We prove universality theorems ("Murphy's Laws") for representation schemes of fundamental groups of closed 3-dimensional manifolds. We show that germs of SL(2,C)-representation schemes of such groups are essentially the same as germs of schemes of over rational numbers.
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This paper explores representation spaces of knot groups into SL(n,C).
problem Understanding representation spaces of knot groups into SL(n,C).
method General introduction to representation spaces, discussion of tangent space vs. representation scheme, and recent results on knot groups.
result Presentation of recent results on representation and character varieties of knot groups into SL(n,C).
Neural networks learn task-specific features, influenced by nonlinearity.
problem Understanding the nature of task-dependent feature learning in neural networks.
method Investigation of fully-connected, wide neural networks using Bayesian framework.
result The nature of internal representations depends on neuronal nonlinearity, leading to analog, redundant, or sparse coding schemes.
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular schemes to construct a similarity graph, i.e., pairwise distance based scheme an…
Two new coding schemes improve the efficient communication of noisy data.
problem Efficient communication of noisy data in machine learning.
method Ordered Random Coding (ORC) and Hybrid Coding Scheme.
result Improved coding schemes over existing approaches.
Paper shows strong convergence rates for fractional processes using Ornstein-Uhlenbeck representations.
problem Understanding and improving Monte Carlo schemes for fractional volatility models.
method Numerical discretizations of fractional processes using Ornstein-Uhlenbeck representations.
result Strong convergence rates of arbitrarily high polynomial order for fractional processes.
The paper extends lossy coding to nonlinear latent representations.
problem Learning finite-dimensional coding schemes with nonlinear reconstruction maps.
method Generalizes Maurer--Pontil framework to nonlinear maps, connects to generative modeling, and provides generalization bounds.
result Established a connection to approximate generative modeling and presented generalization bounds.
Study SL(2,C) character schemes for finitely generated groups.
problem Characterize SL(2,C) representations of finitely generated groups.
method Define coordinate rings and equations for SL(2,C) character schemes.
result Explicit equations for character schemes of finitely presented groups.
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies, we propose efficient dictionary learning schemes to solve several practical for…
MMD-B-Fair learns fair representations by minimizing MMD test power.
problem Learning fair representations of data while preserving target attributes.
method Kernel two-sample testing and block testing schemes.
result Minimizing MMD test power allows hiding sensitive attribute information.
Federated learning improves with adaptive hyper-parameters and representation matching.
problem Heterogeneous client data leads to divergent local models in federated learning.
method Representation matching and adaptive hyper-parameters.
result Significant performance and robustness improvements in federated learning.
Maximizes mutual information to improve graph neural networks performance.
problem Loss of information between nodes in GNNs aggregation and iteration schemes.
method Explores mutual information maximization in the aggregation and iteration scheme of GNNs.
result Improves state-of-the-art performance on graph tasks.
We give a new proof of the Jantzen sum formula for integral representations of Chevalley schemes over Spec Z. This is done by applying the fixed point formula of Lefschetz type in Arakelov geometry to generalized flag varieties. Our proof involves the computation of the equivariant Ray-Singer torsion for all equivarian…
Governance, Risk, and Regulation: A Framework for Improving Efficiency in Kenyan Pension Fundsq-fin.RM
Study improves pension scheme efficiency in Kenya through governance and risk management.
problem Limited research on efficiency of Kenyan pension schemes under governance structures.
method Quantitative panel regression analysis on 128 Kenyan pension schemes over 7 years.
result Employee board members have a significant positive effect on pension scheme efficiency.
New representation of curves helps prove complex geometry result.
problem Understanding cohomologically stable curves in projective space.
method Using commuting matrix polynomials to represent curves and show isomorphism to hyperkähler quotient.
result Hilbert scheme isomorphic to a hyperkähler quotient.
AWARE improves graph prediction by aggregating walks with attention schemes.
problem Improving graph prediction accuracy using walk aggregation.
method Integrates attention schemes into walk-aggregating GNNs.
result AWARE outperforms existing methods in graph-level prediction tasks.
New geometric quantisation scheme for hyper-Kähler manifolds.
problem Quantising hyper-Kähler manifolds with symmetry.
method Constructing unitary quantum representations of isometries.
result Decomposition of quantum representations into irreducibles.
Introduces REVE, a regularization scheme that compresses class conditioned entropy.
problem Improving generalization performance of deep learning models.
method Identifies a variable responsible for final prediction, compresses class conditioned entropy, introduces a variational upper bound, and integrates a tractable loss into training.
result Demonstrates the efficiency of REVE on various neural networks and datasets.
Regularized LAEs learn principal components efficiently.
problem Learning optimal linear representations with LAEs.
method Proper regularization schemes (non-uniform ℓ2 and nested dropout).
result Convergence to optimal representation is slow due to ill-conditioning.
Neural networks improve ocean temperature forecasting and data interpolation.
problem Forecasting and reconstructing sea surface temperature from satellite data.
method Patch-level neural network representations that mimic numerical integration schemes.
result Neural networks outperform other data-driven models in forecasting and missing data interpolation.
Lectures on link homology and its algebraic/geometric models.
problem Defining and understanding link homology.
method Definition and properties of Khovanov-Rozansky triply graded homology, and three geometric models.
result Three geometric models for link homology: braid varieties, Hilbert schemes, and affine Springer fibers.
The Runge-Kutta-Legendre scheme improves pricing American options and other derivatives.
problem Pricing American options and other derivatives with improved accuracy and stability.
method Runge-Kutta-Legendre finite difference scheme applied to Black-Scholes and Heston models.
result Improved convergence and stability compared to existing schemes.
We construct harmonic morphisms on the compact simple Lie group G2. The construction uses eigenfamilies in a representation theoretic scheme.
Unified theory linking atom-centered and message-passing models for molecular properties.
problem Combining atom-centered and message-passing models for accurate molecular property prediction.
method Generalizing ACDC framework to include multi-centered information, providing a complete linear basis for regression.
result Unified understanding of atom-centered and message-passing models, providing a coherent foundation.
A new method for learning network representations that avoids information bias and sparsity.
problem Information bias and sparsity in network representation learning.
method A spreading-activation schema for learning node embeddings in network structures.
result Significant improvement in various real-world network analysis tasks.
Language models improve clinical prediction models using EHR data.
problem Limited patient data for training clinical prediction models.
method Using patient representation schemes from natural language processing.
result 3.5% mean improvement in AUROC on five prediction tasks.
We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme is to approximate the kernel fu…
EigenNoise provides a competitive word vector initialization scheme without pre-training data.
problem Improving word vector initialization without pre-training data.
method EigenNoise uses a dense, independent co-occurrence model to initialize word vectors.
result EigenNoise can approach GloVe performance without pre-training data.
Proposes SHADE, a new regularization scheme for deep learning.
problem Improving classification performance in deep learning.
method SHADE uses information theory to define a prior based on conditional entropy, decoupling representation learning from data fitting.
result Empirically validated improvements over standard regularization schemes.
Proposes SHADE, a new regularization scheme for deep learning.
problem Improving classification performances in deep learning.
method SHADE uses information theory to define a prior based on conditional entropy, decoupling representation learning from data fitting.
result Empirically validated improvements over common regularization schemes.
New LFR algorithm ensures fair predictions with theoretical guarantees.
problem Ensuring fairness in AI algorithms for social decision-making.
method Proposes a new adversarial training scheme using IPM with a parametric family of discriminators.
result Theoretical guarantee of fairness in final prediction models.
Ideal attribution mechanisms track model interactions for faithful watermarks.
problem Ensuring models provide transparent and fair attribution decisions.
method Introducing ideal attribution mechanisms and a ledger for tracking model interactions.
result A unified framework for evaluating watermarking schemes, clarifying attainable guarantees.
New method learns chaotic dynamics from noisy, partial data.
problem Learning chaotic dynamics from noisy, partially observed data.
method Bayesian formulation, neural-network ODE representation, EM-like procedures, state-of-the-art assimilation schemes.
result Recover and reproduce chaotic dynamics, including Lyapunov exponents.
Study of Hilbert schemes and Coulomb branches of hypertoric varieties.
problem Understanding the geometry and topology of Coulomb branches of hypertoric varieties.
method Investigation of transverse equivariant Hilbert schemes and Hamiltonian reductions, proposing new metrics.
result Coulomb branches of hypertoric varieties can be constructed as Hilbert schemes or Hamiltonian reductions.
Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie for the selection of groups of correlated variables. To investigate on the statistical properties of this scheme and in particular on its consistency properties, we set up …
The paper optimizes querying schemes for crowdsourced classification using XOR queries.
problem Optimizing querying schemes for crowdsourced classification.
method Modeling crowdsourced labeling/classification as source coding problem, leveraging connections to channel coding.
result Provides querying schemes with almost optimal number of queries, each involving a constant number of labels.
A coloring scheme improves graph neural networks for node disambiguation.
problem Improving graph neural networks' ability to distinguish identical node attributes.
method Introducing a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate node attributes.
result CLIP is a universal approximator of continuous functions on graphs with node attributes.
New clustering methods use motifs to organize networks.
problem Organizing directed graphs efficiently.
method Construct clustering methods parametrized by motifs.
result New clustering methods can organize networks.
This paper investigates the classical and quantum elementary systems with Newton-Hoooke symmetry. A complete classification is given by explicit computation. In addition, we present an application example of quantization using the Moyal scheme.
Progressive stochastic binarization improves deep network inference efficiency.
problem Efficient inference of deep networks with reduced memory and computational resources.
method A progressive stochastic binarization scheme for deep networks that uses small integers and fixed shifts.
result Matches the accuracy of previous binarized approaches and reduces inference costs by up to 33%.
We conjecture an expression for the dimensions of the Khovanov-Rozansky HOMFLY homology groups of the link of a plane curve singularity in terms of the weight polynomials of Hilbert schemes of points scheme-theoretically supported on the singularity. The conjecture specializes to our previous conjecture relating the HO…
The continuum-of-urns scheme, generalized beta and Indian buffet processes, and hierarchies thereofmath.PR
We describe the combinatorial stochastic process underlying a sequence of conditionally independent Bernoulli processes with a shared beta process hazard measure. As shown by Thibaux and Jordan [TJ07], in the special case when the underlying beta process has a constant concentration function and a finite and nonatomic …
Based on the analogies between knot theory and number theory, we study a deformation theory for SL_2-representations of knot groups, following after Mazur's deformation theory of Galois representations. Firstly, by employing the pseudo-SL_2-representations, we prove the existence of the universal deformation of a given…
This paper proposes a new weight representation scheme for efficient model compression and performance enhancement.
problem Challenges in achieving performance enhancement on devices due to irregular sparse matrix representations.
method Fine-grained and unstructured pruning method combined with structured weight encryption.
result Achieved high compression ratios and performance on various deep learning models.
Researchers extend geometric quantization to complex Abelian Lie supergroups.
problem Quantization of super Kähler structures on complex Abelian Lie supergroups.
method Extended geometric quantization scheme to super Kähler setting, constructed unitary representation.
result Irreducible subrepresentations of the constructed representation are determined by the moment map.
CSI detects novelty by contrasting shifted instances, outperforming existing methods.
problem Detecting samples from outside the training distribution.
method Contrastive learning with distributionally shifted augmentations.
result CSI outperforms existing methods in various novelty detection scenarios.
A new method represents rod shapes as paths in special Euclidean algebra.
problem Representing the shapes of rods and framed curves for mechanical analysis.
method Representing shapes as paths in the special Euclidean algebra.
result The method avoids expensive reconstruction and interpolation in rod mechanics.
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.