arXiv research

LLA shows strong performance in Bayesian optimization but has unbounded search space issues.

AlphaCFG discovers alpha factors using grammar-guided search.

New reshaping method improves hyperparameter search over random search.

The game of Chinese Checkers is a challenging traditional board game of perfect information that differs from other traditional games in two main aspects: first, unlike Chess, all checkers remain indefinitely in the game and hence the branching factor of the search tree does not decrease as the game progresses; second,…

The paper proves homotopy equivalences for spaces of unbounded Fredholm operators.

Unbounded convex domains have zero mean curvature on disconnected boundaries.

Many engineering problems require identifying feasible domains under implicit constraints. One example is finding acceptable car body styling designs based on constraints like aesthetics and functionality. Current active-learning based methods learn feasible domains for bounded input spaces. However, we usually lack pr…

Constructs unbounded Kasparov product for sphere embeddings into Euclidean space.

New PAC-Bayes training method improves model generalization for unbounded loss.

Bayesian optimization has recently emerged as a popular and efficient tool for global optimization and hyperparameter tuning. Currently, the established Bayesian optimization practice requires a user-defined bounding box which is assumed to contain the optimizer. However, when little is known about the probed objective…

We present a version of the equivariant gradient degree defined for equivariant gradient perturbations of an equivariant unbounded self-adjoint operator with purely discrete spectrum in Hilbert space. Two possible applications are discussed.

We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.

Study ancient solutions on graphs with unbounded Laplacians, generalizing previous results.

Symplectic method solves infinite-dimensional Schrödinger equations.

New algorithm tackles multiclass transductive online learning with unbounded labels.

New neural network rates for unbounded domains with weighted Sobolev spaces.

Short note shows unbounded dimensions in Fano K-moduli spaces.

New approach finds solutions to games with unbounded controls.

UDN adapts depth to data complexity, outperforming standard neural networks.

New method for manifold fitting under unbounded noise.

Geometric model of unbounded sl3 laminations with tropical coordinates.

New RL policy for unbounded state space with stability guarantee.

In this work, we study a new approach to optimizing the margin distribution realized by binary classifiers. The classical approach to this problem is simply maximization of the expected margin, while more recent proposals consider simultaneous variance control and proxy objectives based on robust location estimates, in…

New approach to concentration inequalities for unbounded state space dynamical systems.

A new language for neural architecture search decouples search spaces and algorithms.

New analysis shows a gap between Gaussian RKHS and neural networks on unbounded domains.

Solves open problem on universally consistent online learning with unbounded losses.

A new framework generates large hierarchical search spaces for neural architectures.

Using results from our companion article [arXiv:1112.4824v2] on a Schauder approach to existence of solutions to a degenerate-parabolic partial differential equation, we solve three intertwined problems, motivated by probability theory and mathematical finance, concerning degenerate diffusion processes. We show that th…

A method to reduce memory usage in NAS by pruning the search space.

We factorize the Dirac operator on the Connes-Landi 4-sphere in unbounded KK-theory. We show that a family of Dirac operators along the orbits of the torus action defines an unbounded Kasparov module, while the Dirac operator on the principal orbit space -an open quadrant in the 2-sphere- defines a half-closed chain. W…

Two new algorithms improve performance in adversarial bandits with unbounded losses.

New framework for conformal equivariant cycles in KK-theory.

Statistical model checking for PCTL on MDPs using reinforcement learning.

We produce solutions to the Kähler-Ricci flow emerging from complete initial metrics $g_0$ which are $C^0$ Hermitian limits of Kähler metrics. Of particular interest is when $g_0$ is Kähler with unbounded curvature. We provide such solutions for a wide class of $U(n)$-invariant Kähler metrics $g_0$ on $n$ dimensional c…

GP-PSRL achieves sublinear regret for continuous control with unbounded state space.

A real valued function $\varphi$ of one variable is called a metric transform if for every metric space $(X,d)$ the composition $d_\varphi = \varphi\circ d$ is also a metric on $X$. We give a complete characterization of the class of approximately nondecreasing, unbounded metric transforms $\varphi$ such that the trans…

Algorithm learns diffusion processes with high-dimensional state spaces.

We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform maps. A unified treatment is given to the large scale dimension and the small scale …

einspace expands NAS search space to include diverse neural architectures.

Recent advances in Neural Architecture Search (NAS) have produced state-of-the-art architectures on several tasks. NAS shifts the efforts of human experts from developing novel architectures directly to designing architecture search spaces and methods to explore them efficiently. The search space definition captures pr…

New groups found in hyperbolic space with infinite fields of definition.

Approaches to learning Bayesian networks from data typically combine a scoring function with a heuristic search procedure. Given a Bayesian network structure, many of the scoring functions derived in the literature return a score for the entire equivalence class to which the structure belongs. When using such a scoring…

We establish the factorization of Dirac operators on Riemannian submersions of compact spin$^c$ manifolds in unbounded KK-theory. More precisely, we show that the Dirac operator on the total space of such a submersion is unitarily equivalent to the tensor sum of a family of Dirac operators with the Dirac operator on th…

Develops thermodynamic formalism for quasimorphisms on negatively curved spaces.

New model reduces matrix factorization bias, yielding truly low-rank solutions.

We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an arbitrarily small positive optimality gap of $δ$ in $\tilde{O}(1/\sqrtδ)$ computation…

We introduce the quasi-hyperbolicity constant of a metric space, a rough isometry invariant that measures how a metric space deviates from being Gromov hyperbolic. This number, for unbounded spaces, lies in the closed interval $[1,2]$. The quasi-hyperbolicity constant of an unbounded Gromov hyperbolic space is equal to…