We prove a natural inequality which implies the known lower bounds for the -dimensional Hausdorff measure of nodal sets for smooth compact manifolds.
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Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Modelsstat.ML
The natural gradient method has been used effectively in conjugate Gaussian process models, but the non-conjugate case has been largely unexplored. We examine how natural gradients can be used in non-conjugate stochastic settings, together with hyperparameter learning. We conclude that the natural gradient can signific…
A natural occurrence of shift equivalence in a purely algebraic setting constitutes the subject matter of the following short exposition.
We classify -spaces that admit a certain natural -symmetric structure. We further determine the maximal antipodal sets of these structures.
Consider a general machine learning setting where the output is a set of labels or sequences. This output set is unordered and its size varies with the input. Whereas multi-label classification methods seem a natural first resort, they are not readily applicable to set-valued outputs because of the growth rate of the o…
PixL2R maps natural language to pixel-based rewards for RL, improving sample efficiency.
problem Sparse reward settings in RL limit applicability to complex problems.
method Directly maps natural language descriptions to pixel-based rewards for guiding RL.
result Language-based rewards significantly improve sample efficiency in policy learning.
A new method uses natural gradients for efficient distribution optimization.
problem Challenges in computing natural gradients for many distributions.
method Reframe optimization as a surrogate distribution with easy natural gradient computation.
result Expands set of distributions efficiently targetable with natural gradients.
In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact manifold with boundary and the case of a closed manifold pair. This approach also g…
Introduces a natural parallel translation for navigation data.
problem Navigation data geometric representation and parallelism.
method Introduces a natural parallel translation using Riemannian parallelism.
result The natural parallel translation preserves the Randers norm and has a finite-dimensional holonomy group.
A method for predicting credal sets in classification tasks using conformal prediction.
problem Designing methods for learning credal set predictors in machine learning.
method Incorporates conformal prediction for predicting credal sets in classification tasks.
result Conformal credal sets are guaranteed to be valid with high probability.
Study evaluates how well question-answering models generalize to new data types.
problem Generalization of question-answering models to new data types.
method Constructed new test sets from different domains and evaluated models' performance.
result Models show significant performance drops when tested on new data types.
We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides with the invariant distribution induced by the set of fixed vectors of the isotropy. This extends a known result on compact naturally reductive spaces. We also address the study of the quotient by the foliation of symmetry.
In this paper, we extend the formal definition of topological surgery by introducing new notions in order to model natural phenomena exhibiting it. On the one hand, the common features of the presented natural processes are captured by our schematic models and, on the other hand, our new definitions provide the theoret…
We consider several natural sets of curves associated to a given Teichmüller disc, such as the systole set or cylinder set, and study their coarse geometry inside the curve graph. We prove that these sets are quasiconvex and agree up to uniformly bounded Hausdorff distance. Furthermore, we describe two operations on cu…
New methods using natural gradient for structured optimization.
problem Structured optimization problems.
method Structured second-order methods via natural gradient descent.
result Efficiency demonstrated on non-convex and deep learning problems.
Study relaxes identification assumptions for natural direct effects in non-randomized settings.
problem Identifying causal direct effects under unmeasured confounding.
method Developed relaxed conditions for identifying natural direct effects in non-randomized settings.
result Identified natural direct effect under unmeasured confounding conditions.
In [5], P. Lecomte conjectured the existence of a natural and conformally invariant quantization. In [7], we gave a proof of this theorem thanks to the theory of Cartan connections. In this paper, we give an explicit formula for the natural and conformally invariant quantization of trace-free symbols thanks to the meth…
We describe the connected components of the complement of a natural "diagonal" of real codimension 1 in a stratum of quadratic differentials on CP1. We establish a natural bijection between the set of these connected components and the set of generic configurations that appear on such "flat spheres". We also prove that…
New algorithm for online convex minimization over integer lattice.
problem Online decision-making with nonlinear combinatorial objectives.
method Introduces online -convex minimization and proposes efficient algorithms.
result Tight regret bound for full information setting algorithm.
The author studies regions foliated by 1D families of functions and their applications.
problem Understanding regions represented as foliated forms and natural smooth maps onto them.
method Investigates natural smooth maps respecting canonical projections and moment maps, focusing on foliated regions.
result Discusses the 1st derivative of functions and critical sets in foliated regions.
We determine the structure of the -Lie superalgebra generated by a set of carefully chosen natural operators of an orientable WSD manifold of rank three. This Lie superalgebra is formed by global sections of a natural Lie superalgebra bundle, and turns out to be a product of $\mathbf{sl}(4,\C)$ with the full special…
We review two strands of conceptual approaches to the formal representation of a decision maker's non-knowledge at the initial stage of a static one-person, one-shot decision problem in economic theory. One focuses on representations of non-knowledge in terms of probability measures over sets of mutually exclusive and …
Paper proposes a natural hedging framework with graphical assessment for longevity risk management.
problem Lack of a unified framework for natural hedging and graphical risk assessment.
method Structured natural hedging framework integrated with a graphical risk metric.
result Demonstrates flexibility, interpretability, and practical value for longevity risk management.
Study shows perceptual boost of visual attention varies with task difficulty and size.
problem Understanding how task-dependent the perceptual boost of visual attention is in natural settings.
method Designed and trained neural networks on various visual tasks, comparing results to baseline.
result Perceptual boost of attention is stronger with more difficult tasks and weaker with larger task sets.
We introduce the fibred toric varieties as equivariant bundles over lower dimensional toric varieties. An equivalent characterization is that the natural morphisms on them degenerate to bundle projections in the context of variation of toric varieties as GIT quotients. Our main observation is that these…
Rank-1 Approximation of Inverse Fisher for Natural Policy Gradients in Deep Reinforcement Learningcs.LG
Paper presents a rank-1 approximation method for natural policy gradients in deep RL.
problem Computing natural gradients requires inverting the Fisher Information Matrix, which is computationally expensive.
method Develops a rank-1 approximation to the inverse Fisher Information Matrix for efficient natural policy optimization.
result The rank-1 approximation converges faster and has similar sample complexity to stochastic policy gradient methods.
Smooth compactness for spaces of asymptotically conical self-expanders of mean curvature flowmath.DG
We show compactness in the locally smooth topology for certain natural families of asymptotically conical self-expanding solutions of mean curvature flow. Specifically, we show such compactness for the set of all two-dimensional self-expanders of a fixed topological type and, in all dimensions, for the set of self-expa…
Deep Sets improve reinforcement learning agent's object-centered navigation and generalization.
problem Improving reinforcement learning agents' ability to generalize to unseen objects and goals.
method Combining object-wise permutation invariant networks (Deep Sets) and gated-attention mechanisms.
result Agent demonstrates strong generalization to out-of-distribution goals in a procedurally-generated 2D world.
New Einstein metrics found on orthogonal groups without natural reductivity.
problem Finding non-naturally reductive Einstein metrics on orthogonal groups.
method Using real flag manifolds and symmetry assumptions on left-invariant metrics.
result Obtained new invariant Einstein metrics on $\SO(n)$.
BONG optimizes Bayesian inference online with natural gradient descent.
problem Sequential Bayesian inference in online settings.
method Bayesian online natural gradient (BONG) approach based on variational Bayes.
result BONG outperforms other online VB methods in non-conjugate settings.
Paper discusses natural quasiconvexity and its relation to decomposable sums in risk measures.
problem Understanding natural quasiconvexity and its implications in risk measures.
method Relates natural quasiconvexity to decomposable sums, proposes a general treatment of convexity index, and proves equivalence for certain spaces.
result Natural quasiconvexity and convexity are equivalent for conditional risk measures on spaces under mild conditions.
James bundlesmath.AT
We study cubical sets without degeneracies, which we call square sets. These sets arise naturally in a number of settings and they have a beautiful intrinsic geometry; in particular a square set C has an infinite family of associated square sets J^i(C), i=1,2,..., which we call James complexes. There are mock bundle pr…
We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [C] and [CM2], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces.
Deep learning has improved performance on many natural language processing (NLP) tasks individually. However, general NLP models cannot emerge within a paradigm that focuses on the particularities of a single metric, dataset, and task. We introduce the Natural Language Decathlon (decaNLP), a challenge that spans ten ta…
Multiple gapsmath.LO
We consider the notion of multiple gap as a finite set of ideals that cannot be separated. We study the different types of such objects that can be found in the Boolean algebra of subsets of the natural numbers modulo finite sets.
A new method compares image classifiers using adaptive sampling of natural images.
problem Evaluation of image classifiers on small, fixed test sets may not generalize to real-world images.
method Adaptive sampling from a large corpus of unlabeled images to maximize classifier discrepancies measured by WordNet hierarchy.
result Human labeling of model-dependent image sets reveals relative classifier performance.
We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with the…
Complex Valued Analytic Torsion for Flat Bundles and for Holomorphic Bundles with (1,1) Connectionsmath.DG
The work of Ray and Singer which introduced analytic torsion, a kind of determinant of the Laplacian operator in topological and holomorphic settings, is naturally generalized in both settings. The couplings are extended in a direct way in the topological setting to general flat bundles and in the holomorphic setting t…
Automates translating natural language to Verilog for digital design.
problem Manual translation of natural language specifications to Verilog is time-consuming and error-prone.
method Fine-tuned GPT-2 to derive Verilog from English, using a dataset of design tasks.
result GPT-2 achieved 94.8% correct translation across simple and abstract design tasks.
Current approaches for predicting sets from feature vectors ignore the unordered nature of sets and suffer from discontinuity issues as a result. We propose a general model for predicting sets that properly respects the structure of sets and avoids this problem. With a single feature vector as input, we show that our m…
The paper is concerned with defining a topology on the set of ideals of codimension d of the algebra C^\infty(M,R) with M being a compact smooth manifold. Its main property is that it is compact Hausdorff and it contains as a subspace the configuration space of d distinct unordered points in M and therefore provides a …
Many Machine Reading and Natural Language Understanding tasks require reading supporting text in order to answer questions. For example, in Question Answering, the supporting text can be newswire or Wikipedia articles; in Natural Language Inference, premises can be seen as the supporting text and hypotheses as question…
Using geodesic length functions, we define a natural family of real codimension 1 subvarieties of Teichmüller space, namely the subsets where the lengths of two distinct simple closed geodesics are of equal length. We investigate the point set topology of the union of all such hypersurfaces using elementary methods. Fi…
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat…
Unified model for sequence labeling and classification.
problem Efficiently perform multiple sequence labeling tasks.
method Generative framework with shared natural language output space.
result Significant improvements in few-shot and low-resource slot labeling.
A new class of Higgs bundles is introduced in a natural setting. Existence and nonexistence results for Higgs-Hermitian-Yang-Mills metrics are proved.
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers via a Poisson point process with mean measure on the power set of . Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, an…
We prove some results concerning the boundary of a convex set in $\H^n$. This includes the convergence of curvature measures under Hausdorff convergence of the sets, the study of normal points, and, for convex surfaces, a generalized Gauss equation and some natural characterizations of the regular part of the Gaussian …