The paper calculates topological complexity for non-tree graphs and banana graphs.
problem Determining topological complexity for non-tree graphs and banana graphs.
method Analyzes fully articulated graphs and banana graphs, completing previous results for trees.
result Shows that unordered configuration spaces can have lower topological complexity than ordered ones.
Unified framework designs LK structures using integer twists on non-manifold meshes.
problem Binary twisting limits topological possibilities and structural behaviors.
method Generalizes twist formulation to arbitrary integer labels for non-manifold meshes.
result Integer twists enable full connectivity and dynamic folding/articulation.
Human infants can discover words directly from unsegmented speech signals without any explicitly labeled data. In this paper, we develop a novel machine learning method called nonparametric Bayesian double articulation analyzer (NPB-DAA) that can directly acquire language and acoustic models from observed continuous sp…
New tools for constructing fixed point sets in digital topology.
problem Constructing fixed point sets in digital topology.
method Defining excludable points and articulation points, and showing their exclusion from freezing sets.
result Excludable points and articulation points can be excluded from all freezing sets.
Paper tackles shape graph registration using neural networks.
problem Constrained registration of shape graphs with varying nodes and edges.
method Shape-Graph Matching Network (SGM-net) with an elastic shape metric loss function.
result State-of-the-art matching performance and reduced computational cost.
Improved model predicts interactions in complex systems better than previous methods.
problem Predicting interactions in complex systems like social networks or physical dynamics.
method Factorized Neural Relational Inference (fNRI) model that separates interactions into layers.
result fNRI significantly outperforms original NRI in edge and trajectory prediction.
H. Masur and J. Smillie proved precisely which singularity index lists arise from pseudo-Anosov mapping classes. In search of an analogous theorem for outer automorphisms of free groups, Handel and Mosher ask: Is each connected, simplicial, (2r-1)-vertex graph the ideal Whitehead graph of a fully irreducible outer auto…
We show that conically smooth stratified spaces embed fully faithfully into ∞-categories. This articulates a stratified generalization of the homotopy hypothesis proposed by Grothendieck. As such, each ∞-category defines a stack on conically smooth stratified spaces, and we identify the descent conditions…
We show how to construct, for each r≥3, an ageometric, fully irreducible φ∈Out(Fr) whose ideal Whitehead graph is the complete graph on 2r−1 vertices. This paper is the second in a series of three where we show that precisely eighteen of the twenty-one connected, simplicial, five-vertex graphs are ideal …
Anisotropic minimal graphs over half-spaces are flat.
problem Characterizing minimal graphs over half-spaces.
method Maximum principle and fully nonlinear PDE theory.
result Anisotropic minimal graphs over half-spaces are flat.
FC-GAGA forecasts traffic using a novel gating mechanism.
problem Forecasting multivariate time-series, especially with graph relationships.
method Learnable fully connected hard graph gating mechanism for fully connected time-series forecasting.
result Competitive or better performance than existing algorithms without graph knowledge.
Bayesian deep learning for graphs improves graph classification and prediction tasks.
problem Graph classification reproducibility issues and lack of uncertainty quantification.
method Developed a Bayesian Deep Learning framework for graph learning, considering discrete and continuous edge features.
result Produces unsupervised embeddings for graph classification tasks reaching state-of-the-art performance.
HOTCAKE compresses CNNs by decomposing kernels into smaller parts.
problem Compressing deep CNNs without significant accuracy loss.
method Input channel decomposition, guided Tucker rank selection, higher order Tucker decomposition, fine-tuning.
result HOTCAKE produces highly compressed CNN models with good accuracy.
Graphs indistinguishable by GNNs are fully characterized.
problem Limited expressiveness of GNNs in distinguishing non-isomorphic graphs.
method Theory of covering spaces to characterize GNN equivalence classes.
result Arbitrarily many non-isomorphic graphs that GNNs cannot distinguish.
Continues study on special Lagrangian graphs and flow solutions.
problem Long time existence and convergence of a class of fully nonlinear flows.
method Analyzes special Lagrangian graphs with prescribed second boundary conditions.
result Long time existence and convergence for a family of special Lagrangian graphs.
We provide an example in each rank of an ageometric fully irreducible outer automorphism whose ideal Whitehead graph has a cut vertex. Consequently, we show that there exist examples in each rank of Handel-Mosher axis bundles that are not just a single axis, as well as of "nongeneric" behavior in the sense of the "trai…
Decentralized learning of personalized models and collaboration graphs without central coordination.
problem Training personalized models and collaboration graphs in a decentralized manner without a central coordinator.
method Alternates between training models given the graph and updating the graph given the models, using peer-to-peer exchanges.
result Communication-efficient approach that avoids exchanging personal data, with benefits demonstrated on synthetic and real datasets.
New graph CNN layers improve accuracy on graph datasets.
problem Graph data relations are better represented as graphs, not grids.
method Proposed new graph CNN layers for vertex and edge features.
result Improved classification accuracy on graph datasets.
This paper explains spectral clustering and its equivalence to PCA, breaking it into fully connected and multi-connected cases.
problem Understanding the mathematics behind spectral clustering and its equivalence to PCA.
method Dividing spectral clustering into two categories based on graph connectivity and proving the equivalence to PCA.
result Spectral clustering and PCA are equivalent, with specific proofs for fully connected and multi-connected graphs.
Improved BP algorithm outperforms loopy BP in MAP inference.
problem Limited understanding and poor performance of belief propagation in graphs with loops.
method Introduced α belief propagation, a minimization of localized α-divergence. result Significantly outperforms loopy BP in fully-connected graphs for MAP inference.
BayGo framework optimizes decentralized learning in multi-agent networks.
problem Information heterogeneity in multi-agent networks.
method Bayesian learning and graph optimization framework with fast convergence.
result Estimation error decreases exponentially with each iteration.
Improved knowledge graph embedding using taxonomic information.
problem Learning about domains in knowledge graphs using embedding models.
method Minimal modifications to existing knowledge graph completion methods to incorporate taxonomic information.
result Our model is fully expressive, respecting subclass and subproperty information.
Method learns graph-structured data segments using deep learning.
problem Segmenting data structured by an adjacency graph.
method Graph-structured contrastive loss for deep learning.
result Achieved state-of-the-art performance on 3D point cloud segmentation.
The paper connects link symmetries to finite subgroups of O(3).
problem Understanding symmetries of flat fully augmented links.
method Developed a dictionary linking graph automorphisms to link symmetries, constructing infinite link classes.
result Symmetry groups of b-prime flat fully augmented links match finite subgroups of O(3).
A neural network learns efficient parametrizations of product shape spaces.
problem Efficiently parametrize complex shape spaces with high computational costs.
method Developed a neural network architecture that separately learns approximations for low-dimensional factors and combines them.
result Demonstrated the effectiveness of the approach on synthetic and real data.
New method synthesizes piano training data, improving transcription performance.
problem Lack of large piano datasets limits note onset transcription models.
method Synthesizes arbitrary training data, models piano dynamics, avoids disentanglement problem.
result Achieves good transcription performance on MAPS dataset and excellent generalization.
Researchers solve a complex equation to embed graphs with negative curvature.
problem Embedding graphs in Rn+1 with negative Gauss curvature. method Solving a fully nonlinear Monge-Ampère equation using energy estimates and Nash-Moser iteration.
result Local solvability of the fully nonlinear equation for negative curvature.
This paper proposes a method to reveal task relationships in multi-task learning models using sparse graphs.
problem Understanding the underlying task relationships in multi-task learning models.
method Proposes a bilevel formulation of multi-task learning that induces sparse graphs.
result The method improves interpretability of multi-task learning models without sacrificing generalization performance.
Graph neural network simplifies to linear model with attention mechanisms.
problem Semi-supervised learning with limited labeled data.
method Proposes a graph neural network removing fully-connected layers and replacing them with attention mechanisms.
result Attention-based graph neural network outperforms existing methods on benchmark datasets.
We describe a graph-based semi-supervised learning framework in the context of deep neural networks that uses a graph-based entropic regularizer to favor smooth solutions over a graph induced by the data. The main contribution of this work is a computationally efficient, stochastic graph-regularization technique that u…
New algorithm tackles multi-agent bandits with heavy-tailed data.
problem Maximizing system performance in multi-agent settings with heavy-tailed data.
method Algorithm exploits hub-like structures and synchronization among clients.
result Regret bound of O(M1−α1logT) for homogeneous settings, O(MlogT) for heterogeneous. A novel fully asynchronous scheme for distributed reinforcement learning over networks.
problem Policy evaluation in distributed reinforcement learning over networks.
method Design of a stochastic average gradient (SAG) based distributed algorithm and push-pull augmented graph approach.
result The proposed algorithm converges at a linear rate of \(\mathcal{O}(c^k)\) with \(c\in(0,1)\) and \(k\) increasing by one per node update.
The study classifies subgroups of outer automorphisms of free products.
problem Classifying subgroups of outer automorphisms of free products.
method Geometric tool: boundaries of relative factor graphs and equivalence classes of arational trees.
result Every finitely generated subgroup either contains a relatively fully irreducible automorphism or virtually preserves a conjugacy class.
Paper proposes DAG-DB for learning discrete DAGs via backpropagation.
problem Learning Directed Acyclic Graphs (DAGs) from data.
method DAG-DB uses Discrete Backpropagation with I-MLE and Straight-Through Estimation.
result DAG-DB learns DAGs effectively using probabilistic sampling and backpropagation.
Method to create Heegaard splittings for graph manifolds.
problem Constructing Heegaard splittings of graph manifolds.
method Method to construct Heegaard splittings of oriented graph manifolds with orientable bases.
result A method to create Heegaard splittings of oriented graph manifolds.
We examine graphs that contain a non-trivial link in every embedding into real projective space, using a weaker notion of unlink than was used by Flapan, et al. We call such graphs intrinsically linked in projective space. We fully characterize such graphs with connectivity 0,1 and 2. We also show that only one Peterse…
New communication topologies improve deep reinforcement learning performance.
problem Improving performance of learning agents in distributed reinforcement learning.
method Examined four graph families for communication topologies and found Erdos-Renyi random graphs to outperform fully connected topologies.
result Erdos-Renyi random graphs can improve performance of distributed learning agents.
The purpose of this paper is to give a simpler proof to the problem of controllability of a Hilbert snake \cite{PeSa}. Using the action of the Möbius group of the unit sphere on the configuration space, in the context of a separable Hilbert space. We give a generalization of the Theorem of accessibility contained in \c…
The Frame Problem (FP) is a puzzle in philosophy of mind and epistemology, articulated by the Stanford Encyclopedia of Philosophy as follows: "How do we account for our apparent ability to make decisions on the basis only of what is relevant to an ongoing situation without having explicitly to consider all that is not …
A decentralized policy achieves logarithmic regret for multi-agent MAB problems with communication constraints.
problem Decentralized policy for multi-agent MAB problems with option availability and communication constraints.
method Upper Confidence Bound (UCB) algorithms with non-stationary stochastic communication protocol.
result Guaranteed logarithmic regret for non-fully connected spatial graphs with communication constraints.
We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(F_n) are stable, meaning that a quasi-geodesic wi…
We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtai…
In this paper, a class of fully nonlinear flows with nonlinear Neumann type boundary condition is considered. This problem was solved partly by the first author under the assumption that the flow is the parabolic type special Lagrangian equation in R2n. We show that the convexity is preserved for solution…
PFPN uses particle filtering to improve character control in physics-based simulations.
problem Premature commitment to suboptimal actions in high-dimensional continuous control problems for articulated characters.
method Proposes a particle-based action policy using particle filtering to dynamically explore and discretize the action space.
result Demonstrates better imitation performance and robustness to external perturbations compared to Gaussian policies.
The paper counts conjugacy classes in Out(F_N) using hyperbolic spaces.
problem Counting conjugacy classes in the outer automorphism group Out(F_N).
method Analyzing f.g. groups with non-elementary WPD actions on hyperbolic spaces.
result The number of conjugacy classes grows exponentially with radius.
New method improves curvature estimates for stable surfaces.
problem Curvature estimates for stable surfaces in Rn+1. method Replacing Young's inequality with Hölder's inequality simplifies and improves curvature estimates.
result The new method yields a strictly smaller constant and a natural extension to CMC settings.
New communication topologies improve deep reinforcement learning efficiency.
problem Optimizing communication topology for faster and more robust learning in deep reinforcement learning.
method Introduced alternative network topologies (Erdos-Renyi random graphs) and compared their performance with fully-connected and star topologies.
result Erdos-Renyi random graphs outperform fully-connected networks in deep reinforcement learning tasks.
TUDataset provides benchmark datasets for graph learning.
problem Lack of meaningful benchmark datasets and standardized evaluation procedures for graph learning.
method Collection and standardization of 120 graph datasets from various applications.
result Standardized evaluation procedures and baseline experiments provided.