We present an efficient, principled, and interpretable technique for inferring module assignments and for identifying the optimal number of modules in a given network. We show how several existing methods for finding modules can be described as variant, special, or limiting cases of our work, and how the method overcom…
We discuss several open problems in classical Knot Theory and we develop techniques that allow us to study them: Lagrangian tangles, skein modules and Burnside groups.
Investigates adjustments on Lie group crossed modules for gauge theory.
problem Existence and classification of adjustments on crossed modules of Lie groups.
method Differentiation/integration correspondence with infinitesimal adjustments; Lie algebra techniques.
result Infinitesimal adjustments exist if and only if the Kassel-Loday class lies in the image of the Chern-Weil homomorphism.
This paper is a presentation, where we compute the HOMFLYPT Skein module of singular links in the 3-sphere. This calculation is based on some results previously proved by Rabenda and the author on Markov traces on singular Hecke algebras, as well as on classical techniques that allow to pass from the framework of Marko…
Self-modulation improves GAN performance across various settings.
problem Training GANs is challenging due to inconsistent performance.
method Introduces self-modulation, allowing generator feature maps to adapt to input noise.
result Reduces FID by 5%-35% in empirical studies.
New bases found for Kauffman bracket skein module of fibered torus.
problem Computing Kauffman bracket skein module of fibered 3-manifolds.
method Constructed bases for Kauffman bracket skein module of product annulus and circle, then applied to (β,2)-fibered torus. result Found a new basis for KBSM of (β,2)-fibered torus. Computational study of prime knots in specific spaces.
problem Tabulation and classification of prime knots in lens spaces.
method Computational techniques, skein modules, hyperbolic structures.
result Established amphichiral knots and distinguished knots by skein modules.
A deep learning subsampling technique improves modulation classification accuracy.
problem Improving modulation classification accuracy in wireless communication systems.
method Proposes a data-driven subsampling strategy using deep neural networks to simulate signal removal.
result Improves classification accuracy to higher levels than traditional methods.
Extends ambient modules to hidden space for better generative model training.
problem Lack of practical methods for applying ambient modules to hidden space of generators.
method Extend ambient modules to hidden space, provide uniqueness condition and strategy.
result Practical method for ambient hidden generator in adversarial training process.
Dynamic information balancing reduces catastrophic forgetting in modular neural networks.
problem Catastrophic forgetting in neural networks when learning multiple tasks.
method Dynamic Information Balancing (DIB) using reinforcement learning to adaptively route inputs based on module information load.
result DIB combined with EWC regularization outperforms models with similar capacity and EWC regularization.
We study optimal investment strategies that maximize expected utility from consumption and terminal wealth in a pure-jump asset price model with Markov-modulated (regime switching) jump-size distributions. We give sufficient conditions for existence of optimal policies and find closed-form expressions for the optimal v…
Optimized CNNs for AMC on edge devices reduce complexity without sacrificing accuracy.
problem Developing efficient DL models for AMC on resource-constrained edge devices.
method Pruning, quantization, and knowledge distillation techniques applied to CNNs.
result Optimized models maintain or improve AMC accuracy with reduced complexity.
Metareasoning optimizes modular systems by dynamically adjusting configurations.
problem Maximizing system utility in high-stakes tasks with modular subsystems.
method Employing reinforcement learning with rich contextual representations to dynamically adjust module configurations.
result Significant improvement in system performance across various reinforcement learning techniques.
Developed a new statistic to test binary regime switching models.
problem Testing the model assumption of binary regime switching extension of GBM.
method Proposed a new discriminating statistics and identified an admissible class of regime switching candidate models.
result Sampling distribution of the test statistics differs significantly between different regime switching models.
CycleGAN-VC2 improves voice conversion without parallel data.
problem Challenges in non-parallel voice conversion.
method Improved CycleGAN-VC with three techniques: two-step adversarial losses, 2-1-2D CNN generator, and PatchGAN discriminator.
result CycleGAN-VC2 significantly reduces the gap between converted and target speech.
Paper introduces RKHM for more explicit variable structures analysis.
problem Explicitly analyzing structures among variables.
method Orthonormal systems in Hilbert C∗-modules, RKHM. result Theoretical and practical procedures for RKHM orthonormalization.
Researchers compute the skein module of a solid torus using braids.
problem Computing the HOMFLYPT skein module of S1imesS2. method Braid-theoretic techniques to solve an infinite system of equations.
result The free part of the skein module is generated by the empty link, with all other elements being torsion.
A standard technique for understanding underlying dependency structures among a set of variables posits a shared conditional probability distribution for the variables measured on individuals within a group. This approach is often referred to as module networks, where individuals are represented by nodes in a network, …
Paper proposes a time-frequency analysis method for blind modulation classification in MIMO systems.
problem Blind modulation classification in MIMO systems with overlapping signals and unknown channel parameters.
method Time-frequency analysis using windowed short-time Fourier transform, conversion to RGB spectrogram images, convolutional neural network for classification, decision fusion.
result Proposed scheme achieves high classification accuracy at different SNRs, outperforming existing methods.
New method proves representation stability for linear groups, resolving homological questions.
problem Proving representation stability for linear groups over fields of characteristic zero.
method Introducing a technique for quantitative representation stability theorems.
result Vanishing result for higher syzygies of VIC- and SI-modules.
Machine learning predicts extreme events from spectral data.
problem Predicting extreme events in nonlinear systems from limited data.
method Trained a neural network to correlate spectral and temporal properties of optical fibre modulation instability.
result Predicted temporal probability distribution from high-dynamic range spectral data.
In this paper, we study the interplay between modules and sub-objects in holomorphic Poisson geometry. In particular, we define a new notion of "residue" for a Poisson module, analogous to the Poincaré residue of a meromorphic volume form. Of particular interest is the interaction between the residues of the canonical …
PICLE uses probabilistic models to efficiently evaluate and compose modules for continual learning.
problem Challenging search space of module compositions in continual learning.
method Probabilistic framework to cheaply compute module compositions' fitness.
result First modular CL algorithm to achieve perceptual, few-shot, and latent transfer.
Paper proposes continuous residual layers for graph neural networks.
problem Low-pass filtering effect in GCN-based models.
method Integrates Ordinary Differential Equations (ODE) to produce outputs of continuous residual layers.
result Continuous residual layers achieve better results than non-residual modules in multiple layers.
Let Δ be a trivial knot in the three-sphere. For every finite cyclic group G of odd order, we construct a G-equivariant Khovanov homology with coefficients in the filed $\F_{2}$. This homology is an invariant of links up to isotopy in (S3,Δ). Another interpretation is given using the categorification of the …
Details of quantum knot invariant calculations using a specific SU(3)_q-module are given which distinguish the Conway and Kinoshita-Teresaka pair of mutant knots. Features of Kuperberg's skein-theoretic techniques for SU(3)_q invariants in the context of mutant knots are also discussed.
Framework uses physics knowledge to improve spatiotemporal prediction with limited data.
problem Challenges in modeling physical systems with limited real-world data.
method Physics-aware meta-learning with auxiliary tasks, incorporating PDE-independent spatial and temporal modules.
result Framework outperforms in spatiotemporal prediction tasks with limited data.
Meta-learning approach discovers task-specific modules for few-shot tasks.
problem Meta-learning large models with limited task-specific data.
method Bayesian shrinkage for automatic discovery of task-specific and general modules.
result Outperforms existing meta-learning methods in domains with little task data and long adaptation horizons.
In the last chapter of his book "The Algebraic Theory of Modular Systems " published in 1916, F. S. Macaulay developped specific techniques for dealing with " unmixed polynomial ideals " by introducing what he called " inverse systems ". The purpose of this paper is to extend such a point of view to differential module…
Paper introduces RKHM and KME for richer data analysis.
problem Lack of rich data structures in kernel methods.
method Proposes RKHM and KME for functional data analysis.
result RKHM captures structural properties in functional data.
In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators (D-modules), and reformulate the composition series and branching problems for objects in the Bernstein-Gelfand-Gelfand pa…
UT module refines VAE latent space, improving disentanglement and interpretability.
problem Irregular latent distributions cause posterior collapse and misalignment in VAEs.
method UT module uses G-KDE clustering, GM modeling, and PIT to transform latent space into uniform distribution.
result UT module enhances disentanglement and interpretability of latent representations.
Neural network optimizes MRI pipeline for better brain activity analysis.
problem Inaccurate parameter setting across MRI pipeline modules.
method Converted pipeline into a deep neural network, jointly optimising parameters.
result Adaptive spatial smoothing module improves brain decoding accuracy.
Deep learning improves automatic modulation classification from subsampled data.
problem Automatic recognition of wireless communication signal modulations from imperfect data.
method Developed and tested Convolutional Long Short-term Deep Neural Network (CLDNN), LSTM, and ResNet architectures.
result Achieved high classification accuracy (around 90%) at high SNR with minimal training data.
New bases for Kauffman bracket skein module of genus 2 handlebody.
problem Finding new bases for Kauffman bracket skein module of genus 2 handlebody.
method Using parting technique to convert elements in the Przytycki-basis to open braid form, defining an ordering relation, and relating the bases via matrix relations.
result Introducing BH2 as a more natural basis for KBSM(H2) and suitable for computing modules of 3-manifolds obtained from H2 by surgery. New techniques prove bounded acyclicity results for semi-simplicial sets.
problem Homological stability of semi-simplicial sets and groups.
method Combinatorial techniques in simplicial bounded cohomology.
result Slope-1/2 stability results for certain groups. In this paper, we compute the graph skein algebra of the punctured disk with two holes. Then, we apply the graph skein techniques developed here to establish necessary conditions for a spatial graph to have a symmetry of order p, where p is a prime. The obstruction criteria introduced here extend some results obtai…
The linking genotype to phenotype is the fundamental aim of modern genetics. We focus on study of links between gene expression data and phenotype data through integrative analysis. We propose three approaches. 1) The inherent complexity of phenotypes makes high-throughput phenotype profiling a very difficult and labor…
The powerful character variety techniques of Culler and Shalen can be used to find essential surfaces in knot manifolds. We show that module structures on the coordinate ring of the character variety can be used to identify detected boundary slopes as well as when closed surfaces are detected. This approach also yields…
The paper addresses uncalibrated uncertainty estimates for object localization.
problem Uncalibrated uncertainty estimates for object localization in safety-critical applications.
method Adapting a technique for calibrating regression models to object localization.
result Calibrated model provides more reliable uncertainty estimates.
PC-RNN reconstructs MRI images from undersampled data with more details.
problem Recovering fine details from undersampled MRI data.
method Pyramid Convolutional RNN (PC-RNN) with three ConvRNN modules for multi-scale reconstruction.
result PC-RNN outperforms other methods in recovering more details from MRI images.
A new quandle from link modules helps identify link properties.
problem Identifying link properties from their modules.
method Defining quandle operations on multivariate Alexander modules.
result The fundamental multivariate Alexander quandle determines the link module sequence.
Classifies modules of surface-knots in terms of their properties.
problem Characterizing modules of surface-knots in terms of their properties.
method Using homology and covering spaces, the reduced first module is characterized.
result The reduced first module for every genus g is characterized in terms of properties of a finitely generated module.
New method learns both module structure and sequencing in neural networks.
problem Learning only the parameters and order of execution of neural modules.
method Expands the approach to learn the internal structure of modules, including the ordering and combination of arithmetic operators.
result Performance comparable to hand-designed modules achieved without extra supervisory signals.
Paper disproves a Smith conjecture about sphere actions.
problem Smith conjecture about sphere actions with two fixed points.
method Induction of group representations to show counterexamples.
result Negative answer to Smith conjecture for specific groups.
AFS uses attention to select features efficiently.
problem Efficiently selecting features from high-dimensional data.
method AFS combines an attention module and a learning module to address feature selection challenges.
result AFS outperforms state-of-the-art feature selection algorithms in accuracy and stability.
The document provides tables of prehomogeneous and étale modules for reductive algebraic groups.
problem Classifying and tabulating prehomogeneous and étale modules for reductive algebraic groups.
method Classification and tabulation of prehomogeneous and étale modules based on existing work and the author's determination.
result Tables of prehomogeneous and étale modules for reductive algebraic groups with up to two simple factors.
Curvature defined for Hilbert modules and Kasparov modules.
problem Defining and studying curvature in Hilbert modules and Kasparov modules.
method Introduced curvature for densely defined universal connections on Hilbert C∗-modules relative to spectral triples. result Curvature only depends on the represented form of the universal connection modulo junk forms.