arXiv research

Develops CPL for optimal prediction set length and validity.

Proposes a differentiable STFT for more efficient optimization of hop length.

New approach finds minima of geodesic lengths for non-uniform fillings.

New algorithm reduces regret bounds for Bayesian optimization with unknown hyperparameters.

Paper finds optimal shapes for minimizing average lengths of billiard trajectories in specific polygons.

Paper introduces a differentiable STFT for continuous window length optimization.

Improved phylogenetic tree reconstruction using flexible branch length distributions.

Paper estimates optimal ROC curve arc length and AUC, improving classification performance.

Optimizes treatment duration to maximize quality-adjusted lifetime.

Paper introduces length measures for curves and convex shapes, proving isoperimetric and distance properties.

We present Rotated Adaptive Tetra-iterated Quantizer (RATQ), a fixed-length quantizer for gradients in first order stochastic optimization. RATQ is easy to implement and involves only a Hadamard transform computation and adaptive uniform quantization with appropriately chosen dynamic ranges. For noisy gradients with al…

Develops optimal transport in Lorentzian spaces with synthetic curvature bounds.

Given $φ$ a pseudo-Anosov map, let $\ell_\mathcal{T}(φ)$ denote the translation length of $φ$ in the Teichmüller space, and let $\ell_\mathcal{C}(φ)$ denote the stable translation length of $φ$ in the curve graph. Gadre--Hironaka--Kent--Leininger showed that, as a function of Euler characteristic $χ(S)$, the minimal po…

New insights show embedding lengths correlate with semantic properties.

Non-parametric estimators improve quickest changepoint detection under irregular sequence lengths.

DeepCO uses deep learning for offline combinatorial optimization in warehouse operations.

Bayesian Optimization (BO) has become a core method for solving expensive black-box optimization problems. While much research focussed on the choice of the acquisition function, we focus on online length-scale adaption and the choice of kernel function. Instead of choosing hyperparameters in view of maximum likelihood…

Let $D$ be a Riemannian 2-disc of area $A$, diameter $d$ and length of the boundary $L$. We prove that it is possible to contract the boundary of $D$ through curves of length $\leq L + 200d\max\{1,\ln {\sqrt{A}\over d} \}$. This answers a twenty-year old question of S. Frankel and M. Katz, a version of which was asked …

CAPO optimizes LLM prompts more efficiently and cost-effectively.

Let $M$ be a Riemannian $2$-sphere. A classical theorem of Lyusternik and Shnirelman asserts the existence of three distinct simple non-trivial periodic geodesics on $M$. In this paper we prove that there exist three simple periodic geodesics with lengths that do not exceed $20d$, where $d$ is the diameter of $M$. We a…

The study examines translation lengths of pseudo-Anosov maps on curve graphs.

The paper studies properties of optimal metrics associated to curves on surfaces.

Sharp bounds found on shortest geodesic on punctured spheres.

Lower bounds on geodesic lengths for spheres with Willmore energy.

Clarifies definitions of global hyperbolicity in various spaces.

The paper develops algorithms to minimize queue length regret in a communication system.

A simple text model shows word lengths follow Zipf's law.

We construct a counterexample to a conjectured inequality L<2D, relating the diameter D and the least length L of a nontrivial closed geodesic, for a Riemannian metric on the 2-sphere. The construction relies on Guillemin's theorem concerning the existence of Zoll surfaces integrating an arbitrary infinitesimal odd def…

The Efficient Global Optimization (EGO) algorithm uses a conditional Gaus-sian Process (GP) to approximate an objective function known at a finite number of observation points and sequentially adds new points which maximize the Expected Improvement criterion according to the GP. The important factor that controls the e…

Bayesian optimization reduces RNN architecture search time.

Study shows not all smooth paths are optimal in certain geometric structures.

Transformers learn chain-of-thought reasoning for longer problems, proving length generalization.

The Minimum Description Length (MDL) principle states that the optimal model for a given data set is that which compresses it best. Due to practial limitations the model can be restricted to a class such as linear regression models, which we address in this study. As in other formulations such as the LASSO and forward …

We analyze differences between two information-theoretically motivated approaches to statistical inference and model selection: the Minimum Description Length (MDL) principle, and the Minimum Message Length (MML) principle. Based on this analysis, we present two revised versions of MML: a pointwise estimator which give…

Paper analyzes regret bounds for unconstrained online optimization.

Gradient flow of curve length on Sobolev metrics preserves convexity.

An online framework optimizes efficiency in conformal prediction with a target miscoverage rate.

Optimal inequalities found between Riemannian and Hilbert metrics in convex projective domains.

Sine activation functions enable two-layer neural networks to learn modular addition more efficiently.

Short proof for ideal polygons with near optimal orthogeodesic decomposition.

The study quantifies the information needed for causal queries at different levels of Pearl's hierarchy.

We present an asymptotic criterion to determine the optimal number of clusters in k-means. We consider k-means as data compression, and propose to adopt the number of clusters that minimizes the estimated description length after compression. Here we report two types of compression ratio based on two ways to quantify t…

Algorithm minimizes regret and converges to equilibria in Markov games.

This paper proves a conjecture about trisections with a specific length.

Transformer pretraining yields strong EB performance without explicit adaptation.

New online conformal prediction methods minimize strongly adaptive regret and achieve near-optimal coverage.

SentenceMIM learns rich latent representations for variable-length language data.

Normalization techniques such as Batch Normalization have been applied successfully for training deep neural networks. Yet, despite its apparent empirical benefits, the reasons behind the success of Batch Normalization are mostly hypothetical. We here aim to provide a more thorough theoretical understanding from a clas…