On a compact complex manifold we study the behaviour of strong Kähler with torsion (strong KT) structures under small deformations of the complex structure and the problem of extension of a strong KT metric. In this context we obtain the analogous result of Miyaoka extension theorem. Studying the blow-up of a strong KT…
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48 results for “KT structures”
PSI-KT improves KT accuracy and interpretability in learning materials.
problem Optimizing learning materials selection and timing for understanding and retention.
method Hierarchical generative approach using Bayesian inference.
result Superior multi-step predictive accuracy and scalable inference.
We present the construction of a large class of homogeneous KT, HKT and QKT manifolds, , using an invariant metric on and the canonical connection. For this a decomposition of the Lie algebra of is employed, which is most easily described in terms of colourings of Dynkin diagrams of simple Lie algebras. KT…
A strong KT (SKT) manifold consists of a Hermitian structure whose torsion three-form is closed. We classify the invariant SKT structures on four-dimensional solvable Lie groups. The classification includes solutions on groups that do not admit compact four-dimensional quotients. It also shows that there are solvable g…
Generalized Kernel Thinningstat.ML
Improves probability distribution compression with KT algorithm.
problem Efficiently compressing probability distributions.
method Kernel thinning (KT) algorithm with four improvements.
result KT yields tighter, dimension-free guarantees for any kernel.
We use the procedure of reduction of Courant algebroids to reduce strong KT, hyper KT and generalized Kaehler structures on Courant algebroids. This allows us to recover results from the literature as well as explain from a different angle some of the features observed there in. As an example, we prove that the moduli …
We introduce and study a notion of `Sasaki with torsion structure' (ST) as an odd-dimensional analogue of Kähler with torsion geometry (KT). These are normal almost contact metric manifolds that admit a unique compatible connection with 3-form torsion. Any odd-dimensional compact Lie group is shown to admit such a stru…
Proposes a new KT technique for deep representation learning.
problem Efficient knowledge transfer for representation learning tasks.
method Trains a student model maintaining mutual information with teacher model.
result Outperforms existing KT techniques and allows new applications.
Study the geometry and symmetries of moduli spaces of connections on KT manifolds.
problem Investigate the geometry and symmetries of moduli spaces of Hermitian-Einstein and instanton connections on KT manifolds.
method Analyze the geometry and symmetries of moduli spaces of Hermitian-Einstein and instanton connections on KT manifolds, using vector fields and connections with skew-symmetric torsion.
result The geometry of moduli spaces can be modeled on principal bundles with specific fibre and base spaces.
On astheno-Kaehler metricsmath.DG
A Hermitian metric on a complex manifold of complex dimension is called {\em astheno-Kähler} if its fundamental -form satisfies the condition . If , then the metric is {\em strong KT}, i.e. is -closed. By using blow-ups and the …
Some selected applications of KT and HKT geometries in string theory, supergravity, black hole moduli spaces and hermitian geometry are reviewed. It is shown that the moduli spaces of a large class of five-dimensional supersymmetric black holes are HKT spaces. In hermitian geometry, it is shown that a compact, conforma…
Enhances supervised learning speed with KT algorithm.
problem Speed up supervised learning tasks with minimal loss.
method Generalizes kernel thinning to supervised learning, combining NW and KRR with KT.
result KT-based estimators offer superior computational and statistical efficiency.
Investigating the Robustness of Knowledge Tracing Models in the Presence of Student Concept Driftcs.LG
KT models struggle with student concept drift, but BKT remains the most stable.
problem Impact of student concept drift on KT models.
method Applied four KT models to five academic years of data.
result KT models generally degrade in performance with concept drift, BKT remains stable.
KT models improved slightly with synthetic student data.
problem Limited access to real student data and lack of diversity in public datasets.
method Simulated student data using three statistical strategies and tested on KT baselines.
result Synthetic data can lead to similar performance as real data.
Kernel Treeletsstat.ML
KT combines treelets with kernel functions for hierarchical clustering.
problem Hierarchical clustering of non-numeric data.
method Combines treelets and kernel functions to handle non-numeric data.
result KT effectively clusters non-numeric data.
SKVMN improves KT models by tracing student knowledge states and dependencies.
problem Tackling limitations of existing KT models in deep learning.
method Proposes SKVMN, a deep learning model unifying recurrent and memory capacities.
result Significantly outperforms state-of-the-art KT models on multiple datasets.
This note records two results which were inexplicably omitted from our paper on Pin structures on low dimensional manifolds, [KT]. Kirby chose not to be listed as a coauthor. A Pin^- structure on a surface F induces a quadratic enhancement of the mod 2 intersection form, q: H_1(F;Z/2Z) -> Z/4Z Theorem 1.1 says that q v…
Reduction of HKT-Structuresmath.DG
KT-geometry is the geometry of a Hermitian connection whose torsion is a 3-form. HKT-geometry is the geometry of a hyper-Hermitian connection whose torsion is a 3-form. We identify non-trivial conditions for a reduction theory for these types of geometry.
New algorithms reduce private bandit regret to nearly non-private levels.
problem Differentially private adversarial bandits and expert advice.
method Conversion of non-private algorithms to private, new algorithms for bandits and expert advice.
result Improved regret bounds for private bandits, sublinear for small ε.
qDKT improves KT models by considering individual question outcomes.
problem Ignoring question-specific outcomes leads to inaccurate learner skill tracking.
method qDKT incorporates graph Laplacian regularization and uses a fastText-inspired initialization scheme.
result qDKT achieves state-of-the-art performance in predicting learner outcomes.
This paper classifies Hermitian structures on 6-dimensional nilmanifolds M=G/L for which the fundamental 2-form is d d-bar closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is described when G is the complex Heisenberg group, and explicit solutions are obta…
The paper describes Hermitian non-Kähler structures on complex flag manifolds.
problem Understanding Hermitian non-Kähler structures on products of principal S¹-bundles.
method Using representation theory of complex simple Lie algebras and Cartan-Ehresmann connections.
result Explicit description of Hermitian non-Kähler manifolds and families of complex structures.
Quantization of a Lagrangian field system essentially depends on its degeneracy and implies its BRST extension defined by sets of non-trivial Noether and higher-stage Noether identities. However, one meets a problem how to select trivial and non-trivial higher-stage Noether identities. We show that, under certain condi…
A Hermitian metric on a complex manifold is called strong Kähler with torsion (SKT) if its fundamental 2-form is -closed. We review some properties of strong KT metrics also in relation with symplectic forms taming complex structures. Starting from a -dimensional SKT Lie algebra $\mathfr…
New algorithm for multiarmed bandits with variable, unbounded delays achieves similar regret bounds.
problem Variable, unbounded delays in multiarmed bandits.
method Introduces a new algorithm that skips rounds with excessively large delays and uses a doubling scheme.
result Achieves the same regret bound as Exp3 with variable, unbounded delays.
Develops Hamilton-Jacobi theory for non-conservative field theories in k-contact geometry.
problem Analyzes non-conservative field theories, especially dissipative systems.
method Introduces evolution k-contact k-vector fields and develops two Hamilton-Jacobi theories.
result Recover ordinary contact Hamilton-Jacobi theory as k=1, and enlarges application range.
MOTS improves Thompson sampling to match minimax bounds for bandit problems.
problem Achieving optimal regret bounds for Thompson sampling in multi-armed bandit problems.
method Proposes MOTS, a variant of Thompson sampling that clips arm sampling.
result Proves MOTS achieves minimax optimal regret bounds .
New constraints on space and adaptivity in bandits force more batches and memory use.
problem Simultaneous space and adaptivity constraints in stochastic bandits.
method Proved lower bounds and constructed an algorithm with near-minimax regret.
result Near-minimax regret requires more batches and memory than previously thought.
New algorithm improves multiclass classification regret bound.
problem Improving multiclass classification with bandit feedback.
method Developed a new bandit classification algorithm.
result Guaranteed regret of , improving over classical algorithms.
Paper defines and proves a new analytic index for Fredholm operators.
problem Defining the analytic index rigorously for families of Fredholm operators.
method Based on Segal's ideas, new definition under weaker continuity assumptions.
result New definition agrees with Atiyah-Singer index when applicable.
Improved analysis shows Maillard sampling achieves optimal regret bounds.
problem Optimal regret bounds for K-armed bandit problem.
method Improved analysis of Maillard sampling (MS) to achieve asymptotical optimality and minimax regret bound.
result MS achieves both asymptotical optimality and minimax regret bound of √(KT log T).
Con-TS optimizes wireless link throughput with latency constraints.
problem Optimizing rate selection for wireless links with latency constraints.
method Proposes Con-TS, a constrained Thompson sampling algorithm for stochastic MAB problems.
result Con-TS achieves upper bounds on expected constraint violations and throughput loss.
New algorithm FEWA tackles rotting bandits with improved regret bounds.
problem Non-stationary rewards in recommendation systems.
method FEWA constructs moving averages of increasing windows to identify high-reward arms.
result FEWA achieves better regret bounds for rotting bandits than previous methods.
In this paper, we consider the symmetries of the Dirac operator derived from a connection with skew-symmetric torsion. We find that the generalized conformal Killing-Yano tensors give rise to symmetry operators of the massless Dirac equation, provided an explicitly given anomaly vanishes. We show that this gives rise t…
Defines holomorphic differential forms on complex manifolds over commutative Banach algebras.
problem Defines holomorphic differential forms on complex manifolds over commutative Banach algebras.
method Defines -holomorphic vector bundles and differential forms on -manifolds.
result Defines cohomology groups as -modules, providing a new perspective on cohomology.
Optimal multiclass U-calibration error found to be Θ(√KT).
problem Online multiclass U-calibration with low regret for all bounded proper losses.
method Follow-the-Perturbed-Leader algorithm and lower bound construction.
result Optimal U-calibration error is Θ(√KT).
For a Kähler Manifold , the "symplectic Dolbeault operators" are defined using the symplectic spinors and associated Dirac operators, in complete analogy to how the usual Dolbeault operators, and , arise from Dirac operators on the canonical complex spinors on . We give special atte…
Virtual twin groups map to symmetric groups, revealing automorphism structure.
problem Understanding homomorphisms between virtual twin groups and symmetric groups.
method Using irreducible right-angled Coxeter groups and right-angled Artin groups.
result A complete description of homomorphisms between virtual twin groups and symmetric groups, including the structure of the automorphism group of .
The paper finds global Darboux coordinates for a new family of symplectic forms on the deformation space of -structures.
problem Finding global Darboux coordinates for a specific family of symplectic forms.
method Study of complete Lagrangian fibrations and application to the deformation space of -structures.
result Global Darboux coordinates for a new family of symplectic forms are found.
Sharp bounds for Kirby-Thompson invariants of knotted surfaces computed.
problem Computing sharp lower bounds for Kirby-Thompson invariants of knotted surfaces.
method Using dual curve complex distances to compute invariants.
result Exact values of KT-invariants computed for knotted surfaces with bridge number ≤ 6.
Using a combinatorial approach described in a recent paper of Manolescu, Ozsváth, and Sarkar we compute the Heegaard-Floer knot homology of all knots with at most 12 crossings as well as the invariant for knots through 11 crossings. We review the basic construction of \cite{MOS}, giving two examples that can be wor…
New algorithms avoid a dominant lower-order term in heavy-tailed loss settings.
problem Prediction with heavy-tailed losses without prior knowledge.
method Adaptive algorithms that avoid the maximum of losses as a lower-order term in regret.
result Improved regret bounds of and .
New algorithm for bandits with delayed action effects, reducing regret.
problem Delayed impact of actions in multi-armed bandits.
method Formulated a new bandit setting with delayed action effects, proposed an algorithm with regret bound.
result Achieved a regret of and showed a matching lower bound.
Squint bound improved by removing term.
problem Improving the Squint bound by removing the term.
method Using the Krichevsky--Trofimov algorithm to change the prior.
result Removed the term from the Squint bound.
Paper optimizes FTPL for adversarial and stochastic bandits with specific tail distributions.
problem Optimizing Follow-the-Perturbed-Leader (FTPL) policy for bandit problems.
method Analyzes FTPL with Fréchet-type tail distributions in adversarial and stochastic settings.
result FTPL with certain Fréchet-type tail distributions achieves regrets in adversarial bandits.
RKT model improves knowledge tracing by considering exercise relations and student forget behavior.
problem Traditional KT models fail to consider both exercise relations and student forget behavior.
method RKT model uses relation-aware self-attention to incorporate exercise relations and student forget behavior.
result RKT model outperforms state-of-the-art KT methods on real-world datasets.
Improved online Lasso reduces regret in sparse linear contextual bandits.
problem Sparse linear contextual bandit problem with inefficient sampling.
method Perturbed adversary approach to alleviate sampling inefficiency.
result Online Lasso achieves regret bound.
A Simple and Optimal Policy Design with Safety against Heavy-Tailed Risk for Stochastic Banditsstat.ML
New policy optimizes risk and optimality in stochastic bandits.
problem Optimizing risk in stochastic bandits with heavy-tailed risk.
method Designing policies with worst-case optimality for expected regret and light-tailed risk distribution.
result Achieves worst-case optimality for expected regret and light-tailed risk distribution.