INNs improve acceptance rates in electron spectra analysis.
problem Analyzing electron spectra from near-critical laser-plasmas.
method Invertible Neural Networks (INNs) for forward and inverse modeling.
result INNs significantly increase acceptance rates up to a factor of 10.
INNs can approximate diverse functions despite layer restrictions.
problem Can INNs approximate sufficiently diverse functions?
method Developed a theoretical framework based on differential geometry to simplify the approximation problem of diffeomorphisms.
result INNs have the universal approximation property.
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of param…
This work tackles exploding inverses in INNs, revealing and mitigating their numerical non-invertibility.
problem Exploding inverses in INNs cause numerical non-invertibility, leading to failures in various tasks.
method Derived bi-Lipschitz properties of INN building blocks, proposed regularizers for local invertibility, and stable INN designs for global invertibility.
result Bi-Lipschitz properties and stable INN designs are crucial for addressing numerical non-invertibility.
CF-INNs can approximate any invertible function, resolving a long-standing problem.
problem Whether CF-INNs can approximate any invertible function.
method Demonstrated CF-INNs are universal approximators for invertible functions by showing a convenient criterion.
result CF-INNs are universal approximators for invertible functions.
The Information Bottleneck (IB) objective uses information theory to formulate a task-performance versus robustness trade-off. It has been successfully applied in the standard discriminative classification setting. We pose the question whether the IB can also be used to train generative likelihood models such as normal…
INNs produce interval-valued uncertainty scores for DNNs.
problem Uncertainty quantification in deep neural networks.
method Data-driven interval propagating network using interval arithmetic.
result INNs produce sensible lower and upper bounds for prediction error.
INN method refines clean labeled data from noisy labels.
problem Handling noisy labels in deep neural networks.
method INN method based on memorization effect at neighbor regions.
result INN method resolves memorization effect shortcomings.
Study bi-Lipschitz equivalence of mixed polynomials under specific conditions.
problem Classify bi-Lipschitz equivalence of mixed polynomials with inner non-degeneracy.
method Defined metric links and introduced new data to determine bi-Lipschitz equivalence.
result Neither Newton boundary nor C-face diagram is an invariant for bi-Lipschitz equivalence.
An automorphism α of a group G is normal if it fixes every normal subgroup of G setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group G, Inn(G) has finite index in the subgroup Autn(G) of normal au…
Let A1,...,Ak be a system of free factors of Fn. The group of relative automorphisms Aut(Fn;A1,...,Ak) is the group given by the automorphisms of Fn that restricted to each Ai are conjugations by elements in Fn. The group of relative outer automorphisms is defined as $Out(F_n;A_1,...,A_k) = Aut(F_n…
Let A=A1,...,Ak be a system of free factors of Fn. The group of relative automorphisms Aut(Fn;A) is the group given by the automorphisms of Fn that restricted to each Ai are conjugations by elements in Fn. The group of relative outer automorphisms is defined as $\m…
Multispectral optical imaging is becoming a key tool in the operating room. Recent research has shown that machine learning algorithms can be used to convert pixel-wise reflectance measurements to tissue parameters, such as oxygenation. However, the accuracy of these algorithms can only be guaranteed if the spectra acq…
ISR creates analytical relationships from data via invertible maps.
problem Creating analytical relationships from datasets.
method Combines INNs and EQL, using invertible maps and sparsity promoting regularization.
result ISR can serve as a normalizing flow for density estimation and solve inverse problems.
Stochastic gradient descent (SGD) has been the dominant optimization method for training deep neural networks due to its many desirable properties. One of the more remarkable and least understood quality of SGD is that it generalizes relatively well on unseen data even when the neural network has millions of parameters…
Intraductal papillary mucinous neoplasm (IPMN) is a precursor to pancreatic ductal adenocarcinoma. While over half of patients are diagnosed with pancreatic cancer at a distant stage, patients who are diagnosed early enjoy a much higher 5-year survival rate of 34% compared to 3% in the former; hence, early diagno…
In this paper we study different questions concerning automorphisms of quandles. For a conjugation quandle Q=Conj(G) of a group G we determine several subgroups of Aut(Q) and find necessary and sufficient conditions when these subgroups coincide with the whole group Aut(Q). In particular, we p…
Study of profinite quandles with constructions and characterizations.
problem Characterizing and constructing profinite quandles.
method Several constructions and characterizations of profinite quandles from profinite groups and other quandles.
result Characterization of algebraically connected profinite quandles in terms of $\widehat{\Inn(Q)}$.
AutoPQ automates quantile forecasting for smart grids, reducing workload and environmental impact.
problem Accurate and unbiased uncertainty quantification in probabilistic forecasting for smart grid operations.
method AutoPQ uses a conditional Invertible Neural Network (cINN) to generate quantile forecasts from point forecasts, automating model selection and hyperparameter optimization.
result AutoPQ outperforms state-of-the-art methods while reducing computational effort and environmental impact.
Study confirms non-injective monodromy for even genus 4 translation surfaces.
problem Characterizing monodromy of translation surfaces in even genus 4.
method Analysis of orbifold classifying spaces and finite-type Artin groups.
result Monodromy of Heven(6) contains a non-abelian free group of rank 2. Factorization Machine (FM) is a widely used supervised learning approach by effectively modeling of feature interactions. Despite the successful application of FM and its many deep learning variants, treating every feature interaction fairly may degrade the performance. For example, the interactions of a useless featur…
Logical neural networks solve mazes by filling dead ends, but not all methods generalize well.
problem Understanding how logical neural networks extrapolate solutions to mazes.
method Examined recurrent and implicit neural networks trained on maze-solving tasks.
result Models fail to generalize well to diverse maze sizes, suggesting limitations in learning scalable algorithms.
New MIP methods improve training of integer-valued neural networks.
problem Training integer-valued neural networks with limited data and resources.
method Formulated new MIP models to optimize training efficiency and handle more data.
result Significantly outperforms previous state-of-the-art methods in accuracy, training time, and data usage.
Generates samples conditioned on labels using optimal transport.
problem Estimating conditional distributions for specific labels.
method Wasserstein geodesic generator based on optimal transport theory.
result Learned conditional distributions and optimal transport maps.
The paper classifies Finsler surfaces satisfying the T-condition or σT-condition.
problem Characterizing Finsler surfaces based on specific tensor conditions.
method Analyzing Finsler surfaces in dimensions n≥3, proving conditions equivalence, and solving PDEs.
result All Finsler surfaces satisfying the T-condition or σT-condition are classified.
The paper develops a new approach to conditional risk measures using modular convex analysis.
problem Developing a new method for conditional risk measures.
method Random modular approach to conditional certainty equivalents and niveloids in the conditional L∞-space. result Retrieves a conditional variational formula for optimized certainty equivalents and applies it to the conditional entropic risk measure.
Paper constructs solutions to Bogomolny equations with specific boundary and asymptotic conditions.
problem Constructing solutions to Bogomolny equations with given boundary and asymptotic conditions.
method Using generalized Nahm pole boundary condition and real symmetry breaking condition.
result Solutions analogous to instanton solutions, satisfying different asymptotic conditions.
We extend probabilistic programming to handle conditioning on marginal distributions.
problem Conditioning probabilistic programs on marginal distributions of observable variables.
method We define and implement stochastic conditioning, allowing inference in probabilistic programs conditioned on marginal distributions.
result We demonstrate the effectiveness of stochastic conditioning in various real-life scenarios.
New tests for conditional copulas based on decision trees.
problem Testing constancy of conditional dependence structure given conditioning events.
method Data-driven decision trees to maximize differences in conditional Kendall's tau.
result Asymptotic distributions of test statistics under the null hypothesis.
Paper finds necessary condition for logarithmic Minkowski problem in higher dimensions.
problem Logarithmic Minkowski problem in higher dimensions.
method Established a necessary condition through generalization and refinement of previous work.
result Generalizes and refines necessary condition for logarithmic Minkowski problem.
This paper introduces a neural operator for probabilistic conditioning.
problem Probabilistic conditioning of random variables X given Y. method Develops a single operator that maps any joint density to its conditional, approximated by neural operators.
result Neural operators can approximate the conditioning operator to arbitrary accuracy.
CSI method learns conditional distributions by estimating flow equations.
problem Learning conditional distributions in generative models.
method Estimates probability flow equations to transport reference to target distribution.
result Derives explicit expressions for conditional drift and score functions.
New conditional risk measures called conditional generalized quantiles defined and characterized.
problem Developing new risk measures for dynamic risk assessment.
method Propose and characterize conditional generalized quantiles using expected utility model and equivalent conditions.
result Characterized conditional generalized quantiles as well-defined and equivalent to a conditional first order condition.
A new method for learning conditional distributions using ODEs and neural networks.
problem Learning conditional distributions efficiently and accurately.
method Conditional Föllmer Flow, discretized with Euler's method, using nonparametric velocity estimation.
result Effective approximation of target conditional distributions, with convergence results for Wasserstein-2 distance.
Sharp statistical theory for conditional diffusion models.
problem Lack of theoretical foundation for conditional diffusion models.
method Sharp statistical theory with approximation of conditional score function.
result Sample complexity bound that adapts to data distribution smoothness.
An analysis is made of reality conditions within the context of noncommutative geometry. We show that if a covariant derivative satisfies a given left Leibniz rule then a right Leibniz rule is equivalent to the reality condition. We show also that the matrix which determines the reality condition must satisfy the Yang-…
New conditions prevent gaps in optimal control problems.
problem Preventing gaps in optimal control problems with state constraints.
method Developed new sufficient conditions not relying on convexity.
result Derived bounds for the size of the relaxation gap.
We identify conditional parity as a general notion of non-discrimination in machine learning. In fact, several recently proposed notions of non-discrimination, including a few counterfactual notions, are instances of conditional parity. We show that conditional parity is amenable to statistical analysis by studying ran…
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate cas…
Proposes a new method for interpreting feature importance and effects in dependent feature models.
problem Challenges in interpreting feature importance when features are dependent and interactions are present.
method Conditional Subgroup Approach
result Conditional PFI and PDP estimates based on this approach often outperform existing methods.
New boundary conditions solve Cauchy problem for Dirac operators on spacetimes.
problem Understanding non-local boundary conditions for Dirac operators on spacetimes.
method Define and analyze a class of Lorentzian boundary conditions that are local in time and non-local in spatial directions.
result Well-posed Cauchy problem for the Dirac operator is established under these conditions.
We extend CS divergence to conditional distributions and show its advantages in time series data and sequential decision making.
problem Quantifying the closeness between conditional distributions.
method Developed and estimated a conditional Cauchy-Schwarz divergence using kernel density estimation.
result Conditional CS divergence outperforms previous methods in time series clustering and sequential decision making.
The Samuelson condition is not satisfied by tangent lines of quadratic curves.
problem Area condition for Lagrangian 2-web
method Show that the Samuelson condition is not satisfied
result The Samuelson condition is not satisfied by tangent lines of quadratic curves.
We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generali…
A new method tests conditional independence by transforming it into an unconditional problem using transport maps.
problem Testing conditional independence between two random vectors given a third.
method Constructing transport maps to transform conditional independence into unconditional independence, estimating these maps from data using conditional continuous normalizing flow models.
result The proposed method is validated through simulations and real-data analysis, demonstrating practical effectiveness.
DG algorithms often fail to generalize well in limited domains, highlighting necessary vs. sufficient conditions.
problem DG algorithms fail to consistently outperform ERM in limited domains.
method Examined necessary and sufficient conditions for DG, proposing a subspace alignment method.
result DG methods focus on sufficient conditions, often neglecting necessary conditions, leading to generalization failures.
In this paper, we examine higher order difference problems. Using the "squeezing" argument, we derive both Euler's condition and the transversality condition. In order to derive the two conditions, two needed assumptions are identified. A counterexample, in which the transversality condition is not satisfied without th…
Study on estimating conditional risk in machine learning.
problem Estimating expected loss of prediction models given input features.
method Analyzed in classification and regression settings, showing equivalence to standard regression. Developed theoretical insights and empirical validation.
result Conditional risk calibration is distinct from existing uncertainty quantification problems.