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Navid Safaei

Publications and source records attributed to Navid Safaei.

4 recordsLinked to original sources

MathNet: a Global Multimodal Benchmark for Mathematical Reasoning and Retrieval

Mathematical problem solving remains a challenging test of reasoning for large language and multimodal models, yet existing benchmarks are limited in size, language coverage, and task diversity. We introduce MathNet, a high-quality, large-scale, multimodal, and multilingual dataset of Olympiad-level math problems together with a benchmark for evaluating mathematical reasoning in generative models and mathematical retrieval in embedding-based systems. MathNet spans 47 countries, 17 languages, and two decades of competitions, comprising 30,676 expert-authored problems with solutions across diverse domains. In addition to the core dataset, we construct a retrieval benchmark consisting of mathematically equivalent and structurally similar problem pairs curated by human experts. MathNet supports three tasks: (i) Problem Solving, (ii) Math-Aware Retrieval, and (iii) Retrieval-Augmented Problem Solving. Experimental results show that even state-of-the-art reasoning models (78.4% for Gemini-3.1-Pro and 69.3% for GPT-5) remain challenged, while embedding models struggle to retrieve equivalent problems. We further show that retrieval-augmented generation performance is highly sensitive to retrieval quality; for example, DeepSeek-V3.2-Speciale achieves gains of up to 12%, obtaining the highest scores on the benchmark. MathNet provides the largest high-quality Olympiad dataset together with the first benchmark for evaluating mathematical problem retrieval, and we publicly release both the dataset and benchmark at https://mathnet.mit.edu.

cs.AI

Rationality of the inner products of spherical $s$-distance $t$-designs for $t \geq 2s-2$, $s \geq 3$

We prove that the inner products of spherical $s$-distance $t$-designs with $t \geq 2s-2$ (Delsarte codes) and $s \geq 3$ are rational with the only exception being the icosahedron. In other formulations, we prove that all sharp configurations have rational inner products and all spherical codes which attain the Levenshtein bound, have rational inner products, except for the icosahedron.

math.CO

On spherical 4-distance 7-designs

We investigate spherical 4-distance 7-designs by studying their distance distributions. We compute these distance distributions and use their product (an integer) to derive certain divisibility conditions relating the dimension $n$ and the cardinality $M$ of our designs. It follows that $n$ divides $12M$ and $n+1$ divides $4M^2$. This result provides a good base for computer experiments to support the folklore conjecture that the only spherical 4-distance 7-designs are the tight spherical 7-designs. We then proceed with a computer assisted proof of this conjecture in all dimensions $n \leq 1000$.

math.CO

On 3-distance spherical 5-designs

Inspired by a recently formulated conjecture by Bannai et al. we investigate spherical codes which admit exactly three different distances and are spherical 5-designs. Computing and analyzing distance distributions we provide new proof of the fact (due to Levenshtein) that such codes are maximal and rule out certain cases towards a proof of the conjecture.

math.CO