Large language models have made substantial progress on mathematical reasoning, but existing benchmarks typically evaluate well-specified problems with final answers, step-by-step solutions, or complete proofs. They do not capture collaborative open-problem solving: a setting in which participants propose partial arguments, identify gaps or errors in prior steps, repair flawed reasoning, and gradually synthesize incremental contributions into a proof. We introduce CrowdMath, a dataset of 164 expert-annotated progress chains from the MIT PRIMES–Art of Problem Solving (AoPS) CrowdMath program (2016–2025), a collaborative research initiative whose discussions have led to peer-reviewed publications. Each chain traces a multi-participant forum discussion from an open-problem statement to a completed proof. Posts are labeled by their functional roles in the evolving solution process, including partial progress, proof completion, erroneous reasoning, and error identification. We define evaluation tasks and benchmark six frontier models. Models achieve 83–88% accuracy on next-post prediction, suggesting that they can follow the local flow of mathematical discussion. However, they struggle to identify the functional significance of individual contributions with the best model achieving only 0.42 macro-F1 on post-role classification. CrowdMath exposes a gap between solving well-specified mathematical problems and understanding collaborative mathematical progress as it unfolds.

The ability of large language models (LLMs) to “learn in context” based on the provided prompt has led to an explosive growth in their use, culminating in the proliferation of AI assistants such as ChatGPT, Claude, and Bard. These AI assistants are known to be robust to minor prompt modifications, mostly due to alignment techniques that use human feedback. In contrast, the underlying pre-trained LLMs they use as a backbone are known to be brittle in this respect. Building high-quality backbone models remains a core challenge, and a common approach to assessing their quality is to conduct few-shot evaluation. Such evaluation is notorious for being highly sensitive to minor prompt modifications, as well as the choice of specific in-context examples. Prior work has examined how modifying different elements of the prompt can affect model performance. However, these earlier studies tended to concentrate on a limited number of specific prompt attributes and often produced contradictory results. Additionally, previous research either focused on models with fewer than 15 billion parameters or exclusively examined black-box models like GPT-3 or PaLM, making replication challenging. In the present study, we decompose the entire prompt into four components: task description, demonstration inputs, labels, and inline instructions provided for each demonstration. We investigate the effects of structural and semantic corruptions of these elements on model performance. We study models ranging from 1.5B to 70B in size, using ten datasets covering classification and generation tasks. We find that repeating text within the prompt boosts model performance, and bigger models (≥30B) are more sensitive to the semantics of the prompt. Finally, we observe that adding task and inline instructions to the demonstrations enhances model performance even when the instructions are semantically corrupted. The code is available at this URL.

Large language models can solve new tasks without task-specific fine-tuning. This ability, also known as in-context learning (ICL), is considered an emergent ability and is primarily seen in large language models with billions of parameters. This study investigates if such emergent properties are strictly tied to model size or can be demonstrated by smaller models trained on reduced-scale data. To explore this, we simplify pre-training data and pre-train 36 causal language models with parameters varying from 1 million to 165 million parameters. We show that models trained on this simplified pre-training data demonstrate enhanced zero-shot capabilities across various tasks in simplified language, achieving performance comparable to that of pre-trained models six times larger on unrestricted language. This suggests that downscaling the language allows zero-shot learning capabilities to emerge in models with limited size.Additionally, we find that these smaller models pre-trained on simplified data demonstrate a power law relationship between the evaluation loss and the three scaling factors: compute, dataset size, and model size.