2 citations · 2 across the 7 of their papers we have counts for
9 papers
Denoising Score Matching in Diffusion Models: The Effect of Rank Constraints on Generalization
Anand Jerry George, Nicolas Macris
Architectural biases restrict the class of functions that a diffusion score network can represent, but their effect on generalization remains poorly understood. We study denoising…
Separable decompositions of 2xn states with operator Schmidt rank three
Perrine Vantalon, Nicolas Macris
We prove that every bipartite state of a qubit coupled to an -level system whose operator Schmidt rank equals three can be written as a mixture of pure prod…
Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Data
Anand Jerry George, Nicolas Macris
We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifo…
Analysis of Diffusion Models for Manifold Data
Anand Jerry George, Rodrigo Veiga, Nicolas Macris
We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of…
Sampling in High-Dimensions using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations
Anand Jerry George, Nicolas Macris
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transp…
Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves
Anand Jerry George, Rodrigo Veiga, Nicolas Macris
We theoretically investigate the phenomena of generalization and memorization in diffusion models. Empirical studies suggest that these phenomena are influenced by model complexity…
The PRODSAT phase of random quantum satisfiability
Joon Lee, Nicolas Macris, Jean Bernoulli Ravelomanana +1
The -QSAT problem is a quantum analog of the famous -SAT constraint satisfaction problem. We must determine the zero energy ground states of a Hamiltonian of qubits consi…
Rectangular Rotational Invariant Estimator for High-Rank Matrix Estimation
Farzad Pourkamali, Nicolas Macris
We consider estimating a matrix from noisy observations coming from an arbitrary additive bi-rotational invariant perturbation. We propose an estimator which is optimal among the c…
Stochastic Gradient Flow Dynamics of Test Risk and its Exact Solution for Weak Features
Rodrigo Veiga, Anastasia Remizova, Nicolas Macris
We investigate the test risk of continuous-time stochastic gradient flow dynamics in learning theory. Using a path integral formulation we provide, in the regime of a small learnin…