We introduce the notion of partial presimplicial set and construct its geometric realization. We show that any semiadequate diagram yields a partial presimplicial set leading to a geometric realization of the almost-extreme Khovanov homology of the diagram. We give a concrete formula for the homotopy type of this geome…
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48 results for “Realizable Setting”
Improved multi-group learning with group-realizable concepts.
problem Enhancing multi-group learning efficiency.
method Empirical risk minimization over group-realizable concepts.
result Improved sample complexity in group-realizable settings.
Study compares adaptive vs fixed query learning methods.
problem Comparing adaptive and fixed query learning methods for task approximation.
method Examined in-context and agentic learning in two settings: unrestricted and realizable.
result Adaptivity does not hinder performance in unrestricted setting but can in realizable setting.
Incorrect parity-based descriptions of realizable Gauss diagrams found, but bipartite graphs provide a valid approach.
problem Incorrect descriptions of realizable Gauss diagrams using parity conditions.
method Used bipartite graphs to describe realizable Gauss diagrams.
result Realizable Gauss diagrams can be accurately described using bipartite graphs.
Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet diverse examples. Under a probabilistic setting for discrete input spaces, we focus …
Study shows certain mapping class groups cannot be realized as subgroup of homeomorphisms.
problem Proving non-realizability of specific mapping class groups.
method Analyzing compactly supported and full mapping class groups of surfaces with genus 3 or order 6 symmetries.
result Proven non-realizability of mapping class groups for surfaces with genus 3 or order 6 symmetries.
We study geometric realization questions of curvature in the affine, Riemannian, almost Hermitian, almost para Hermitian, almost hyper Hermitian, almost hyper para Hermitian, Hermitian, and para Hermitian settings. We also express questions in Ivanov-Petrova geometry, Osserman geometry, and curvature homogeneity in ter…
New DP algorithms achieve near-optimal regret bounds for online learning problems.
problem Online learning problems with zero-loss solutions and differential privacy constraints.
method Developed new Differentially Private algorithms with near-optimal regret bounds.
result Achieved near-optimal regret bounds for various online prediction and convex optimization problems.
New active learning framework for multiclass classification beyond realizability assumption.
problem Active learning in non-realizable settings with convex model classes.
method Surrogate risk minimization, epoch-based fitting, aggregation of models.
result Achieves label and sample complexity comparable to prior work in non-realizable settings.
VOLARE provides standardized realized volatility measures from financial data.
problem Lack of standardized realized volatility measures from ultra-high-frequency data.
method Asset-specific pipeline for cleaning and sampling data, providing a wide range of realized estimators.
result Comprehensive set of realized estimators for equities, exchange rates, and futures.
Affine realizations with affine state processes for stochastic partial differential equationsmath.PR
The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.
Characterizes statistical complexity of realizable regression in PAC and online learning.
problem Understanding the statistical complexity of realizable regression in both PAC and online learning settings.
method Introduces minimax instance optimal learners, novel and combinatorial dimensions to characterize learnability.
result Characterizes which classes of real-valued predictors are learnable and provides necessary conditions for learnability.
Neural networks cannot approximate certain functions in Sobolev spaces, leading to unbounded parameter growth.
problem Non-closedness of sets of neural networks in Sobolev spaces.
method Construction of sequences of neural networks whose realizations converge to functions not realizable by neural networks.
result Sets of realized neural networks are not closed in order- Sobolev spaces for .
We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian manifold. This requires extending the Tricerri-Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen …
Dehn twists on K3-type 4-manifolds are not homotopy coherently Nielsen realizable.
problem Homotopy coherent Nielsen realization problem for Dehn twists on 4-manifolds
method Using family Seiberg-Witten theory
result Failure of the classical Nielsen realization problem in K3-type 4-manifolds
Unified framework for realizable and agnostic learning.
problem Lack of a unified theory for realizable and agnostic learnability.
method Three-line blackbox reduction.
result Unified understanding across various learning settings.
On Query-efficient Planning in MDPs under Linear Realizability of the Optimal State-value Functioncs.LG
TensorPlan algorithm finds δ-optimal policies with poly queries under linearly realizable state-value function.
problem Efficient planning in MDPs with linearly realizable state-value function.
method TensorPlan algorithm using poly simulator queries.
result First algorithm with polynomial query complexity using only linear-realizability of a single competing value function.
Boosting is a widely used machine learning approach based on the idea of aggregating weak learning rules. While in statistical learning numerous boosting methods exist both in the realizable and agnostic settings, in online learning they exist only in the realizable case. In this work we provide the first agnostic onli…
Study apple tasting feedback in online binary classification, providing new insights into minimax expected mistakes.
problem Online binary classification with partial feedback (apple tasting).
method Combinatorial analysis, Littlestone dimension, Effective width.
result Established a trichotomy of minimax expected mistakes in the realizable setting.
Investigates conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.
problem Conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.
method Analysis of GKM graphs and fiber bundles, counterexamples, and classification of twist automorphisms.
result Realizability of fiber bundles of GKM graphs depends on the twist automorphism and can be decided in terms of the classification.
New algorithms for interactive learning match minimax bounds efficiently.
problem Interactive learning in the realizable setting with computational efficiency.
method General framework, computationally efficient algorithms, Monte Carlo hit-and-run sampling.
result Sample complexities quantifiable in terms of combinatorial quantities, computationally efficient.
Neural network training is usually accomplished by solving a non-convex optimization problem using stochastic gradient descent. Although one optimizes over the networks parameters, the main loss function generally only depends on the realization of the neural network, i.e. the function it computes. Studying the optimiz…
We develop a tractable model of realization utility that studies the role of reference-dependent S-shaped preferences in a dynamic investment setting with reinvestment. Our model generates both voluntarily realized gains and losses. It makes specific predictions about the volume of gains and losses, the holding periods…
Study online learning with set-valued feedback, showing differences between deterministic and randomized approaches.
problem Online learning with set-valued feedback, where labels are sets rather than single labels.
method Introduced new combinatorial dimensions (Set Littlestone and Measure Shattering) to characterize learnability.
result Characterized deterministic and randomized online learnability, and established bounds for various learning settings.
In this paper we focus on compacta which possess a neighbourhood basis that consists of nested solid tori . We call these sets toroidal. In \cite{hecyo1} we defined the genus of a toroidal set as a generalization of the classical notion of genus from knot theory. Here we introduce the se…
Researchers solved a complex problem for a specific type of 4-manifolds.
problem Realizing mapping classes of finite order on del Pezzo surfaces.
method Synthesized results from reflection group theory and 4-manifold topology.
result Provided both positive and negative examples of realizability.
We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian random field. In this setting, the posterior distribution on the objective func…
Theory extends optimal learning rates without realizability assumption.
problem Agnostic binary classification without realizability assumption.
method Identifies tetrachotomy of optimal rates and combinatorial structures.
result Optimal universal rates for binary classification in agnostic setting.
New algorithms improve label complexity for active multi-distribution learning.
problem Active multi-distribution learning with improved label complexity.
method Developed new algorithms for active multi-distribution learning and established improved label complexity upper and lower bounds.
result Improved label complexity upper and lower bounds for active multi-distribution learning.
Efficient RL algorithm for MDPs with linear realizability, achieving optimal regret bound.
problem Efficient reinforcement learning under linear realizability assumption for MDPs with stochastic dynamics.
method Frozen Policy Iteration algorithm that uses high-confidence data and freezes policy for well-explored states.
result Achieves optimal regret bound of for linear (contextual) bandits.
We consider a classical N. Steenrod's problem on realization of homology classes by images of the fundamental classes of manifolds. It is well-known that each integral homology class can be realized with some multiplicity as an image of the fundamental class of a manifold. Our main result is an explicit purely combinat…
4 flat 3-manifolds realized in hyperbolic 4-space.
problem Realizing flat 3-manifolds in hyperbolic 4-space.
method Using finite-volume hyperbolic 4-manifolds with cusp sections.
result 6 closed orientable flat 3-manifolds realized as cusp sections.
Study robust online learning with adversarial perturbations.
problem Learning robust classifiers in the presence of adversarial perturbations.
method Formulated as an online learning problem, considered both realizable and agnostic learnability, defined new dimension controlling mistake/regret bounds.
result Showed new dimension controls mistake/regret bounds, generalized to multiclass hypothesis classes.
In this paper, we will show that the projection does not have a section; i.e. the braid group cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary point-wise and marked points in the interior as a set. We also give a new proof of a result o…
We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. Basing our estimator…
Study of loss functions for learning to defer, proving consistency.
problem Learning to defer in machine learning.
method Introduced a family of surrogate losses parameterized by and proved their consistency.
result Proved realizable -consistency and Bayes-consistency of specific surrogate losses.
As a first step to understand how complicated attractors for dynamical systems can be, one may consider the following realizability problem: given a continuum , decide when can be realized as an attractor for a homeomorphism of . In this paper we introduce toroidal sets as th…
In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK\cap P are also discussed, where gK is a coset space in G.
Analytic realization of Thom-Smale complex for G-manifolds.
problem Realizing Thom-Smale complex for G-manifolds with Lie group action.
method Using G-invariant Witten instanton complex associated with a Morse-Bott function.
result Generalized Thom-Smale complex for G-manifolds including horizontal direction influence.
Bayesian model improves asset price forecasting using realized volatility.
problem Improving asset price forecasting accuracy.
method Integrates dynamic gamma process with DLMs for price and realized volatility.
result Significant improvements in asset price forecasting compared to standard models.
Comparative learning combines realizable and agnostic settings for two hypothesis classes, reducing sample complexity.
problem Learning with two hypothesis classes in a more general setting than single hypothesis classes.
method Introduces comparative learning, defines mutual VC dimension and Littlestone dimension, and applies insights to multiaccuracy and multicalibration.
result Sample complexity of comparative learning is characterized by mutual VC dimension and Littlestone dimension.
Study shows realizable learnability doesn't imply agnostic learnability for distributions.
problem Learnability and robustness of distribution classes.
method Analyzes the relationship between learnability and robustness for distribution learning.
result Realizable learnability does not imply agnostic learnability for distributions.
New protocol for online learning with partial feedback, extending classical methods.
problem Learning with partial feedback where only one acceptable label is observed per round.
method Introducing a collection version space to address the lack of direct extension of classical methods.
result Characterization of learnability in set-realizable regime using Partial-Feedback Littlestone dimension and Partial-Feedback Measure Shattering dimension.
Solves a problem related to Nielsen realization for certain groups.
problem Whether a cocompact proper topological manifold is equivariantly homotopy equivalent to a classifying space.
method Assumes a zero-dimensional singular set and uses properties of hyperbolic groups and aspherical manifolds.
result Solves the problem for specific groups containing a normal torsion-free subgroup.
Paper tackles sample-efficient RL for linearly realizable MDPs with limited revisiting.
problem Sample-efficient reinforcement learning for linearly realizable MDPs with limited revisiting.
method Develops a new sampling protocol that allows for backtracking and revisiting states in a controlled manner.
result Achieves polynomial sample complexity scaling with feature dimension, horizon, and inverse sub-optimality gap.
Given a finite subgroup G of the mapping class group of a surface S, the Nielsen realization problem asks whether G can be realized as a finite group of homeomorphisms of S. In 1983, Kerckhoff showed that for S a finite-type surface, any finite subgroup G may be realized as a group of isometries of some hyperbolic metr…
Paper integrates real data into probabilistic models using Fourier transform.
problem Learning from constrained data sets in high dimensions.
method Functional approach based on weak formulation of Fourier transform of probability measures.
result Estimation of posterior probability measures for QoI and QoI with control parameter.
In this paper, we first discuss the regular level set of a nonsingular Smale flow (NSF) on a 3-manifold. The main result about this topic is that a 3-manifold admits an NSF flow which has a regular level set homeomorphic to if and only if . T…