arXiv subjects

Simon Mahns

Publications and source records attributed to Simon Mahns.

5 recordsLinked to original sources

arXiv2026

A problem of Andrews and Dhar on partitions

This paper is motivated by a broad question about AI-assisted mathematics: can an AI system help discover and certify an explicit bijection between two infinite sequences of complicated combinatorial sets already known to be equinumerous? The challenge is to find a reversible structure explaining that equality uniformly across the sequence. We give an affirmative test case in the setting of a partition problem. Andrews and Dhar introduced two partition families $\mathcal{C}_3(n)$ and $\mathcal{D}_3(n)$, and for "nonexceptional'' $n$, they asked for a bijective proof of their equality \[ |\mathcal{C}_3(n)|=\frac{|\mathcal{D}_3(n)|}{3}. \] We prove a residue-class equidistribution theorehm for $\mathcal{D}_3(n)$ that identifies a "canonical third'' subset $\mathcal{D}_3^{(0)}(n)\subseteq \mathcal{D}_3(n)$. Answering their question, we construct a bijection \[ \iota_n:\mathcal{C}_3(n)\longrightarrow \mathcal{D}_3^{(0)}(n) \] as a highly structured composition of four maps. AxiomProver autonomously produced and Lean-verified the equidistribution theorem. The bijection was found through human--AxiomProver collaboration, and the theorem was autoformalized and verified by the system.

math.CO↗

arXiv2026

ABC implies that Ramanujan's tau function misses almost all primes

Lehmer conjectured that Ramanujan's tau-function never vanishes. In a related direction, a folklore conjecture asserts that infinitely many primes arise as absolute values of Ramanujan's tau-function. Recently, Xiong showed that these prime values form a subset of the primes with density at most $2/11$. Assuming the $abc$ Conjecture, we prove the stronger upper bound \[ S(X):=\#\{\ell\le X:\ \ell\ \text{prime and } |\tau(n)|=\ell \text{ for some } n\ge 1\} = O(X^{13/22}), \] which implies that Ramanujan's tau-function misses a density 1 subset of the primes. We give a heuristic suggesting that $S(X)$ should nevertheless be infinite, with predicted order of magnitude \[ S(X)\asymp \frac{C X^{\frac{1}{11}}}{(\log X)^2}. \] The main engine in this note was formalized and produced automatically in Lean/Mathlib by AxiomProver from a natural-language statement of the problem.

math.NT↗

arXiv2025

Agentic Operator Generation for ML ASICs

We present TritorX, an agentic AI system designed to generate functionally correct Triton PyTorch ATen kernels at scale for emerging accelerator platforms. TritorX integrates open-source large language models with a custom linter, JIT compilation, and a PyTorch OpInfo-based test harness. This pipeline is compatible with both real Meta Training and Inference Accelerator (MTIA) silicon and in hardware simulation environments for next-generation devices. In contrast to previous kernel-generation approaches that prioritize performance for a limited set of high-usage kernels, TritorX prioritizes coverage. Our system emphasizes correctness and generality across the entire operator set, including diverse data types, shapes, and argument patterns. In our experiments, TritorX successfully generated kernels and wrappers for 481 unique ATen operators that pass all corresponding PyTorch OpInfo tests (over 20,000 in total). TritorX paves the way for overnight generation of complete PyTorch ATen backends for new accelerator platforms.

cs.DC↗

arXiv2025

LLM-as-a-Prophet: Understanding Predictive Intelligence with Prophet Arena

Forecasting is not only a fundamental intellectual pursuit but also is of significant importance to societal systems such as finance and economics. With the rapid advances of large language models (LLMs) trained on Internet-scale data, it raises the promise of employing LLMs to forecast real-world future events, an emerging paradigm we call "LLM-as-a-Prophet". This paper systematically investigates such predictive intelligence of LLMs. To this end, we build Prophet Arena, a general evaluation benchmark that continuously collects live forecasting tasks and decomposes each task into distinct pipeline stages, in order to support our controlled and large-scale experimentation. Our comprehensive evaluation reveals that many LLMs already exhibit impressive forecasting capabilities, reflected in, e.g., their small calibration errors, consistent prediction confidence and promising market returns. However, we also uncover key bottlenecks towards achieving superior predictive intelligence via LLM-as-a-Prophet, such as LLMs' inaccurate event recalls, misunderstanding of data sources and slower information aggregation compared to markets when resolution nears.

cs.AI↗

arXiv2025

AI Realtor: Towards Grounded Persuasive Language Generation for Automated Copywriting

This paper develops an agentic framework that employs large language models (LLMs) for grounded persuasive language generation in automated copywriting, with real estate marketing as a focal application. Our method is designed to align the generated content with user preferences while highlighting useful factual attributes. This agent consists of three key modules: (1) Grounding Module, mimicking expert human behavior to predict marketable features; (2) Personalization Module, aligning content with user preferences; (3) Marketing Module, ensuring factual accuracy and the inclusion of localized features. We conduct systematic human-subject experiments in the domain of real estate marketing, with a focus group of potential house buyers. The results demonstrate that marketing descriptions generated by our approach are preferred over those written by human experts by a clear margin while maintaining the same level of factual accuracy. Our findings suggest a promising agentic approach to automate large-scale targeted copywriting while ensuring factuality of content generation.

cs.AI↗