP and system performance in scaled deployments and under diverse data heterogeneity.

Poaching poses significant threats to wildlife and biodiversity. A valuable step in reducing poaching is to forecast poacher behavior, which can inform patrol planning and other conservation interventions. Existing poaching prediction methods based on linear models or decision trees lack the expressivity to capture complex, nonlinear spatiotemporal patterns. Recent advances in generative modeling, particularly flow matching, offer a more flexible alternative. However, training such models on real-world poaching data faces two central obstacles: imperfect detection of poaching events and limited data. To address imperfect detection, we integrate flow matching with an occupancy-based detection model and train the flow in latent space to infer the underlying occupancy state. To mitigate data scarcity, we adopt a composite flow initialized from a linear-model prediction rather than random noise which is the standard in diffusion models, injecting prior knowledge and improving generalization. Evaluations on datasets from two national parks in Uganda show consistent gains in predictive accuracy.

The widespread use of Large Language Models (LLMs) in many applications marks a significant advance in research and practice. However, their complexity and hard-to-understand nature make them vulnerable to attacks, especially jailbreaks designed to produce harmful responses. To counter these threats, developing strong detection methods is essential for the safe and reliable use of LLMs. This paper studies this detection problem using the Contextual Co-occurrence Matrix, a structure recognized for its efficacy in data-scarce environments. We propose a novel method leveraging the latent space characteristics of Contextual Co-occurrence Matrices and Tensors for the effective identification of adversarial and jailbreak prompts. Our evaluations show that this approach achieves a notable F1 score of 0.83 using only 0.5% of labeled prompts, which is a 96.6% improvement over baselines. This result highlights the strength of our learned patterns, especially when labeled data is scarce. Our method is also significantly faster, speedup ranging from 2.3 to 128.4 times compared to the baseline models.

Accurate prediction of clinical outcomes using Electronic Health Records (EHRs) is critical for early intervention, efficient resource allocation, and improved patient care. EHRs contain multimodal data, including both structured data and unstructured clinical notes that provide rich, context-specific information. In this work, we introduce a unified framework that seamlessly integrates these diverse modalities, leveraging all relevant available information through a two-stage architecture for clinical risk prediction. In the first stage, a fine-tuned Large Language Model (LLM) extracts crucial, task-relevant information from clinical notes, which is enhanced by graph-based retrieval of external domain knowledge from sources such as a medical corpus like PubMed, grounding the LLM's understanding. The second stage combines both unstructured representations and features derived from the structured data to generate the final predictions. This approach supports a wide range of clinical tasks. Here, we demonstrate its effectiveness on 30-day readmission and in-hospital mortality prediction. Experimental results show that our framework achieves strong performance, with AUC scores of $0.84$ and $0.92$, respectively, despite these tasks involving severely imbalanced datasets, with positive rates ranging from approximately $4\%$ to $13\%$. Moreover, it outperforms all existing baselines and clinical practices, including established risk scoring systems. To the best of our knowledge, this is one of the first frameworks for healthcare prediction which enhances the power of an LLM-based graph-guided knowledge retrieval method by combining it with structured data for improved clinical outcome prediction.

The widespread adoption of large language models (LLMs) such as ChatGPT, Gemini, and DeepSeek has significantly changed how people approach tasks in education, professional work, and creative domains. This paper investigates how the structure and clarity of user prompts impact the effectiveness and productivity of LLM outputs. Using data from 243 survey respondents across various academic and occupational backgrounds, we analyze AI usage habits, prompting strategies, and user satisfaction. The results show that users who employ clear, structured, and context-aware prompts report higher task efficiency and better outcomes. These findings emphasize the essential role of prompt engineering in maximizing the value of generative AI and provide practical implications for its everyday use.