b=0
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Exact output statistics of Icart's encoding in the exceptional \(j=0\) case
Announce Type: cross Abstract: Icart's encoding is a classical deterministic map from finite fields to elliptic curves and a basic ingredient in early hash-to-curve constructions. We determine the exact one-output distribution of this map in the exceptional \(j=0\) case. More precisely, for \[ E_{0,b}:Y^2=X^3+b,\ q\equiv2\pmod3, \] we compute the complete fibre distribution of \(f_{0,b}:\mathbb F_q\to E_{0,b}(\mathbb F_q)\).
Approximation by short exponential sums with geometric error decay based on Gauss quadrature
Announce Type: new Abstract: We present new short exponential sum approximations of length $N$ for $f_1(x)=\frac{1}{a+x}$ with $a>0$ on $[0, \infty)$ and for $f_2(x)= {\mathrm e}^{-x^2/2\sigma}$ with $\sigma>0$ on ${\mathbb R}$ with geometric error decay ${\rho}^{-2N}$ for user-defined $N \ge 2$ and $\rho > The approximations are built over consecutive intervals $[b_j, \, b_{j+1}) \subset [0, \infty)$, $j \in {\mathbb N}_{0}$, with interval lengths that depend on $\rho$ and grow...
Bit-counting complexity classes
arXiv:2606.04406v1 Announce Type: new Abstract: We define a new family of complexity classes called bit-counting complexity classes, since membership depends not merely on the number of accepting paths, but also on the binary profile of that number. We study the relationship between this new family of complexity classes and the classical complexity classes. We prove that the classical complexity class ${\bf PP}$ is contained in our comparison based bit-counting complexity classes ${\bf...
The LD_DEBUG environment variable (2012)
The LD_DEBUG environment variable Originally published 23 April 2012, updated 10 September 2019 (add link to troubleshooting tool), updated 18 October 2019 (moved to Jekyll), updated 3 April 2023 with links to other tools Development of large systems using many shared (dynamically) loaded libraries can sometimes lead to some frustrating bugs that are difficult to diagnose. These bugs often arise because there a few different versions of libraries on the system and the “wrong” version gets...
Normalization Equivariance for Arbitrary Backbones, with Application to Image Denoising
arXiv:2605.08193v3 Announce Type: replace Abstract: Normalization Equivariance (NE) is a structural prior that improves robustness to distribution shift in image-to-image tasks. A function $f$ is normalization equivariant iff $f(a y + b\mathbf{1}) = a f(y) + b\mathbf{1}$ for all $a>0$ and $b\in\mathbb{R}$. Existing NE methods constrain every internal layer to NE-compatible operations. These constraints add runtime cost and exclude standard transformer components such as softmax attention and...
Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks
Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks This post is a high-level explainer for my Master’s thesis, which involves designing hardware architectures for ultrafast inference and online learning using the Kolmogorov-Arnold Network (KAN) architecture. I’ll assume familiarity with standard machine learning concepts, as well as some understanding of hardware and digital circuits; read my previous post here for the latter. Please read the two papers below for more...
One-Shot Klein Cutting Planes for Lipschitz Geodesically Convex Optimization in Hyperbolic Space
arXiv:2605.17540v4 Announce Type: replace Abstract: Motivated by the COLT 2023 open problem of Criscitiello, Mart\'inez-Rubio, and Boumal on deterministic first-order methods for Lipschitz geodesically convex optimization on Hadamard manifolds, we study hyperbolic space \[ \HH^d_{-\kappaC^2} =\{X\in\R^{d+1}:\ipL{X}{X}=-1,\ X_0>0\}, \qquad \ip{U}{V}_X=\kappaC^{-2}\ipL{U}{V}. For every geodesically convex $M$-Lipschitz function \[ f:\bar B_{\HH}(x_0,r)\to\R,\qquad s=\kappaC r, \] we give a...
Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks
Announce Type: cross Abstract: This paper studies how efficiently deep ReLU neural networks can approximate and learn smooth functions. When the error is measured in $L^p([0,1]^d)$ norm and the approximator is a network with width $W$ and depth $L$, recent works have proven the supper approximation rate $\mathcal{O}((WL)^{-2s/d})$ for Besov space $\mathcal{B}^s_{q,r}([0,1]^d)$ under the Sobolev embedding condition $s/d>1/q-1/p$. In order to overcome the curse of dimensionality in this rate,...
Revenue Guarantees of No-Swap-Regret Dynamics in First Price Auctions
arXiv:2606.06085v1 Announce Type: new Abstract: We study the revenue of approximate correlated equilibrium in discrete first price auctions - the set of allowable bids is $\mathcal{B} = \{0, 1/k, \dots, 1 - 1/k, 1\}$ for some $k \in \mathbb{N}$. We show that the revenue of any $\epsilon$-approximate correlated equilibrium is at least $v_2 - \Theta(1/k)- \Theta(\epsilon k^2)$, where $v_2 \geq 0$ is the second-highest valuation. Our results establish the first polynomial convergence rates on...
A Low-rank Interpolatory Projection Algorithm for Solving Large-scale T-Sylvester Equations
arXiv:2606.05640v1 Announce Type: new Abstract: This paper considers large-scale T-Sylvester equations of the form $AX - X^\top E^\top + B_1B_2^\top = 0$, which admit a low-rank solution. It is shown that when the unique solution of the T-Sylvester equation is low-rank, the problem naturally reduces to a tangential interpolation problem via oblique projection. The specific interpolation points and tangential directions needed to obtain the low-rank solution are not known a priori, thus...