arXiv subjects

Sam Silver

Publications and source records attributed to Sam Silver.

3 recordsLinked to original sources

arXiv2026

A note on the self-intersection of rational unicuspidal curve with one Puiseux pair

For any $(p,q)$, we proved the existence of a rational unicuspidal curve with one Puiseux pair $(p,q)$ in an algebraic surface, with a self-intersection which realizes the upper bound $m_{p,q}$ conjectured by the first-named author in \cite{C}, thus strengthening the symplectic version of the result in \cite{C}. These ``optimal" curves were obtained by examining two infinite families of rational bicuspidal curves, one in $CP^2$ and one in $CP^1\times CP^1$. In order to facilitate the computations, we derived certain recursive identities, and as a byproduct, we obtained a new formula for the bound $m_{p,q}$, which is more amenable to computations and gives us better insight concerning the nature of the bound. As a byproduct of this investigation, a formula for the last entry of the multiplicity sequence of the singularity was also found.

math.AG↗

arXiv2025

The Morita $(\infty,2)$-category of a monoidal category as a $2$-complicial set

We provide an explicit and elementary construction of the Morita $(\infty,2)$-category of a monoidal category which satisfies minimal conditions. We construct it as a $3$-coskeletal $2$-complicial set, in which the vertices encode the monoids, the edges encode the bimodules, the triangles encode the bimodule maps out of a balanced tensor product, and tetrahedra encode composition of bimodule maps. The marked edges encode invertible bimodules, and the marked triangles encode bimodule isomorphisms with a balanced tensor product.

math.CT↗

arXiv2025

Language Models can perform Single-Utterance Self-Correction of Perturbed Reasoning

Large Language Models (LLMs) have demonstrated impressive mathematical reasoning capabilities, yet their performance remains brittle to minor variations in problem description and prompting strategy. Furthermore, reasoning is vulnerable to sampling-induced errors which autoregressive models must primarily address using self-correction via additionally-generated tokens. To better understand self-correction capabilities of recent models, we conduct experiments measuring models' ability to self-correct synthetic perturbations introduced into their Chain of Thought (CoT) reasoning. We observe robust single-utterance intrinsic self-correction behavior across a range of open-weight models and datasets, ranging from subtle, implicit corrections to explicit acknowledgments and corrections of errors. Our findings suggest that LLMs, including those not finetuned for long CoT, may possess stronger intrinsic self-correction capabilities than commonly shown in the literature. The presence of this ability suggests that recent "reasoning" model work involves amplification of traits already meaningfully present in models.

cs.CL↗