This is an exposition of some recent results on ECS manifolds, by which we mean pseudo-Riemannian manifolds of dimensions greater than 3 that are neither conformally flat nor locally symmetric, and have parallel Weyl tensor. All ECS metrics are indefinite. We state two classification theorems, describing the local stru…
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48 results for “ECS manifolds”
Researchers describe the metric structure of compact ECS manifolds.
problem Understanding the metric structure of compact rank-one ECS manifolds.
method Analyzing pseudo-Riemannian manifolds with nonzero parallel Weyl tensor.
result Compact rank-one ECS manifolds are either translational or noncompact.
Compact ECS manifolds have a simple topological structure.
problem Understanding the structure of compact ECS manifolds.
method Review of basic facts, construction of examples, and proof of a topological structure result.
result Compact rank-one ECS manifolds are bundles over S^1 with fibers being leaves of D⊥.
Study on rank-one ECS manifolds, focusing on dilational type.
problem Characterizing ECS manifolds with specific properties.
method Analyzing properties of pseudo-Riemannian manifolds with parallel Weyl tensor.
result Generic compact rank-one ECS manifolds are either translational or locally homogeneous.
Compact ECS manifolds are proven to be bundles over the circle.
problem Compact ECS manifolds and their local structure.
method Proof of a specific result for compact rank-one ECS manifolds.
result Compact rank-one ECS manifolds, not locally homogeneous, are bundles over the circle.
New insights into compact rank-one ECS manifolds, proving they are bundles over circles.
problem Understanding the structure of compact rank-one ECS manifolds.
method Analyzing the properties of pseudo-Riemannian manifolds with parallel Weyl tensor.
result Compact rank-one ECS manifolds are bundles over the circle with specific leaf structures.
New compact ECS manifolds with rank 2 discovered, differing from previous rank 1 examples.
problem Finding new compact ECS manifolds with rank 2.
method Constructing new examples of compact pseudo-Riemannian manifolds with parallel Weyl tensor, rank 1 or 2.
result New compact ECS manifolds of rank 2, locally homogeneous, and geodesically incomplete.
Corrected misstatements about invariant rank in ECS manifold papers.
problem Misstated invariant rank (d=1 instead of d=2) in several papers on ECS manifolds.
method Identified the class of examples with d=1, explained why d=2, and listed corrections.
result Corrected papers to accurately state d=2 for ECS manifolds.
The reduced thin-sandwich equations (RTSE) appear within Wheeler's thin-sandwich approach towards the Einstein constraint equations (ECE) of general relativity. It is known that these equations cannot be well-posed in general, but, on closed manifolds, sufficient conditions for well-posedness have been established. In …
Compact 3D Cotton-parallel manifolds are always conformally flat.
problem Understanding the properties of compact 3D Cotton-parallel manifolds.
method Analyzing the Cotton tensor and its parallelism condition.
result Compact 3D Cotton-parallel manifolds are conformally flat.
Elliptically-Contoured Tensor-variate Distributions with Application to Improved Image Learningstat.ME
Improved image learning using elliptically contoured tensor-variate distributions.
problem Inadequate statistical analysis for tensor-valued data, especially with heavier or lighter tails.
method Developed a family of elliptically contoured tensor-variate distributions and derived their properties and procedures for estimation.
result Tensor-variate classification rules and tensor-on-tensor regression better predict and characterize data than TVN-based methods.
EC method calibrates neural networks by matching average confidence to correct label proportion.
problem Overoptimism in neural network prediction confidence.
method Expectation consistency (EC) post-training rescaling of weights.
result EC achieves similar calibration performance to temperature scaling (TS) but is based on a principled Bayesian principle.
STAS selects optimal spatio-temporal scales for bias correction in precipitation forecasts.
problem Limited prior data and fixed ST scale in existing BCoPs lead to biases in numerical weather predictions.
method End-to-end deep-learning BCoP model STAS with SFM/TFM to automatically adjust spatial and temporal scales.
result STAS outperforms 8 published BCoP methods on threat scores (TS).
Develops confidence intervals for ECE, a measure of model calibration.
problem Ensuring the calibration of probabilistic predictions in machine learning models.
method Develops confidence intervals for the Expected Calibration Error (ECE), considering top-1-to- calibration.
result Shows asymptotic normality and different convergence rates for calibrated and miscalibrated models, developing methods to construct valid confidence intervals.
ECS evaluates synthetic CXR images' distributional fidelity.
problem Evaluating synthetic CXR images' distributional fidelity under privacy constraints.
method Characteristic function transforms of feature embeddings.
result ECS uncovers clinically relevant distributional discrepancies.
Meta-ensemble scheme allocates queries to EC nodes for reduced latency.
problem Efficiently allocating queries to EC nodes to minimize latency.
method Combining ensemble models to decide query allocation based on node and query characteristics.
result Meta-ensemble scheme outperforms traditional allocation methods in reducing query processing latency.
Paper analyzes ECE bias and provides bounds for its estimation.
problem Understanding the estimation bias in ECE for machine learning models.
method Information-theoretic approach to analyze bias in uniform mass and uniform width binning strategies.
result Established upper bounds on ECE estimation bias and optimal number of bins.
Protein contacts contain important information for protein structure and functional study, but contact prediction from sequence remains very challenging. Both evolutionary coupling (EC) analysis and supervised machine learning methods are developed to predict contacts, making use of different types of information, resp…
A new algorithm reduces regret in multi-player bandits without collision info.
problem Decentralized multi-player multi-armed bandits with no collision info.
method EC-SIC algorithm using optimal error correction coding for reward statistics.
result Regret approaches that of centralized with collision info.
Enhanced tabular benchmarks for energy-efficient neural architecture search.
problem Energy consumption in deep learning models.
method Introducing EC-NAS, an enhanced tabular benchmark with energy consumption data.
result EC-NAS reveals a balance between energy usage and accuracy in neural architecture search.
New measure EC assesses node contributions in nonlinear, time-varying systems.
problem Existing node contribution measures assume linear, time-invariant dynamics, failing for complex, real-world systems.
method Defined 'emergent contribution (EC)' as a dynamical leverage measure from Jacobians of differentiable models.
result EC diverges from average controllability under persistent regime switching and sign reversal, identifying limits of local linearization.
This work characterizes topological descriptors of graph products and their expressive power.
problem Capturing multiscale structural information in graph products using topological descriptors.
method Analysis of various filtrations on graph products, including Euler characteristic and persistent homology.
result Persistent homology of graph products contains more information than individual graphs.
Transform ANNs into interpretable decision trees.
problem Lack of interpretability in ANNs.
method Developed two MDT algorithms: EC-DT and Extended C-Net.
result Extended C-Net generates the most compact and effective trees.
A new method improves few-shot event classification accuracy.
problem Few-shot event classification for unseen event types.
method Extensively exploit matching information in the support set during training.
result Improves event classification accuracy by up to 10%.
Global pairwise network alignment (GPNA) aims to find a one-to-one node mapping between two networks that identifies conserved network regions. GPNA algorithms optimize node conservation (NC) and edge conservation (EC). NC quantifies topological similarity between nodes. Graphlet-based degree vectors (GDVs) are a state…
Study on deep neural networks using concentration inequalities and optimal stopping.
problem Understanding the performance and structure of stochastic deep neural networks.
method Introduced concentration inequalities for SDNN outputs and an EC classifier. Determined the optimal number of layers via an optimal stopping procedure.
result Optimal number of layers for SDNNs determined via an optimal stopping procedure.
A new framework evaluates LLM calibration in open-ended QA.
problem Evaluating LLM calibration in open-ended QA settings.
method Sem-ECE framework: sampling answers, grouping by semantic classes, and using frequencies as confidence.
result Sem-ECE estimators are unbiased and Sem achieves smaller calibration error.
The use of EEG biometrics, for the purpose of automatic people recognition, has received increasing attention in the recent years. Most of current analysis rely on the extraction of features characterizing the activity of single brain regions, like power-spectrum estimates, thus neglecting possible temporal dependencie…
Study new ECS structures in 5D Minkowski compactifications of M-theory.
problem Characterize geometries of supersymmetric compactifications to 5D Minkowski space.
method Define and classify ECS structures, relate to hypermultiplet moduli.
result Classify ECSs and find their moduli, relating to hypermultiplet moduli.
Simple algorithm achieves distance to calibration error of at most 2√T+1.
problem Achieving distance to calibration error of O(√T) in adversarial setting.
method An extremely simple, efficient, deterministic algorithm.
result Obtains distance to calibration error at most 2√T+1.
EControl improves fast distributed optimization with compression and error control.
problem Stable convergence issues in distributed training with compression.
method Proposes EControl to regulate error compensation and prove fast convergence.
result Proves fast convergence for EControl in various convex settings without additional assumptions.
BYOV combines SSL and Bayesian methods for uncertainty estimation.
problem Model uncertainty in applications.
method Combines Bootstrap Your Own Latent (BYOL) and Bayes by Backprop (BBB).
result BYOV improves model calibration and reliability with various augmentations.
Recently, neuro-inspired episodic control (EC) methods have been developed to overcome the data-inefficiency of standard deep reinforcement learning approaches. Using non-/semi-parametric models to estimate the value function, they learn rapidly, retrieving cached values from similar past states. In realistic scenarios…
Restoring Calibration for Aligned Large Language Models: A Calibration-Aware Fine-Tuning Approachcs.LG
The paper addresses poor calibration in fine-tuned LLMs after preference alignment.
problem Poor calibration in fine-tuned Large Language Models (LLMs) after preference alignment.
method Proposes a calibration-aware fine-tuning approach to restore calibration without compromising model performance.
result Demonstrates the effectiveness of the proposed methods through extensive experiments.
New decision-theoretic calibration error metric improves prediction reliability.
problem Improving the reliability of predictions for decision-making.
method Proposed Calibration Decision Loss (CDL) and an efficient algorithm to achieve near-optimal CDL.
result Near-optimal CDL guarantees vanishing payoff loss from miscalibration.
Paper proposes a method to predict MOBA game winners with calibrated confidence.
problem Predicting MOBA game winners with noisy data and uncertain noise.
method A novel confidence-calibration method considering data uncertainty.
result Achieves outstanding expected calibration error (ECE) of 0.57%.
New metrics improve uncertainty estimation on graph data.
problem Current GNNs focus only on nodewise scores, limiting uncertainty estimation.
method Proposed edgewise metrics for uncertainty estimation on graphs.
result GNN models with structured prediction perform better in uncertainty estimation.
Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective multiplicative factor for inputs to the last softmax layer. On non-neural models the exist…
New method calibrates classifier probabilities with guaranteed coverage.
problem Inaccurate probability estimates by classifiers in high-risk applications.
method Adaptive temperature scaling algorithm for conformal prediction.
result Improves calibration error measures and standard metrics across various tasks.
New method improves calibration of neural networks by targeting robust margins and local smoothness.
problem Poor calibration of neural networks, leading to unreliable confidence estimates.
method Intervene on training procedure by targeting robust margins and local smoothness.
result Improved out-of-sample calibration without sacrificing accuracy.
This post introduces model calibration and evaluation measures, highlighting issues with a common measure.
problem Ensuring model confidence accurately reflects true outcomes.
method Explains common calibration definition, ECE, and its drawbacks.
result New evaluation measures needed for comprehensive model calibration.
Decades of research on the neural code underlying spatial navigation have revealed a diverse set of neural response properties. The Entorhinal Cortex (EC) of the mammalian brain contains a rich set of spatial correlates, including grid cells which encode space using tessellating patterns. However, the mechanisms and fu…
In an era where accumulating data is easy and storing it inexpensive, feature selection plays a central role in helping to reduce the high-dimensionality of huge amounts of otherwise meaningless data. In this paper, we propose a graph-based method for feature selection that ranks features by identifying the most import…
Proposes CCE to assess point-wise reliability of neural network predictions.
problem Overconfidence and misaligned predictive distributions in neural networks.
method Introduces Conditional Congruence (CCE) metric using conditional kernel mean embeddings.
result CCE exhibits correctness, monotonicity, reliability, and robustness in high-dimensional regression tasks.
New method calibrates confidence for object detection and segmentation models.
problem Intrinsically miscalibrated confidence estimates in object detection and segmentation models.
method Introduces multivariate confidence calibration for object detection and segmentation, extending ECE.
result Improves calibration, positively impacts segmentation quality.
Paper introduces kernel methods for detecting anomalous changes in remote sensing imagery.
problem Detecting anomalous changes in remote sensing imagery.
method Nonlinear extension of Gaussian and elliptically contoured distribution algorithms using reproducing kernel Hilbert space.
result Improved detection accuracy and reduced false-alarm rates compared to linear formulations.
Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. Th…
New methods reduce bias in estimating calibration error.
problem Reducing bias in estimating calibration error.
method Synthesizing model outputs and using equal-mass bins.
result Two reliable calibration-error estimators found: debiased estimator and ECE_sweep.