Understanding Curriculum Learning in Large Language Models via Cross-Difficulty Optimization Dynamics

Curriculum learning has been widely adopted in the post-training of large language models by organizing training data from easy to hard. However, its effectiveness varies substantially across reasoning tasks, suggesting that no single curriculum is universally optimal and raising a fundamental question: what determines when curriculum learning works? In this paper, we answer this question by analyzing the optimization dynamics induced by different curriculum schedules. We show that the transfer relationship between different difficulty levels characterizes the optimization dynamics induced by curriculum learning, which in turn explains the effectiveness of different curriculum schedules, and formalize this relationship as Relative Transfer, a principled measure of cross-difficulty knowledge transfer. Based on this measurement, we derive Transfer-aware Dynamic Curriculum Sampling (TDCS), which dynamically adjusts the sampling distribution according to the estimated transfer relationship throughout training. Extensive experiments on multiple reasoning benchmarks demonstrate that TDCS consistently outperforms representative scheduling strategies across different tasks, model scales, and training paradigms. More importantly, our work provides a unified optimization-based explanation of curriculum learning through cross-difficulty transfer.

Evaluating and Calibrating LLM Confidence on Questions with Multiple Correct Answers

Confidence calibration is essential for making large language models (LLMs) reliable, yet existing training-free methods have been primarily studied under single-answer question answering. In this paper, we show that these methods break down in the presence of multiple valid answers, where disagreement among equally correct responses leads to systematic underestimation of confidence. To enable a systematic study of this phenomenon, we introduce MACE, a benchmark of 12,000 factual questions spanning six domains with varying numbers of correct answers. Experiments across 15 representative calibration methods and four LLM families (7B-72B) reveal that while accuracy increases with answer cardinality, estimated confidence consistently decreases, causing severe miscalibration for questions with mixed answer counts. To address this issue, we propose Semantic Confidence Aggregation (SCA), which aggregates confidence over multiple high-probability sampled responses. SCA achieves state-of-the-art calibration performance under mixed-answer settings while preserving strong calibration on single-answer questions.

Do LVLMs Know What They Know? A Systematic Study of Knowledge Boundary Perception in LVLMs

Large vision-language models (LVLMs) demonstrate strong visual question answering (VQA) capabilities but are shown to hallucinate. A reliable model should perceive its knowledge boundaries-knowing what it knows and what it does not. This paper investigates LVLMs' perception of their knowledge boundaries by evaluating three types of confidence signals: probabilistic confidence, answer consistency-based confidence, and verbalized confidence. Experiments on three LVLMs across three VQA datasets show that, although LVLMs possess a reasonable perception level, there is substantial room for improvement. Among the three confidences, probabilistic and consistency-based signals are more reliable indicators, while verbalized confidence often leads to overconfidence. To enhance LVLMs' perception, we adapt several established confidence calibration methods from Large Language Models (LLMs) and propose three effective methods. Additionally, we compare LVLMs with their LLM counterparts, finding that jointly processing visual and textual inputs decreases question-answering performance but reduces confidence, resulting in an improved perception level compared to LLMs.