Profile entropy measures learnability and compressibility of discrete distributions.
problem Understanding the learnability and compressibility of discrete distributions.
method Investigates profile entropy, showing its role in estimation, inference, and compression.
result Profile entropy is a fundamental measure unifying estimation, inference, and compression.
New summary measures reveal geometric structure in weighted measures on manifolds.
problem Lack of geometric information in standard weight-only summaries.
method Heat-kernel entropy profiles, tracking nonuniformity across scales.
result Geometric effective sample size discounts nearby or duplicate particles.
New theorems on compactness and finiteness for specific types of self-shrinkers.
problem Characterizing rotationally symmetric self-shrinkers with constraints.
method Compactness and finiteness theorems for self-shrinkers with specific symmetries and constraints.
result Existence of entropy minimizing self-shrinkers diffeomorphic to S1imesSn−1 for each n≥2. The paper explores inequalities for strongly-convex sets in weighted Riemannian manifolds.
problem Investigating dilation type inequalities on weighted Riemannian manifolds.
method Introducing dilation profile and comparing it with model space under lower weighted Ricci curvature bounds.
result Showed several functional inequalities related to various entropies.
Earlier studies have shown that stock market distributions can be well described by distributions derived from Tsallis entropy, which is a generalization of Shannon entropy to non-extensive systems. In this paper, Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler relative entropy (KLRE) to…
A new framework for adaptive behavior using reusable value profiles.
problem Adaptive behavior in changing environments requires switching among value-control regimes, but maintaining separate parameters for each situation is impractical.
method Introduces value profiles: reusable bundles of parameters assigned to hidden states, allowing for state-conditional strategy recruitment without independent parameters for each context.
result Profile-based models outperform simpler alternatives in probabilistic reversal learning, suggesting belief-dependent control of adaptive behavior.
We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed point regardless of the shape of demand curves for a wide class of probability di…
Sharp Gaussian isoperimetry proven along Ricci flow.
problem Proving sharp Gaussian isoperimetric inequality for Ricci flow.
method Using monotonicity formula to prove inequality.
result Exact Gaussian enlargement theorem and concentration estimates.
Study quantifies how LLMs capture higher-order statistical structure using cumulant expansion.
problem Understanding how LLMs internalize statistical structure during next-token prediction.
method Cumulant-expansion framework treating softmax entropy as perturbation around center distribution.
result Cumulants reveal distinct signatures for mathematical vs. general text prompts, quantifying feature-learning dynamics.
New efficient algorithm for approximate PML distribution.
problem Computing the profile maximum likelihood (PML) distribution efficiently.
method Exploiting sparsity structure and new matrix rounding algorithm.
result First provable computationally efficient implementation of PseudoPML.
New method uses asymmetric Tsallis relative entropy for better risk assessment in financial portfolios.
problem Improving risk assessment for financial portfolios using asymmetric data.
method Generalized Tsallis relative entropy (ATRE) for asymmetric distributions of returns.
result ATRE shows better risk-return profiles, especially during market crashes.
Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form (ρ(λX))λ≥0, where ρ is a convex risk measure and X a random variable, and we call such a curve a \emph{liqu…
This paper demonstrates two novel methods to estimate the global SNR of speech signals. In both methods, Deep Neural Network-Hidden Markov Model (DNN-HMM) acoustic model used in speech recognition systems is leveraged for the additional task of SNR estimation. In the first method, the entropy of the DNN-HMM output is c…
Calculates local Granger causality for Gaussian and nonlinear systems.
problem Understanding causal influence in complex systems.
method Vector autoregression and information-theoretic approach.
result Local Granger causality offers a robust and fast method for time-directed information transfer.
The paper measures semantic information production in generative models using information theory.
problem Measuring when semantic decisions are made during generative model training.
method Using an online formula for the optimal Bayesian classifier, the paper estimates conditional entropy and determines time intervals for highest information transfer.
result Semantic information transfer is highest in intermediate stages of diffusion, with different classes making decisions at different times.
Study shows translators can have non-removable singularities at infinity but eventually converge to unique planes.
problem Understanding singularities and convergence of translators at infinity.
method Global analysis of quasilinear soliton equations, sharp non-standard elliptic decay estimates, and potential theory.
result Finite entropy, finite genus translators converge to uniquely determined planes at infinity.
Study error bounds and optimal schedules for Masked Diffusions with factorized approximations.
problem Analyzing trade-offs between computation and accuracy in Masked Diffusion Models.
method Provided general error bounds and identified optimal schedules based on data distribution information profiles.
result Identified optimal schedule sizes for Masked Diffusion Models.
Flatsomatic compresses cancer mutation data with VAEs, maintaining predictive power.
problem Compressing somatic mutation profiles in cancer while preserving predictive power.
method Flatsomatic uses a Variational Auto Encoder (VAE) with MLP architecture, optimizing evidence lower bound and beta-VAE for latent space regularization.
result Flatsomatic embeddings maintain predictive power of original data, reducing dimensionality from 8,298 to 64.
New method shows data-driven causal studies can be misleading.
problem Misattribution of causality in data-driven earth science studies.
method Subsample-based ensemble approach for robust causality analysis.
result Transfer entropy-based causal graphs can be spurious.
A new covariance estimator reduces dimensionality in high-dimensional undersized samples.
problem Challenges in estimating covariance matrices for high-dimensional data with fewer samples.
method Maximum Entropy Covariance (MEC) estimator that combines covariance matrices from different response categories.
result MEC estimator improves efficiency in dimension reduction methods like SIR and SAVE.
A method to produce personalized classification models to automatically review online dating profiles on Tinder is proposed, based on the user's historical preference. The method takes advantage of a FaceNet facial classification model to extract features which may be related to facial attractiveness. The embeddings fr…
The resolution and calibration of pure spectra of minority components in measurements of chemical mixtures without prior knowledge of the mixture is a challenging problem. In this work, a combination of band target entropy minimization (BTEM) and target partial least squares (T-PLS) was used to obtain estimates for sin…
A method to describe Riemann surfaces using graph profiles is proposed.
problem Describing Riemann surfaces in a graph-theoretic framework.
method Graph profiles to represent Riemann surfaces, establishing necessary and sufficient conditions for their existence.
result A criterion for the existence of Riemann surfaces with a given signature.
In cheminformatics, compound-target binding profiles has been a main source of data for research. For data repositories that only provide positive profiles, a popular assumption is that unreported profiles are all negative. In this paper, we caution audience not to take this assumption for granted, and present empirica…
Method controls extrapolation in prediction profiles for statistical and machine learning models.
problem Avoiding invalid predictions due to extrapolation in prediction profiles.
method Genetic algorithm optimization over constrained factor regions.
result Optimal factor settings without constraint are often invalid and extrapolated.
Background: While machine learning (ML) models are rapidly emerging as promising screening tools in critical care medicine, the identification of homogeneous subphenotypes within populations with heterogeneous conditions such as pediatric sepsis may facilitate attainment of high-predictive performance of these prognost…
We equip many non compact non simply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly non generic property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new result…
We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincaré profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by Benjamini--Schramm--Timár. In this paper we focus on properties of the Poincaré profiles of groups with …
Logarithmic separation profile in hyperbolic groups shows hierarchical structure.
problem Understanding hierarchical structure in hyperbolic groups with logarithmic separation.
method Proving groups with logarithmic separation split over cyclic groups and providing counterexamples.
result Not all groups with hierarchical structure have logarithmic separation profile.
Framework detects shape shifts in functional profiles using Fréchet mean and shape invariant model.
problem Detecting shape shifts in functional profiles.
method Combining Fréchet mean and shape invariant model for interpretable parameterization of profile deviations.
result Potential shifts in shape deformation process distinguished by significant shifts in amplitude and/or phase.
Study compares isoperimetric profiles on manifolds with integral Ricci curvature bounds.
problem Comparing isoperimetric profiles on manifolds with integral Ricci curvature bounds.
method Extending previous work, the study uses integral bounds on Ricci curvature to prove comparison results for isoperimetric profile functions.
result Comparison results for the Isoperimetric profile function in manifolds with integral bounds on Ricci curvature.
There has been a rapid proliferation of machine learning/deep learning (ML) models and wide adoption of them in many application domains. This has made profiling and characterization of ML model performance an increasingly pressing task for both hardware designers and system providers, as they would like to offer the b…
We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide range of learning tasks. In particular, for every alphabet size k and desired…
Estimates lower bounds for isoperimetric profiles and improves on previous estimates for specific manifolds.
problem Estimating lower bounds for isoperimetric profiles of specific Riemannian manifolds.
method Explicit lower bounds for isoperimetric profiles of Riemannian product manifolds.
result Improved lower bounds for isoperimetric profiles and Yamabe constants.
In the context of sub-Riemannian Heisenberg groups Hn, n \geq 1, we shall study Isoperimetric Profiles, which are closed compact hypersurfaces having constant horizontal mean curvature, very similar to ellipsoids. Our main goal is to study the stability of Isoperimetric Profiles.
Paper describes profiles of multivariate normal distributions and novel estimators for mutual information.
problem Estimating mutual information for complex distributions.
method Analytical description of profiles, introduction of Bend and Mix Models, Monte Carlo estimation.
result Bend and Mix Models accurately estimate mutual information profiles and provide Bayesian estimates.
Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination of these profiles. The non-negativity constraint is imposed while estimating arch…
Adaptive Nucleus Truncation Improves Long-Form Reasoning
problem Improving long-form reasoning in language models
method Adaptive Nucleus Truncation Sampling (ANTS)
result Significant performance gains across various benchmarks
Random layer-wise pruning profiles are as effective as metric-based ones for various datasets.
problem Reduction of model size and computational resources in neural networks.
method Conducted baseline experiments, developed RL-based search algorithm for finding transferable layer-wise pruning profiles.
result RL-based layer-wise pruning profiles are as good or better than best profiles found on the original dataset via exhaustive search.
Study lampshuffler groups' isoperimetric profiles, refining previous estimates.
problem Relate isoperimetric profiles of lampshuffler groups to their base groups.
method Use lamplighter subgraphs and halo products to find optimal upper bounds.
result Sharp estimates for exponential growth groups, including Brieussel-Zheng groups.
The study analyzes how large language models form and express investor risk profiles.
problem Understanding how large language models (LLMs) form and express investor risk profiles.
method Examined three LLMs (GPT, Gemini, and Llama) and assessed their responses to a standardized risk questionnaire under varying prompts.
result LLMs generally form long-term investment profiles, but they exhibit different risk tolerance levels.
Uniform Lipschitz continuity of isoperimetric profiles in evolving surfaces.
problem Uniform Lipschitz continuity of isoperimetric profiles in evolving surfaces.
method Normalized Ricci flow on compact surfaces.
result Uniform Lipschitz continuity of isoperimetric profiles under normalized Ricci flow.
It is shown that, in dimensions <8, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.
The hypercube's perimeter is significantly larger than expected near half volume.
problem Understanding the isoperimetric profile of the hypercube.
method Analytical proof of perimeter bounds and comparison to Gaussian isoperimetric profile.
result The isoperimetric profile of the hypercube does not converge to the Gaussian profile as dimension increases.
The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.
With the maturation of metabolomics science and proliferation of biobanks, clinical metabolic profiling is an increasingly opportunistic frontier for advancing translational clinical research. Automated Machine Learning (AutoML) approaches provide exciting opportunity to guide feature selection in agnostic metabolic pr…
We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show that such profiles are in a one-parameter family of curves which w…
Develops a method to disaggregate aerosol optical depth into vertical extinction profiles.
problem Uncertainty in measuring aerosol vertical distributions due to limited observations.
method Bayesian nonparametric Gaussian process modeling using meteorological predictors.
result Model reconstructs realistic extinction profiles with well-calibrated uncertainty, outperforming idealized baselines.