Six misconceptions about large language models: A minimal model and diagnostic taxonomy

Large language models (LLMs) increasingly act as agents with little human oversight, so potential mistakes they make can go unnoticed. Users then depend on the model to report what went wrong. An honest model discloses its mistakes, while a deceptive one conceals them. However, it is unclear how current LLMs behave in such situations. In this study, we prefill LLM trajectories with synthetic mistakes. The trajectories resemble real deployments in chat and agentic settings. Models fail to disclose their mistake in 36.4% of chat and 67.1% of agentic rollouts. In 2.4% and 5.3% of rollouts, respectively, they are aware of the mistake in their chain of thought but still deceptively conceal it. Rates vary by model: for instance, Gemini 3.5 Flash knowingly conceals mistakes in up to 19.9% of agentic rollouts. In 11.9% of chat and 51.8% of agentic rollouts, models show no awareness of mistakes, even though they reliably spot them when reviewing the same transcript as an outside observer. Our results show that, as agents take on more tasks with less oversight, users cannot rely on them to self-report possible mistakes. Developers should instead use independent monitors that review agent trajectories, or specifically train models to check their past actions and disclose what they find.

Public leaderboards increasingly suggest that large language models (LLMs) surpass human experts on benchmarks spanning academic knowledge, law, and programming. Yet most benchmarks are fully public, their questions widely mirrored across the internet, creating systematic risk that models were trained on the very data used to evaluate them. This paper presents three complementary experiments forming a rigorous multi-method contamination audit of six frontier LLMs: GPT-4o, GPT-4o-mini, DeepSeek-R1, DeepSeek-V3, Llama-3.3-70B, and Qwen3-235B. Experiment 1 applies a lexical contamination detection pipeline to 513 MMLU questions across all 57 subjects, finding an overall contamination rate of 13.8% (18.1% in STEM, up to 66.7% in Philosophy) and estimated performance gains of +0.030 to +0.054 accuracy points by category. Experiment 2 applies a paraphrase and indirect-reference diagnostic to 100 MMLU questions, finding accuracy drops by an average of 7.0 percentage points under indirect reference, rising to 19.8 pp in both Law and Ethics. Experiment 3 applies TS-Guessing behavioral probes to all 513 questions and all six models, finding that 72.5% trigger memorization signals far above chance, with DeepSeek-R1 displaying a distributed memorization signature (76.6% partial reconstruction, 0% verbatim recall) that explains its anomalous Experiment 2 profile. All three experiments converge on the same contamination ranking: STEM > Professional > Social Sciences > Humanities.

Post-training has become central to turning pretrained large language models (LLMs) into aligned, capable, and deployable systems. Recent progress spans supervised fine-tuning (SFT), preference optimization, reinforcement learning (RL), process supervision, verifier-guided methods, distillation, and multi-stage pipelines. Yet these methods are often discussed in fragmented ways, organized by labels or objectives rather than by the behavioral bottlenecks they address. This survey argues that LLM post-training is best understood as structured intervention on model behavior. We organize the field first by trajectory provenance, which defines two primary regimes: off-policy learning on externally supplied trajectories and on-policy learning on learner-generated rollouts. We then interpret methods through two recurring roles -- effective support expansion, which makes useful behaviors more reachable, and policy reshaping, which improves behavior within already reachable regions -- together with a complementary systems-level role, behavioral consolidation, which preserves, transfers, and amortizes useful behavior across stages and model transitions. Under this view, SFT may serve either support expansion or policy reshaping; preference optimization is usually off-policy reshaping, though online variants move closer to learner-generated states. On-policy RL often improves behavior on learner-generated states, but stronger guidance can also make hard-to-reach reasoning paths reachable. Distillation is often better understood as consolidation rather than only compression, and hybrid pipelines emerge as coordinated multi-stage compositions. Overall, the framework helps diagnose post-training bottlenecks and reason about stage composition, suggesting that progress increasingly depends on coordinated systems design rather than any single dominant objective.