Improved graph clustering for sparse graphs using non-backtracking random walks.
problem Improving graph clustering performance for sparse graphs.
method VEC-NBT uses a non-backtracking random walk to modify VEC, a graph embedding technique.
result VEC-NBT achieves comparable or greater accuracy with shorter walks than VEC for sparser graphs.
DeepBC method computes backtracking counterfactuals in deep causal models.
problem Computing valid counterfactuals in complex causal models.
method DeepBC method using Langevin Monte Carlo or constrained optimization.
result DeepBC provides causally compliant, versatile, and modular counterfactuals.
New approach to counterfactual reasoning in AI and psychology.
problem Challenges to conventional counterfactual reasoning in AI and psychology.
method Formalizes a backtracking approach to counterfactuals within the SCM framework.
result First general account and algorithmisation of backtracking counterfactuals.
New matrix reveals cluster info in sparse directed graphs.
problem Analyzing cluster information in directed graphs.
method Proposed complex non-backtracking matrix integrating Hermitian adjacency matrix and non-backtracking matrix properties.
result The complex non-backtracking matrix holds cluster information, especially for sparse directed graphs.
Backtracking model predicts state-action pairs leading to high-reward states for efficient RL.
problem Efficiently learning from environments where only a few states yield high reward.
method Backtracking model that predicts state-action pairs leading to high-reward states.
result Improves sample efficiency of RL algorithms across various environments and tasks.
A new graph neural network (NBA-GNN) avoids revisiting nodes to improve accuracy.
problem Redundancy in graph neural network updates causes over-squashing and inaccurate recognition.
method Proposes non-backtracking graph neural networks (NBA-GNN) that update messages without revisiting nodes.
result The NBA-GNN alleviates over-squashing and improves performance on graph benchmarks.
Sparse Attentive Backtracking selectively backpropagates long-term dependencies in recurrent networks.
problem Difficulty in learning long-term dependencies in BPTT due to computational impracticality and biased gradient estimates.
method Sparse Attentive Backtracking learns an attention mechanism over past hidden states and selectively backpropagates through high-weight paths.
result Model learns long-term dependencies with fewer backpropagation steps, addressing biased gradient issues.
Spectral method detects communities in sparse hypergraphs, achieving detection threshold.
problem Community detection in sparse hypergraphs.
method Non-backtracking operator and spectral approach.
result Spectral method achieves detection threshold for sparse HSBMs.
New Q-Newton's method avoids saddle points and converges quadratically.
problem Optimizing functions with saddle points and ensuring convergence guarantees.
method Modified New Q-Newton's method with Backtracking line search.
result Theorem for Morse functions: quadratic convergence to local minima.
BRACE generates efficient counterfactual explanations by integrating causal reasoning.
problem Challenges in traditional counterfactual explanations, especially neglecting causal relationships.
method Backtracking counterfactuals with causal reasoning.
result Our method provides deeper insights into model outputs and is computationally efficient.
Backtracking GD proves convergence for general C1 functions, including Deep Learning.
problem Proving convergence of gradient descent for non-Lipschitz functions.
method Backtracking gradient descent method for C1 functions. result Backtracking GD converges for Morse functions and has properties for general C1 functions. Develops active intervals for geodesics in Teichmüller space.
problem Understanding geodesics in Teichmüller space with no backtracking.
method Defines active intervals for subsurfaces along geodesics in Thurston metric.
result Active intervals represent reparametrized quasi-geodesics in curve graphs with bounded movement outside.
Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a more complicated, non-symmetric and higher dimensional operator, related to the n…
New method tightens spectral bounds for percolation in clustered networks.
problem Tight spectral bounds for percolation in sparse networks with clustering.
method Message passing algorithm on triangle-non-backtracking matrix.
result Method gives tighter lower-bound to percolation transition.
Motivated by community detection, we characterise the spectrum of the non-backtracking matrix B in the Degree-Corrected Stochastic Block Model. Specifically, we consider a random graph on n vertices partitioned into two equal-sized clusters. The vertices have i.i.d. weights {φu}u=1n with second moment $Φ…
Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here we introduce a…
New method detects communities in complex hypergraphs, matching theoretical limits.
problem Detecting communities in non-uniform hypergraphs with varying hyperedge sizes.
method Developed a spectral theory for weighted non-backtracking operators on non-uniform hypergraphs.
result Achieved the Kesten-Stigum bound for weak recovery in a general class of non-uniform HSBMs.
New findings support a new community recovery threshold for Stochastic Block Model with many communities.
problem Recovering communities in Stochastic Block Model with more than sqrt(n) communities.
method Counting specific motifs to achieve polynomial-time community recovery above a new threshold.
result LDP fails below the new threshold, but polynomial-time recovery is possible above it.
Backtracking Gradient Descent method converges to critical points in Banach spaces.
problem Finding convergence conditions for Backtracking Gradient Descent in Banach spaces.
method Local Backtracking GD procedure with weak topology convergence.
result Weak convergence of sequence to critical points, no saddle points for generic choices.
Quasi-geodesics in Out(F_n) are not always geodesics, with backtracking in free factors.
problem Characterizing quasi-geodesics in Out(F_n) and their properties.
method Analysis of various paths in Out(F_n) and construction of counterexamples.
result Quasi-geodesics in Out(F_n) can backtrack in free factors, unlike in mapping class groups.
Improves generative models by optimizing rewards and sample editing.
problem Efficiently generating high-reward samples with structural constraints.
method Introduces MDM-VGB, a discrete diffusion sampler that augments unmasking generation with reward-guided remasking.
result MDM-VGB achieves quadratic complexity and robustness to noise, outperforming heuristics like best-of-N. Boosting Variational Inference improves posterior approximations with adaptive step-sizes.
problem Limited resources hinder the widespread adoption of Boosting Variational Inference.
method Characterized global curvature impact, introduced local curvature, and developed an approximate backtracking algorithm.
result New theoretical convergence rates and experimental validation demonstrate improved performance.
Unified spectral clustering for sparse networks with heterogeneous degrees.
problem Efficiently detecting communities in sparse networks with varying degrees.
method Developed a parametrized regularized Laplacian matrix for spectral clustering.
result Improved parametrization accounts for network heterogeneity and community hardness.
New method uses robust estimators for Newton's method in empirical risk minimization.
problem Improving robustness in empirical risk minimization.
method Robust Newton's method with gradient and Hessian replaced by robust estimators.
result Faster convergence rates in high-dimensional settings.
The study proves unique path lifting properties and their implications on quotient spaces and covering maps.
problem Understanding unique path lifting properties and their implications on quotient spaces and covering maps.
method The study uses group actions on R-trees and path lifting properties to prove the main results. result Every map of manifolds with the unique path lifting property is a covering map.
Local search improves GFlowNets' ability to generate high-reward samples.
problem GFlowNets struggle with over-exploration in high-reward space.
method Local search focusing on high-reward samples via backtracking and reconstruction.
result Significant performance improvement in biochemical tasks.
HollowFlow speeds up likelihood evaluation for large-scale models.
problem Prohibitive scaling of sample likelihood computations in flow-based models.
method Introduces HollowFlow, a flow-based generative model using a NoBGNN with a block-diagonal Jacobian structure.
result Achieves up to O(n^2) speed-up in likelihood evaluation for large systems.
A new method backtracks through a few key past states to speed up credit assignment in long sequences.
problem Computational inefficiency of back-propagation through time for long sequences.
method Sparse attentive backtracking using learned attention mechanisms to skip connections.
result Matches or outperforms regular BPTT and truncated BPTT in tasks with long-term dependencies.
New method learns search policies by inspecting and improving past roll-outs.
problem Learning good search policies for complex combinatorial spaces.
method Retrospective imitation learning, improving policy through past roll-outs.
result Policy can iteratively scale up to larger problems.
Researchers compute large quantum invariants for 3-manifolds.
problem Computing large values of Turaev-Viro invariants for 3-manifolds.
method Optimized backtracking algorithm, lattice point counting, preprocessing strategy, multi-precision arithmetics.
result Experimentally verified improvements over state-of-the-art implementations, supporting volume conjecture.
Improved DANE algorithm for faster convergence in distributed machine learning.
problem Challenges in convergence of DANE algorithm for general convex functions.
method Introducing variants of DANE with backtracking line search and heavy-ball method.
result Proved global and local convergence rates for quadratic and non-quadratic strongly convex functions.
New scheme adapts batch size for faster variance-reduced algorithms.
problem Slowness of variance-reduced algorithms due to large batch size.
method Eliminates backtracking line search, adapts batch size via history stochastic gradients.
result Significantly reduces overall complexity for SVRG and SARAH/SPIDER.
New method quantifies network cycles to enhance community detection.
problem Challenges in detecting communities in networks, especially in sparse graphs.
method Renewal non-backtracking random walks (RNBRW) to quantify cyclic structure.
result RNBRW improves community detection algorithms, especially in sparse graphs.
This paper allows unbounded learning rates in gradient descent for better convergence.
problem Proving convergence of gradient descent with unbounded learning rates.
method Introducing a function h(t) to control the learning rates and proving convergence under Armijo's condition.
result Convergence of the sequence {x_n} is proven under specific conditions on the cost function f.
The paper develops methods for unconstrained optimization on Riemannian manifolds.
problem Optimization on Riemannian manifolds with general functions.
method Developed explicit versions of gradient descent and Newton's method for Riemannian optimization.
result The algorithms either converge to a local minimum or diverge to infinity, depending on the function and manifold properties.
Paper tackles sample-efficient RL for linearly realizable MDPs with limited revisiting.
problem Sample-efficient reinforcement learning for linearly realizable MDPs with limited revisiting.
method Develops a new sampling protocol that allows for backtracking and revisiting states in a controlled manner.
result Achieves polynomial sample complexity scaling with feature dimension, horizon, and inverse sub-optimality gap.
Local algorithms perform well on SDP relaxations of graph bisection problems.
problem Understanding the performance of local algorithms on SDP relaxations of graph bisection problems.
method Used dual witness construction and harmonic measure on limiting Galton-Watson tree.
result Simple local algorithms are at most 8/9 suboptimal for graph bisection problems.
New methods solve MI problems with locally Lipschitz operators, improving solution efficiency.
problem Solving monotone inclusions with locally Lipschitz continuous operators.
method Primal-dual extrapolation methods using backtracking line search.
result Improved operation complexity for solving MI problems.
We show that the driving force behind the regularizing effect of Laplacian smoothing on surface elements is the popular mean ratio quality measure. We use these insights to provide natural generalizations to polygons and polyhedra. The corresponding functions measuring the quality of meshes are easily seen to be convex…
We consider the problem of clustering partially labeled data from a minimal number of randomly chosen pairwise comparisons between the items. We introduce an efficient local algorithm based on a power iteration of the non-backtracking operator and study its performance on a simple model. For the case of two clusters, w…
Paper uses RL and diffusion models to solve Bayesian inverse problems.
problem Bayesian inverse problems with latent biases.
method Relative Trajectory Balance (RTB) for RL, conditional diffusion models, off-policy backtracking exploration.
result RTB improves diffusion model posteriors for inverse problems.
Paper introduces a privacy-preserving line search method for optimization.
problem Optimization performance depends on step size tuning, which is difficult and privacy-sensitive.
method Introduces a stochastic adaptive line search algorithm that satisfies differential privacy.
result The algorithm efficiently uses privacy budget and outperforms existing private optimizers.
Transformer learns to search through reinforcement learning, mimicking DFS.
problem Understanding how transformers learn search capabilities in RL.
method Two-head transformer, depth-wise curriculum, discounted returns.
result Transformer policy generalizes depth and prioritizes high-probability branches.
New findings on community recovery in SBM with many communities.
problem Determining community recovery conditions in SBM with more than sqrt(n) communities.
method Constructing motifs and counting them to prove community recovery above the proposed threshold.
result Proving community recovery above the proposed threshold in SBM with K >= sqrt(n) communities.
Novel SAAG variants reduce variance in large-scale learning.
problem Reduction of variance in noisy gradient approximations for large-scale machine learning.
method Proposed SAAG-III and IV variants with SBAS for step size determination.
result Proved linear convergence of SAAG-IV for all smoothness and strong-convexity combinations.
Community detection is a fundamental problem in network analysis with many methods available to estimate communities. Most of these methods assume that the number of communities is known, which is often not the case in practice. We study a simple and very fast method for estimating the number of communities based on th…
Efficient algorithms solve joint graphical lasso problems.
problem Learning graphical models from sparse data.
method Proximal gradient procedures with ADMM backtracking option.
result Proposed algorithms achieve high accuracy and precision.
New formula refutes random CSPs with fewer constraints.
problem Refuting random constraint satisfaction problems efficiently.
method Introduced a non-backtracking matrix and proved an Ihara-Bass formula.
result Efficiently refutes random CSPs with fewer constraints.