Humans need to study only a handful of well-written textbooks to master a discipline and attempt its hardest problems. We argue that an ideal self-evolution method should share the same property, that is autonomously learning from raw training material for transferable problem-solving capability. However, we still lack a direct measurement for it. We introduce StudyBench, a controlled physics benchmark that directly measures how efficiently a self-evolution method converts training material into capability. We organise the test set into an Application Set, consisting of difficult textbook problems and evaluating absorption ability, and a Transfer Set, consisting of olympiad-level problems and evaluating transfer ability. Benchmarking representative self-evolution methods across three base models, we find that improvements on the Application Set rarely translate to the harder Transfer Set. A guidance ablation exposes a Guidance Gap: even the strongest method closes only a small fraction of what the same material unlocks when supplied as in-context guidance. Besides, every method hits a Compute Plateau, saturating well before exhausting its compute budget. The remaining gap is therefore a method problem rather than a data or compute problem. By offering a clean and controlled benchmark, StudyBench turns self-evolution progress from an open-ended pursuit into a measurable target for future research. Our code is released at https://github.com/thunlp/StudyBench.
Neural networks can learn algebraic operations from finite examples, but it remains unclear whether this ability transfers across mathematically equivalent representations of the same operation. We study this question through multiplication in finite fields under changes of basis. The Galois action organizes basis representations into orbits, and bases in the same orbit induce the same coordinate multiplication map. This structure allows us to separate learning multiplication from transferring it to basis representations that are not used for training. We examine several ways of providing or recovering the relevant orbit structure, including invariant labels, basis matrices, orbit recognition, and algebraic decomposition. Our main approach trains a model to predict the Galois action between basis representations. Repeated applications of the learned transformation are then used to construct a canonical representative for each orbit, which supports multiplication on held-out bases through exact canonical matching. This provides a concrete mechanism for converting a learned algebraic symmetry into an invariant representation that can be used for transfer.
Extracting abstract causal structures and applying them to novel situations is a hallmark of human intelligence. While Large Language Models (LLMs) and Vision Language Models (VLMs) have shown strong performance on a wide range of reasoning tasks, their capacity for interactive causal learning -- inducing latent structures through sequential exploration and transferring them across contexts -- remains uncharacterized. Human learners accomplish such transfer after minimal exposure, whereas classical Reinforcement Learning (RL) agents fail catastrophically. Whether state-of-the-art Artificial Intelligence (AI) models possess human-like mechanisms for abstract causal structure transfer is an open question. Using the OpenLock paradigm requiring sequential discovery of Common Cause (CC) and Common Effect (CE) structures, here we show that models exhibit fundamentally delayed or absent transfer: even successful models require initial environmental-specific mapping -- what we term environmental grounding -- before efficiency gains emerge, whereas humans leverage prior structural knowledge from the very first solution attempt. In the text-only condition, models matched or exceeded human discovery efficiency. In contrast, visual information -- in both the image-only and text-and-image conditions -- overall degraded rather than enhanced performance, revealing a broad reliance on symbolic processing rather than integrated multimodal reasoning. Models further exhibited systematic CC/CE asymmetries absent in humans, suggesting heuristic biases rather than direction-neutral causal abstraction. These findings reveal that large-scale statistical learning does not produce the decontextualized causal schemas underpinning human analogical reasoning, establishing grounding-dependent transfer as a fundamental limitation of current LLMs and VLMs.