A prevailing narrative in LLM post-training holds that supervised fine-tuning (SFT) memorizes while reinforcement learning (RL) generalizes. We revisit this claim for reasoning SFT with long chain-of-thought (CoT) supervision and find that cross-domain generalization is not absent but conditional, jointly shaped by optimization dynamics, training data, and base-model capability. Some reported failures are under-optimization artifacts: cross-domain performance first degrades before recovering and improving with extended training (a dip-and-recovery pattern), so short-training checkpoints can underestimate generalization. Data quality and structure both matter: low-quality solutions broadly hurt generalization, while verified long-CoT traces yield consistent cross-domain gains. Model capability is essential: stronger models internalize transferable procedural patterns (e.g., backtracking) even from a toy arithmetic game, while weaker ones imitate surface verbosity. This generalization is asymmetric, however: reasoning improves while safety degrades, reframing the question from whether reasoning SFT generalizes to under what conditions and at what cost.

Large language models (LLMs) can perform remarkably complex tasks, yet the fine-grained details of how these capabilities emerge during pretraining remain poorly understood. Scaling laws on validation loss tell us how much a model improves with additional compute, but not what skills it acquires in which order. To remedy this, we propose the **Implicit Curriculum Hypothesis**: pretraining follows a compositional and predictable curriculum across models and data mixtures. We test this by designing a suite of simple, composable tasks spanning retrieval, morphological transformations, coreference, logical reasoning, and mathematics. Using these tasks, we track emergence points across four model families spanning sizes from 410M-13B parameters. We find that **emergence orderings** of when models reach fixed accuracy thresholds are strikingly consistent ($\rho = .81$ across 45 model pairs), and that composite tasks most often emerge after their component tasks. Furthermore, we find that this structure is encoded in model representations: tasks with similar function vector representations also tend to follow similar trajectories in training. By using the space of representations derived from our task set, we can effectively predict the training trajectories of simple held-out compositional tasks throughout the course of pretraining ($R^2 = .68$--$.84$ across models) without previously evaluating them. Together, these results suggest that pretraining is more structured than loss curves reveal: skills emerge in a compositional order that is consistent across models and readable from their internals.

Software auditing is an increasingly critical task in the era of rapid code generation. While LLM-based auditors have demonstrated strong potential, their effectiveness remains limited by misalignment with the highly complex, domain-specific nature of bug detection. In this work, we introduce BugScope, a framework that mirrors how human auditors learn specific bug patterns from representative examples and apply this knowledge during code auditing. BugScope structures auditing into three steps: seed identification, context retrieval, and bug detection, and aligns LLMs to each step by analyzing real bug reports and mutated examples, and distilling concise, reusable guidelines. On a curated dataset of 33 real-world bugs from 21 widely used open-source projects, BugScope achieves 86.05\% precision and 87.88\% recall, corresponding to an F1 score of 0.87. By comparison, leading industrial tools such as Claude Code (with Claude Opus 4.6) and Cursor BugBot achieve F1 scores of only 0.51 and 0.43, respectively. Beyond benchmarks, large-scale evaluation on real-world projects such as the Linux kernel uncovered 184 previously unknown bugs, of which 78 have already been fixed and 7 explicitly confirmed by developers. Our code is available at (https://anonymous.4open.science/r/BugScope-40C4).

Large language models are increasingly used as proxies for human cognition, but do they reason like humans when beliefs conflict with new evidence? We study this question through \emph{belief revision}, that is, how agents update their beliefs in light of contradictions. Cognitive psychology has shown that humans favor \emph{explanation-based revision}: they first generate explanations for the conflict, such as identifying conditions under which a general rule admits exceptions, and revise accordingly. In this paper, we develop a Bayesian model that decomposes this process into two orthogonal components: \emph{what} to revise and \emph{how broadly} to generalize to similar instances. We first run three human-subject experiments on simple, everyday abstract and grounded scenarios to evaluate how people revise their beliefs, and use this data to test our model's predictions. We then evaluate three frontier LLMs (GPT, Claude, Gemini) on the same scenarios and show that while LLMs match human rule-targeting rates, they consistently fail to generalize: both humans and LLMs target the directly contradicted beliefs, but humans propagate revisions to related beliefs while LLMs revise only the directly contradicted instance.