Paper shows braid groups can't be realized geometrically.
problem Cannot geometrically realize braid groups as homeomorphisms.
method Showed non-existence of a section for the projection map.
result Braid groups cannot be realized geometrically.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,181 papers · 148 categories
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48 results for “Non-realizable setting”
New algorithms reduce collaborative PAC learning sample complexity.
problem Collaborative PAC learning with reduced sample complexity.
method Design of new algorithms for both realizable and non-realizable settings.
result Sample complexity is times the worst-case sample complexity for learning a single task.
Proofs non-realizability of mapping class group via homeomorphisms, resolves Thurston's conjecture.
problem Non-realizability of mapping class group via homeomorphisms
method Short and elementary proof, rigidity results for actions on Euclidean spaces
result Proof of non-realizability of mapping class group via homeomorphisms
The pure braid group cannot be realized as area-preserving homeomorphisms.
problem Realizing the pure braid group inside area-preserving homeomorphisms.
method Using rotation numbers to show non-realizability.
result The pure braid group has no realization inside area-preserving homeomorphisms.
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.
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 method for distributional off-policy evaluation using Bellman residual minimization.
problem Learning return distribution from offline data generated by a different policy.
method Energy Bellman Residual Minimizer (EBRM) method.
result Established finite-sample error bound for EBRM estimator.
New algorithm SELECT minimizes satisficing regret in bandits.
problem Minimizing regret in bandit optimization with satisficing arms.
method SELECT algorithm for satisficing regret minimization.
result SELECT achieves constant expected satisficing regret.
We construct non-constructible simplicial -spheres with vertices and non-constructible, non-realizable simplicial -balls with vertices for .
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.
P. M. Akhmetiev used a controlled version of the stable Hopf invariant to show that any (continuous) map N -> M between stably parallelizable compact n-manifolds, n\ne 1,2,3,7, is realizable in R^{2n}, i.e. the composition of f with an embedding M\subset R^{2n} is C^0-approximable by embeddings. It has been long believ…
Paper tackles MLR prediction error without assuming realizable models.
problem Prediction error in mixture of linear regressions without realizable assumptions.
method Developed algorithms for list-decoding MLR predictions and minimized empirical risk.
result Alternating minimization algorithm finds best fit lines in non-realizable settings.
For every compact surface of finite type (possibly with boundary components but without punctures), we show that when is sufficiently large there is no lift of the surface braid group to , the group of diffeomorphisms preserving marked points and restricting to t…
Paper solves the Hurwitz existence problem using fiber products.
problem Determining when a combinatorial map datum corresponds to a holomorphic map.
method Using fiber products of holomorphic maps between Riemann surfaces.
result Proves non-realizability of many branch data and constructs new data.
Active learning reconstructs hierarchical tree cuts from leaf similarity.
problem Reconstructing hierarchical tree cuts from pairwise leaf similarity.
method Pairwise similarity over tree leaves; active learning; regret and query complexity bounds.
result Theoretical guarantees on statistical error and practical linear-time implementations.
The article enumerates doubly symmetric diagrams for knots up to 18 crossings.
problem Enumerating doubly symmetric diagrams for knots.
method Developed an enumeration strategy for prime knots given by doubly symmetric diagrams.
result Determined all cases of doubly symmetric diagrams up to 18 crossings.
Torelli group cannot be realized as area-preserving homeomorphisms.
problem Realization of the Torelli group as area-preserving homeomorphisms.
method Analysis of the Torelli group and its relationship with homeomorphisms.
result The Torelli group has no realization inside the area-preserving homeomorphisms.
Algorithm learns arbitrary ReLU neurons under Gaussian inputs.
problem Learn an arbitrary ReLU activation over Gaussian marginals.
method Statistical Query (SQ) algorithm that outputs a ReLU activation achieving loss.
result First constant factor approximation for arbitrary bias in polynomial time.
S. Parsa's theorems on embedding and linking are simplified and presented.
problem Embedding graphs and simplicial complexes into lower-dimensional spaces.
method Piecewise linear (PL) embeddings and combinatorial arguments.
result Graphs and complexes can be embedded into lower dimensions with specific properties.
Generalizes cohomology ring result for combinatorial line arrangements.
problem Cohomology ring of boundary manifold for combinatorial line arrangements.
method Introduced boundary manifold, constructed homology cycles, computed cohomology ring.
result Cohomology ring of boundary manifold is isomorphic to double of Orlik-Solomon algebra.
This paper studies universal rates of ERM for binary classification under agnostic learning.
problem The challenge of achieving universal rates of ERM for binary classification under agnostic learning.
method The paper explores the agnostic universal rates of ERM for binary classification, revealing three possible rates: , , or arbitrarily slow.
result The paper provides a complete characterization of which concept classes fall into each of the three categories of agnostic universal rates.
The study provides error bounds for the generalized Lasso with sub-exponential data.
problem Analyzing the generalized Lasso under sub-exponential data distributions.
method Non-asymptotic analysis using generic chaining-based proof strategy.
result Error bounds for the generalized Lasso can be controlled by two complexity parameters.
This study tightens bounds on how GD and SGD generalize in smooth convex optimization problems.
problem Understanding how GD and SGD generalize in smooth stochastic convex optimization problems.
method Provided tight excess risk lower bounds for GD and SGD under different conditions.
result Lower bounds suggest overfitting occurs and gaps remain in some cases.
New algorithm trains ReLU gates provably in linear time.
problem Training ReLU gates in realizable settings with mild conditions.
method Iterative stochastic algorithm with moment assumptions.
result First recovery of true labels under data-poisoning attacks.
The paper explores embedding Ricci flow solutions in flag manifolds.
problem Realizing Ricci flow solutions as embedded submanifolds.
method Investigation of invariant metrics in flag manifolds, proving global attractors and non-realizable collapses.
result Certain Ricci flow collapses cannot be embedded in Euclidean spaces.
Solves open problem on universally consistent online learning with unbounded losses.
problem Open problem on universally consistent online learning with unbounded losses.
method Constructs random measurable partitions of the instance space.
result Simple memorization rule is optimistically universal for any unbounded loss.
New bandit algorithm works without realizability assumption.
problem Contextual bandit problems without realizability assumption.
method Computes a constrained regression problem in every epoch, ensuring similar regret guarantees as realizability-based algorithms.
result Ensures similar regret guarantees as realizability-based algorithms, up to a misspecification term.
To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate su…
New algorithm optimizes beam and rate allocation in mmWave systems for multiple users.
problem Optimizing beam and rate allocation in mmWave systems for multiple users with limited feedback.
method Introducing SAT-CTS, a combinatorial semi-bandit policy with satisficing objective.
result SAT-CTS achieves finite-time regret bounds and reduces satisficing regret in mmWave systems.
This work characterizes the benefits of averaging schemes widely used in conjunction with stochastic gradient descent (SGD). In particular, this work provides a sharp analysis of: (1) mini-batching, a method of averaging many samples of a stochastic gradient to both reduce the variance of the stochastic gradient estima…
New learner achieves optimal agnostic error in small error regime.
problem Optimizing agnostic learning in the small error regime.
method Careful aggregations of ERM classifiers.
result Achieves error $c \cdot τ+ O \left(\sqrt{\frac{τ(d + \log(1 / δ))}{m}} + \frac{d + \log(1 / δ)}{m}
ight)$, matching lower bound when .
Study shows Julia sets and gasket limit sets are quasiconformally different.
problem Quasiconformal non-equivalence of Julia sets and gasket limit sets.
method Proved quasiconformal non-equivalence of Julia sets and gasket limit sets.
result Julia sets and gasket limit sets are quasiconformally different.
New deep learning model for matching sets of items, preserving exchangeability.
problem Matching two different sets of items while preserving exchangeability.
method Exchangeable deep neural networks architecture and efficient training framework.
result Significant improvements in fashion set recommendation and group re-identification.
Study shows non-symmetric convex sets have full boundary limits.
problem Understanding boundaries of non-symmetric convex sets.
method Proved using proximal limit set analysis.
result Proximal limit set equals full projective boundary for non-symmetric irreducible divisible convex sets.
The paper analyzes set-to-set matching with neural networks, focusing on theoretical generalization.
problem Theoretical analysis of set-to-set matching with neural networks.
method Generalization error analysis of set-to-set matching with neural networks.
result Theoretical insights into the behavior of set-to-set matching models.
Generative model learns to autoencode and generate sets of images.
problem Learning to represent and generate sets of images with unknown number of sets.
method Set Distribution Networks (SDNs) learn set encoder, discriminator, generator, and prior.
result SDNs can reconstruct and generate sets of images with preserved attributes.
Study on cold and freezing sets in digital images.
problem Properties of cold sets in digital images.
method Analysis of properties and relationships between cold and freezing sets.
result Examined relationships between cold and freezing sets.
Paper solves whether zero sets are mapping degree sets.
problem Whether finite sets containing zero are mapping degree sets.
method Examined oriented closed connected manifolds of the same dimension.
result Affirmative answer given for both integer and rational settings.
Maps sets to probability distributions to minimize information loss.
problem Learning to map sets to probability distributions to preserve information.
method Relates set operations to probability distribution interpolations and demonstrates a preliminary solution.
result Experimental results show the effectiveness of the set embedding approach.
Unified framework for generating set-valued outputs.
problem Handling unordered set outputs with varying sizes.
method Sequential Set Generation (SSG) framework.
result SSG outperforms baseline methods in experiments.
New model predicts sets from feature vectors without discontinuity issues.
problem Discontinuity issues in predicting sets from feature vectors.
method General model that respects set structure, auto-encodes point sets, predicts bounding boxes, and attributes.
result Model successfully predicts sets from a single feature vector without discontinuity.
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.
We introduce the concept of hereditarily non uniformly perfect sets, compact sets for which no compact subset is uniformly perfect, and compare them with the following: Hausdorff dimension zero sets, logarithmic capacity zero sets, Lebesgue 2-dimensional measure zero sets, and porous sets. In particular, we give an exa…
Study dynamics and topology of flows near non-saddle sets or W-sets.
problem Understanding the dynamics and topology of flows near specific invariant sets.
method Cohomological relations and global properties analysis.
result Dynamical classification of surfaces and robustness of non-saddle-sets.
Bayesian optimization for set inputs using approximate set kernels.
problem Permutation-invariant optimization over sets with black-box functions.
method Developed a Bayesian optimization method with set kernel, efficient approximate set kernel, and constrained acquisition function.
result Our method outperforms other methods in numerical experiments.
The study explores mapping degree sets and their properties for manifolds.
problem Understanding the structure and properties of mapping degree sets for manifolds.
method Analyzes the properties of mapping degree sets and their relationships with self-mapping degree sets.
result Not every multiplicative set containing 0,1 is a self-mapping degree set.
This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.
problem Determining if minimum-volume confidence sets for multinomial outcomes are disjoint.
method Enumerating and covering the continuous regions of the exact p-value function to study the geometry of minimum-volume confidence sets.
result The geometry of minimum-volume confidence sets for multinomial parameters is studied, providing insights into their structure and properties.
Model learns set representations through optimized permutations.
problem Challenges in learning set representations due to permutation-invariance.
method Proposes a Permutation-Optimisation module to learn set permutations.
result Achieves state-of-the-art results on various set learning tasks.