Mathematical Foundations and Methods for Post-Training, Inference, and Evaluation of Large Language Models
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".
Deadline for manuscript submissions: 31 March 2027 | Viewed by 46
Editor
Interests: machine learning; data mining; large language models; pattern recognition; distributed systems
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Large language models (LLMs) have emerged as transformative tools across science and engineering, yet the mathematical principles that govern their post-training, inference, and evaluation remain insufficiently understood. Post-training techniques, including supervised fine-tuning (SFT), reinforcement learning from human feedback (RLHF), and direct preference optimization (DPO), can be formulated as a family of stochastic optimization and game-theoretic problems involving non-convex loss landscapes, distributional shift, and reward misspecification; rigorous analysis of their convergence, stability, and generalization properties is essential for principled algorithm design. The inference stage poses equally rich mathematical challenges: deploying billion-parameter models under real-world latency and memory constraints requires advances in numerical approximation theory, including low-bit quantization error analysis, structured matrix factorization, speculative decoding with draft-model acceptance guarantees, and combinatorial search algorithms for test-time compute scaling. The evaluation of LLM capabilities further demands robust statistical and information-theoretic frameworks, ranging from hypothesis testing and contamination-resistant benchmark design to the calibration theory of LLM-as-a-judge systems and process-level reward verification via probabilistic reasoning.
This Special Issue invites original contributions that advance the mathematical foundations, algorithmic theory, and computational methods underlying any of these three interconnected stages. Topics of interest for publication include, but are not limited to: optimization theory for alignment, approximation guarantees for model compression, statistical methodology for evaluation, as well as studies that reveal deep mathematical connections across post-training, inference, and evaluation. For example, we encourage investigations into how the geometry of the loss landscape shapes inference-time efficiency, or how information-theoretic bounds inform the design of both reward models and evaluation protocols.
Prof. Dr. Kan Li
Guest Editor
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Keywords
- large language models
- optimization theory for post-training
- numerical approximation for efficient inference
- statistical methodology for LLM evaluation
- reinforcement learning and game theory
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