Lorentz-Finsler geometry reveals new and old inequalities.
problem Finding new inequalities using Lorentz-Finsler geometry.
method Applying reverse Cauchy-Schwarz and reverse triangle inequalities in Lorentz-Finsler geometry.
result Proved new and refined inequalities, including refinements of Aczél's inequality.
The paper generalizes the Cauchy-Schwarz-Bunyakovsky inequality and applies it to elasticity problems.
problem Applying the Cauchy-Schwarz-Bunyakovsky inequality to elasticity problems.
method Presentation of discrete and integral forms, n-dimensional generalizations, and strengthened CBS inequality.
result The strengthened CBS inequality is crucial for elasticity problems.
Introduces Cauchy-Schwarz divergence for domain adaptation.
problem Evaluating discrepancy between source and target domains in unsupervised domain adaptation.
method Introduces Cauchy-Schwarz divergence as a measure for evaluating discrepancy between marginal and conditional distributions.
result CS divergence offers a tighter generalization error bound than Kullback-Leibler divergence.
We establish in this note some Cauchy-Schwarz-type inequalities on compact Kähler manifolds, which generalize the classical Khovanskii-Teissier inequalities to higher-dimensional cases. Our proof is to make full use of the mixed Hodge-Riemann bilinear relations due to Dinh and Nguye^n. A proportionality p…
New method improves deep neural network performance in regression tasks.
problem Improving generalization, robustness, and explainability of deep neural networks in regression.
method Developed a new Information Bottleneck approach using Cauchy-Schwarz divergence.
result Demonstrated superior performance on six real-world regression tasks.
We use the intrinsic area to define a distance on the space of homothety classes of convex bodies in the n-dimensional Euclidean space, which makes it isometric to a convex subset of the infinite dimensional hyperbolic space. The ambient Lorentzian structure is an extension of the intrinsic area form of convex bodies…
Improved Cauchy-Schwarz inequality for L1 and L2 norms.
problem Refining the classical Cauchy-Schwarz inequality for different norms.
method Developed a new inequality for p and q with q>p>2. result Demonstrated a new bound for the L1 norm in terms of Lp and Lq norms. New Schwarz Lemma for Bergman metrics in bounded domains.
problem Finding bounds for Bergman metrics in bounded domains.
method Using Cauchy-Schwarz inequality from probability theory.
result Established a new Schwarz Lemma for Bergman metrics.
We extend CS divergence to conditional distributions and show its advantages in time series data and sequential decision making.
problem Quantifying the closeness between conditional distributions.
method Developed and estimated a conditional Cauchy-Schwarz divergence using kernel density estimation.
result Conditional CS divergence outperforms previous methods in time series clustering and sequential decision making.
We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' vers…
Multithreshold Entropy Linear Classifier (MELC) is a density based model which searches for a linear projection maximizing the Cauchy-Schwarz Divergence of dataset kernel density estimation. Despite its good empirical results, one of its drawbacks is the optimization speed. In this paper we analyze how one can speed it…
Classifies reversible and strongly reversible elements in quaternionic groups.
problem Classifying reversible and strongly reversible elements in quaternionic groups.
method Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
result Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
The paper classifies reversible and strongly reversible elements in Hermitian isometry groups.
problem Classifying reversible and strongly reversible elements in Hermitian isometry groups.
method Classification through group theory and algebraic manipulation.
result New classification of strongly reversible elements in Sp(n).
This paper classifies reversible and strongly reversible elements in affine groups.
problem Classifying reversible and strongly reversible elements in affine groups.
method Identifying affine transformations and using conjugacy by involutions.
result Classification of reversible and strongly reversible elements in affine groups.
New neural net learns time-reversible symplectic dynamics.
problem Lack of time-reversibility in neural networks for symplectic systems.
method Proposes a new neural network architecture for time-reversible symplectic systems.
result Demonstrates learning of time-reversible symplectic dynamics from data.
A new trading strategy using reinforcement learning for statistical arbitrage.
problem Traditional statistical arbitrage models rely on model assumptions and price deviations from a long-term mean.
method Empirical reversion time metric, reinforcement learning framework, and state space optimization.
result Optimal mean reversion strategy identified through reinforcement learning.
Algebraic method reveals criterion for quaternionic Möbius group reversibility.
problem Characterizing reversibility in quaternionic Möbius group elements.
method Purely algebraic approach using matrix entries and conjugacy invariants.
result Explicit criterion for reversibility in terms of matrix entries.
Recent studies have shown that online portfolio selection strategies that exploit the mean reversion property can achieve excess return from equity markets. This paper empirically investigates the performance of state-of-the-art mean reversion strategies on real market data. The aims of the study are twofold. The first…
A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodes…
Sharp stability results for reverse isoperimetric inequalities in 2D.
problem Reverse isoperimetric inequalities in the plane.
method Stability analysis of λ-convex bodies and convex bodies with smooth boundaries. result Sharp stability results for reverse isoperimetric inequalities, including inradius and Cheeger inequalities.
Let G be a group. An element g in G is called reversible if it is conjugate to g−1 within G, and called strongly reversible if it is conjugate to its inverse by an order two element of G. Let HHn be the n-dimensional quaternionic hyperbolic space. Let PSp(n,1) be the i…
Boundary rigidity proven for non-reversible Finsler metrics.
problem Recovering non-reversible Finsler metrics from boundary distance data.
method Sum of reversible Finsler norm and closed 1-form, boundary rigidity results.
result 1-form can be uniquely recovered from boundary distance data.
On-line portfolio selection has attracted increasing interests in machine learning and AI communities recently. Empirical evidences show that stock's high and low prices are temporary and stock price relatives are likely to follow the mean reversion phenomenon. While the existing mean reversion strategies are shown to …
Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.
problem Approximating target distributions in conditional diffusion models.
method Using finite Gaussian mixtures with ReLU-network logits as reverse kernels, reducing the problem to static conditional density approximation.
result The resulting neural reverse-kernel class is dense in conditional KL divergence under exact terminal matching.
New knots not rationally concordant to their reverses found.
problem Identifying knots not rationally concordant to their reverses.
method Infinite family of knots constructed, rational knot concordance group analyzed.
result Infinite rank subgroup in rational knot concordance group.
The paper classifies reversible elements in Seifert-fibered spaces and braid groups.
problem Classifying reversible elements in Seifert-fibered spaces and braid groups.
method Classification of reversible elements in Fuchsian groups, application to Seifert-fibered groups, and analysis of 3-torsion elements.
result Classification and analysis of reversible and 3-torsion elements in Seifert-fibered spaces and braid groups.
Reverse annealing boosts quantum matrix factorization performance.
problem Improving quantum matrix factorization performance.
method Combining forward and reverse annealing for nonnegative/binary matrix factorization.
result Combination of forward and reverse annealing significantly improves performance.
TRS-ODENs learn dynamics with time-reversal symmetry for more efficient learning.
problem Learning dynamics with time-reversal symmetry for more efficient learning.
method Proposed a loss function and a new framework (TRS-ODENs) to learn dynamics efficiently.
result TRS-ODENs can learn dynamics from noisy and complex trajectories efficiently.
Paper proves rigidity theorems for geodesically reversible Finsler metrics.
problem Understanding geodesically reversible Finsler metrics in closed manifolds.
method Applied theory of volumes and areas on Finsler spaces to establish rigidity theorems.
result Partial explanation of the scarcity of geodesically reversible Finsler metrics in closed manifolds.
Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.
problem Testing identity of reversible Markov chains from a single trajectory.
method Using lumping-congruent Markov embeddings, the problem is simplified to testing symmetric chains over a larger state space.
result Achieves state-of-the-art sample complexity for identity testing.
Proof of reverse isoperimetric inequality for black holes.
problem Reverse isoperimetric inequality for black holes in Einstein gravity.
method Geometric-analytic approach.
result Reversal of the usual isoperimetric inequality is explained by curved backgrounds governed by Einstein's equations.
New algorithm learns bridged diffusion processes without time-reversals.
problem Learning bridged diffusion processes efficiently and accurately.
method Score matching with Doob's h-transform, avoiding time-reversals.
result Outperforms existing methods in learning bridged diffusion processes.
Consider the problem of pricing options on forwards in energy markets, when spot prices follow a geometric multi-factor model in which several rates of mean reversion appear. In this paper we investigate the role played by slow mean reversion when pricing and hedging options. In particular, we determine both upper and …
Characterizes isometries between non-reversible Finsler manifolds.
problem Understanding isometries in non-reversible Finsler manifolds.
method Generalization of Myers-Nakai Theorem for Riemannian manifolds, modification of function spaces to accommodate asymmetric structure.
result Functional characterization of isometries between non-reversible Finsler manifolds.
New method trains neural samplers to sample from multi-modal distributions efficiently.
problem Mode-seeking behavior of reverse KL divergence hinders effective sampling from multi-modal target distributions.
method Minimizing reverse diffusive KL divergence along diffusion trajectories of model and target densities.
result Demonstrated enhanced sampling performance across various multi-modal distributions.
New ODE solvers improve training efficiency and accuracy.
problem Training Neural ODEs requires efficient and accurate gradient calculation.
method Presented algebraically reversible ODE solvers that are time and memory efficient, calculate exact gradients, and are numerically stable.
result Reversible solvers strictly improve upon previous architectures in efficiency and accuracy.
This paper describes an improvement in Deep Q-learning called Reverse Experience Replay (also RER) that solves the problem of sparse rewards and helps to deal with reward maximizing tasks by sampling transitions successively in reverse order. On tasks with enough experience for training and enough Experience Replay mem…
A new sampler speeds up Bayesian mixture models.
problem Sampling from Bayesian finite mixture models is slow and hard.
method Introduces a non-reversible sampling scheme for Bayesian finite mixture models.
result The new sampler outperforms classical samplers in many scenarios, especially during convergence.
Classifies orientation-reversing homeomorphisms of even periods on surfaces.
problem Classifying orientation-reversing homeomorphisms of even periods on surfaces.
method Following the approach of [1] and correcting errors in [1] for the case of periods multiple of 4.
result Classification for orientation-reversing homeomorphisms of periods multiple of 4.
We continue our study of geometric analysis on (possibly non-reversible) Finsler manifolds, based on the Bochner inequality established by the author and Sturm. Following the approach of the Γ-calculus a la Bakry et al, we show the dimensional versions of the Poincare--Lichnerowicz inequality, the logarithmic Sobolev…
A quandle orbit's orientation is problematic when reversed.
problem The natural orientation-reversal of quandle orbits is unsuitable for medial quandles.
method Defined the orientation-reversal of a quandle orbit by inverting translations, observed it's unsuitable for medial quandles.
result The natural orientation-reversal of quandle orbits is unsuitable for medial quandles.
PETRA enables parallel training of deep models with reversible architectures.
problem Challenges in parallelizing deep model training.
method Introduces PETRA, a novel approach for parallelizing gradient computations in reversible architectures.
result Achieves competitive accuracies on CIFAR-10, ImageNet32, and ImageNet using ResNet models.
New method detects inconsistencies in AHP matrices using triadic preference reversals.
problem Challenges in assessing consistency in AHP pairwise comparison matrices.
method Triadic preference reversals to detect inconsistencies between pairs of elements.
result 97% accuracy in detecting inconsistencies, significantly surpassing traditional methods.
RER improves sample complexity by updating in reverse order.
problem Theoretical analysis limits RER's convergence rate.
method Tighter analysis for larger learning rates and longer sequences.
result RER converges faster with larger learning rates and longer sequences.
The paper proves a reverse isoperimetric inequality and applies it to analyze surface flows.
problem Analyzing the negative gradient flow of the Willmore energy plus volume.
method Proved a quantitative reverse isoperimetric inequality and applied it to the flow.
result Initial surfaces converge to a round point in finite or infinite time.
Extended elliptical slice sampling for infinite-dimensional spaces, proving reversibility.
problem Proving reversibility of elliptical slice sampling in infinite-dimensional spaces.
method Extended elliptical slice sampling to infinite-dimensional separable Hilbert spaces, providing an alternative proof of reversibility.
result The approach yields a positive semi-definite Markov operator, proving reversibility.
SARD improves deep learning clinical prediction performance.
problem Deep learning models struggle to match linear models in healthcare predictions.
method Reverse Distillation to initialize deep models, combined with contextual and temporal embeddings.
result SARD outperforms state-of-the-art methods on clinical prediction outcomes.
Study homology products on loop spaces with orientation reversal.
problem Computing homology products on loop spaces with orientation reversal.
method Defined transfer product on loop space quotients using transfer maps and Chas-Sullivan loop product.
result Computed homology of loop spaces with orientation reversal and defined product.