We examine several aspects of explicability of a classification system built from neural networks. The first aspect is the pairwise explicability, which is the ability to provide the most accurate prediction when the range of possibilities is narrowed to just two. Next we consider explicability in development, which me…
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41 results for “Explicability”
We solve the twistor equation on all indecomposable Lorentzian symmetric spaces explicity.
New framework for fairness in machine learning models using SHAP values and adversarial learning.
problem Fairness of model predictions, especially for unprivileged groups.
method Develops a new fairness definition and a framework using SHAP values and adversarial learning to mitigate bias.
result Models produced are fairer and performant, demonstrating the approach on various datasets.
In Random Forests, proximity distances are a metric representation of data into decision space. By observing how changes in input map to the movement of instances in this space we are able to determine the independent contribution of each feature to the decision-making process. For binary feature vectors, this process …
Enhances machine learning interpretability using category theory.
problem Improving machine learning interpretability and social implementation.
method Develops a categorical framework for structured understanding of supervised learning.
result Introduces the Gauss-Markov Adjunction for clarifying residuals and parameters.
An earlier article with Francis Bonahon introduced new invariants for pseudo-Anosov diffeomorphisms of surface, based on the representation theory of the quantum Teichmuller space. We explicity compute these quantum hyperbolic invariants in the case of the 1-puncture torus and the 4-puncture sphere.
The relations between the infinite dimensional geometry of -conformal symmetries at , Berezin quantization of the Lobachevskii plane and Karasev-Maslov asymptotic quantization are explicated. Some aspects of the ``approximate'' representation theory are discussed.
A generalized flag manifold is a homogeneous space of the form , where is the centralizer of a torus in a compact connected semisimple Lie group . We classify all flag manifolds with four isotropy summands and we study their geometry. We present new -invariant Einstein metrics by solving explicity the Ei…
Recently, Honda, Kazez and Matic described an adapted partial open book of a compact contact 3-manifold with convex boundary by generalizing the work of Giroux in the closed case. They also implicitly established a one-to-one correspondence between isomorphism classes of partial open book decompositions modulo positive…
We explicate a number of notions of algebraic laminations existing in the literature, particularly in the context of an exact sequence of hyperbolic groups. These laminations arise in different contexts: existence of Cannon-Thurston maps; closed geodesics exiting ends of manifolds; dual to …
The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of -spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a …
Empirical investigation of a quantum field theory of forward ratescond-mat.stat-mech
A new test of a wide class of interest rate models is proposed and applied to a recently developed quantum field theoretic model and the industry standard Heath-Jarrow-Morton model. This test is independent of the volatility function unlike other tests previously proposed in the literature. It is found that the HJM mod…
This work aims to reduce inexplicable errors in deep neural networks by obtaining class-level semantics and penalizing misclassifications.
problem Deep neural networks misclassify images, leading to inexplicable errors that can harm trust and societal impact.
method Obtain class-level semantics, propose Weighted Loss Functions (WLFs), and train classifiers with these methods.
result Trained networks have more explicable failure modes and comparable accuracy to existing methods.
We show that the universal odd Chern form, defined on the stable unitary group , extends to the loop group in a way that is closed with respect to an equivariant-type differential. This provides an odd analogue to the Bismut-Chern form. We also describe the associated transgression form, the so-called Bismut-Ch…
Generalised regularisation equals robustness for exotic function classes.
problem Adversarial examples highlight the need for robust models in exotic function classes.
method Equality result linking distributional robustness and Lipschitz regularisation.
result Certified robustness of Lipschitz-regularised models with mild assumptions.
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
problem The distribution of holonomy on compact hyperbolic 3-manifolds is not uniformly distributed.
method An asymptotic count of closed geodesics by their length and holonomy, and analysis of spectral parameters.
result A normalized, smoothed bias count of holonomy is distributed according to a probability distribution, controlled by the number of zero spectral parameters.
New approach to nonuniform learnability using measure theory.
problem Nonuniform learnability of hypotheses with varying sample sizes.
method Measure theoretic approach to redefine nonuniform learnability, introducing a new algorithm (Generalize Measure Learnability).
result Achieved statistical consistency in learning countable hypothesis classes.
This paper explores geometric and analytic aspects of Lojasiewicz inequalities on vector bundles.
problem Understanding growth and stability conditions for real-analytic functions over vector bundles.
method Outline theory of functionals and variational problems over vector bundles, explore applications to real-analytic functionals.
result Describes the energy functional on $S^{n-1$ as a functional over a vector bundle.
Paper proposes a modified fairness constraint to address shortcomings of counterfactual fairness.
problem Counterfactual fairness is not a necessary condition for algorithmic fairness.
method Analyzed hypothetical scenario and explicated discrimination to develop causal relevance fairness.
result Causal relevance fairness is a modified constraint that circumvents shortcomings of counterfactual fairness.
Machine learning uses invariant theory to restrict function classes.
problem Creating function classes that respect physical law constraints.
method Using equivariant machine learning and Malgrance's method to parameterize functions.
result Explicitly parameterizes equivariant functions between linear spaces.
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.
Neural network predicts daily power consumption with high accuracy.
problem Middle-term power consumption prediction in the energy sector.
method Incorporates trend, seasonality, and weather conditions in a shallow Neural Network.
result Excellent density forecast results on one-year test set.
Finsler connection preserving the two-vector angle under the indicatrix-inhomogeneous treatmentmath.DG
The Finsler spaces in which the tangent Riemannian spaces are conformally flat prove to be characterized by the condition that the indicatrix is a space of constant curvature. In such spaces the Finslerian normalized two-vector angle can be explicated from the respective two-vector angle of the associated Riemannian sp…
For semi-supervised techniques to be applied safely in practice we at least want methods to outperform their supervised counterparts. We study this question for classification using the well-known quadratic surrogate loss function. Using a projection of the supervised estimate onto a set of constraints imposed by the u…
Dendrogram of mixing measures: Hierarchical clustering and model selection for finite mixture modelsstat.ME
New method uses dendrograms for better mixture model selection and clustering.
problem Selecting the correct number of components in finite mixture models.
method Hierarchical clustering tree derived from overfitted latent mixing measures.
result Consistently selects the true number of mixing components and optimal convergence rate for parameter estimation.
Study on identifying most preferred policy in bandits with vector-valued rewards.
problem Identifying the most preferred policy in bandits with vector-valued rewards.
method Derive a novel lower bound on sample complexity, design the Preference-based Track and Stop (PreTS) algorithm, and derive a new concentration inequality.
result The sample complexity of PreTS is asymptotically tight.
New framework improves interpretability of trainable prompts.
problem Improving task-specific LLM performance with soft prompts remains a black-box method.
method Developed a theoretical framework for evaluating interpretability of trainable prompts, inspired new objective functions.
result Found a fundamental trade-off between interpretability and task performance in trainable prompts.
Though used extensively, the concept and process of machine learning (ML) personalization have generally received little attention from academics, practitioners, and the general public. We describe the ML approach as relying on the metaphor of the person as a feature vector and contrast this with humanistic views of th…
New model forecasts power consumption with high accuracy over months to years.
problem Probabilistic forecasting of power consumption in a middle-term horizon.
method Combines traditional time-series analysis with weather conditions using Gaussian Process.
result Promising results in Out-of-Sample density forecasts up to one year.
Continuous control imitation learning fails if expert actions are smooth.
problem Continuous control imitation learning fails if expert actions are smooth.
method Study of imitation learning in discrete-time, continuous state-and-action control systems.
result Any smooth, deterministic imitator policy suffers exponentially larger error than the expert.
A new method for faster optimization on statistical manifolds.
problem Slow convergence of first-order methods in manifold optimization.
method Dual Riemannian Newton method on manifolds with dual connections.
result Local quadratic convergence of the dual Riemannian Newton method.
Unified approach for estimating quantiles of potential outcomes using inverse estimating equations.
problem Estimating quantiles of potential outcomes for causal inference.
method Inverse estimating equations and moment function.
result Unified approach to estimate mean and quantiles of potential outcomes.
This paper argues for decolonizing AI alignment by incorporating open-source Hinduism concepts.
problem Coloniality in AI development and deployment, particularly in alignment practices.
method Proposes three forms of openness: model, societal, and excluded knowledge openness, using Hindu viśe\d{s}a-dharma.
result AI alignment should be decolonialized to avoid moral absolutism and better align with desired values.
This paper opens the series of articles supplemental to the series (hep-th/9405050,q-alg/9610026,q-alg/9611003,q-alg/9611019,funct-an/9611003), which also lies in lines of general ideology exposed in the review (mp_arc/96-477). The main purpose of the activity, which has its origin and motivation presumably in the auth…
The paper argues for interpreting neural networks as approximating the true posterior, enhancing in-context learning.
problem The limitations of traditional MLE interpretation in large-scale, single-epoch training setups.
method Demonstrates the power of interpreting neural networks as approximations of the true posterior, using experiments to predict generalizations.
result Models become robust in-context learners by effectively composing knowledge from their training data, revealing surprising generalizations.
A salient approach to interpretable machine learning is to restrict modeling to simple models. In the Bayesian framework, this can be pursued by restricting the model structure and prior to favor interpretable models. Fundamentally, however, interpretability is about users' preferences, not the data generation mechanis…
Adversarial Networks and Autoencoders: The Primal-Dual Relationship and Generalization Boundsstat.ML
Since the introduction of Generative Adversarial Networks (GANs) and Variational Autoencoders (VAE), the literature on generative modelling has witnessed an overwhelming resurgence. The impressive, yet elusive empirical performance of GANs has lead to the rise of many GAN-VAE hybrids, with the hopes of GAN level perfor…
Paper explains learning property of logistic and softmax losses for balanced and imbalanced class data.
problem Understanding and optimizing loss functions for deep neural networks with class imbalances.
method Analyzing necessary conditions for convergence of logistic and softmax losses in CNNs.
result Proposes a novel reweighted logistic loss function that improves performance over softmax loss.
Unified framework for analyzing neural networks in high dimensions.
problem Understanding neural networks' efficiency in high-dimensional data.
method Statistical physics techniques, including replica method and approximate message-passing algorithms.
result Unified analysis of various machine learning architectures and tasks.
STNN-DDI predicts drug interactions using substructure-aware neural networks.
problem Predicting drug-drug interactions (DDIs) to avoid side effects in poly-drug treatments.
method Designing a novel Substructure-ware Tensor Neural Network (STNN-DDI) that learns a 3-D tensor of substructure-substructure interactions.
result Significant improvement in AUC, AUPR, Accuracy, and Precision compared to state-of-the-art models.
Dynamical systems are widely used in science and engineering to model systems consisting of several interacting components. Often, they can be given a causal interpretation in the sense that they not only model the evolution of the states of the system's components over time, but also describe how their evolution is af…