arXiv:2602.09924v3 Announce Type: replace-cross Abstract: Running LLMs with extended reasoning on every problem is expensive, but determining which inputs actually require additional compute remains challenging. We investigate whether their own likelihood of success is recoverable from their internal representations before generation, and if this signal can guide more efficient inference. We train linear probes on pre-generation activations to predict policy-specific success on math and coding tasks, substantially outperforming surface features such as question length and TF-IDF. Using E2H-AMC, which provides both human and model performance on identical problems, we show that models encode a model-specific notion of difficulty that is distinct from human difficulty, and that this distinction increases with extended reasoning. Leveraging these probes, we demonstrate that routing queries across a pool of models can exceed the best-performing model whilst reducing inference cost by up to 70\% on MATH, showing that internal representations enable practical efficiency gains even when they diverge from human intuitions about difficulty. Our code is available at: https://github.com/KabakaWilliam/llms_know_difficulty

arXiv:2603.12270v1 Announce Type: cross Abstract: Knowledge distillation from large language models (LLMs) assumes that the teacher's output distribution is a high-quality training signal. On reasoning tasks, this assumption is frequently violated. A model's intermediate representations may encode the correct answer, yet this information is lost or distorted through the vocabulary projection, where prompt formatting and answer-token choices creates brittle, noisy outputs. We introduce \method{}, a distillation framework that bypasses this bottleneck by training lightweight probes on frozen teacher hidden states and using the probe's predictions, rather than output logits, as supervision for student training. This simple change yields consistent improvements across four reasoning benchmarks (AQuA-RAT, ARC Easy/Challenge, and MMLU), with gains most pronounced under limited data. Probes trained on intermediate representations provide cleaner labels than the teacher's own outputs, effectively denoising the distillation signal. \method{} requires no architectural changes to student or teacher, is architecture-agnostic, and adds minimal compute since probe training is cheap and teacher representations can be cached. By exploiting internal representations, \method{} enables practitioners to extract more value from large teacher models without additional training data or architectural complexity.