The paper analyzes numerical instability in variational flows and proposes a diagnostic method.
problem Numerical instability in variational flows affects sampling, density evaluation, and ELBO estimation.
method Treated variational flows as dynamical systems, used shadowing theory for theoretical guarantees, and developed a diagnostic procedure.
result Despite numerical instability, results from variational flows can be accurate enough for practical applications.
Deep neural networks struggle with numerical instability during training.
problem Numerical instability in gradient descent training of deep neural networks.
method Analysis of floating-point arithmetic and gradient descent in ReLU neural networks.
result It is highly unlikely for ReLU networks to maintain a superlinear number of affine pieces during training.
NGRC shows numerical instabilities with short lags and high-degree polynomials.
problem Numerical instabilities in NGRC feature matrix.
method Combining numerical linear algebra and dynamical systems theory, we study feature matrix conditioning. We evaluate different numerical algorithms for solving the regularized least-squares problem.
result SVD-based training achieves accurate forecasts without regularization, preferable for short lags and high-degree polynomials.
A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For example, real-time studies of instabilities in nonlinear fibre optics frequently …
The square root of Fredholm determinants causes numerical instabilities in option pricing models.
problem Numerical instabilities in Fourier-based option pricing for the Volterra Stein-Stein model.
method Characterization of determinant crossing behavior, derivation of transform to handle crossings, efficient algorithms.
result Significant improvement in accuracy and reduction in computational cost for Fourier-based pricing.
This work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in numerical instability due to division by zero. We propose a variation on the flow that removes the nu…
New findings on optimal transport gradient for generative models, addressing numerical instabilities.
problem Numerical instabilities in training Wasserstein Generative Adversarial Networks (WGAN).
method Valid differentiation theorem for entropic regularized transport, semi-discrete gradient formulation, and optimization algorithm.
result Existence of optimal transport gradient for generative models under specified conditions.
Slow feature analysis (SFA) is a method for extracting slowly varying features from a quickly varying multidimensional signal. An open source Matlab-implementation sfa-tk makes SFA easily useable. We show here that under certain circumstances, namely when the covariance matrix of the nonlinearly expanded data does not …
Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of the algorithm is a graph where nodes represent clusters and edges represent the …
Improved ANN-based Monte Carlo simulation for Higgs decay events.
problem Accurate simulation of Higgs boson decay events.
method Monte Carlo simulation using an Artificial Neural Network (ANN) with improved training algorithm.
result The ANN simulation of Higgs decay is within 0.7% of the true value and achieves 26% unweighting efficiency.
Bayesian neural network predicts planetary instability.
problem Predicting planetary instability in compact systems.
method Novel Bayesian neural network trained on raw orbital elements.
result Model predicts planetary instability times with high accuracy and robust generalization.
We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated R…
We study analytically and numerically Minsky instability as a combination of top-down, bottom-up and peer-to-peer positive feedback loops. The peer-to-peer interactions are represented by the links of a network formed by the connections between firms, contagion leading to avalanches and percolation phase transitions pr…
Investigates stability of piecewise flat Ricci flow using analysis and simulations.
problem Stability of piecewise flat Ricci flow.
method Linear stability analysis and numerical simulations.
result Adaptations avoided numerical instability and led to convergence to smooth solutions.
Investment diversification affects financial stability, depending on network connectivity.
problem Analyzing stability of financial networks with diversified portfolios.
method Random matrix dynamical model with portfolio rebalancing, considering heterogeneity and diversification effects.
result Stability/instability transition depends on the largest eigenvalue of the random matrix.
Adversarial attacks against neural networks in a regression setting are a critical yet understudied problem. In this work, we advance the state of the art by investigating adversarial attacks against regression networks and by formulating a more effective defense against these attacks. In particular, we take the perspe…
We present an approach for efficiently training Gaussian Mixture Model (GMM) by Stochastic Gradient Descent (SGD) with non-stationary, high-dimensional streaming data. Our training scheme does not require data-driven parameter initialization (e.g., k-means) and can thus be trained based on a random initialization. Furt…
Fractal learning rate schedules accelerate vanilla gradient descent.
problem Difficulty in tuning learning rates in iterative optimization.
method Introduce Chebyshev learning rate schedule for gradient descent.
result Locally unstable updates can lead to convergence in deep learning.
We study the emergence of instabilities in a stylized model of a financial market, when different market actors calculate prices according to different (local) market measures. We derive typical properties for ensembles of large random markets using techniques borrowed from statistical mechanics of disordered systems. …
We improve current instability-based methods for the selection of the number of clusters k in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously unaccounted driver of cluster instability. We show that our normalized instability mea…
A new method for robust product Markovian quantization overcomes numerical instabilities.
problem Numerical instabilities in the PMQ algorithm limit its adoption, especially for stochastic volatility models.
method Reformulated PMQ as standard vector quantization, applying accelerated Lloyd's algorithm for robustness.
result The method overcomes numerical instabilities and extends applicability to stochastic volatility models.
FCA improves fair clustering by optimizing utility and fairness.
problem Balancing fairness and utility in clustering.
method FCA alternates between aligning data and optimizing cluster centers in an aligned space.
result FCA achieves a superior trade-off between fairness and utility.
Two new PCA variants improve financial data analysis.
problem Numerical instability and nonstationarity in PCA for finance.
method Iterated and exponentially weighted moving PCA variants using Ogita-Aishima iteration.
result Improved stability and adaptability in financial data analysis.
Study on market instability in multi-agent trading with price impact and transaction costs.
problem Analyzing market instability in multi-agent trading with price impact and transaction costs.
method Analytical and numerical methods to study Nash equilibria and stability conditions.
result Conditions on model parameters determine market stability, including scaling of market impact and transaction cost.
Modeling HFT interactions reveals market instability.
problem Market instability caused by HFT dynamic coupling.
method Developed a recurrence relations framework to model HFT interactions.
result Unexpected latency and feedback can trigger market instability.
New proof of instability for certain Einstein metrics.
problem Einstein metrics on specific 4-manifolds.
method Proving instability of conformally Kähler, Einstein metrics.
result Proven instability of certain Einstein metrics.
Study stability and instability of Ricci-flat metrics under generalized Ricci flow.
problem Stability and instability of Ricci-flat metrics under Ricci flow.
method Analysis of generalized Ricci flow for Ricci-flat metrics and vanishing 3-forms.
result Dynamical stability and instability results for Ricci-flat metrics and vanishing 3-forms.
Some exotic compact objects possess evanescent ergosurfaces: timelike submanifolds on which a Killing vector field, which is timelike everywhere else, becomes null. We show that any manifold possessing an evanescent ergosurface but no event horizon exhibits a linear instability of a peculiar kind: either there are solu…
Interval Neural Networks detect instabilities in image reconstructions.
problem Detecting instabilities in deep learning image reconstructions.
method Employed uncertainty quantification methods with Interval Neural Networks.
result Interval Neural Networks effectively reveal image reconstruction instabilities.
Note on instabilities in super-time-stepping methods for Heston model.
problem Instabilities in super-time-stepping methods applied to Heston model.
method Exploration of explicit super-time-stepping schemes (RK-Chebyshev, RK-Legendre) for Heston model.
result Relevance of stability remarks beyond super-time-stepping schemes.
Binary perceptron's instability linked to replica symmetry breaking.
problem Understanding the relationship between algorithmic instability and replica symmetry breaking in binary perceptron learning.
method Established the connection between algorithmic instability and replica symmetry breaking by comparing the instability condition around the fixed point to the instability for breaking the replica symmetric solution of the free energy function.
result The instability condition around the algorithmic fixed point is identical to the instability for breaking the replica symmetric saddle point solution of the free energy function.
New research shows hyperbolic embeddings are useful for global consistency tasks in graphs.
problem The usefulness of hyperbolic representations in graph learning tasks.
method Computed hyperbolic embeddings for node classification and link prediction tasks, addressing optimization issues at zero curvature.
result Hyperbolic embeddings are more effective for tasks requiring global consistency, while Euclidean models are superior for other tasks.
The study examines stability and instability of Poincaré-Einstein metrics using Ricci flow.
problem Stability and instability of Poincaré-Einstein metrics.
method Variant of expander entropy for asymptotically hyperbolic manifolds, local positive mass theorem, volume comparison.
result Characterization of stability and instability in terms of local positive mass theorem and volume comparison.
Many industrial machine learning (ML) systems require frequent retraining to keep up-to-date with constantly changing data. This retraining exacerbates a large challenge facing ML systems today: model training is unstable, i.e., small changes in training data can cause significant changes in the model's predictions. In…
Study shows instability of naked singularities in perfect fluid models.
problem Instability of naked singularities in Einstein equations coupled with isothermal perfect fluid.
method Investigated spherically symmetric self-similar naked singularities under C1,α perturbations of an external massless scalar field. result Spherically symmetric self-similar naked singularities are unstable to trapped surface formation.
Study on spectral stability of Riemannian coverings.
problem Stability of eigenvalues in Riemannian coverings.
method Analysis of Laplacian eigenvalues under finite coverings.
result Necessary conditions for spectral stability or instability.
Clinical models can be unstable, leading to unreliable predictions.
problem Stability of clinical prediction models developed using statistical or machine learning methods.
method Simulation and case studies of statistical and machine learning approaches to show instability in model predictions.
result Model instability often leads to miscalibration of predictions in new data.
In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricia…
A data-driven approach predicts morphological development under structural instability.
problem Understanding and predicting spatiotemporal complexities of morphogenesis under structural instability.
method Machine-learning framework based on physical modeling of morphogenesis.
result Identification of key bifurcation characteristics and prediction of history-dependent development.
Study shows instability of naked singularities in scalar field models.
problem Stability of naked singularities in spherically symmetric Einstein-Scalar field systems.
method Analysis of a family of incoming null cones becoming increasingly singular.
result Naked singularities are unstable to black hole formation under certain perturbations.
New recommendations improve Gaussian process accuracy and stability.
problem Numerical instabilities and poor test likelihoods in iterative Gaussian process learning.
method Investigated CG tolerance, preconditioner rank, and Lanczos decomposition rank. Recommended small CG tolerance and large root decomposition size.
result L-BFGS-B optimizer achieves convergence with fewer gradient updates, improving Gaussian process accuracy.
Study shows instability of certain MOTSs with continuous symmetry.
problem Stability of MOTSs with continuous symmetry.
method Analysis of initial data sets with continuous symmetry and non-preserved MOTSs.
result Exotic MOTSs are unstable except in exceptional cases.
We stabilize MI-based losses by adding a regularization term, improving their performance and stability.
problem Instability of MI-based losses in machine learning.
method Added a novel regularization term to stabilize MI-based losses.
result Regularization stabilizes training and improves the performance of MI-based losses.
New method stabilizes probabilistic ODE solvers for high accuracy.
problem Numerical instability in high-order ODE solvers.
method Accurate initialisation, coordinate change preconditioner, square-root implementation.
result Probabilistic ODE solvers can now achieve high order (up to 11) with stability.
The paper studies stability and instability of minimal submanifolds in complex Einstein spaces.
problem Stability and instability of minimal submanifolds in complex Einstein spaces.
method Computation of index and nullity, investigation of stability, and algorithm for higher eigenvalues.
result Criterion for instability of minimal submanifolds in some cases.
The study examines the stability of Einstein metrics on Sasaki Einstein and nearly parallel G2 manifolds.
problem Linear instability of Einstein metrics on Sasaki Einstein and nearly parallel G2 manifolds.
method Analysis of the second and third Betti numbers for Sasaki Einstein and nearly parallel G2 manifolds.
result Positive second and third Betti numbers lead to linear instability for the respective manifolds.
Paper extends Simons theorem to F-Yang-Mills connections for instability.
problem Tackles instability of F-Yang-Mills connections. method Extends Simons theorem to F-Yang-Mills connections using Kobayashi-Ohnita-Takeuchi's method. result Derives a sufficient condition for instability of non-flat F-Yang-Mills connections. Using numerical simulations of the axisymmetric Navier-Stokes equations with swirl on a no-slip flat boundary, Hsu-Notsu-Yoneda [J. Fluid Mech. 2016] observed the creation of a high-vorticity region on the boundary near the axis of symmetry. In this paper, using a differential geometric approach, we prove that such flo…