Guillemin trace formula adapted for group actions.
problem Distributional trace for proper, cocompact group actions.
method Developing an equivariant version of the distributional trace.
result Equivariant Guillemin trace formula for group actions.
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48 results for “distributional trace”
We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rank structure of its updates to ac…
We provide rigorous guarantees on learning with the weighted trace-norm under arbitrary sampling distributions. We show that the standard weighted trace-norm might fail when the sampling distribution is not a product distribution (i.e. when row and column indexes are not selected independently), present a corrected var…
A new method predicts student skill success rates in real-time.
problem Accurate and explainable prediction of student skill success rates in real-time.
method Performance Distribution Tracing (PDT) using a Dynamic Bayesian Network with continuous random variables.
result PDT provides both explainability and accuracy in real-time predictions of student skill success rates.
The flat trace of geodesic Koopman operators varies with negatively curved surfaces.
problem Understanding how the flat trace of geodesic Koopman operators changes with variations of negatively curved surfaces.
method Computing the first variation of the flat trace as a distribution and analyzing its leading singularity.
result The leading singularity coefficient is a linear functional of length variations, forcing marked lengths to be locally constant.
CausalSim corrects bias in trace-driven simulations for more accurate results.
problem Bias in trace-driven simulations due to system conditions during trace collection.
method CausalSim learns a causal model of system dynamics and latent factors from an RCT to remove bias from trace data.
result CausalSim reduces simulation errors by 53% and 61% compared to baselines, providing more accurate insights.
We prove the analogue of Weyl's law for a noncommutative Riemannian manifold, namely the noncommutative two torus equipped with a general translation invariant conformal structure and a Weyl conformal factor. This is achieved by studying the asymptotic distribution of the eigenvalues of the perturbed L…
Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.
problem Optimal transportation between Gaussian distributions with different dimensions.
method Entropic Gromov-Wasserstein and inner product Gromov-Wasserstein, with closed-form expressions and von Neumann's trace inequality.
result Closed-form expressions for the entropic IGW and its unbalanced variant between Gaussian distributions.
Ray tracing sampler improves neural network sampling efficiency and resilience.
problem Sampling neural network posterior distributions efficiently and robustly.
method Markov Chain Monte Carlo using ray tracing through likelihood space.
result Significantly higher resilience to gradient heating compared to HMC.
We study a "div-grad type" sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub-Riemannian manifold. We prove a short time asymptotic expansion of the heat trace up to any order. Our main result holds true for any smooth measure on the manifold, but it has a spec…
Improved reasoning model by sampling from power distribution without additional training.
problem Efficiently sampling from a sharpened distribution to improve reasoning models.
method Entropy-Cut Metropolis-Hastings algorithm that identifies key decision points for resampling.
result The method consistently improves reasoning models across various datasets.
Trace norm regularization is a popular method of multitask learning. We give excess risk bounds with explicit dependence on the number of tasks, the number of examples per task and properties of the data distribution. The bounds are independent of the dimension of the input space, which may be infinite as in the case o…
This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.
A trace formula for foliated flows on closed manifolds.
problem Establishing a trace formula for foliated flows on closed manifolds.
method Using leafwise currents and cohomologies, a trace formula is derived involving infinitesimal data from closed orbits and preserved leaves.
result A trace formula is proven for foliated flows on closed manifolds, solving a conjecture by C. Deninger.
SHMM models human mobility from GPS and text data, overcoming text sparsity.
problem Modeling human mobility from semantic trace data, especially addressing text sparsity.
method SHMM is a multi-modal spherical hidden Markov model that jointly models location, time, and text embeddings on a unit sphere using vMF distribution.
result SHMM outperforms state-of-the-art models in next location prediction and has lower training cost.
Bayesian generative models can flag performance loss, bias, and out-of-distribution image contentcs.LG
SLUG method detects bias and out-of-distribution content in generative models.
problem Generative models can underrepresent certain groups and fail on out-of-distribution data.
method SLUG: A new uncertainty quantification method for VAEs combining Laplace approximations and stochastic trace estimators.
result SLUG's UQ score correlates with bias and out-of-distribution content.
A general approach to proving that the length spectrum of a compact Riemannian manifold is an invariant of the Laplace spectrum comes from considering the wave trace, a spectrally determined tempered distribution. The Poisson relation states that the singularities of the wave trace can only occur at lengths of closed g…
A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be u…
We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of normalized orbital integrals associated to the hyperbolic conjugacy classes of this …
Study of torus surgeries on knot traces, finding exotic surfaces and traces.
problem Understanding exotic surfaces and traces through torus surgeries.
method Realizing annulus twisting as torus surgery, using key technical insight.
result Exotic elliptic surfaces and traces discovered, improving known geography.
Classifies knot traces with specific trisection genus limits.
problem Classifying knot traces with specific trisection genus limits.
method Classifying knot traces with specific trisection genus limits.
result Infinitely many knots have traces with trisection genus 3 and 4, and arbitrarily large trisection genus.
TRACE improves conformal prediction for multi-dimensional outputs.
problem Challenges in constructing valid and informative conformal prediction regions for multi-dimensional outputs.
method TRACE uses transport alignment in diffusion and flow matching models to define nonconformity scores.
result TRACE yields valid and adaptive conformal prediction regions for multimodal and non-convex distributions.
Consider a Riemannian symmetric space of non-compact type, where denotes a connected, real, semi-simple Lie group with finite center, and a maximal compact subgroup of . Let be its Oshima compactification, and the regular representation of on $\widet…
Formula derived for zeta functions of 3D foliated systems.
problem Analyzing zeta functions of 3D Riemannian foliated dynamical systems.
method Relating dynamical spectral -functions to zeta functions using the distributional dynamical Lefschetz trace formula.
result Proved a regularized determinant formula for zeta functions.
Paper derives trace formula for magnetic Laplacian at zero energy.
problem Trace formula for magnetic Laplacian at zero energy.
method Generalizes Gutzwiller trace formula, focuses on zero energy level.
result Derives trace formula at zero energy level.
In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.
In many environments only a tiny subset of all states yield high reward. In these cases, few of the interactions with the environment provide a relevant learning signal. Hence, we may want to preferentially train on those high-reward states and the probable trajectories leading to them. To this end, we advocate for the…
This paper proposes a methodology for host-based anomaly detection using a semi-supervised algorithm namely one-class classifier combined with a PCA-based feature extraction technique called Eigentraces on system call trace data. The one-class classification is based on generating a set of artificial data using a refer…
Prospects for Money Transfer Modelsphysics.soc-ph
Recently, in order to explore the mechanism behind wealth or income distribution, several models have been proposed by applying principles of statistical mechanics. These models share some characteristics, such as consisting of a group of individual agents, a pile of money and a specific trading rule. Whatever the trad…
New methods derive a generalized Frenkel trace formula for Lie groups.
problem Deriving a generalized Frenkel trace formula for Lie groups.
method Applying supersymmetric localization to quantum mechanical and gauged sigma models.
result Presented two complementary approaches for the derivation of the trace formula.
Examines a new type of analytic torsion on Riemannian manifolds.
problem Analyzing a new trace formula for Riemannian manifolds.
method Uses residue-trace instead of spectral zeta function quasi-trace.
result Defines and examines the residue analytic torsion.
Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.
problem Deriving and generalizing the Selberg trace formula.
method Supersymmetric localization principle and path integral derivation.
result Derives Selberg trace formula on arbitrary compact Riemann surfaces and generic compact locally symmetric spaces.
Introduces a new model for mapping matrices to matrices, subsuming linear regression.
problem Learning matrix-to-matrix mappings from data.
method Partial trace regression model, leveraging quantum information theory.
result Relevance demonstrated in matrix-to-matrix regression and positive semidefinite matrix completion.
Quantum probability theory reveals hidden structure in joint probability distributions.
problem Understanding hidden structure in joint probability distributions.
method Modeling joint probability distributions as density operators and applying partial trace.
result Decoding extra information in reduced density operators that captures subsystem interactions.
Proposes CLRS-Text, a new benchmark for evaluating LM reasoning capabilities.
problem Lack of transferable benchmarks for evaluating reasoning capabilities of language models.
method Developed a textual version of the CLRS benchmark, generating diverse algorithmic tasks.
result Demonstrates a novel challenge for the LM reasoning community and validates prior work.
We trace the initiative by Professor Meghnad Saha to develop a (statistical) physics model of market economy and his search for the mechanism to constrain the entropy maximized width of the income distribution in a society such that the spread of inequality can be minimized.
L-spaces and knot tracesmath.GT
New findings on knots and their traces, distinguishing L-space knots by their 0-trace.
problem Characterizing knots by their traces and Dehn surgeries.
method Combining Heegaard Floer homology with surface homeomorphisms and dynamics.
result The 0-trace detects every L-space knot, contrasting with characterizing surgeries.
This paper investigates the strength of the trace field as a commensurability invariant of hyperbolic 3-manifolds. We construct an infinite family of two-component hyperbolic link complements which are pairwise incommensurable and have the same trace field, and infinitely many 1-cusped finite volume hyperbolic 3-manifo…
We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.
Clarifies a trace for Heisenberg operators on contact manifolds.
problem Calculating the index of Heisenberg elliptic operators on contact manifolds.
method Introduced a new trace on Heisenberg pseudodifferential operators and constructed a cocycle in periodic cyclic cohomology.
result Simplified the construction of the trace on Heisenberg pseudodifferential operators.
Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.
problem Analyzing the magnetic Laplacian on compact hyperbolic surfaces.
method Computed the trace formula for magnetic Laplacian energies above the Mane critical level.
result Asymptotic behavior of trace formula coefficients near the Mane critical level.
Sharp inequality found on three-balls for fourth order Sobolev traces.
problem Fourth order Sobolev trace inequality on three-balls.
method Established through equivalence to a third order Sobolev inequality on two-spheres.
result Sharp fourth order Sobolev trace inequality on three-balls.
Infinite knots have non-integer trace values.
problem Finding knots with non-integer trace values.
method Proved existence of infinitely many non-homeomorphic hyperbolic knot complements with specific trace properties.
result Infinitely many non-homeomorphic hyperbolic knot complements with non-integer trace values.
Introduces expected eligibility traces for more efficient credit assignment in reinforcement learning.
problem Efficiently assigning credit to states and actions in reinforcement learning.
method Introduces expected eligibility traces, allowing updates to counterfactual sequences.
result Substantial improvements in temporal-difference learning can be achieved with expected traces.
Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.
problem Optimizing estimation of Kernel Stein Discrepancy from samples.
method Identifying and comparing minimax scales for U-statistic and V-statistic.
result Hilbert-Schmidt norm of Stein covariance operator gives optimal scale.
Quantum trace map defined for 3-manifolds with torus boundaries.
problem Quantifying topological structures of 3-manifolds with torus boundaries.
method Defining a quantum trace map from skein module to a quantum torus module.
result Established a 3D quantum trace map for 3-manifolds with torus boundaries.
New knots found that resist trace detection.
problem Knots not detected by any trace.
method Extended existing results to new knots.
result Knots exist that share traces with infinitely many distinct knots and are not detected by any trace.
Quantum heat tracesmath-ph
We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction formulas expressing these new invariants in terms of some integral transforms of the u…