New quantum kernels avoid overfitting by combining local and global components.
problem Exponential concentration in quantum kernels leads to overfitting.
method Local-global quantum kernels combining small subsystem and full-system measurements.
result Demonstrated benign overfitting in local-global quantum kernels.
This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds (with boundary and corners), similarly to the toric case, but their associated in…
Improves deep learning robustness by enforcing local and global compactness.
problem Deep neural networks' vulnerability to adversarial attacks.
method Proposes Adversary Divergence Reduction Network (ADRN) that enforces local/global compactness and clustering assumption.
result Augmenting adversarial training with ADRN components improves robustness.
Combines local and global samplers for efficient sampling.
problem Limited learning accuracy in regions with little data.
method Explore-Exploit Markov chain Monte Carlo strategy (Ex2MCMC) result Proves V-uniform geometric ergodicity of Ex2MCMC. Purpose: Lung nodules have very diverse shapes and sizes, which makes classifying them as benign/malignant a challenging problem. In this paper, we propose a novel method to predict the malignancy of nodules that have the capability to analyze the shape and size of a nodule using a global feature extractor, as well as …
Decomposes spillover effects under misspecified exposure mappings.
problem Modeling outcomes as functions of own treatment and a misspecified exposure mapping of others' treatments.
method Pseudo-true estimands and local-global extension for structured misspecification.
result Sharp asymptotic decomposition into direct, local, and global components.
We present a fairly general construction of unbounded representatives for the interior Kasparov product. As a main tool we develop a theory of C^1-connections on operator * modules; we do not require any smoothness assumptions; our sigma-unitality assumptions are minimal. Furthermore, we use work of Kucerovsky and our …
A multiplicatively closed, horizontal foliation on a Lie groupoid may be viewed as a "pseudoaction" on the base manifold M. A pseudoaction generates a pseudogroup of transformations of M in the same way an ordinary Lie group action generates a transformation group. Infinitesimalizing a pseudoaction, one obtains the…
cKAM improves adaptive sampling by incorporating a cyclical stepsize scheme.
problem Adaptive Metropolis algorithms can get stuck in local modes.
method cKAM uses a cyclical stepsize scheme to encourage exploration and escape from local modes.
result cKAM successfully escapes local modes and converges to the true posterior distribution.
New method improves feature selection in tree-based models.
problem Previous feature selection methods in tree-based models lack sufficient regularization and sub-optimal performance.
method Developed a new gain penalization approach for tree-based models that allows for flexible feature-specific importance weights.
result The new method improves out-of-sample performance, especially with correlated features.
We study local, global and local-to-global properties of threefolds with certain singularities. We prove criteria for these threefolds to be rational homology manifolds and conditions for threefolds to satisfy rational Poincaré duality. We relate the topological Euler characteristic of elliptic Calabi-Yau threefolds wi…
New mesh network preserves symmetries in deep learning.
problem No existing mesh processing architecture is equivariant to all symmetries.
method Equivariant attention-based mesh network using relative tangential features.
result The network achieves improved performance and is equivariant to various transformations.
Paper bounds Kähler manifolds' diameter using Orlicz spaces and complex Monge-Ampère equations.
problem Establishing diameter bounds for Kähler manifolds in Orlicz spaces.
method Proving a priori estimates for solutions of complex Monge-Ampère equations in Orlicz spaces using Kołodziej's and Guo-Phong-Tong-Wang's approaches.
result Uniform estimates for Green's function and its gradient for Kähler metrics.
Deep neural networks perform well on local tasks but struggle with global tasks.
problem Understanding the limitations of overparameterized deep neural networks in learning global functions.
method Introduced k-local and k-global functions to study the interplay between depth and function locality. result Depth is beneficial for learning local functions but detrimental to learning global functions.
Novel approach combines local and global brain changes for AD prediction.
problem Detecting Alzheimer's disease through local and global brain changes.
method Patch-based 3D-CNNs combined with global topological features for multi-scale brain tissue connectivity.
result Average precision score of 0.95 for classifying cognitively normal subjects and AD patients (prevalence ~55%).
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that can model latent (dependent) variables, and directed mixed graphs (DMGs) that c…
PerCDL learns personalized dictionaries for physiological signals combining global and local structures.
problem Representing datasets with both global and local structures in human physiological signals.
method Personalized Convolutional Dictionary Learning (PerCDL) that combines a global and personalized local dictionary.
result PerCDL effectively learns interpretable representations for human locomotion data.
Paper introduces v-CMC linking causality and utility.
problem Linking causality and utility for value theory.
method Developed a new causal independence principle (v-CMC) and proved its equivalence.
result Equivalence of local, global, and decomposition versions of v-CMC.
Graph representation learning is to learn universal node representations that preserve both node attributes and structural information. The derived node representations can be used to serve various downstream tasks, such as node classification and node clustering. When a graph is heterogeneous, the problem becomes more…
Foundation models fail to preserve continuous geometry, identified as the Geometric Alignment Tax.
problem Continuous geometry is lost in foundation models due to discrete categorical bottlenecks.
method Controlled ablations on synthetic systems and evaluation of 14 biological models using rate-distortion theory and MINE.
result Replacing cross-entropy with a continuous head reduces geometric distortion by up to 8.5x.
This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. S…
Study federates measurement of demographic disparities from quantile sketches.
problem Misalignment of fairness goals with siloed data collection and privacy regulations.
method Federated auditing of demographic parity through score distributions, using Wasserstein--Frechet variance and quantile summaries.
result Proposes a one-shot, communication-efficient protocol to estimate global disparity and its decomposition.
The absolute Galois group of 3-manifolds determines their structure up to homeomorphism.
problem Determining the structure of 3-manifolds using their absolute Galois groups.
method Defined a relative absolute Galois group for 3-manifolds and used Chebotarev density properties and Hilbert ramification theory.
result Two branched covers of the three-sphere over a stably Chebotarev link are homeomorphic if and only if their absolute Galois groups are isomorphic.
Study on unique spacetime extensions in 1+1 dimensions with applications to weak null singularities.
problem Understanding unique spacetime extensions across null boundaries in 1+1 dimensions.
method Analyzing the C0- and C1-structures of continuous spacetime extensions. result Extensions can have the same C0-structure but different C1-structures. New method uses deep neural networks to interpolate spatiotemporal data.
problem Scalable interpolation of spatiotemporal data from growing earth observation systems.
method Bayesian deep learning with random feature expansions.
result Competitive or superior results compared to existing methods.
TSInsight improves interpretability of deep time-series models.
problem Lack of interpretability methods for time-series data.
method Attach auto-encoder to classifier with sparsity-inducing norm, fine-tune based on gradients and reconstruction penalty.
result TSInsight effectively boosts interpretability of deep time-series models.
Enhances stock return prediction using LLMs and hybrid models.
problem Insufficient use of semantic information and alignment of LLMs with stock features.
method LG model with three strategies for global information modeling and SCRL for embedding alignment.
result Superior performance in Rank Information Coefficient and returns compared to models relying only on stock features.
New method clusters multimodal data with consistency.
problem Multimodal clustering with unaligned data.
method Conjugate mixture models and EM algorithm.
result Consistent multimodal clustering achieved.
This paper analyzes saddle points and minimax points in non-convex smooth games.
problem Understanding local optimal points in non-convex smooth games.
method Comprehensive analysis of local minimax points, including their optimality conditions and stability.
result Local saddle points are uniformly local minimax points under mild continuity assumptions.
The paper introduces closed-form expressions for interpreting Tsetlin Machines.
problem Interpreting complex Tsetlin Machines with a large number of clauses.
method Developed closed-form expressions for local and global interpretability of Tsetlin Machines.
result The expressions enable real-time feature importance assessment and data clustering.
This paper studies the problem of data-adaptive representations for big, distributed data. It is assumed that a number of geographically-distributed, interconnected sites have massive local data and they are interested in collaboratively learning a low-dimensional geometric structure underlying these data. In contrast …
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.
The paper studies continuous submodular functions and their optimization.
problem Maximizing continuous submodular functions in poly. time.
method Characterization of continuous submodularity, operations preserving it, and algorithms for constrained maximization.
result Continuous submodularity is equivalent to a weak DR property, leading to continuous DR-submodular functions with the full DR property.
AI model predicts stock prices using social media data and hybrid neural networks.
problem Predicting stock price movements during the COVID-19 pandemic.
method Integrates social media trends and historical stock data using a hybrid CNN-BLSTM framework.
result The proposed framework outperforms traditional models in predicting stock price movements.
We propose a mathematical model for the word-of-mouth communications among stock investors through social networks and explore how the changes of the investors' social networks influence the stock price dynamics and vice versa. An investor is modeled as a Gaussian fuzzy set (a fuzzy opinion) with the center and standar…