This paper tackles incomplete multi-view clustering with spectral perturbation theory.
problem Realistic clustering scenario where data instances are missing in certain views.
method Spectral perturbation theory and matrix completion method for incomplete similarity matrix.
result The minimization of perturbation risk bounds maximizes the final fusion result across all views.
We present in this paper an empirical framework motivated by the practitioner point of view on stability. The goal is to both assess clustering validity and yield market insights by providing through the data perturbations we propose a multi-view of the assets' clustering behaviour. The perturbation framework is illust…
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.
Paper proposes an efficient algorithm to compute minimum adversarial perturbation for NN classifiers.
problem Computing the minimum adversarial perturbation for Nearest Neighbor classifiers.
method Formulated as a list of convex quadratic programming problems, solved using efficient algorithms.
result Shows dual solutions as valid lower bounds for adversarial perturbation, aiding robustness verification.
Image classifiers are sensitive to small changes, affecting most images in a class.
problem Sensitivity of image classifiers to small perturbations.
method Demonstrated sensitivity for any classifier over images, showing that for most classes, a tiny perturbation can change the classification of a majority of images.
result Image classifiers are sensitive to small perturbations, affecting most images in a class.
Generalizes Fefferman's structure to CR three-manifolds with additional data.
problem Finding conditions for conformal isometry and existence of metrics.
method Introduces perturbations of Fefferman's conformal circle bundle and investigates existence of metrics.
result Provides conditions for existence of metrics satisfying Einstein equations.
We study the classical action functional $\SMC_V$ on the free loop space of a closed, finite dimensional Riemannian manifold M and the symplectic action $\AMC_V$ on the free loop space of its cotangent bundle. The critical points of both functionals can be identified with the set of perturbed closed geodesics in M.…
Study fusion methods for financial image views to improve robustness against attacks.
problem Improving robustness of financial image views for next-day direction prediction.
method Same-source multi-view learning with early fusion and late fusion, using OHLCV and technical-indicator views, and evaluating pixel-space L-infinity attacks.
result Early fusion can suffer negative transfer under noisy settings, while late fusion is more reliable once labels stabilize.
Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed input results in the model outputting an incorrect answer with high confidence. Ear…
Develops a method to predict system behavior under disruptions.
problem Predicting changes in system behavior due to external perturbations.
method Counterfactual distribution regression for structured inference.
result Generalizes behavior predictions from natural to disrupted states.
Framework for causal discovery using multi-modal data.
problem Failure of representation learning in causal tasks.
method Statistical and computational framework combining representation learning and causal inference.
result Effective use of observational and perturbational data for causal discovery.
We investigate the links between various no-arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein. No-arbitrage conditions, either in this abstract setting or in the case of a market consisting of European Call options, give rise to …
Given the ability to directly manipulate image pixels in the digital input space, an adversary can easily generate imperceptible perturbations to fool a Deep Neural Network (DNN) image classifier, as demonstrated in prior work. In this work, we propose ShapeShifter, an attack that tackles the more challenging problem o…
Unified view of gradient-based algorithms for stochastic convex composite optimization.
problem Optimization of stochastic convex composite functions.
method Extend the concept of estimate sequence to cover various gradient-based methods.
result Generic convergence proof and new adaptive SVRG variant.
We examine the issue of sensitivity with respect to model parameters for the problem of utility maximization from final wealth in an incomplete Samuelson model and mainly, but not exclusively, for utility functions of positive power-type. The method consists in moving the parameters through change of measure, which we …
Paper develops robust Bayesian models for linear regression under adversarial perturbations.
problem Ensuring reliable machine learning models under data perturbations.
method Formulates adversarial Bregman divergence loss, computes adversarial perturbation, introduces adversarially robust posteriors, derives generalization certificates.
result Derives first rigorous generalization certificates for adversarially robust Bayesian linear regression.
Paper establishes lower bounds for Gaussian process bandit optimization under various perturbation models.
problem Lower bounds for Gaussian process bandit optimization in noisy and robust settings.
method Novel proof techniques for standard and robust settings, including deterministic strategies.
result Demonstrates inevitable joint dependence of cumulative regret on corruption level and time horizon in robust settings.
New method generates universal adversarial perturbations across different image sources.
problem Certifying robustness of deep learning models with universal adversarial perturbations across various image sources.
method Few-shot learning approach using bilevel optimization and learning-to-optimize techniques.
result Improved attack success rate and faster performance compared to existing methods.
Minimalistic attacks reveal deep RL policies' vulnerabilities with little perturbation.
problem Tackling the vulnerability of deep reinforcement learning policies to minimal perturbations.
method Three key settings: black-box policy access, fractional-state adversary, and tactically-chanced attack. Formulated adversarial attacks on six Atari games.
result Deep RL policies can be significantly fooled by minimal perturbations, even in 0.01% of the input state.
This research deconstructs GANs into formulation, generalization, and optimization components.
problem Improving the performance and stability of GANs.
method Proposes a perturbation view of GANs, introduces Cascade GANs, and develops principles for GAN generalization and optimization.
result Demonstrates a fundamental trade-off in GAN approximation and statistical errors, and proposes a new GAN architecture with zero minimax duality gap.
The study proves rigidity and non-rigidity of spherical caps in mean curvature.
problem Understanding mean curvature rigidity and non-rigidity on spherical caps.
method Used a Tangency Principle to prove rigidity and constructed counterexamples for non-rigidity.
result Contrast between rigidity and non-rigidity phenomena on spherical caps.
Deeper quantum circuits can improve performance on unseen data, contrary to traditional views.
problem Understanding scaling behavior of parameterized quantum circuits and their generalization.
method Gradient-based PQCs, add-one-in perturbation techniques, spectral properties of random matrices.
result Gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying double descent behavior.
The study examines the long-term behavior of mean curvature flows in closed 3-manifolds.
problem Understanding the long-term behavior of mean curvature flows in closed 3-manifolds.
method The approach involves constructing piecewise almost regular flows and applying perturbative arguments.
result The study constructs minimal surfaces in 3-manifolds via parabolic methods.
Study character varieties of tangles to map immersed curves in the pillowcase.
problem Characterizing holonomy-perturbed traceless SU(2) character varieties.
method Examining marked tangles as endomorphisms in the cobordism category and using holonomy-perturbed traceless character variety functor.
result Endomorphisms of immersed curves in the pillowcase have the same image.
We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres in compact perturbations of Schwarzschild-anti-deSitter are uniquely isoperimetric. This is relevant in the context of the asymptotically …
A method for identifying joint and individual subspaces from multi-view data.
problem Unclear conditions for reliably identifying joint and individual subspaces from noisy, high-dimensional measurements.
method Rigorously quantifies conditions based on signal rank, principal angles, and noise levels. Characterizes spectrum perturbations of product of projection matrices.
result Estimates joint and individual subspaces more accurately than existing approaches in simulations and real-world applications.
A new oversampling framework generates minority samples by perturbing majority classes.
problem Oversampling in imbalanced classification often neglects majority classes, leading to samples spread across the minority space.
method Introduces a counterfactual objective to generate new minority samples by perturbing majority samples.
result Generated minority samples are near the decision boundary and significantly outperform state-of-the-art methods.
Unified view of stochastic optimization methods with improved convergence and robustness.
problem Stochastic convex composite optimization with noise.
method Estimate sequence approach, accelerated algorithms, robust strategies.
result Optimal complexity accelerated SVRG algorithm robust to noise.
Proposes a new framework for balancing average- and worst-case performance in machine learning.
problem Robustness issues in machine learning, especially in safety-critical domains.
method Probabilistic robustness framework that balances average- and worst-case performance.
result Effective algorithm balances average- and worst-case performance with lower computational cost.
Study SOLV geometry using monopole Floer homology.
problem Prove SOLV rational homology sphere Y is an L-space.
method Apply Fourier analysis on solvable groups to show irreducible solutions do not exist for certain metrics.
result Y is an L-space geometrically proven.
Proposes robust features for adversarial attacks.
problem Learning robust models to adversarial perturbations is hard.
method Develops robust features by leveraging spectral properties of dataset geometry.
result Establishes strong connections between robust features and spectral geometry.
General equilibrium is the dominant theoretical framework for economic policy analysis at the level of the whole economy. In practice, general equilibrium treats economies as being always in equilibrium, albeit in a sequence of equilibria as driven by external changes in parameters. This view is sometimes defended on t…
Improved FTPL algorithm reduces regret in predictable minimax games.
problem Online learning and minimax games with predictable loss sequences.
method Optimistic modification of FTPL with dual regularization view.
result Tighter regret bounds for predictable sequences, O(T−1/2) accuracy. Enhances safety of 3D object detection neural networks.
problem Ensuring robustness and safety of 3D object detection systems.
method Symbolic error propagation, specialized loss function, safety-aware non-max-inclusion algorithm.
result Improved safety and robustness of 3D object detection neural networks.
New bounds for private matrix approximation using Gaussian noise and Dyson Brownian Motion.
problem Private approximation of symmetric matrices with Gaussian noise.
method Viewing Gaussian noise as Dyson Brownian Motion to track eigenvalue and eigenvector evolution.
result Improved bounds on Frobenius-distance utility for private matrix approximation.
We introduce certain spherically symmetric singular Ricci solitons and study their stability under the Ricci flow from a dynamical PDE point of view. The solitons in question exist for all dimensions n+1≥3, and all have a point singularity where the curvature blows up; their evolution under the Ricci flow is in sh…
The paper connects neural network ensembles to Bayesian inference using variational methods.
problem Explaining the behavior of ensemble methods in neural networks.
method Deriving conditions for ensemble optimization to reduce divergence to the posterior distribution.
result Ensemble methods can be a valid alternative to approximate Bayesian inference.
Geometric formalism views optimization algorithms as discrete connections, revealing their algebraic curvature and flatness properties.
problem Understanding and optimizing the behavior of iterative optimization algorithms.
method Introducing a geometric and operator-theoretic formalism where optimization algorithms are encoded by coupled channels (drift and diffusion) whose algebraic curvature measures the deviation from ideal reversibility.
result Flat connections correspond to methods whose updates commute up to higher order, achieving minimal numerical dissipation and preserving stability.
SAVeD detects dataset versions without metadata, improving accuracy and separation.
problem Difficulty in identifying similar versions of structured datasets.
method Contrastive learning with modified SimCLR pipeline, generating and contrasting augmented table views.
result SAVeD achieves higher accuracy and separation scores on unseen tables.
Study explores bias-variance in adversarial machine learning.
problem Understanding adversarial machine learning's impact on bias and variance.
method Investigates bias-variance trade-offs in deep neural networks using MSE and cross-entropy.
result Derives bias-variance trade-offs for classification and regression.
Stability of catenoid in hyperbolic space proven without symmetry assumptions.
problem Stability of catenoid in hyperbolic space.
method Profile construction, modulation analysis, integrated local energy decay, vectorfield method.
result Nonlinear asymptotic stability of catenoid for n≥5 without symmetry assumptions. New aggregation method improves GNN robustness to structural perturbations.
problem Graph Neural Networks (GNNs) are vulnerable to adversarial attacks that manipulate graph structure.
method Proposes a robust aggregation function with a breakdown point of 0.5, inspired by robust statistics.
result Improves GNN robustness by a factor of 3 on Cora ML and 5.5 on Citeseer, and 8 for low-degree nodes.
In many settings, we have multiple data sets (also called views) that capture different and overlapping aspects of the same phenomenon. We are often interested in finding patterns that are unique to one or to a subset of the views. For example, we might have one set of molecular observations and one set of physiologica…
Generalizes Hodge correlators using quantum master equation concepts.
problem Developing a mathematical framework for non-acyclic Chern-Simons theory.
method Introduces a DG Lie algebra of uni-trivalent graphs with loops satisfying a Maurer-Cartan equation.
result Arithmetic analogue of effective action and quantum master equation.
Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased import…
Adversarial examples are augmented data points generated by imperceptible perturbation of input samples. They have recently drawn much attention with the machine learning and data mining community. Being difficult to distinguish from real examples, such adversarial examples could change the prediction of many of the be…
Advances robustness of metric learning by adversarial margin in input space.
problem Improving robustness of metric learning algorithms.
method Imposing adversarial margin in input space, minimizing perturbation loss.
result Enlarged adversarial margin improves generalization and robustness.
New task aligns molecular structure with gene expression changes.
problem Modeling the relationship between chemical structure and gene expression changes.
method Developed a cross-modal small molecule retrieval task and a coordinated deep learning approach to align chemical structure and gene expression profiles.
result Demonstrated the feasibility of the new task and highlighted the limitations of current data and systems.