On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it

• URL: http://arxiv.org/abs/2301.03662v1
• Date: Mon, 9 Jan 2023 20:14:30 GMT
• Title: On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it
• Authors: Camilo Garcia Trillos, Nicolas Garcia Trillos
• Abstract summary: We propose iterative algorithms to solve adversarial problems in a variety of supervised learning settings interest. Our algorithms can be interpreted as suitable ascent-descent dynamics in Wasserstein spaces.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose iterative algorithms to solve adversarial problems in a variety of supervised learning settings of interest. Our algorithms, which can be interpreted as suitable ascent-descent dynamics in Wasserstein spaces, take the form of a system of interacting particles. These interacting particle dynamics are shown to converge toward appropriate mean-field limit equations in certain large number of particles regimes. In turn, we prove that, under certain regularity assumptions, these mean-field equations converge, in the large time limit, toward approximate Nash equilibria of the original adversarial learning problems. We present results for nonconvex-nonconcave settings, as well as for nonconvex-concave ones. Numerical experiments illustrate our results.

Related papers

• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers. We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Dilute neutron star matter from neural-network quantum states [58.720142291102135]
  Low-density neutron matter is characterized by the formation of Cooper pairs and the onset of superfluidity. We model this density regime by capitalizing on the expressivity of the hidden-nucleon neural-network quantum states combined with variational Monte Carlo and reconfiguration techniques.
  arXiv  Detail & Related papers  (2022-12-08T17:55:25Z)
• Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery [3.06483729892265]
  We introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term.
  arXiv  Detail & Related papers  (2022-11-20T00:46:33Z)
• An Exponentially Converging Particle Method for the Mixed Nash Equilibrium of Continuous Games [0.0]
  We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function. This problem arises for example in game-inspired machine learning applications, such as distributionally-robust learning. We introduce and analyze a particle-based method that enjoys guaranteed local convergence for this problem.
  arXiv  Detail & Related papers  (2022-11-02T17:03:40Z)
• A note on large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum games [0.0]
  Finding equilibria points in continuous minimax games has become a key problem within machine learning. Recent developments have shifted from pure equilibria to focusing on mixed equilibria points. We show that the sequence of empirical measures of the particle system satisfies a large deviation principle as the number of particles grows to infinity.
  arXiv  Detail & Related papers  (2022-06-30T10:29:21Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
  convergence rate analysis of the mean field Langevin dynamics is presented. $p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
  arXiv  Detail & Related papers  (2022-01-25T17:13:56Z)
• Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories [13.3638879601361]
  We consider systems of interacting particles or agents, with dynamics determined by an interaction kernel. We introduce a nonparametric inference approach to this inverse problem, based on a regularized maximum likelihood estimator. We show that a coercivity condition enables us to control the condition number of this problem and prove the consistency of our estimator.
  arXiv  Detail & Related papers  (2020-07-30T01:28:06Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)
• The entanglement membrane in chaotic many-body systems [0.0]
  In certain analytically-tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables, reduces to an effective theory of an entanglement membrane'' in spacetime. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries.
  arXiv  Detail & Related papers  (2019-12-27T19:01:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.