Improve exposition and explain metric bundle equivalence.
problem Improving exposition and explaining metric bundle equivalence.
method Improved exposition and appendix explaining equivalence of flaring conditions.
result Equivalence of flaring conditions explained.
New feature mapping approach improves recommendation accuracy and explainability.
problem Balancing recommendation accuracy and explainability using metadata.
method Maps uninterpretable features to interpretable aspect features, minimizing both prediction and interpretation losses.
result Strong performance in recommendation and explainability, eliminating metadata need.
This paper evaluates and improves metrics for identifying important features in machine learning models.
problem Evaluation metrics for explainable AI are limited by multicollinearity and model accuracy.
method Proposes Expected Accuracy Interval (EAI) to predict model accuracy with multicollinearity.
result EAI is a useful metric for identifying important features in models with multicollinearity.
Explain convexity of K-energy leading to unique metrics.
problem Uniqueness of constant scalar curvature Kahler metrics and extremal metrics.
method Convexity of K-energy along weak geodesics in Kahler potentials.
result Uniqueness of extremal metrics up to automorphisms.
New methods for explaining Random Forest predictions using case-based reasoning.
problem Lack of explainability for black-box machine learning models like Random Forests.
method Extracting distance metric from Random Forests to identify prototypes, critics, counter-factuals, and semi-factuals.
result Identified special points from training datasets to explain Random Forest predictions.
Survey of spectral, probabilistic, and deep metric learning methods.
problem Developing effective distance metrics for various machine learning tasks.
method Divided into spectral, probabilistic, and deep approaches, covering various techniques and their applications.
result Comprehensive overview of metric learning methods, including new developments and applications.
The paper introduces metrics to quantify information discarding in DNNs.
problem Understanding how input information is discarded during neural network processing.
method Developed two entropy-based metrics to measure pixel-wise and reconstruction uncertainty.
result The metrics provide new insights into DNN performance and information processing efficiency.
XAI-Bench releases synthetic datasets for evaluating feature attribution methods.
problem Evaluating and comparing feature attribution methods is challenging.
method Released synthetic datasets and benchmarking library.
result Efficiently evaluates feature attribution methods across various metrics.
Survey reviews explainability in AI for healthcare, emphasizing trust and transparency.
problem Lack of transparency hinders AI adoption in healthcare.
method Comprehensive literature review to guide explainable AI design.
result Quantitative evaluation metrics are needed for some explainability properties.
This paper reviews MDS, Sammon mapping, and Isomap, explaining their theory and applications.
problem Exploring multidimensional data structures and mappings.
method Explains classical MDS, metric MDS, kernel classical MDS, Sammon mapping, Isomap, and their applications.
result Detailed understanding of MDS, Sammon mapping, and Isomap methods.
The paper introduces metrics to objectively evaluate interpretability methods.
problem Lack of objective evaluation metrics for interpretability methods.
method Proposes a set of metrics to evaluate interpretability methods along simplicity and broadness.
result Validated metrics on different benchmark tasks and showed their utility in method selection.
Defines globalness measure for explainers using optimal transport.
problem Challenges in evaluating and comparing explainability methods.
method Axiomatic definition and proof of Wasserstein Globalness measure.
result Wasserstein Globalness measure facilitates meaningful comparison and selection of explainers.
timeXplain bridges AI and time series, making predictions understandable.
problem Making time series classifier predictions interpretable.
method Developed a framework that combines time series data with model-agnostic explainers.
result timeXplain improves the interpretability of time series classifiers.
Unified metric c-Eval evaluates feature-based explanations by perturbation.
problem Lack of consensus on evaluating feature-based local explanations.
method Introduces c-Eval metric and framework to quantify explanation quality.
result c-Eval captures the importance of input features and is applicable in adversarial-robust models.
Paper proposes metrics to evaluate AI explanations without ground truth.
problem Challenges in evaluating neural network explanations without ground truth.
method Designs four metrics to evaluate explanation results.
result New insights into neural network interpretation methods.
This note explains Ricci flow method for Kähler-Einstein metrics.
problem Existence problem of Kähler-Einstein metrics.
method Ricci flow method based on Cao.H.D and Yau.S.T's papers, with additional estimates from Jian Song and Weinkove's note.
result Illustrates and details the Ricci flow method for Kähler-Einstein metrics.
AI techniques explain synthetic tabular data weaknesses.
problem Challenges in evaluating synthetic tabular data quality.
method Apply explainable AI to a binary detection classifier.
result Reveals inconsistencies, unrealistic dependencies, or missing patterns in synthetic data.
Method generates visual explanations for similarity models without classification.
problem Lack of visual explanations for similarity models trained without classification loss.
method Gradient-based visual attention using learned feature embeddings.
result Attention maps improve model performance and can be used as constraints.
Paper proposes Coalitional BAE to improve explainability of unsupervised deep learning models.
problem Improving explainability of Autoencoder's predictions.
method Introduces Coalitional BAE, inspired by agent-based system theory, to reduce correlation in explanations.
result Improved quality of explanations using Coalitional BAE on publicly available datasets.
We give a new construction of Ricci-flat self-dual metrics which is a natural extension of the Gibbons--Hawking ansatz. We also give characterisations of both these constructions, and explain how they come from harmonic morphisms.
WGAN uses a smoother metric to train GANs better.
problem Difficulty in training GANs.
method Introducing Wasserstein GAN to improve GAN training.
result Wasserstein GAN improves training stability and effectiveness.
Paper explores new Kähler metrics from old, aiming to solve YTD conjecture.
problem Extending classical extremal Kähler metrics to include new objects.
method Surveying recent works on weighted extremal Kähler metrics and the YTD conjecture.
result Survey of recent research on weighted extremal Kähler metrics.
These notes are based on my lectures at IMA summer program "Symmetries and Overdetermined Systems of Partial Differential Equations." Here I try to explain basic ideas of the ambient metric construction by studying the Szego kernel of the sphere.
New metrics constructed dual to specific wave-like geometries.
problem Constructing metrics dual to general plane-fronted wave Lorentzian metrics.
method Explains construction of extremal and non-Kähler almost-Kähler metrics.
result Constructs canonical almost-Kähler metrics dual to general plane-fronted wave Lorentzian metrics.
Study identifies key aspects of explainable ML for clinical trust.
problem Lack of concrete definitions for usable explanations in clinical settings.
method Surveyed clinicians from two specialties to understand their needs for explainability.
result Characterized specific aspects of explainability that improve trust in ML models.
Theory explains why neural nets better learn Calabi-Yau metrics.
problem Learning Calabi-Yau metrics with neural networks.
method Developed a theory of metric flows in neural network space.
result Finite-width neural networks learn Calabi-Yau metrics better than fixed kernel methods.
ExpO regularizes models to improve their explainability.
problem Improving the interpretability of black-box models.
method ExpO is a hybridization of regularization and post-hoc explanation systems.
result Post-hoc explanations for ExpO-regularized models have better explanation quality.
In this note we explain how a flow in the space of Riemmanian metrics (including Ricci's \cite{mt}) induces one in the space of pseudoconnections.
Toolkit and taxonomy for diverse AI explainability methods.
problem Diverse stakeholder needs for AI explanations.
method Open-source software toolkit with eight explainability methods and evaluation metrics.
result Taxonomy helps navigate explanation methods.
This short note has been written as an Oberwolfach report for the workshop "Differentialgeometrie im Grossen". We discuss properties of metric spaces that at almost all points admit a tangent metric space. We explain why, under some mild assumptions, the tangents are almost surely subFinsler Carnot groups. We mention s…
Explains old and new non-Kähler metrics on compact manifolds.
problem Coexistence and behavior of non-Kähler metrics on compact complex manifolds.
method Focus on specific types of non-Kähler metrics, describe constructions and properties.
result Mechanism for constructing nilmanifolds with desired metrics.
ID-ExpO fine-tunes neural networks for more faithful explanations.
problem Improving the faithfulness of explanations for complex machine learning models.
method Differentiable insertion/deletion metric-aware regularizers for optimization.
result Fine-tuned predictors produce more faithful explanations.
Proposes a simple method to explain aleatoric uncertainty in neural networks.
problem Lack of transparent explanations for uncertainty estimates in AI models.
method Adapting a neural network with Gaussian output to estimate predictive variance and applying explainers to the variance output.
result The proposed method explains uncertainty more reliably than complex approaches and outperforms them in most settings.
A 4-manifold is constructed with some curious metric properties; or maybe it is many 4-manifolds masquerading as one, which would explain why it looks curious. Anyway, knots in the 3-sphere with complete finite volume hyperbolic metrics on their complements play a role in this story.
Explains visual metrics on hyperbolic space boundaries.
problem Understanding the geometry of hyperbolic spaces.
method Construction of visual metrics, quasisymmetries, and invariants.
result Detailed examples and applications of Gromov's round trees.
This research improves demand forecasting by predicting complete probability density functions using machine learning.
problem Forecasting complete probability density functions for better operational decision making.
method Supervised machine learning method 'Cyclic Boosting' for explainable predictions.
result Predicted probability density functions are fully explainable and avoid 'black-box' models.
Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the classification of general toric anti-self-dual metrics given in an earlier paper (math.DG/06…
Yau proved an existence theorem for Ricci-flat Kähler metrics in the 1970's, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions…
Metric graphs have subgraphs with entropy at least λ.
problem Finding subgraphs with high entropy in metric graphs.
method Proving existence of subgraphs with entropy at least λ for graphs of rank r with entropy 1.
result Metric graphs have subgraphs with entropy at least λ.
We explain how the formal aspects of the theory of Kahler-Einstein metrics can be developed in the framework of moment maps. The central result we use is the Berndtsson convexity theorem, which is interpreted as defining a metric on the space of complex structures. We discuss some applications of these ideas to the Kah…
These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in computational anatomy.
Local decision boundary approximation improves model explanations for complex models.
problem Challenges in explaining complex, opaque machine learning models.
method Train a variational autoencoder to learn a latent space and map it to meaningful attributes. Use these attributes to approximate the local decision boundary and explain model predictions.
result Can recover latent attributes that determine class decisions in a new benchmark data set.
We discuss whether it is possible to reconstruct a metric by its unparameterized geodesics, and how to do it effectively. We explain why this problem is interesting for general relativity. We show how to understand whether all curves from a sufficiently big family are umparameterized geodesics of a certain affine conne…
PDD detects concept drift using explainable AI, improving model performance in dynamic environments.
problem Detecting and adapting to concept drift in predictive models.
method Profile Drift Detection (PDD) using Partial Dependence Profiles (PDPs).
result PDD outperforms existing methods in detecting concept drift and maintaining high predictive performance.
DiSeNE generates interpretable node embeddings without supervision.
problem Lack of interpretability in unsupervised node embeddings.
method Disentangled representation learning with novel objective functions and metrics.
result DiSeNE produces interpretable node embeddings aligned with graph structure.
AI system predicts acute critical illness from EHRs with explainability.
problem Lack of clinical interpretability in AI predictions for acute critical illness.
method Developed an explainable AI early warning score (xAI-EWS) system.
result System provides clinicians with insights into EHR data explaining predictions.
New metric assesses reliability of AI explanations.
problem Unreliable AI explanations under realistic conditions.
method Explanation Reliability Index (ERI) metrics quantifying stability under four axioms.
result Widespread reliability failures in popular explanation methods.
We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive index of symmetry. We also study the geometry of the quotients by the so-called foliation of symmetry…