While language models (LMs) excel in natural language tasks, their ability to learn impossible languages--those that violate the structural, cognitive, or logical constraints that make human languages learnable and functional--remains debatable. This controversy is further fueled by a divide between linguistic theorists and empirical researchers working with small-scale LMs. To address this controversy, we introduce semantic coherence. This concept measures how effectively semantic information is expressed in language structures and examines the learning capabilities of LMs across multiple scales. By fine-tuning billion-parameter LMs on impossible language samples, we demonstrate that larger LMs achieve similar performance on impossible and possible languages, whereas million-parameter LMs exhibit significant degradation when trained on impossible languages. This performance gap widens as semantic complexity increases. We further show that scaling up the LM size fundamentally shifts the learning focus from grammatical rules to semantic understanding, with billion-scale LMs exhibiting a threefold reduction in sensitivity to low-level linguistic perturbations while maintaining stable performance under high-level semantic perturbations.
Curriculum learning (CL), which orders training data from easy to hard, has become a popular strategy for improving reasoning in large language models (LLMs). Yet prior work employs disparate difficulty metrics and training setups, leaving open fundamental questions: When does curriculum help? Which direction—forward or reverse—is better? And does the answer depend on what we measure? We address these questions through a unified offline evaluation framework that decomposes curriculum difficulty into five complementary dimensions: Problem Difficulty, Model Surprisal, Confidence Margin, Predictive Uncertainty, and Decision Variability. Through controlled post-training experiments on mathematical reasoning benchmarks with Llama3.1-8B, Mistral-7B, and Gemma3-4B, we find that: (i) no curriculum strategy dominates universally—the relative effectiveness of forward versus reverse CL depends jointly on model capability and task complexity; (ii) even within a single metric, samples at different difficulty levels produce distinct gains depending on task demands; and (iii) Task-aligned curricula focus on shaping the model’s final representations and generalization, whereas inner-state curricula modulate internal states such as confidence and uncertainty. Our findings challenge the notion of a universal curriculum strategy and offer actionable guidance across model and task regimes, with some metrics indicating that prioritizing decision-uncertain samples can further enhance learning outcomes.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表