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How abundant are good interpolators?

Announce Type: cross Abstract: Let $S$ be the set of unit norm linear classifiers $\theta \in \mathbb{R}^d$ which correctly classify every point of a labeled dataset $(X_i,y_i)_{i=1}^n$, $X_i \in \mathbb{R}^d$, $y_i \in \{-1,+1\}$, with a possibly negative margin $\kappa$ fixed in advance. Under two natural data-generating distributions of the $(X,y)$ pairs -- a Gaussian mixture model and a logistic model with Gaussian features -- and in the proportional regime $n/d \to \alpha$ with small...

arXiv CS 5d ago

Blow-ups of order types of positive density

Announce Type: cross Abstract: Order types are an equivalence relation between point configurations that capture their combinatorial and convexity properties. Let $P$ be a $\kappa$-colored sequence of $n \ge d+1$ points in general position in $\mathbb{R}^d$. Let $\rho$ be a $\kappa$-colored order type on $k \le d+1$ points that has positive density on $P$; that is, for some constant $\delta >0$, there are $\delta \cdot \binom{n}{k}$ $k$-point subsequences of $P$ that have the same order type...

arXiv CS 1d ago

Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks

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Hacker News 23h ago

A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space

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arXiv CS 2d ago

Infinite sequences with optimal diaphony, periodic $L_2$-discrepancy, and beyond

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arXiv CS 5d ago

The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space

Announce Type: new Abstract: Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the $\textbf{Euclidean Fallacy}$: representing SE(3) poses as flat $\mathbb{R}^{12}$ vectors. This approximation induces (1) manifold drift violating SO(3) constraints, (2) broken equivariance under coordinate transformations, and (3) non-geodesic trajectories with excessive kinematic cost. We introduce $\textbf{Lie...

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Magenta RealTime 2: Open and Local Live Music Models

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Hacker News 5d ago

Approximate Algorithms for Chamfer Distance Under Translation

arXiv:2605.25280v2 Announce Type: replace Abstract: Given two sets of points A and B, $|A| = m$, $|B| = n$, the Chamfer distance from $A$ to $B$ is defined as $\operatorname{CD}(A,B) = \sum_{a\in A} \min_{b\in B} d(a,b)$, where $d$ is a distance metric. Chamfer distance is a popular measure of dissimilarity between two sets of points that has seen increasing usage in computer vision and information retrieval as a substitute for the more computationally demanding Earth Mover's distance.

arXiv CS 8d ago

General Convex Agreement with Near-Optimal Communication

arXiv:2602.21411v2 Announce Type: replace Abstract: Byzantine Agreement (BA) considers a setting of $n$ parties out of which up to $t$ can be byzantine (malicious), and requires the honest parties to agree on an input subject to a condition called \emph{validity}: if all honest parties have input $v$, the output agreed upon must be $v$. Convex Agreement (CA) strengthens BA by requiring the output agreed upon to lie in the convex hull of the honest parties' inputs. This validity condition...

arXiv CS 2d ago

Row-Stochastic Matrices Can Provably Outperform Doubly Stochastic Matrices in Decentralized Learning

arXiv:2511.19513v3 Announce Type: replace Abstract: Decentralized learning often involves a weighted global loss with heterogeneous node weights $\lambda$. We revisit two natural strategies for incorporating these weights: (i) embedding them into the local losses to retain a uniform weight (and thus a doubly stochastic matrix), and (ii) keeping the original losses while employing a $\lambda$-induced row-stochastic matrix. Although prior work shows that both strategies target the same...

arXiv CS 9d ago