The study develops methods to summarize team passing strategies from soccer data.
problem Modeling spatial passing networks across multiple games with varying positions.
method Multiresolution tensor decomposition and Poisson nonnegative block term decomposition.
result Automatic production of network motifs at different levels of detail.
We analyze oversquashing in topological message-passing using relational structures.
problem Oversquashing in topological message-passing remains understudied.
method A unifying axiomatic framework that bridges graph and topological message-passing.
result Potential to advance topological deep learning.
Message passing is the key to graph neural networks, but new terms are needed to avoid confusion.
problem Current methods of graph neural networks cannot solve all problems over given input graphs.
method Demonstrates that any function of interest can be expressed using pairwise message passing over a modified graph.
result Message passing is the fundamental approach for graph neural networks, and new terms are needed to avoid confusion.
Optimizes reinforcement learning by prioritizing sets of samples over individual ones.
problem Limits exploration and improvement on harder examples due to focusing on isolated samples.
method Proposes Pass@K Policy Optimization (PKPO) to optimize for sets of samples that maximize reward when considered jointly.
result Optimization with novel low variance unbiased estimators for pass@k and its gradient leads to significant pass@k gains.
The study predicts pass completion probability in NFL games.
problem Estimating the likelihood of NFL pass completion.
method Machine learning algorithm using distance measures and random forest model.
result Developed a method to predict pass completion probability.
QPass evaluates soccer players' passes based on intrinsic value.
problem Lack of quantitative evaluation of players' contributions to team strategy.
method Developed QPass methodology to quantify player pass value.
result Players losing ball possession can lead to better chances of winning.
New group shows knots can't always be simplified.
problem Understanding concordance in long virtual knots.
method Introduced long virtual knot concordance group and proved a band-pass invariant not a concordance invariant.
result For every concordance class, there exists a knot not band-pass equivalent to the original or other specific knots.
ADMP-GNN dynamically adjusts message-passing layers for better graph learning performance.
problem Fixed message-passing steps in GNNs do not account for nodes' varying computational needs.
method Proposes ADMP-GNN, which dynamically adjusts the number of message-passing layers for each node.
result Improves performance on node classification tasks compared to baseline GNN models.
A new knot move preserves pass-move equivalence and differs in count.
problem Defining and analyzing a new knot move.
method Introducing the 1-2-move and comparing it to pass-move and #-move. result Equivalence under 1-2-move for knots is equivalent to pass-move equivalence. SGD performs optimally with multiple passes on hard learning problems.
problem Statistical optimality of SGD on hard learning problems.
method Stochastic gradient descent with multiple passes over data.
result Multiple passes lead to statistically optimal predictions on hard problems.
New method for nonlinear filtering and smoothing using factor graphs.
problem Handling deterministic nonlinear transformations in factor graphs.
method Approximate Gaussian message passing rules for factor graphs with Markov property.
result Proposed nonlinear modified Bryson-Frazier smoother.
New MCMC algorithm reduces subset selection passes to 2 for optimal k-dimensional subspace approximation.
problem Subset selection for k-dimensional subspace approximation with ε-approximation. method MCMC sampling algorithm reducing passes to 2 for p=2 case, poly(k/ε) size subset. result Subset selection of nearly optimal size in 2 passes, (1+ε) approximation. Complete classification of links up to specific moves.
problem Classifying links using specific local moves.
method Clasper theory.
result Complete classification of links up to clasp-pass moves.
New graph coarsening method preserves GNN message-passing signals.
problem Preserving GNN message-passing on coarsened graphs.
method Proposed a new oriented message-passing operation for coarsened graphs.
result Improved node classification results compared to naive methods.
Study on convergence of graph neural networks on random graphs.
problem Convergence of message passing graph neural networks on large random graphs.
method Extended convergence results to a broad class of aggregation functions using McDiarmid inequality.
result Non-asymptotic bounds for convergence quantified with high probability.
Optimal learning rates achieved with multi-pass stochastic gradient methods.
problem Improving learning rates in stochastic gradient methods with multiple passes and mini-batches.
method Analysis of learning properties with multiple passes and mini-batches, considering step-size, number of passes, and mini-batch size.
result Optimal finite sample bounds can be achieved by early-stopping and larger step-sizes are allowed with mini-batches.
DG improves policy gradient efficiency by selectively backpropagating only valuable samples.
problem Expensive backward passes in policy gradient methods reduce efficiency.
method Introduces 'delight' as a forward-pass signal of learning value and a Kondo gate to selectively backpropagate.
result Selective backpropagation reduces backward pass costs without sacrificing learning quality.
Stochastic Gradient Descent can overfit after just a few passes, contrary to initial expectations.
problem Understanding the out-of-sample performance of multi-pass SGD in stochastic convex optimization.
method Analysis of multi-pass SGD in the stochastic convex optimization model.
result Multi-pass SGD can lead to significant overfitting after just a few passes, contrary to initial expectations.
The paper explores different types of knot unknotting numbers using various local moves.
problem Investigating the unknotting numbers of knots using different local moves.
method Examined ribbon-move and pass-move on 2-knots and 1-knots, and high-dimensional-pass-move on high-dimensional knots.
result Found examples and bounds for various unknotting numbers associated with different local moves.
One-pass algorithm finds small subset for ℓp subspace approximation with additive error.
problem Finding a small subset of data points for ℓp subspace approximation. method One-pass subset selection with additive approximation guarantee for p∈[1,∞). result First one-pass algorithm with additive error for ℓp subspace approximation. Study virtualized Delta, Sharp, and Pass moves for oriented virtual knots and links.
problem Conditions for unknotting oriented virtual knots and links.
method Local moves (Delta, Sharp, Pass) for oriented virtual links.
result Lower bounds for the unknotting numbers are proven and shown to be best possible.
A guide to using low-pass graph filters for network data.
problem Understanding and processing graph data with low-pass filters.
method Definition and application of low-pass graph filters to graph data.
result Low-pass filters effectively retain lower frequency graph data contents.
We investigate minimal surfaces passing a given curve in R3. Using the Frenet frame of a given curve and isothermal parameter, we derive the necessary and sufficient condition for minimal surface. Also we derive the parametric representation of two minimal surface families passing a circle and a helix as examples.
New algorithm reduces memory usage for multi-pass bandit problems.
problem Memory-efficient multi-pass bandit algorithms for large action spaces.
method Develops a B-pass algorithm with O(1) memory that achieves optimal regret. result Sharp memory-regret trade-off: O(1) memory suffices for Θ(T1/2) regret in B passes. Full-batch GD outperforms one-pass SGD in learning a single-index model with quadratic activation.
problem Learning a single-index model with quadratic activation using gradient descent.
method Full-batch gradient descent compared to one-pass stochastic gradient descent (SGD) on a correlation loss.
result Full-batch GD requires only n≃d samples for strong recovery, while one-pass SGD requires n≳dlogd samples. Topo-MLP learns network representations without message passing.
problem Lack of efficient higher-order network modeling methods.
method Proposes Topo-MLP, a simplicial neural network algorithm using MLP and HONC loss.
result Demonstrates improved robustness and efficiency in representation learning.
SGM generalizes well with varying number of passes and step sizes.
problem Generalization of stochastic gradient methods with multiple passes.
method Analysis of stability and approximation properties controlled by step-size and number of passes.
result The number of passes and step-size control implicit regularization.
Proposes a new method for predicting missing relations in knowledge graphs.
problem Predicting missing relations between entities in knowledge graphs.
method Relational message passing method considering only edge features without entity IDs.
result PathCon method outperforms state-of-the-art methods significantly.
This paper analyzes multi-pass SGD for least squares, improving generalization bounds.
problem Improving generalization bounds for multi-pass SGD in the least squares problem.
method Develops an instance-dependent excess risk bound for least squares in the interpolation regime.
result SGD performs worse than GD instance-wise but saves computational time.
Introduces P-tensors for generalized higher-order message passing in graph neural networks.
problem Expanding the expressive power of graph neural networks through higher-order structures.
method Introduces P-tensors to define the most general form of permutation equivariant message passing.
result Achieves state-of-the-art performance on molecular datasets.
MPLP learns neural network weights by treating operations as message-passing agents.
problem Training neural networks using gradient-based methods.
method MPLP abstracts neural network operations as message-passing agents, updating internal states and passing messages.
result MPLP outperforms traditional gradient-based methods on simple feed-forward neural networks.
Paper interprets contrastive learning dynamics using message passing.
problem Lack of rigorous understanding of contrastive learning dynamics.
method Casts contrastive objective into message passing scheme on augmentation graph.
result The learning dynamics of contrastive learning can be theoretically characterized.
New distribution simplifies covariance matrix inference.
problem Efficient inference for covariance matrices in large models.
method Incorporates Inverse G-Wishart distribution for variational message passing.
result Elegant and succinct expression of variational message passing fragments.
A pass-move and a $#$-move are local moves on oriented links defined by L.H. Kauffman and H. Murakami respectively. Two links are self pass-equivalent (resp. self $#$-equivalent) if one can be deformed into the other by pass-moves (resp. $#$-moves), where non of them can occur between distinct components of the link. T…
Agent uses message passing to optimize robot navigation, balancing exploration and exploitation.
problem Optimizing robot navigation in continuous-valued spaces with uncertainty.
method Autoregressive active inference agent using message passing on a factor graph.
result Agent modulates action based on predictive uncertainty, leading to better model of dynamics.
Bayesian online learning algorithm for one-pass data, achieving frequentist validity and uncertainty quantification.
problem Theoretical limitations in Bayesian online learning, especially in the one-pass setting.
method Proposed a new Bayesian online learning algorithm with a warm-start phase for the one-pass regime, establishing convergence rates and valid uncertainty quantification.
result The sequentially updated posterior attains optimal convergence rates and valid uncertainty quantification without diverging mini-batch sample sizes.
New method explains GNNs using power iteration clustering.
problem Mysterious mechanism of message passing in GNNs.
method Subspace power iteration clustering (SPIC) models.
result Message passing in GNNs can be understood through power iteration.
SGMM clusters data in one pass, reducing dimensionality.
problem Clustering high-dimensional data efficiently.
method One-pass sparsification of Gaussian mixture model.
result SGMM achieves clustering accuracy with reduced computational cost.
Single-pass algorithm for low-rank approximation of matrix products.
problem Efficiently computing low-rank approximations of matrix products.
method A single pass algorithm that retains additional summary information about matrices A and B.
result Comparable spectral norm guarantees to existing two-pass methods with improved performance.
Introduces Spectral Graph Network combining spatial and spectral message passing.
problem Relational reasoning in graph structured data.
method Applies message passing to both spatial and spectral domains of a graph.
result Promotes efficient training with fewer iterations and robustness to edge dropout.
Convex message passing algorithms converge to a fixed point.
problem Understanding convergence properties of convex message passing methods.
method Proving convergence of coordinate descent applied to piecewise-affine convex objectives, and showing this applies to various message passing methods.
result The iterates converge to a fixed point of the method, and the algorithm terminates in a known number of iterations.
New algorithms accelerate MAP inference in Markov fields with faster convergence.
problem Finding the most likely configuration in discrete-valued Markov random fields.
method Entropy-regularized linear programming with accelerated gradient methods.
result Accelerated algorithms find optimal solutions faster, especially when the LP is tight.
Combines PCA and message passing for better graph node embeddings.
problem Challenges of learning long-range dependencies in graph data.
method PCAPass: PCA + message passing for unsupervised node embeddings.
result Empirically shows competitive performance on node classification benchmarks.
The paper sets limits for GNNs solving PDEs to avoid under-reaching phenomenon.
problem Under-reaching phenomenon in GNNs solving PDEs.
method Sharp lower bounds for message-passing iterations based on PDE characteristics.
result Proposed lower bounds ensure efficient information propagation in GNNs.
Counterexample disproves Spencer-Brown's claim about parity-pass algorithm.
problem Disproving Spencer-Brown's claim about the parity-pass algorithm and its relation to edge colorings.
method Provided a counterexample to Spencer-Brown's algorithm on non-polar pentagons.
result The parity-pass algorithm does not necessarily terminate in an extendable edge coloring.
Study uncovers tactical line-breaking passes in football using clustering.
problem Detecting and analyzing line-breaking passes in football matches.
method Unsupervised clustering-based framework using event and tracking data.
result Introduced tactical metrics to quantify pass effectiveness.
Model trains passing events on a bridge using multilevel Gaussian process.
problem Represent aggregate train-passing events from a bridge monitoring system.
method Formulate a combined model with low-rank approximation hierarchical Gaussian process, incorporating domain expertise as constraints.
result Allow for simulation of previously unobserved train types.
New method solves group synchronization with cycle-edge message passing.
problem Solving group synchronization with adversarial or uniform corruption and small noise.
method Cycle-edge message passing procedure using cycle consistency information.
result Exact recovery and linear convergence guarantees under adversarial corruption.