A new method trains deep neural networks for open set domain adaptation without negative open set difference.
problem Training deep neural networks for open set domain adaptation without negative open set difference.
method Proposes a new upper bound of target-domain risk, including source-domain risk, ε-open set difference (Δε), distributional discrepancy, and constant. Uses gradient descent for source-domain risk and Δε, and adversarial training for distributional discrepancy. Trains DNNs via minimizing the new upper bound. result Shows state-of-the-art performance on benchmark datasets.
The aim of unsupervised domain adaptation is to leverage the knowledge in a labeled (source) domain to improve a model's learning performance with an unlabeled (target) domain -- the basic strategy being to mitigate the effects of discrepancies between the two distributions. Most existing algorithms can only handle uns…
New bounds on inscribed triangles in arbitrary planar domains.
problem Finding inscribed triangles in arbitrary planar domains with specific angle constraints.
method Proving the existence of uniformly fat triangles and not-too-fat triangles in bounded open sets.
result Existence of a maximal number Θ (between 0 and 60) for inscribed triangles with angles ≥ Θ degrees.
This paper reviews information theory in open-world machine learning.
problem Lack of a unified theoretical foundation for open-world machine learning.
method Synthesis of information theoretic approaches.
result Established a pathway toward provable and trustworthy open world intelligence.
Study on covering probability of random balls in bounded open sets.
problem Probability of covering a bounded open set E with random balls of radius δ. method Geometric conditions and partition of E; lower bounds using good partitions. result Lower bounds to the probability of covering E with balls tend to 1 as Nexp(−δn). Sharp bounds on hyperbolic metrics in Ptolemaic spaces are derived.
problem Finding sharp bounds on hyperbolic metrics in Ptolemaic spaces.
method Construction of metrics on open subsets of Ptolemaic spaces.
result Sharp parameter bounds for hyperbolic and strongly hyperbolic metrics are derived.
Often, when dealing with real-world recognition problems, we do not need, and often cannot have, knowledge of the entire set of possible classes that might appear during operational testing. In such cases, we need to think of robust classification methods able to deal with the "unknown" and properly reject samples belo…
The VC-dimension of a set system is a way to capture its complexity and has been a key parameter studied extensively in machine learning and geometry communities. In this paper, we resolve two longstanding open problems on bounding the VC-dimension of two fundamental set systems: k-fold unions/intersections of half-s…
End-to-end PGL framework tackles open-set domain shift.
problem Real-world domain shift with unknown additional classes.
method Episodic training in graph neural network with adversarial learning.
result Guarantees tighter upper bound of target error.
Can certain shapes be drawn with a pencil and eraser?
problem Characterizing which planar sets can be drawn with a pencil and eraser.
method Analyzes the properties of sets drawable with a pencil and eraser, using open and closed unit disks.
result Drawability cannot be characterized by local obstructions.
Linear contextual bandit is an important class of sequential decision making problems with a wide range of applications to recommender systems, online advertising, healthcare, and many other machine learning related tasks. While there is a lot of prior research, tight regret bounds of linear contextual bandit with infi…
We consider the problem of online planning in a Markov Decision Process when given only access to a generative model, restricted to open-loop policies - i.e. sequences of actions - and under budget constraint. In this setting, the Open-Loop Optimistic Planning (OLOP) algorithm enjoys good theoretical guarantees but is …
A classical result due to Blaschke states that for every analytic self-map f of the open unit disk of the complex plane there exists a Blaschke product B such that the zero sets of f and B agree. In this paper we show that there is an analogue statement for critical sets, i.e. for every analytic self-map f of…
Abstract reviews known and open questions on spaces with lower Ricci bounds.
problem Understanding the structure and regularity of spaces with lower Ricci curvature bounds.
method Review of known results and presentation of open questions.
result Presentation of new open questions in the field.
For each Cantor set C in R3, all points of which have bounded local genus, we show that there are infinitely many inequivalent Cantor sets in R3 with complement having the same fundamental group as the complement of C. This answers a question from Open Problems in Topology and has as an application a simple c…
A coordinate cone in R^n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is a defnable in an o-minimal structure over the reals, open bounded subset of R^n such that its intersection with any translation of any coordinate cone is connected. This can be viewed as a …
Upper bound for conjugate radius in open manifolds with scalar curvature and spectrum constraints.
problem Bounding the conjugate radius of open manifolds with specific curvature and spectrum conditions.
method Established an upper bound using scalar curvature and bottom-of-spectrum constraints.
result For certain conditions, the conjugate radius is no more than π.
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, ha…
The study extends curvature bounds to non-smooth spaces and proves stability of mean curvature.
problem Proving curvature bounds in non-smooth spaces.
method Extending results from smooth Riemannian manifolds to non-smooth RCD spaces.
result Stability of mean curvature bounds under uniform convergence.
Let (M,g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.
We give lower bounds for the fundamental tone of open sets in submanifolds with locally bounded mean curvature in N×R, where N is an n-dimensional complete Riemannian manifold with radial sectional curvature KN≤κ. When the immersion is minimal our estimates are sharp. We also show that …
Learning linear predictors with the logistic loss---both in stochastic and online settings---is a fundamental task in machine learning and statistics, with direct connections to classification and boosting. Existing "fast rates" for this setting exhibit exponential dependence on the predictor norm, and Hazan et al. (20…
Open category detection is the problem of detecting "alien" test instances that belong to categories or classes that were not present in the training data. In many applications, reliably detecting such aliens is central to ensuring the safety and accuracy of test set predictions. Unfortunately, there are no algorithms …
New SVM margin bound improves generalization in machine learning.
problem Improving SVM margin bounds for better generalization.
method Stable sample compression schemes to derive new data-dependent generalization bounds.
result Proves a new optimal SVM margin bound with a log factor improvement.
In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space R^n with n >= 1 suffices, as does e.g. the Cantor space. In particular, intuitionistic logic cannot…
Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then we prove that the immersion f : M --> D can be chosen so that the limit sets of …
We first show that for a bounded pseudoconvex domain with a manifold quotient of finite-volume in the sense of Kahler-Einstein measure, the identity component of the automorphism group of this domain is semi-simple without compact factors. This partially answers an open question in [Fra95]. Then we apply this result in…
New sample complexity bounds for linear predictors and neural networks, focusing on initialization.
problem Understanding sample complexity for vector-valued linear predictors and neural networks, especially under initialization-dependent conditions.
method Size-independent bounds on Frobenius norm distance from a fixed reference matrix, applying to vector-valued predictors and neural networks.
result Established new sample complexity bounds for feed-forward neural networks, resolving open questions and introducing a new learnable problem.
Paper resolves open problems on sample complexity in binary hypothesis testing.
problem Open problems in distributed simple binary hypothesis testing under information constraints.
method One-shot lower bound on Bayes error, streamlined sample complexity formula, reverse data-processing inequality.
result Optimally tight sample complexity bounds for communication-constrained simple binary hypothesis testing.
Limits of manifolds with Kato bound on Ricci curvature are rectifiable.
problem Understanding limits of manifolds with specific curvature bounds.
method Proving rectifiability of limits of manifolds with Kato bound on Ricci curvature.
result Rectifiability of limits of manifolds with Kato bound on Ricci curvature.
The study examines spectral properties of the Laplacian on forms for open Riemannian manifolds.
problem Investigating spectral properties of the Laplacian on forms for open Riemannian manifolds.
method Finding sufficient conditions for the Weyl criterion to hold for the Lp-spectrum of the Laplacian on k-forms, proving the decomposition of the Lp-spectrum, and analyzing the resolvent set of the Laplacian. result The Lp-spectrum of the Laplacian on k-forms over hyperbolic space is described in detail. We give lower bounds for the fundamental tone of open sets in minimal submanifolds immersed into warped product spaces of type Nn×fQq, where f∈C∞(N). We also study the essential spectrum of these minimal submanifolds.
We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call "two-convexity". This statement is used to prove a number of rigidity statements in comparison geometry.
The set of Clifford bundles of bounded geometry over open manifolds can be endowed with a metrizable uniform structure. For one fixed bundle E we define the generalized component $\gencomp (E)$ as the set of Clifford bundles E′ which have finite distance to E. If D, D′ are the associated generalized Dirac ope…
The abstract discusses embedding manifolds in open books and contact structures.
problem Embedding manifolds in open books and contact structures.
method Using open book embeddings and contact structures, the abstract proves embedding theorems for various manifolds.
result Closed manifolds can be embedded in open books and contact structures.
Reduces bounded loss learning to binary classification.
problem Universal consistency of non-i.i.d. processes with bounded loss.
method Constructive reduction to binary classification.
result Any bounded loss output setting can be reduced to binary classification.
In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a bounded domain (with smooth boundary) in a given complete (not compact a priori) Riemannian manifold with Ricci bounded below . For this, we use test functions for the Rayleigh quotient subordinated to a family of open se…
New research shows exponential lower bounds for planning in MDPs with linearly-realizable optimal action-value functions.
problem Determining the minimum number of queries needed for sound planners in MDPs with linear function approximation.
method Analyzing fixed-horizon and discounted MDPs with a generative model, showing lower bounds on the number of queries required.
result Sound planners need at least exponential number of queries in both fixed-horizon and discounted settings.
Study shows area-minimizing submanifolds are mostly rough, not smooth.
problem Understanding the smoothness of area-minimizing submanifolds.
method Proved non-smoothness by contradiction and established Hausdorff dimension bounds.
result Area-minimizing submanifolds are not generically smooth, resolving a conjecture.
For p∈(1,2] and a bounded, convex, nonempty, open set Ω⊂R2 let μp(Ωˉ,⋅) be the p-capacitary curvature measure (generated by the closure Ωˉ of Ω) on the unit circle S1. This paper shows that such a problem of prescribing μp on a planar convex domain: "Given a finite…
Novel approach to universal online learning for bounded losses, closing open problems.
problem Characterizing processes for universal online learning under non-i.i.d. conditions.
method Characterization of processes admitting strong and weak universal learning, introduction of optimistically universal learning rule.
result Introduction of a novel 1NN algorithm that is optimistically universal for bounded losses.
Consider a sequence of minimal varieties M_i in a Riemannian manifold N such that the boundary measures are uniformly bounded on compact sets. Let Z be the set of points at which the areas of the M_i blow up. We prove that Z behaves in some ways like a minimal variety without boundary: in particular, it satisfies the s…
New approach for online learning with adaptive adversaries, simpler and more effective.
problem Online learning with adaptive adversaries, especially in bandits and MDPs.
method Uses standard unbiased estimators and a simple increasing learning rate schedule, aided by logarithmically homogeneous self-concordant barriers and strengthened Freedman's inequality.
result First high-probability regret bounds for adversarial bandits and MDPs, resolving open problems.
Study fine Pólya-Szegő inequalities in metric spaces with applications.
problem Fine Pólya-Szegő rearrangement inequalities in metric spaces.
method Theory of Sobolev and BV functions, synthetic Ricci bounds, isoperimetric inequality.
result New geometric and functional inequalities under Ricci lower bounds.
The paper proves properties of open manifolds with positive isotropic curvature.
problem Characterizing complete noncompact manifolds with positive isotropic curvature.
method Ricci flow with surgery on open orbifolds with isolated singularities.
result Open manifolds are diffeomorphic to a connected sum of spherical manifolds and cylinders.
Improved bounds for neural network approximations of functions.
problem Bounding the width of neural networks for function approximation.
method Extending Radon-based norms to bounded open sets and deriving new approximation bounds.
result Improved sparse approximation bounds for neural networks.
In [J.Birman, V.Gebhardt, J.Gonzalez-Meneses, Conjugacy in Garside groups I: cyclings, powers and rigidity] authors asked: (open question 2) is the size of USS of a rigid pseudo-Anosov braid is bounded above by some polynomial in the number of strands and the braid length? We answer this question in the negative.
The study proves that sets with constant nonlocal curvature are composed of equal balls under certain conditions.
problem Characterizing sets with constant nonlocal curvature.
method Analyzing measurable sets in R^d with constant nonlocal h-mean curvature under a suitable integrability assumption.
result Finite unions of equal balls are the only sets with constant nonlocal curvature under the given conditions.