The paper computes characteristic classes for Lie group representations.
problem Computing characteristic classes for Lie group representations.
method The paper outlines a procedure to compute characteristic classes of irreducible representations of Lie groups, expressing them as polynomial functions in the highest weight.
result The paper expresses characteristic classes of Lie group representations as polynomial functions in the highest weight.
The paper studies highest weight representations of Lie superalgebras and their geometric realizations.
problem Understanding highest weight representations of Lie superalgebras and their geometric realizations.
method Analyzes representations of Lie superalgebras and their geometric realizations on Hermitian superspaces.
result Discovers geometric realizations of highest weight representations of Lie superalgebras.
Study shows bounds on Hausdorff dimension for limit sets of projective Anosov representations.
problem Understanding Hausdorff dimensions of limit sets for projective Anosov representations.
method Proved bounds on Hausdorff dimension using critical exponents associated to highest weight and simple root.
result Hausdorff dimension of symmetric limit set is bounded by critical exponents.
Study the asymptotic behavior of analytic torsion for hyperbolic orbifolds.
problem Understanding the asymptotic behavior of analytic torsion for hyperbolic orbifolds.
method Analyzing sequences of representations associated to rays of highest weights.
result Asymptotic behavior of analytic torsion for hyperbolic orbifolds is understood.
TQFT used to study symplectic group modules.
problem Calculating dimensions and characters of specific modules.
method Applied Topological Quantum Field Theory (TQFT).
result Explicit formulae for dimensions and characters.
Paper refines Alesker-Bernig-Schuster theorem, proving Hodge-Riemann relations for Euclidean balls.
problem Understanding translation-invariant valuations and their geometric implications.
method Explicit construction of highest weight vectors and analysis of natural operations on these vectors.
result Proof of Hodge-Riemann relations for Euclidean balls, extending geometric inequalities.
We define invariants for colored oriented spatial graphs by generalizing CM invariants, which were defined via non-integral highest weight representations of Uq(sl2). We apply the same method to define Yokota's invariants, and we call these invariants Yokota type invariants. Then we propose a volume conjecture of t…
The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branch…
Study on eigenvalues of Laplace operator on 1-forms for symmetric spaces.
problem Investigating the first eigenvalue of the Laplace operator on 1-forms in compact inner symmetric spaces.
method Analyzing the Casimir eigenvalue of the highest root for the isotropy representation.
result The first eigenvalue of the Laplace operator on 1-forms is the Casimir eigenvalue of the highest root.
Verma Howe duality connects tensor products of Verma modules to LKB representations.
problem Understanding the relationship between tensor products of Verma modules and LKB representations.
method Established a quantized version of Verma Howe duality and used it to prove the simplicity of LKB representations.
result LKB representations arise from the quantized Verma Howe duality and are shown to be simple modules.
BetaDataWeighter learns weights for unlabelled data to improve self-supervised learning accuracy.
problem Improving unsupervised representations with domain shift between unlabelled and target data.
method Learning Bayesian instance weights for unlabelled data to prioritize useful instances.
result BetaDataWeighter achieves highest average accuracy and prunes up to 78% of images without significant loss in accuracy.
Study asymptotics of unitary matrix elements in quantum mechanics.
problem Asymptotic behavior of unitary matrix elements in quantum mechanics.
method Uses Berezin-Toeplitz quantization and symplectic geometry.
result Recover asymptotics of Wigner's d-matrix elements for spin representations.
New categorification method for infinite braids.
problem Categorifying highest-weight projectors for infinite braids.
method Limiting colored Khovanov-Rozansky homology of infinite braids.
result Partial isomorphism between HOMFLY-PT homology of braids and infinite torus knots.
Quantum Racah matrices for R=[2,2] are fully described and evaluated.
problem Calculating Racah matrices for quantum groups U_q(sl_N).
method Eigenvalue hypothesis for most matrices, highest weight method for degenerate cases.
result Complete Racah matrices for |R| ≤ 4, allowing calculation of HOMFLY polynomials.
This work is a continuation of the former paper in which principal bundles are given by compact spin toric manifolds and compact connected semisimple Lie groups. In this paper, ambient manifolds are assumed to be compact toric manifolds and Lie groups are compact connected. The main result is that locally smooth manifo…
Paper finds better words for topic models by reranking top words.
problem Top words in topic models are not always representative.
method Reranking words by considering marginal probability over every topic.
result Reranked top words are more representative of topics.
Unified approach to aggregating models and preferences.
problem Consistent aggregation of models and preferences.
method Formal definition and weighted averaging of models and preferences.
result All rational aggregation rules are weighted averages of highest-ranked models/experts.
New homology for infinite multi-colored braids, completing previous work.
problem Categorification of highest-weight projectors for infinite braids.
method Defining limiting Khovanov-Rozansky homology for semi-infinite braids.
result Categorifies highest-weight projectors for a large class of braids.
URT layer improves few-shot image classification across diverse domains.
problem Few-shot image classification in multi-domain settings.
method Meta-learns to dynamically re-weight and compose domain-specific representations.
result Sets new state-of-the-art on Meta-Dataset.
Extends Lawrence's representations to integral Uqsl(2) Verma-modules and braid groups.
problem Integrating Lawrence's representations into Uqsl(2) Verma-modules and braid groups. method Defining homological operators and showing they provide a representation for Uqsl(2), establishing isomorphisms and preserving key properties. result Recovering an integral version of Kohno's theorem for Verma-modules and braid group representations.
A hybrid model reduces graph complexity for improved classification accuracy.
problem High computational complexity and large number of parameters in higher-order graph convolutional networks.
method Weight sharing mechanism and novel fusion pooling layer to reduce parameters and complexity.
result The proposed model achieves highest classification accuracy with fewer trainable parameters.
Classifies and constructs intertwining differential operators between vector bundles over real projective space.
problem Classifying and constructing intertwining differential operators between vector bundles over RP2. method Utilizes SL(3,R)-intertwining differential operators, BGG resolution, and representation theory. result Irreducible unitary highest weight modules of SU(1,2) at reduction points classified by Cartan and PRV operators. Paper presents new matrix formats for deep neural networks that improve inference efficiency.
problem High computational cost of dot product operations in deep neural networks.
method Develops new matrix formats with bounded complexity by entropy of weight matrices.
result Up to x90 energy savings and x5 speed ups in dot product operations.
Efficient RNNs on FPGA using structured matrices improve energy efficiency 35.7x.
problem Irregular network structure after pruning degrades RNN performance and energy efficiency.
method Use block-circulant matrices to compress and accelerate RNNs in FPGA.
result Achieved maximum energy efficiency improvement of 35.7x compared to ESE.
The paper calculates HOMFLY polynomials for 3-strand knots using a new method.
problem Systematic description of colored knot polynomials for arbitrary representations.
method Efficient highest-weight method to find inclusive Racah matrices.
result Explicitly found HOMFLY polynomials for 3-strand knots and confirmed conjectures.
We study the interplay between the minimal representations of the orthogonal Lie algebra g=so(n+2,C) and the \emph{algebra of symmetries} S(□r) of powers of the Laplacian □ on Cn. The connection is made through the construction of highest weight repres…
Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its applications to a concrete construction of some natural equivariant operators that a…
In the present paper, we study the Sp-module structure of the cokernel of the Johnson homomorphism of the mapping class groups of surfaces. We detect the Sp-irreducible components with highest weight [1^k] (and [k]) in the cokernel. We also show that the multiplicities of them is equal to one.
The ``Links-Gould invariant'' is a two-variable Laurent polynomial invariant of oriented (1,1) tangles, which is derived from the representation of the braid generator associated with the one-parameter family of four dimensional representations with highest weights (0,0|a) of the quantum superalgebra U_q[gl(2|1)]. We u…
Test-asset construction affects factor model performance.
problem How test assets are constructed impacts factor model performance.
method Forming characteristic-unsorted random portfolios and varying stock selection, initial weighting, holding, and rebalancing.
result Test-asset construction shifts factor model rankings materially.
The paper calculates Racah matrices for up to 3 strands of knots and links.
problem Systematic description of colored knot and link invariants.
method Highest weight method and use of Racah matrices.
result Explicit answers for Racah matrices and colored polynomials for 3-strand knots and links.
Conformal Bayes under label shift: post-hoc calibration vs. in-training adaptation
problem Bayesian prediction sets under label shift
method Post-hoc calibration vs. In-training adaptation
result Both strategies achieve valid coverage equally in an unbiased training regime
Study on default clustering in large networks using graph theory.
problem Understanding the impact of defaults in large interconnected systems.
method Law of large numbers applied to graph dynamics, singular value decomposition of adjacency matrix.
result Identification of components with highest contagion impact using eigenvalues.
Two approaches improve conformal Bayes for label shift, one post-hoc and one in-training.
problem Improving prediction sets for target domain under label shift.
method Two complementary approaches: post-hoc calibration and in-training adaptation.
result In-training adaptation achieves up to 43% width reduction at unchanged coverage.
Characterizes flag geometries for Hitchin representations in SL3(R).
problem Understanding flag geometries associated with Hitchin representations in SL3(R).
method Geometric characterization based on invariant foliations and refraction flows.
result Constructs refraction flows for positive roots in general sl_n(R), with highest root flows being C^1+α.
Paper identifies key CpG methylation sites for breast cancer.
problem Early detection and treatment of breast cancer.
method Used machine learning on TCGA dataset to classify cancer vs. non-cancer samples.
result Reduced model with 25 key CpG sites achieves over 94% accuracy.
New technique trains DNNs with fewer weights, saving memory and energy.
problem Training deep neural networks requires many weights, increasing memory and energy costs.
method Constrain weight updates to those with highest gradients, regenerating others.
result Pruned networks maintain accuracy while significantly reducing weight count and memory usage.
The paper studies weak singular Hermite-Einstein structures on homogeneous vector bundles.
problem Existence of weak singular Hermite-Einstein structures on homogeneous holomorphic vector bundles.
method Using Cartan's highest weight theory, the paper establishes an algebraic criterion for topological splitting and decouples the prescribed mean curvature equation.
result A sufficient algebraic condition for realizing an L2-function as the mean curvature of a singular Hermitian structure on an irreducible homogeneous bundle. Kashaev limits of quantum A-polynomials reveal classical action vanishing and hyperbolic volume deformation.
problem Exploring the Kashaev limits of quantum A-polynomials. method Analyzing the double scaling quasiclassical limit.
result Identifying two phases in the Kashaev limit.
We study the structure of abelian extensions of the group LqG of q-differentiable loops (in the Sobolev sense), generalizing from the case of central extension of the smooth loop group. This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules are…
In this paper we describe all the nilradicals of parabolic subalgebras of split real simple Lie algebras admitting symplectic structures. The main tools used to obtain this list are Kostant's description of the highest weight vectors (hwv) of the cohomology of these nilradicals and some necessary conditions obtained fo…
Researchers find highest volumes for isospectral spherical orbifolds and space forms.
problem Finding the maximum volumes of isospectral spherical orbifolds and space forms.
method Analyzing isospectral properties and calculating volumes of spherical orbifolds and space forms.
result Highest volumes for specific dimensions and conditions of isospectral spherical orbifolds and space forms.
We construct and study a new family of TQFTs based on nilpotent highest weight representations of quantum sl(2) at a root of unity indexed by generic complex numbers. This extends to cobordisms the non-semi-simple invariants defined in (arXiv:1202.3553) including the Kashaev invariant of links. Here the modular categor…
New Feedback Transformer architecture improves model performance by exposing past representations to future.
problem Limitations of Transformers in fully exploiting sequential input.
method Proposes Feedback Transformer exposing all past representations to future.
result Demonstrates improved performance with smaller, shallower models.
This paper explores how representation learning can improve design-based causal inference.
problem Estimating causal effects in design-based studies is challenging due to the need for optimal weights.
method The authors propose an end-to-end estimation procedure that learns a flexible representation to minimize the error in choosing a representation.
result The proposed method is competitive in various causal inference tasks and shows promise for improving design-based weights.
Diffusion models optimize objectives similar to ELBO with Gaussian noise augmentation.
problem Optimizing diffusion models for high perceptual quality.
method Showed diffusion objectives are weighted ELBOs over noise levels, with Gaussian noise augmentation.
result Diffusion objectives equate to ELBO with Gaussian noise augmentation under monotonic weighting.
Study shows Steinberg representation's multiplicity in cohomology of congruence subgroups.
problem Analyzing multiplicity of Steinberg representation in cohomology of congruence subgroups.
method Computation of cohomology of S-arithmetic groups outside a linear range of degrees. result Multiplicity of Steinberg representation is 1 in top-degree cohomology.
New method for sparse autoencoder learning using rank-ordered hidden units.
problem Sparse representation learning without extra hyperparameters.
method Order hidden units by activation, progressively reconstruct input, minimize reconstruction error.
result High sparsity achieved with minimal reconstruction error and robustness.