Modularity component analysis clusters data without centering.
problem Clustering data without centering.
method Developed exact linear relation between modularity matrix eigenvectors and singular vectors.
result Modularity component analysis clusters data similarly to PCA but without centering.
The paper identifies a component of representations mapping modular group elements to isometries with unique fixed points.
problem Characterizing representations of the modular group into isometry groups.
method Analyzing the space of discrete faithful representations of the modular group into Isom(X) for X=SL3(R)/SO(3).
result The space of representations has a component homeomorphic to R^2 x [0,∞), parametrized by Pappus representations and containing Anosov representations.
Study modular concept learning with different oracle interfaces.
problem Learning a concept that is a cross product of component concepts.
method Analyze different types of oracle interfaces and queries.
result Modular concept learning is easier with positive examples and membership queries.
Recursive sketches summarize deep networks, aiding quick analysis and learning.
problem Understanding and analyzing complex deep learning models.
method Developed a recursive sketch mechanism to summarize inputs and outputs of modular deep networks.
result Sketches can identify key components and summarize essential information, even if partially erased.
Describes representations of modular group into SL(3,R)/SO(3).
problem Understanding representations of modular group into isometry group of symmetric space.
method Analyzes connected component of conjugacy classes of representations.
result Certain representations in the component are Anosov.
Enhances multi-modular models by directing information flow between components.
problem Improving predictive performance in multi-modular models with misspecification.
method Introduces Semi-Modular Inference (SMI) with an influence parameter to control information flow between modules.
result SMI allows for tunable and directed information flow, improving prediction in some settings.
RLgraph separates RL tasks into modular components for stability and efficiency.
problem Algorithmic instability, hyper-parameter sensitivity, and distributed communication patterns in RL tasks.
method Introduces RLgraph, a library for RL tasks in static and define-by-run paradigms.
result Robust, testable, and high-performance implementations across different frameworks and backends.
Study analyzes cost-benefit of CBM for unmanned systems.
problem Determining ROI for CBM strategies in unmanned systems.
method MDFTA with MCS for assessing maintenance requirements.
result Different CBM strategies can significantly impact ROI.
Meta-materials simulation sped up with energy surrogates.
problem Challenging simulation of complex meta-materials due to high-fidelity PDEs.
method Learned component-level surrogates using neural networks to model stored potential energy.
result Surrogates enable accurate macroscopic behavior simulation without full structure simulation.
Proves modular operad structure for Riemann surfaces with open and closed boundaries.
problem Understanding modular operads of Riemann surfaces with mixed boundary conditions.
method Proves modular completion, provides finitary presentation, characterizes algebras via morphisms of Frobenius algebras.
result Modular operad structure for Riemann surfaces with mixed boundaries.
We propose a framework for training GANs on composed data, improving model modularity and interpretability.
problem Training GANs on complex, composed data.
method Composition/decomposition framework for adversarially training GANs on composed data.
result Improves modularity, extensibility, and interpretability of GANs.
Improved algorithm for modular links provides upper volume bounds.
problem Understanding the geometry of modular links and Lorenz links.
method Bunch algorithm to study modular links and provide upper volume bounds.
result First upper volume bound independent of word exponents and quadratic in braid index.
Novel convex surrogate for non-modular loss functions.
problem Computational tractability for non-modular loss functions.
method Submodular-supermodular decomposition, slack-rescaling, Lov{á}sz hinge.
result First tractable solution for non-modular loss functions.
The paper studies knots in modular flows using self-covers.
problem Understanding topological properties of modular knots.
method Constructing templates for Anosov flows and studying closed geodesics.
result Explicit construction of an infinite family of links with the trefoil.
A new method integrates forms on Riemann surfaces, leading to modular forms.
problem Integrating differential forms with poles on Riemann surfaces.
method Simple procedure to integrate differential forms with arbitrary holomorphic poles, establishing an analytic theory for integrals over configuration spaces.
result Regularized graph integrals on elliptic curves are almost-holomorphic modular forms.
RNNs solve modular addition tasks using low rank and sparse Fourier structures.
problem Solving modular addition tasks with recurrent neural networks.
method Identified low rank structures and sparse Fourier representations in RNN weights.
result RNNs robust to removing individual frequencies but degrade with more ablation.
New methods for scalable inference in modular models with misspecified sub-models.
problem Model misspecification in multi-modular models complicates evidence combination.
method Variational methods for approximating Cut and SMI posteriors, and Variational Meta-Posterior.
result Feasibility of analysis with multiple cuts using a single set of variational parameters.
Maliciously crafted modular learning components can cause ML systems to malfunction.
problem Security threats posed by modular learning components in machine learning systems.
method Demonstrated logic-bomb attacks on two healthcare ML systems.
result Maliciously modified MLCs can cause 100% success rate misdiagnosis of skin cancer.
Geodesic patterns, shears, and Anosov representations of the modular group.
problem Understanding representations of the modular group into Isom(X).
method Analyzing geodesic patterns, shears, and foliations.
result The Barbot component is homeomorphic to R^2 x [0,∞), with interior and boundary properties.
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.
FinRL-X unifies trading components for AI and rule-based strategies.
problem Inconsistent between research and live deployment in trading platforms.
method Modular architecture integrating data processing, strategy construction, backtesting, and execution.
result Unified protocol supports AI and rule-based trading components without altering execution.
The paper studies the geometric structure of modular curves X1(N) using meromorphic differentials.
problem Understanding the topological complexity of modular curves X1(N). method Using the walls-and-chambers structure of strata of meromorphic differentials.
result Formulas for the number of chambers and effective means to draw the incidence graph of X1(N). Study counts geodesics on modular surface, linking to necklace counting.
problem Counting geodesics on modular surface with specific winding numbers.
method Asymptotic expansion, generating function analysis, correspondence to necklace counting.
result Obtained asymptotic growth rate of m low-lying geodesics in terms of word length.
Proposes a CL technique to improve accuracy and reduce forgetting.
problem Sequential task learners struggle with forgetting information from previous tasks.
method Extracts modular parts of neural networks and estimates task relatedness.
result Remarkable performance gain in robustness to forgetting for EWC and GEM methods.
This review establishes a taxonomy for modular neural networks.
problem Scaling ANNs for complex and multi-disciplinary problems.
method Systematic analysis of modularization techniques in MNNs.
result A universal framework for studying MNNs.
Improved graph clustering with modularity and coarsening for attributes and communities.
problem Inaccurate community detection and computational inefficiency in graph clustering.
method Integrates coarsening and modularity maximization, using a loss function with log-determinant, smoothness, and modularity components.
result Superior clustering outcomes, proven consistent under DC-SBM, and efficient algorithm integration with GNNs and VGAEs.
New algorithms detect changes in non-stationary MABs for better performance.
problem Non-stationary MAB environments where arm reward distributions change over time.
method Modular Detection Augmented Bandit (DAB) procedures with improved performance lower bounds.
result Modular DAB procedures achieve order-optimal regret bounds for various change detectors and bandit algorithms.
Financial markets modeled like brain networks using dMNC.
problem Understanding latent dynamics in financial markets.
method Biologically inspired framework using dMNC.
result Structural persistence, regime shifts, and early warning signals identified.
Theoretical analysis explains why models generalize after overfitting in modular addition.
problem Understanding why models generalize after overfitting in modular addition.
method Theoretical analysis and gradient descent behavior of two-layer quadratic networks and Transformers.
result Two-layer quadratic networks and simple Transformers generalize well after initially overfitting, indicating grokking.
New method for clustering hypergraphs using modularity maximization.
problem Clustering on hypergraphs for various applications.
method Introduced a hypergraph null model and node-degree preserving reduction. Defined a modularity function and used the Louvain algorithm to maximize it. Proposed a refinement method.
result Demonstrated the efficacy and efficiency of the method on real-world datasets.
New method uses hyperspherical geometry to improve community detection.
problem Improving community detection methods in network analysis.
method Mapping networks to points on a hypersphere, then projecting to clustering vectors.
result Modularity maximization is equivalent to minimizing angular distance on the hypersphere.
Study analyzes Colombian firms' export capabilities over 5 years.
problem Understanding specialization in Colombian firms' export products.
method Bipartite network analysis, modularity maximization, Louvain algorithm.
result Firms specialize in exporting specific product categories, forming clusters.
New techniques prove quantum modularity for various functions.
problem Proving quantum modularity of false theta functions and related series.
method Developed techniques including Poisson summation formula and modular series framework.
result Unified approach to proving quantum modularity for various functions.
Study Eisenstein metrics on modular group representations.
problem Harmonic metrics on automorphic vector bundles.
method Eisenstein series construction for metrics.
result Residue of Eisenstein metrics is a harmonic metric.
A novel metric and framework for evaluating gradient norm equality in deep neural networks.
problem Evaluation of gradient norm equality in complex DNNs requires strong assumptions or complex analysis.
method Proposes a novel metric called Block Dynamical Isometry and a modularized statistical framework based on free probability.
result Gradient Norm Equality is a universal philosophy behind initialization, normalization, and network structures.
ModSSC unifies semi-supervised classification for various data types.
problem Fragmented support for semi-supervised classification across different methods, settings, and data types.
method ModSSC is a modular Python framework that supports reproducible and controlled experimentation for semi-supervised classification on heterogeneous data.
result ModSSC enables systematic comparison of semi-supervised learning across various datasets and model backbones.
SLM Lab is a framework for reproducible RL research with modular algorithms.
problem Reproducibility in deep reinforcement learning.
method Modular software framework for RL algorithms, synchronous/asynchronous execution, hyperparameter search, result analysis.
result Comprehensive benchmark and novel RL algorithms (e.g., discrete-AC variant, hybrid training method).
New method finds community structure in networks via nonlinear modularity eigenvectors.
problem Finding a leading module in large networks is computationally infeasible.
method Proposes a nonlinear relaxation of the modularity measure using the spectrum of a nonlinear modularity operator.
result Extremal eigenvalues of the nonlinear modularity operator provide an exact relaxation of the modularity measure.
New mapping class group actions on Hochschild complexes for modular categories.
problem Understanding actions of mapping class groups on Hochschild complexes of modular categories.
method Construction of a symmetric monoidal functor with excision property.
result Homotopy coherent projective action of mapping class groups on Hochschild complexes.
New proof of four squares theorem using projective geometry.
problem Proving every natural number is a sum of four squares.
method Projective differential geometry and modular forms.
result A new geometric approach to Lagrange's theorem.
This research classifies Teichmüller curves in genus 2, proving parity conjectures for specific cases.
problem Classifying imprimitive Teichmüller curves in $\M_2$ related to square-tiled surfaces and modular curves.
method Analyzing square-tiled surfaces and their modular curves, proving parity conjectures for specific cases.
result Established the parity conjecture for Wd2[n] in three cases, showing number of components does not depend on d. We explore the dynamics of the action of the mapping class group in genus 2 on the PSL(2,R)-character variety. We prove that this action is ergodic on the connected components of Euler class 1 and -1, as it was conjectured by Goldman. In the connected component of Euler class 0 there are two invariant open subsets, on …
Hydra boosts efficiency for long-context reasoning in resource-constrained settings.
problem Quadratic complexity of transformers limits long-context reasoning in resource-constrained systems.
method Hydra uses a modular architecture with adaptive routing between sparse global attention, mixture-of-experts, and dual memories.
result Hydra achieves significant throughput and accuracy improvements for long-context reasoning.
We establish several Witten type rigidity and vanishing theorems for twisted Toeplitz operators on odd dimensional manifolds. We obtain our results by combining the modular method, modular transgression and some careful analysis of odd Chern classes for cocycles in odd K-theory. Moreover we discover that in odd dimen…
The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the Euclidean ring of integers of a quadratic imaginary number field. We also obtain the r…
New framework for modular reinforcement learning reduces sample complexity.
problem Achieving independent credit assignment in reinforcement learning.
method Defining modular credit assignment as minimizing algorithmic mutual information, introducing modularity criterion for causal analysis.
result Single-step temporal difference action-value methods meet the modularity criterion, improving sample efficiency.
Researchers analyze Gromov-Witten potentials of elliptic orbifolds, proving modularity.
problem Understanding modularity properties of Gromov-Witten potentials for elliptic orbifolds.
method Developed identities and identities between functions with properties generalizing mock modular forms.
result Complete understanding of modularity transformation properties of Cho, Hong, Kim, and Lau's functions.
This paper develops a new framework to assess crypto portfolio risk using simulation methods.
problem Traditional financial risk models fail to capture crypto market characteristics like volatility and contagion.
method The framework integrates four components: volatility stress testing, hedging, contagion modeling, and Monte Carlo simulation.
result The framework robustly assesses crypto portfolio risk and is validated with real data.