Neighbor embeddings balance attraction and repulsion to visualize data.
problem Visualizing high-dimensional datasets with trade-offs between continuous and discrete structures.
method Neighbor embeddings combine attractive and repulsive forces to visualize data.
result Changing the exaggeration parameter in t-SNE yields a spectrum of embeddings with a trade-off between continuous and discrete structures.
New method improves sample diversity and efficiency from complex distributions.
problem Sampling from intractable un-normalized distributions with high auto-correlation.
method Stein self-repulsive dynamics using a repulsive force to push samples away from past trajectories.
result Significantly decreases auto-correlation and increases effective sample size.
ARS visualization improves t-SNE dynamics with tunable attraction and repulsion.
problem Improve data visualization techniques for complex data sets.
method ARS framework based on t-SNE dynamics with normalized interactions and tunable kernels.
result ARS visualization provides better control over cluster tightness and spacing.
New algorithm detects anomalies by forcing samples to displace mass in low-density regions.
problem Detecting anomalies in datasets.
method Mass Repulsing Optimal Transport (MROT) approach.
result Our algorithm improves anomaly detection over existing methods.
We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated…
We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCM…
Feature normalization prevents collapse in non-contrastive learning dynamics.
problem Non-contrastive learning can collapse into a single point due to lack of repulsive force.
method Extended previous theory based on L2 loss to cosine loss, considering feature normalization.
result Cosine loss induces stable equilibrium, preventing collapse even with insufficient repulsive force.
In earlier work, we provided a general description of the forces of attraction and repulsion, encountered by two parallel vertical plates of infinite extent and of possibly differing materials, when partially immersed in an infinite liquid bath and subject to surface tension forces. In the present study, we examine som…
Stein variational gradient descent (SVGD) is a recently proposed particle-based Bayesian inference method, which has attracted a lot of interest due to its remarkable approximation ability and particle efficiency compared to traditional variational inference and Markov Chain Monte Carlo methods. However, we observed th…
Paper improves particle variational inference by optimizing generalization error bound.
problem Improving the diversity of models in particle variational inference to enhance generalization.
method Develops a new second-order Jensen inequality with a repulsion term based on the loss function, leading to a tighter generalization error bound.
result The proposed PVI optimizes the generalization error bound directly, improving performance compared to existing methods.
In the present work, torsion energy is defined. Its law of conservation is given. It is shown that this type of energy gives rise to a repulsive force which can be used to interpret supernovae type Ia observations, and consequently the accelerating expansion of the Universe. This interpretation is a pure geometric one …
CAMEL embeds data into a manifold using curvature-augmented forces.
problem Data visualization and dimensionality reduction.
method Formulates DR as a physics model with curvature-augmented forces.
result CAMEL outperforms existing methods on benchmark datasets.
The possibility that price dynamics is affected by its distance from a moving average has been recently introduced as new statistical tool. The purpose is to identify the tendency of the price dynamics to be attractive or repulsive with respect to its own moving average. We consider a number of tests for various models…
This work proposes a novel method for estimating the influence that unknown static objects might have over mobile agents. Since the motion of agents can be affected by the presence of fixed objects, it is possible use the information about trajectories deviations to infer the presence of obstacles and estimate the forc…
Study shows global invertibility in nonlinear elasticity with vanishing self-repulsion term.
problem Global invertibility in nonlinear elasticity with a vanishing nonlocal self-repulsion term.
method Proves global invertibility in the Γ-limit of elastic energy with a vanishing nonlocal self-repulsion term. result Global invertibility can be obtained in the Γ-limit of the elastic energy with a vanishing nonlocal self-repulsion term. Repulsive ensembles improve uncertainty estimates in PINNs for differential equations.
problem Improving uncertainty estimates in PINNs for differential equations.
method Employing repulsive ensembles (RE-PINN) with a repulsive term in the loss function.
result Repulsive ensembles produce more accurate uncertainty estimates and higher sample diversity.
Enhances contrastive learning for better representation learning on wild images.
problem Binary partition of views from same and different instances limits CL's performance.
method Doubly Contrastive Learning (CACR) with contrastive attraction and repulsion.
result CACR improves performance and robustness on wild image datasets.
A method to control results of gradient descent unsupervised learning in a deep neural network by using evolutionary algorithm is proposed. To process crossover of unsupervisedly trained models, the algorithm evaluates pointwise fitness of individual nodes in neural network. Labeled training data is randomly sampled an…
Repulsive deep ensembles improve diversity and Bayesian inference.
problem Challenges in maintaining diversity among ensemble members trained independently.
method Introducing a repulsive term in the update rule of deep ensembles.
result Training dynamics of repulsive ensembles follow a Wasserstein gradient flow of KL divergence with the true posterior.
Computer experiments reveal complex knots that don't simplify.
problem Understanding the dynamics of complex knots under self-repulsion.
method Computer simulations of knot theory, focusing on rational knots and tangles.
result Discovered hard unknots and complexified knots that do not reduce to simpler forms under self-repulsion.
FoRDE uses input gradients to improve neural network ensembles.
problem Improving neural network ensembles for robustness and accuracy.
method Proposes FoRDE, an ensemble learning method based on ParVI, which repels function space by input gradients.
result FoRDE significantly outperforms DEs and other ensemble methods in accuracy and calibration.
Study identifies stable configurations of intertwined threads with repulsive interactions.
problem Stable configurations of entangled systems with repulsive interactions.
method Analysis of steepest descent flow of an energy functional.
result Existence and uniqueness of stable configuration of two layers drifting apart at t1/3 rate. This work shows dimension regularization can replace skip-gram negative sampling for graph embeddings, improving efficiency and performance.
problem Efficiently enforcing dissimilarity among node embeddings in graph learning.
method Dimension regularization as an alternative to skip-gram negative sampling.
result Dimension regularization is a more efficient approach to enforcing dissimilarity in graph embeddings.
Randomized feature models learn interaction kernels from agent paths.
problem Learning interaction kernels from noisy agent paths.
method Randomized feature algorithm and sparse regression.
result Pruned features reduce overfitting and lower simulation cost.
New solutions found for elliptic systems with mixed couplings.
problem Existence of fully nontrivial solutions to elliptic systems with mixed couplings.
method Study of fully nontrivial solutions to the system with mixed couplings in a bounded or unbounded domain.
result New existence and multiplicity results of fully nontrivial solutions.
Shielded LMC samples from non-convex spaces with repulsive drift.
problem Sampling from non-convex spaces with convex holes.
method Combining adaptive temperature and repulsive drift.
result Advantages over unconstrained sampling in constrained spaces.
New approach improves multi-head attention by making heads less similar.
problem Multi-head attention can lead to similar features, reducing model expressiveness.
method Proposes a non-parametric approach using Bayesian techniques to make heads repel each other.
result Improves feature diversity, leading to better representations and performance.
Research examines correlations of complex logarithms of lattice points, showing level repulsion and Poissonian behavior.
problem Analyzing correlations of complex logarithms of lattice points.
method Proving existence of pair correlation functions and examining behavior at various scalings.
result Level repulsion observed at linear scaling, Poissonian behavior at sublinear scalings.
Generative adversarial nets (GANs) are widely used to learn the data sampling process and their performance may heavily depend on the loss functions, given a limited computational budget. This study revisits MMD-GAN that uses the maximum mean discrepancy (MMD) as the loss function for GAN and makes two contributions. F…
RePULSe improves language model alignment by reducing undesired outputs without sacrificing overall performance.
problem Aligning language models with human preferences while minimizing undesired outputs.
method Integrates probabilistic inference into RL training to reduce undesired outputs.
result RePULSe achieves a better balance between expected reward and undesired output probability.
The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we prove that such repulsive sampling schemes lowers the variance of the gradient est…
NucleusDiff models atomic nuclei interactions to prevent separation violations in drug design.
problem Maintaining minimum pairwise distance between atoms to avoid separation violations in drug design.
method Enforces distance constraint between atomic nuclei and manifolds in a diffusion model.
result Reduces separation violations by up to 100.00% and enhances binding affinity by up to 22.16%.
This paper introduces repulsive Monte Carlo methods for computing the sliced Wasserstein distance.
problem Computing the integral of a function on the unit sphere using Monte Carlo methods.
method The approach involves using determinantal point processes and repelled point processes to create quadratures for the sliced Wasserstein distance.
result The UnifOrtho estimator is recommended for the computation of the sliced Wasserstein distance in large dimensions.
PPC learns binary codes from data similarities and dissimilarities.
problem Creating efficient binary codes from data similarities and dissimilarities.
method PPC learns binary codes by modeling attractive and repulsive forces in a signed graph.
result PPC achieves superior results in nearest-neighbor searches compared to spectral methods.
We consider the problem of diversity enhancing clustering, i.e, developing clustering methods which produce clusters that favour diversity with respect to a set of protected attributes such as race, sex, age, etc. In the context of fair clustering, diversity plays a major role when fairness is understood as demographic…
The paper studies Möbius energy gradient of helix pairs and finds limiting behavior as coiling ratio increases.
problem Characterizing the limiting behavior of Möbius energy gradient for symmetric helix pairs.
method Complex asymptotics
result The gradient diverges in opposing directions based on radius, approaching 1/2 as coiling ratio increases.
New Gaussian DPP model reveals directionality in data.
problem Negative dependence in data modeling.
method Investigation of Gaussian Determinantal Processes (GDPs) with parametric modulation.
result Parameter modulation introduces directionality in repulsion structure, affecting dependency.
Continuous control tasks in reinforcement learning are important because they provide an important framework for learning in high-dimensional state spaces with deceptive rewards, where the agent can easily become trapped into suboptimal solutions. One way to avoid local optima is to use a population of agents to ensure…
Domain adaptation is transfer learning which aims to generalize a learning model across training and testing data with different distributions. Most previous research tackle this problem in seeking a shared feature representation between source and target domains while reducing the mismatch of their data distributions.…
A new model improves clustering by reducing redundancy in mixture of local EPCAs.
problem Redundancy in traditional mixture models causes ambiguity in clustering.
method Introduced a repulsiveness-encouraging prior and a DPP for diversity in DEPCAM model.
result The method reduces model redundancy and improves clustering performance.
The t-distributed Stochastic Neighbor Embedding (tSNE) algorithm has become in recent years one of the most used and insightful techniques for the exploratory data analysis of high-dimensional data. tSNE reveals clusters of high-dimensional data points at different scales while it requires only minimal tuning of its pa…
The study examines correlations of logarithms of integers at different scalings.
problem Analyzing pair correlations of logarithms of integers at various scalings.
method Examined correlations of logarithms of positive integers at different scalings, proving the existence of pair correlation functions.
result Level repulsion at linear scaling, total loss of mass at superlinear scalings, and Poissonian behavior at sublinear scalings.
The paper proves a Lojasiewicz inequality for maps from the 2-sphere to itself.
problem Analyzing maps from the 2-sphere to itself using Lojasiewicz inequalities.
method Using Lojasiewicz-Simon inequalities and Topping's repulsion estimates, along with a bubble-tree induction argument.
result Polynomial convergence of weak solutions of harmonic map flow on compact domains.
Paper proposes ARB-Loss to improve classification precision in imbalanced datasets.
problem Improving classification precision on minor classes in imbalanced datasets.
method Introduces Attraction-Repulsion-Balanced Loss (ARB-Loss) to balance gradients across different classes.
result ARB-Loss achieves state-of-the-art performance with one-stage training.
Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient sampling algorithm based on the eigendecomposition of…
This paper presents a model of capital accumulation for a large number of heterogenous producer-consumers in an exchange space in which interactions depend on agents' positions. Each agent is described by his production, consumption, stock of capital, as well as the position he occupies in this abstract space. Each age…
Study on capillarity minimizers with nonlocal repulsion and gravity, proving existence and nonexistence.
problem Minimizing an energy functional with capillarity, nonlocal repulsion, and gravity.
method Quantitative isoperimetric inequalities applied to capillarity problem in a half-space.
result Existence and nonexistence of minimizers for various nonlocal kernels and masses.
Spectral portfolio theory links neural networks to wealth dynamics via SGD weight matrices.
problem Understanding wealth dynamics from neural network training.
method Direct identification of weight matrices as portfolio allocation matrices, linking SGD forces to portfolio dynamics.
result Spectral properties of SGD weight matrices transition between additive and multiplicative regimes, influencing wealth dynamics.