arXiv subjects

Feliciano Giuseppe Pacifico

Publications and source records attributed to Feliciano Giuseppe Pacifico.

3 recordsLinked to original sources

arXiv2026

Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes

In this work, Neural ODEs equipped with a curated collection of equilibrium points have been successfully employed for classification tasks. The planted attractors serve as indicators for the target classes, while the velocity field leveraging the universal approximation capabilities of the architecture shapes the dynamical landscape. This process defines the basins of attraction of the trained model, effectively directing each input (provided as an initial condition) toward its corresponding destination target.

cond-mat.dis-nn↗

arXiv2026

Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality

We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models.

cond-mat.dis-nn↗

arXiv2025

Train Stochastic Non Linear Coupled ODEs to Classify and Generate

A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the dynamical system amounts to shaping the architecture of inter-nodes connection to steer the evolution towards the assigned equilibrium, as a function of the class to which the item - supplied as an initial condition - belongs to. Under the stochastic perspective, point attractors are turned into probability distributions, made analytically accessible via the linear noise approximation. The addition of noise proves beneficial to oppose adversarial attacks, a property that gets engraved into the trained adjacency matrix and therefore also inherited by the deterministic counterpart of the optimized stochastic model. By providing samples from the target distribution as an input to a feedforward neural network (or even to a dynamical model of the same typology of the adopted for classification purposes), yields a fully generative scheme. Conditional generation is also possible by merging classification and generation modalities. Automatic disentanglement of isolated key features is finally proven.

cond-mat.dis-nn↗