2 papers
math.NT2026
Generalizations of the Christoffel-Darboux formula and congruences involving Apéry-like numbers
Zhi-Hong Sun
In this paper, we first extend the Christoffel-Darboux formula for orthogonal polynomials to general three-term recurrence sequences, and then investigate the identities and congru…
cs.AI2026
Different Feedback, Different Updates: Selective Self-Learning from User Interactions for Large Language Models
Xuanchen Li, Haitao Li, Yujia Zhou +5
User feedback offers natural supervision for persistent LLM improvement, but a single message may support multiple behavioral changes with different scopes of generalization. We in…