Study feature representations induced by dependence between variables.
problem Learning feature representations from dependent random variables.
method Characterized sufficient and necessary conditions for dependence-induced representations, and provided a family of loss functions.
result Features learned from the family of loss functions can be expressed as the composition of a loss-dependent function and the maximal correlation function.
This paper establishes a mathematical framework for G-CNNs on homogeneous spaces.
problem Designing equivariant neural networks for data with symmetries.
method Using Mackey's theory on induced representations, the paper presents a general framework for G-CNNs.
result G-CNNs are a universal class of equivariant network architectures.
In this note we observe that the notion of an induced representation has an analog for quasi-actions. We then use induced quasi-actions to refine some earlier rigidity results for product spaces.
Study geometric and representation theory of statistical transformation models.
problem Understand relationships between induced structures and actions on measure spaces.
method Investigate geometric properties and symplectic actions on induced structures.
result Show equivariance of action and relationships between tangent bundles and projectivizations.
Proposes bounds on bias from low-dimensional representations in CATE estimation.
problem Bias in CATE estimation due to low-dimensional representations.
method Proposes a refutation framework to estimate bounds on representation-induced confounding bias.
result Demonstrates effectiveness of refutation framework in practice.
Linear disentangled representations improve unsupervised action estimation.
problem Learning linear disentangled representations for unsupervised action estimation.
method Developed a method to induce irreducible representations in VAE models without labeled action sequences.
result Linear disentangled representations are a desirable property for unsupervised action estimation.
Researchers develop multi-utility representations for incomplete preferences linked to risk measures.
problem Handling incomplete preferences induced by set-valued risk measures.
method Established dual representations of set-valued risk measures to create parsimonious and well-behaved multi-utility representations.
result Unified dual representations of set-valued risk measures, linking them to scalar risk measures.
Develops VAEs with graphical models for interpretable representations.
problem Creating interpretable representations in complex, high-dimensional data.
method Incorporates structured graphical models into VAE encoders for approximate variational inference.
result Induces interpretable representations with deep generative models under structural constraints.
We sharpen the construction of representation space in the paper "Principal Series Representations of Infinite Dimensional Lie Groups II: Construction of Induced Representations". We show that the principal series representation spaces constructed there, are completions of spaces of sections of Hilbert bundles rather t…
Paper tackles supervision bottleneck in machine learning.
problem Difficulty in generating supervision signals for learning models.
method Describes several learning paradigms to alleviate the supervision bottleneck.
result Illustrates the benefit of these paradigms in inducing semantic representations from text.
STAR improves equivariant and invariant representation learning by routing projection heads.
problem Redundant feature learning in equivariant and invariant representation learning.
method Soft Task-Aware Routing (STAR) for projection heads specialization.
result Lower canonical correlations between invariant and equivariant embeddings.
Modified group captures braid dynamics, revealing Burau kernel.
problem Detecting the kernel of the Burau representation for braids.
method Defined a modified group Gn3 and its representation. result The modified group's representation detects the Burau kernel.
We present a complete classification and the construction of Mp(2n+2,R)-equivariant differential operators acting on the principal series representations, associated to the contact projective geometry on RP2n+1 and induced from the irreducible Mp(2n,R)-submodules of…
This paper analyzes Barlow Twins' representation efficiency using information-geometric methods.
problem Understanding and comparing the efficiency of self-supervised learning methods.
method Introduces an information-geometric framework to quantify representation efficiency and applies it to Barlow Twins.
result Proves that Barlow Twins achieves optimal representation efficiency (η=1).
DBGAN learns graph node representations by balancing distribution consistency.
problem Graph representation learning overfits due to ignoring data distribution.
method DBGAN uses a structure-aware prior distribution and bidirectional adversarial learning.
result DBGAN achieves better trade-off between robustness and dimensionality.
Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfaces are generated by the Davey -Stewartson hierarchy. Geometrically thes…
A new algorithm maximizes entropy or mutual information for efficient inference of nonstationary Gaussian processes.
problem Nonstationary dynamics in real-world phenomena pose challenges to accurate modeling.
method LISAL algorithm that adaptively maximizes entropy or mutual information on induced latent dynamics and marginal likelihood.
result Efficient inference of nonstationary Gaussian processes for large-scale real-world applications.
The article studies Hamiltonian flows on surface group representations induced by invariant multi-functions.
problem Hamiltonian flows on surface group representations induced by invariant multi-functions.
method Introducing subsurface deformation and proving Poisson commutativity of induced invariant multi-functions.
result Hamiltonian flows on character varieties are of subsurface deformation type and Poisson commute if supporting subsurfaces are disjoint.
In this paper, we introduce a study of prolongations of homogeneous vector bundles. We give an alternative approach for the prolongation. For a given homogeneous vector bundle E, we obtain a new homogeneous vector bundle. The homogeneous structure and its corresponding representation are derived. The prolongation of in…
Study mapping class groups' action on surface homology.
problem Characterize mapping class groups' homology representation.
method Precise characterization of induced homology representation.
result Characterized the image of the homology representation.
New method removes lexical treatment signals to avoid overlap violations in causal inference from text.
problem Overlap violations in estimating causal effects from text due to treatment encoding.
method Masking-based adjustment representations to remove lexical treatment signals.
result Masking improves overlap diagnostics and reduces bias in treatment effect estimates.
We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and lower bounds of good deal pricing bounds are expressed by convex risk measures on …
Via a non degenerate symmetric bilinear form we identify the coadjoint representation with a new representation and so we induce on the orbits a simplectic form. By considering Hamiltonian systems on the orbits we study some features of them and finally find commuting functions under the corresponding Lie-Poisson brack…
Representation costs in data science: Unifying function-space views of parametric methods
problem Analyzing representation costs of parametric data-fitting methods
method Developing a general framework for analyzing representation costs through parameter-space regularizers
result Proving that many natural results hold in this abstract setting, including representer theorems for parametric methods on their native spaces
We study the asymptotic behavior of the twisted Alexander polynomial for the sequence of SL(n ,C)-representations induced from an irreducible metabelian SL(2, C)-representation of a knot group. We give the limits of the leading coefficients in the asymptotics of the twisted Alexander polynomial and related Reidemeister…
There is intense interest in applying machine learning to problems of causal inference in fields such as healthcare, economics and education. In particular, individual-level causal inference has important applications such as precision medicine. We give a new theoretical analysis and family of algorithms for predicting…
Compactifies a component by studying metric degeneration.
problem Compactify the SO(2,3)-Hitchin component.
method Study metric degeneration on a surface in pseudo-hyperbolic space.
result Establish closure in projectivized geodesic currents space.
New insights into Anosov representations of hyperbolic groups.
problem Understanding Anosov representations of relatively hyperbolic groups.
method Proving representations can be interpreted as restricted Anosov representations over flow spaces and showing stability under deformations.
result Representations of certain types are divergent, extended geometrically finite and stable under small deformations.
We classify representations of compact connected Lie groups whose induced action on the unit sphere has an orbit space isometric to a Riemannian orbifold.
A new geometric metric identifies true data changes from parametrization artifacts in high-dimensional representations.
problem Quantifying representation drift in high-dimensional data using Euclidean or cosine distances can misattribute changes due to arbitrary parametrizations.
method Introducing the Fubini Study metric to identify representations that differ only by gauge transformations.
result The Fubini Study metric isolates intrinsic evolution by remaining invariant under gauge-induced fluctuations, providing a diagnostic for meaningful structural changes.
Study genus-three Torelli maps and their fixed point sets in representation varieties.
problem Understanding fixed point sets and representation varieties of genus-three Torelli maps.
method Analyzing fixed point sets and representation varieties of powers of bounding pair maps.
result Determined the number of connected components of fixed point sets and representation varieties.
New groups and subgroups classified with representations and properties.
problem Classifying representations of new groups and subgroups.
method Introduced new groups and subgroups, classified representations into GL_n(C), investigated properties.
result Classified homogeneous 2-local representations of M_kVT_n into eight distinct types.
We define the representation ring of a saturated fusion system F as the Grothendieck ring of the semiring of F-stable representations, and study the dimension functions of F-stable representations using the transfer map induced by the characteristic idempotent of F. We find a…
The paper defines cocycles for positive Anosov representations and constructs affine actions with bounded fundamental domains.
problem Positive Anosov representations into SO(2n,2n−1). method Definition of cocycles and construction of affine actions with fundamental domains.
result Quotient manifolds are homeomorphic to handlebodies.
New task aligns molecular structure with gene expression changes.
problem Modeling the relationship between chemical structure and gene expression changes.
method Developed a cross-modal small molecule retrieval task and a coordinated deep learning approach to align chemical structure and gene expression profiles.
result Demonstrated the feasibility of the new task and highlighted the limitations of current data and systems.
Symplectic spinors and their properties are analyzed for Hodge theory.
problem Decomposing and characterizing symplectic spinors and their derivatives.
method Representation theory, cohomology, and duality of Lie superalgebras.
result Valid Hodge theory for elliptic complexes involving symplectic spinors.
Chaos in cerebellar cells enhances complexity of neural patterns.
problem Understanding how cerebellar granular layer represents complex information.
method Constructed a model of cerebellar granular layer with gap junctions, evaluated using reservoir computing.
result Chaotic dynamics in the cerebellar granular layer produce complex and diverse output patterns.
New formula for knot group representations and hyperbolic structures.
problem Understanding representations of knot groups and their geometric implications.
method Direct algebraic formula for geometric parameters of octahedral decompositions.
result Explicit criterion for critical points in Neumann-Zagier--Yokota potential function.
Graphon autoencoder generates graphs with arbitrary sizes using Chebyshev filters.
problem Generating graphs with arbitrary sizes and arbitrary structures.
method Induces graphons from observed graphs, uses Chebyshev filters for latent representation, and learns encoder and decoder to minimize Wasserstein distance.
result Graphon autoencoder provides a new paradigm for graph generation with good generalizability and transferability.
New concept of relatively dominated representations for higher-rank groups.
problem Understanding geometric finiteness in higher-rank Lie groups.
method Introducing and analyzing relatively dominated representations.
result Groups admitting relatively dominated representations are relatively hyperbolic.
Consistent spectral clustering with fairness constraints on representation graphs.
problem Finding balanced clusters in similarity graphs with fairness constraints.
method Developed variants of unnormalized and normalized spectral clustering for fair planted partitions.
result Consistency results for constrained spectral clustering under fair planted partitions.
In this article we give examples which show that the TQFT representations of the mapping class groups derived from quantum SU(N) for N>2 are generically decomposable. One general decomposition of the representations is induced by the symmetry which exchanges SU(N) representation labels by their conjugates. The respecti…
BriarPatches obscure sensitive attributes to achieve demographic parity.
problem Achieving demographic parity in model predictions.
method Pixel-space interventions that obscure sensitive attributes from classifier representations.
result BriarPatches push downstream predictors towards demographic parity.
A method to train multi-agent reinforcement learning models without intrinsic rewards.
problem Training multi-agent reinforcement learning models with sparse rewards is challenging.
method A learning-based exploration strategy using variational graph autoencoder to generate initial states.
result The method improves the training and performance of multi-agent reinforcement learning models.
We find decomposition series of length at most two for modular representations in positive characteristic of mapping class groups of surfaces induced by an integral version of the Witten-Reshetikhin-Turaev SO(3)-TQFT at the p-th root of unity, where p is an odd prime. The dimensions of the irreducible factors are given…
Given a knot K in an integral homology sphere with exterior N_K, there is a natural action of the cyclic group Z/n on the space of SL(n,C) representations of the knot group π_1(N_K), and this induces an action on the SL(n,C) character variety. We identify the fixed points of this action in terms of characters of metabe…
NURD improves model performance by distilling representations independent of nuisance variables.
problem Models trained under spurious correlations may fail on data with different nuisance-label relationships.
method Developed Nuisance-Randomized Distillation (NURD) to find representations independent of nuisance variables.
result NURD finds representations that perform better regardless of nuisance-label relationships.
A scalable Gaussian process method for large datasets.
problem Handling high number of training instances and high dimensional input data.
method Subspace inducing inputs combined with matrix-preconditioning.
result Improved predictive performances and reduced computational times.