$PLYN polynomial

Latest papers

1. The existence of small defining polynomials for number fields math.NT · 14 Oct · 2 hits

   We prove that every number field of degree $n$ and absolute discriminant $D$ has a defining integral polynomial of degree $n$ whose coefficients are all $O_n(\sqrt D)$ in size, thus resolving a 1998 conjecture…

2. The Physics Is the Network: Fast, Training-Free Neural Emulation cs.LG · 14 Oct · 1 hit

   …substitute for known physics. We investigate PolyNets that couple a continuous-time neural representation of polynomial dynamics with a simple recurrent network for discrete-time integration. When the governing…

3. Petz Recovery through a Single Polar Transformation for Approximate Quantum Error Correction quant-ph · 14 Oct · 1 hit

   …spectrum-weighted loss, which provides a channel specific objective for optimizing the QSVT angles. Uniform polynomial approximation yields an asymptotic error bound that decays exponentially with the number of QSVT…

4. Effective equidistribution of polynomial trajectories in $\operatorname{SL}_3(\mathbb R)/\operatorname{SL}_3(\mathbb Z)$ math.DS · 14 Oct · 5 hits

   For a fixed matrix-polynomial trajectory in $\operatorname{SL}_3(\mathbb R)/\operatorname{SL}_3(\mathbb Z)$, we give a necessary…

5. Tracking a Small Set of Experts in Online Convex Optimization cs.LG · 14 Oct · 2 hits

   …this computational inefficiency is inherent, establishing a separation between the information-theoretic and polynomial-time regret achievable for this problem. Specifically, under the hypergraphic planted-clique…

6. On the Structure of Radical Towers and their Parametrizations math.AG · 14 Oct · 1 hit

   Radical parametrizations describe algebraic varieties by means of nested radicals of polynomials, and their theory relies on three varieties associated with a parametrization, namely, the…

7. Gaussian rigidity and width of measures math.CA · 14 Oct · 1 hit

   Given $0\le m<n$ and a positive Radon measure $\mu$ on $\mathbb R^n$ with at most polynomial growth, assume that it has finite $m$-dimensional \emph{Gaussian discrepancy}, defined as…

8. Hypothesis Selection via Weighted Medians cs.DS · 14 Oct · 1 hit

   …factor and sample complexity. The running time improves the dependence on the failure probability from polynomial to logarithmic in the state-of-the-art bound $\tilde{O}(n\varepsilon^{-2}\delta^{-1})$ of Aamand,…