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Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we…
The rapid escalation from elementary school-level to frontier problems of the difficulty for LLM benchmarks in recent years have weaved a miracle for researchers that we are only inches away from surpassing human intelligence. However, is…
Large language models (LLMs) excel at complex tasks thanks to advances in their reasoning abilities. However, existing methods overlook the trade-off between reasoning effectiveness and efficiency, often encouraging unnecessarily long…
Large language models have made significant progress in mathematical reasoning, which serves as an important testbed for AI and could impact scientific research if further advanced. By scaling reasoning with reinforcement learning that…
As modern scientific instruments generate vast amounts of data and the volume of information in the scientific literature continues to grow, machine learning (ML) has become an essential tool for organising, analysing, and interpreting…
With the rapid development in Transformer-based language models, the reading comprehension tasks on short documents and simple questions have been largely addressed. Long documents, specifically the scientific documents that are densely…
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains…
Increasing interest in reasoning models has led math to become a prominent testing ground for algorithmic and methodological improvements. However, existing open math datasets either contain a small collection of high-quality, human-written…
How can "weak teacher models" such as average human annotators or existing AI systems, effectively supervise LLMs to improve performance on hard reasoning tasks, especially those that challenge and requires expertise or daily practice from…
Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both…
Text simplification is a common task where the text is adapted to make it easier to understand. Similarly, text elaboration can make a passage more sophisticated, offering a method to control the complexity of reading comprehension tests.…
This paper presents a comprehensive evaluation of the performance of state-of-the-art Large Language Models (LLMs) on challenging university-level algorithms exams. By testing multiple models on both a Romanian exam and its high-quality…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
A suite of impressive scientific discoveries have been driven by recent advances in artificial intelligence. These almost all result from training flexible algorithms to solve difficult optimization problems specified in advance by teams of…
Can AI make progress on important, unsolved mathematical problems? Large language models are now capable of sophisticated mathematical and scientific reasoning, but whether they can perform novel research is still widely debated and…
For several years, students visit us on different occasions at the university. But how to bridge from the school curriculum to the contents of the university mathematics? And how to find a focal point at which an active contribute, despite…
Code super-optimization is the task of transforming any given program to a more efficient version while preserving its input-output behaviour. In some sense, it is similar to the paraphrase problem from natural language processing where the…
Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the…
Why bother with fully rigorous proofs when one can very quickly get semi-rigorous ones? Yes, yes, we know how to get a "rigorous" proof of the result stated in the title of this article. One way is the boring, human one, citing some heavy…
Large language models (LLMs) have made impressive progress in handling simple math problems, yet they still struggle with more challenging and complex mathematical tasks. In this paper, we introduce a series of LLMs that employs the…