A new type of random forest improves robustness against noisy data.
problem Noise in test samples damages random forest performance.
method Introduces denoising autoencoders into random forests to identify and correct incorrect decisions.
result Improves estimation accuracy by considering multiple traversal paths for incorrect nodes.
Sparse neural networks training is difficult due to optimization failures and energy landscape issues.
problem Training sparse neural networks leads to suboptimal solutions and optimization failures.
method Investigated optimization dynamics and energy landscape in sparse neural networks.
result Sparse neural networks have a linear path with a monotonically decreasing objective from initialization to a good solution, but not from a bad solution.
Many tasks in computer vision can be cast as a "label changing" problem, where the goal is to make a semantic change to the appearance of an image or some subject in an image in order to alter the class membership. Although successful task-specific methods have been developed for some label changing applications, to da…
Path queries on a knowledge graph can be used to answer compositional questions such as "What languages are spoken by people living in Lisbon?". However, knowledge graphs often have missing facts (edges) which disrupts path queries. Recent models for knowledge base completion impute missing facts by embedding knowledge…
Generative Flow Networks solve shortest path problems in graphs.
problem Finding shortest paths in graphs.
method Generative Flow Networks with flow regularization.
result Training a GFlowNet can solve pathfinding problems in arbitrary graphs.
Computes transition probability between learning tasks, decomposing it into geometry and path difficulty.
problem Predicting success in transfer learning between different learning tasks.
method Decomposes transition probability into two factors: geometry of loss landscapes and path difficulty.
result Derives strict lower bounds on learning complexity, showing that geometry alone is insufficient.
SURF steers scalarization weights to uniformly traverse the Pareto front.
problem Non-uniform coverage of the Pareto front when using scalarization weights.
method Geometric analysis and CDF mapping to select weights for uniform coverage.
result SURF converges to uniform Pareto front coverage under provable conditions.
Automates optimizer design for diverse tasks efficiently.
problem Scalability, generability, and sample efficiency in optimizer search.
method Re-arranged optimizer space into a super-tree, applying tree traversal methods.
result Discover optimizers with only 128 evaluations, surpassing human-designed and prior methods.
The paper sparsifies networks by finding efficient paths in their functional space.
problem Sparsifying neural networks to improve performance and efficiency.
method The authors use the geometry of weight spaces and functional manifolds to find efficient paths (geodesics) in the functional space of neural networks.
result The proposed framework can sparsify networks and improve performance on various tasks.
This paper unifies observability notions for colored graphs and identifies graph modifications to improve observability.
problem Observability of colored graphs and its relationship to graph properties.
method Unified framework of observability notions, graph modifications, and NP-completeness results.
result Identification of graph modifications to improve observability and NP-completeness of one modification problem.
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly trained with backpropagation, like a neural network. Even though this continuity …
Unified approach to verify NN properties using ReLU's unique polytope structure.
problem Lack of robustness and interpretability in ReLU NNs for risk-sensitive applications.
method Identifying and traversing the local polytopes of ReLU NNs, developing an algorithm to verify properties.
result Unified approach to examine network behavior in risk-sensitive settings.
Recently, machine learning algorithms have successfully entered large-scale real-world industrial applications (e.g. search engines and email spam filters). Here, the CPU cost during test time must be budgeted and accounted for. In this paper, we address the challenge of balancing the test-time cost and the classifier …
We study smooth {\sf traversing} vector fields v on compact manifolds X with boundary. A traversing v admits a Lyapunov function f:X→R such that df(v)>0. We show that the trajectory spaces T(v) of {\sf traversally generic} v-flows are {\sf Whitney stratified spaces}, and thus admit tr…
A new method uses string method to explore diffusion models.
problem Understanding the geometry of learned distributions in diffusion models.
method String method to compute continuous paths between samples.
result The string method identifies realistic morphing sequences and transition pathways.
Given a point (the "spider") on a rectangular box, we would like to find the minimal distance along the surface to its opposite point (the "fly" - the reflection of the spider across the center of the box). Without loss of generality, we can assume that the box has dimensions 1×a×b with the spider on one …
The paper proposes a method to improve random forest classification accuracy by weighting trees based on their decision path reliability.
problem Random forests' uniform voting fails to correct errors in regions where incorrect tree representations outnumber correct ones.
method The paper introduces using the structural pattern of each tree's decision path as an instance-adaptive reliability signal to identify and weight more reliable trees.
result Using the proposed method yields a statistically significant accuracy improvement over RF on 36 binary classification benchmarks.
BOSH improves decision-based attacks by optimizing solution paths.
problem Generating optimal adversarial examples for decision-based attacks.
method BOSH-attack uses Bayesian Optimization and Successive Halving to explore solution paths.
result BOSH converges to better solutions with fewer queries.
A new method interprets astrophysical spectra using geometric paths to distinguish line profiles.
problem Tackling the indistinguishability of spectral line profiles under scalar summaries.
method Introduces a geometric representation of line profiles using rough path theory, mapping profiles to a common velocity grid and defining descriptors from path properties.
result Compact descriptors separate morphologies with similar scalar summaries, revealing ordered line structures.
Euler's theorem extended to complex structures.
problem Generalizing Euler's theorem to complex structures.
method Analyzing strongly connected, pure n-dimensional regular CW-complexes. result Evenness of cells is equivalent to generalized cycle decomposition and traversability.
The study calculates the growth rate of reciprocal hyperbolic elements in Hecke groups.
problem Counting reciprocal hyperbolic elements in Hecke groups.
method Analyzes conjugacy classes of hyperbolic elements associated with reciprocal geodesics.
result Determines the asymptotic growth rate and limiting constant of primitive conjugacy classes of reciprocal hyperbolic elements.
New method adapts neural networks without losing prior knowledge.
problem Understanding and enabling flexible adaptation of neural networks.
method Differential geometry framework, functionally invariant paths (FIP).
result Achieves comparable state-of-the-art performance on continual learning and sparsification tasks.
A novel multi-resolution Gaussian process model for efficient time traversal.
problem Inference for long sequences with fast and slow transitions is difficult.
method A novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution.
result The combined model allows efficient inference for arbitrarily long sequences with complex dynamics.
Deep learning predicts information diffusion in complex networks.
problem Predicting information spread in heterogeneous networks with local and threshold limitations.
method Meta-path representation learning for global latent representation of heterogeneous networks, followed by deep learning.
result The proposed HDD approach outperforms existing methods in topic diffusion and cascade prediction.
We prove two theorems about homotopies of curves on 2-dimensional Riemannian manifolds. We show that, for any epsilon > 0, if two simple closed curves are homotopic through curves of bounded length L, then they are also isotopic through curves of length bounded by L + epsilon. If the manifold is orientable, then for an…
We combine Gromov's amenable localization technique with the Poincaré duality to study the traversally generic vector flows on smooth compact manifolds X with boundary. Such flows generate well-understood stratifications of X by the trajectories that are tangent to the boundary in a particular canonical fashion. Sp…
The paper explores holographic structures on exotic spheres and their implications.
problem Understanding holographic structures on exotic spheres.
method Introducing and studying holographic structures on closed manifolds Y. result Generalizing the Holography Theorem to fillable holographic structures on Y. Lazy-CFR improves CFR's efficiency and performance in imperfect information games.
problem Efficiency and performance in imperfect information games with imperfect information.
method Lazy update technique to avoid full traversal of game tree, resulting in a more efficient CFR variant.
result Lazy-CFR achieves better convergence and significantly outperforms vanilla CFR in experiments.
LSDAT reduces query efficiency for decision-based adversarial attacks.
problem Improving query efficiency for decision-based adversarial attacks.
method Low-rank and sparse decomposition (LSD) to craft perturbations.
result LSDAT achieves superior fooling rates with fewer queries.
Predicts node sequences in graphs using multi-order network models.
problem Predicting sequences of node traversals in graphs.
method Combines multiple higher-order network models into a multi-order model, fitting and selecting the optimal maximum order.
result Outperforms state-of-the-art algorithms for next-element and full sequence prediction.
Analyzes geodesic lengths in sparse networks, deriving a distribution.
problem Understanding connectivity and robustness in networked systems.
method Analytic derivation of geodesic length distribution in sparse networks.
result Simple closed-form expression for geodesic length distribution.
Let X be a compact smooth manifold with boundary. In this article, we study the spaces V†(X) and V‡(X) of so called boundary generic and traversally generic vector fields on X and the place they occupy in the space V(X) of all fields (see Theorems \ref{th3.4} and Theo…
The paper explores how a geometric flow can turn a black hole into a traversable wormhole.
problem The study investigates how a static, spherically symmetric black hole can be transformed into a traversable wormhole.
method The approach involves analyzing almost η-Ricci-Yamabe solitons and their geometric coupling with the Hawking temperature. result The geometric flow successfully transforms the black hole into a traversable wormhole, opening the throat and preserving the exact cosmological spacetime.
Study on bandit problems with switching constraints, revealing phase transitions in regret.
problem Stochastic multi-armed bandit problem with switching cost constraints.
method Proved matching upper and lower bounds on optimal regret, provided efficient algorithms.
result Phase transitions in optimal regret rate with respect to switching budget.
A graph traversal algorithm for cold-start news recommendation using named entities.
problem Cold-start news recommendation for articles without user-specific information.
method Graph traversal algorithm and novel weighting scheme for named entities over a knowledge graph.
result Our method produces stronger Pearson correlation to human similarity scores than other cold-start methods.
GAT-RWOS uses graph attention to improve imbalanced data classification.
problem Imbalanced data leads to biased models favoring majority classes.
method Combines GATs and random walks to generate synthetic minority samples.
result Improves classification performance on imbalanced datasets.
A scalable algorithm for GP regression selects relevant covariates efficiently.
problem Scalable variable selection in large GP regression models.
method VGPR algorithm using Vecchia approximation for sparse precision matrix, mini-batch subsampling.
result Improved scalability and accuracy in selecting relevant covariates.
This paper speeds up speech recognition by vectorizing hypotheses and speech.
problem Slowness in beam search during speech recognition.
method Vectorization of hypotheses and speech, parallelism, batch processing, shallow fusion.
result 3.7x speedup achieved by vectorizing hypotheses, 10.5x by GPU.
Method generates counterfactual explanations for graph classifiers.
problem Generating high-quality explanations for graph predictions.
method Permutation equivariant graph variational autoencoder to traverse latent space.
result Empirically validated model is high-performing and robust.
A new method simplifies sampling from complex distributions without using diffusions.
problem Sampling from complex, high-dimensional distributions efficiently.
method Reduces sampling to solving a sequence of 'nice' sampling problems using SLC distributions.
result Shows how to traverse backwards paths using high-accuracy routines for SLC distributions.
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to extra combinatorial constraints, the only practical algorithms to date have been v…
Let Ck1k2 denote the set of all closed curves of class Cr on the sphere S2 whose geodesic curvatures are restricted to lie in (k1,k2), furnished with the Cr topology (for some r>=2 and possibly infinite k1<k2). In 1970, J. Little proved that the space C0+∞ of closed curves ha…
Adapts models incrementally for continual changes in environments.
problem Continual appearance shifts impact machine learning model performance.
method Adversarial approach for lifelong, incremental domain adaptation.
result Improves handling of large appearance changes compared to direct methods.
This paper is the third in a series that researches the Morse Theory, gradient flows, concavity and complexity on smooth compact manifolds with boundary. Employing the local analytic models from \cite{K2}, for \emph{traversally generic flows} on (n+1)-manifolds X, we embark on a detailed and somewhat tedious study …
A framework for navigating environments with spatially correlated obstacles and uncertain blockage status.
problem Navigation in environments with spatially correlated obstacles of uncertain blockage status.
method Modeling spatial correlation with Gaussian Random Field, developing Bayesian belief updates, proposing a two-stage learning framework with offline and online phases.
result Consistent performance gains over baselines in environments with adversarial interruptions or clustered natural hazards.
Paper introduces a new optimisation method combining NG and Hessian Free for sequence training.
problem Overfitting and inefficiency in training DNNs with sequence criteria.
method Combines Natural Gradient and Hessian Free methods for better path traversal on parameter manifold.
result Achieves larger reductions in WER and lower WER compared to NG and HF methods.
In real-world and online social networks, individuals receive and transmit information in real time. Cascading information transmissions (e.g. phone calls, text messages, social media posts) may be understood as a realization of a diffusion process operating on the network, and its branching path can be represented by …
New graph-based algorithms find maxima of functions on graph nodes.
problem Finding the maximum of a function defined on graph nodes.
method Local iterative algorithms, Metropolis-Hastings random walk with different transition kernels.
result Convergence rates for two algorithms derived in terms of total variation distance and hitting times.