arXiv AI
Jul 14
The Ramanujan Challenge For AI
arXiv:2607. 09721v1 Announce Type: cross Abstract: To help evaluate the mathematical skills of current AI systems, we present a set of formulas for fundamental mathematical constants.
Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves
arXiv:2607. 24251v1 Announce Type: cross Abstract: We investigate the extent to which the reduced minimal Weierstrass coefficients of an elliptic curve over $\mathbb{Q}$ may be computed from it's Frobenius traces.
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arXiv AI
Jun 12
Real-rootedness of the Poincar\'e polynomials of $\overline{\mathcal M}_{0,n}$: an AI-assisted proof
arXiv:2605. 29151v2 Announce Type: replace-cross Abstract: We prove real-rootedness for the Poincar\'e polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne--Mumford moduli space $\overline{\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli.
arXiv AI
Jul 28
Computational Experiments in Number Theory
arXiv:2504. 19451v4 Announce Type: replace-cross Abstract: This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory.
arXiv Machine Learning
Jul 21
Computations and ML for surjective rational maps
arXiv:2510. 08093v2 Announce Type: replace-cross Abstract: The present note studies \emph{surjective rational endomorphisms} $f: \mathbb{P}^2 \dashrightarrow \mathbb{P}^2$ with \emph{cubic} terms and the indeterminacy locus $I_f \ne \emptyset$.
Hugging Face Trending Papers
Aug 3
Sharp Root Anti-Concentration via Projective Incidence and Ordered Root Laws
This paper answers the one-dimensional local root anti-concentration questions posed by Balcan, Pegden, and Sharma in the context of online optimization of piecewise-Lipschitz functions. For a homogeneous feature curve and coefficients whose density relative to the uniform law on a symmetric convex body $K$ is bounded by $A$, we show that the worst-case interval-hitting constant equals $A$ times a section-averaged projective incidence speed.
arXiv Machine Learning
Jun 16
Transformers Learn the Mestre-Nagao Heuristic
arXiv:2606. 15036v1 Announce Type: new Abstract: We train a two-layer transformer encoder to classify rational elliptic curves $E/\mathbb{Q}$ of conductor $\leq 10000$ as either rank 0 or rank 1 from the first 128 normalized Frobenius traces.
arXiv AI
Jul 15
Prime Fourier Embeddings: A Principled Basis for Modular Arithmetic
arXiv:2606. 23044v2 Announce Type: replace-cross Abstract: Numbers have algebraic structure that standard neural embeddings often fail to expose.
arXiv AI
Aug 11
Exact Zarankiewicz Values On Two Finite Frontier Slices
arXiv:2608. 08154v1 Announce Type: cross Abstract: The Zarankiewicz number Z(m,n,s,t) is the maximum number of edges in a bipartite graph with parts of orders m and n containing no copy of Ks,t.
arXiv Machine Learning
Aug 4
Sharp Root Anti-Concentration via Projective Incidence and Ordered Root Laws
arXiv:2608. 01670v1 Announce Type: new Abstract: This paper answers the one-dimensional local root anti-concentration questions posed by Balcan, Pegden, and Sharma in the context of online optimization of piecewise-Lipschitz functions.
arXiv Machine Learning
Aug 4
Detecting Nonproperness of Likelihood Equations
arXiv:2608. 01976v1 Announce Type: cross Abstract: Given an algebraic statistical model, a challenging problem is classifying the data according to the number of positive critical points of the likelihood function.
arXiv AI
Jul 8
Tangent classes of matroids and wonderful compactifications
arXiv:2607. 05835v1 Announce Type: cross Abstract: For every loopless matroid $M$ and every Feichtner--Yuzvinsky building set $\mathcal{G}$ containing the top flat, we construct an integral tangent class $T_{M,\mathcal{G}}^{\mathbb{Z}}\in K_{\mathbb{Z}}(M,\mathcal{G})$; in the realizable case it specializes to the class of the tangent bundle of the corresponding wonderful compactification, it recovers the Hilbert series of the Chow ring through Hirzebruch--Riemann--Roch, and it satisfies the expected Chern-alpha lower bounds.
arXiv Machine Learning
Jul 10
Tubular Neighbourhoods of Pfaffian Sets and Applications to Neural Networks
arXiv:2607. 08370v1 Announce Type: cross Abstract: We derive bounds for the volume of tubular neighbourhoods of smooth Pfaffian hypersurfaces, generalising known results for algebraic varieties.