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Vaios Laschos

Vaios Laschos appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.PRMachine Learningmath-phmath.MPmath.OCmath.APmath.CA

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Published work

8 published item(s)

preprint2026arXiv

In-context learning to predict critical transitions in dynamical systems

Critical transitions - abrupt, often irreversible changes in system dynamics - arise across human and natural systems, often with catastrophic consequences. Real-world observations of such shifts remain scarce, preventing the development of reliable early warning systems. Conventional statistical and spectral indicators, such as increasing variance, tend to fail under realistic conditions of limited data and correlated noise, whereas existing deep learning classifiers do not extrapolate beyond their training data distribution. In this work, we introduce TipPFN, an in-context learning (ICL) framework that uses a prior-data fitted network to infer a system's proximity to a critical transition. Trained on our novel synthetic data generator, which is based on canonical bifurcation scenarios coupled to diverse, randomized stochastic dynamics, TipPFN flexibly capitalizes on contexts of various sizes, complexity and dimensionalities. We demonstrate robust, state-of-the-art early detection of critical transitions in previously unseen tipping regimes, sim-to-real examples, and real-world observations in both ICL and zero-shot settings.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Risk-Sensitive Partially Observable Markov Decision Processes as Fully Observable Multivariate Utility Optimization problems

We provide a new algorithm for solving Risk Sensitive Partially Observable Markov Decisions Processes, when the risk is modeled by a utility function, and both the state space and the space of observations is finite. This algorithm is based on an observation that the change of measure and the subsequent introduction of the information space that is used for exponential utility functions, can be actually extended for sums of exponentials if one introduces an extra vector parameter that tracks the "expected accumulated cost" that corresponds to each exponential. Since every increasing function can be approximated by sums of exponentials in finite intervals, the method can be essentially applied for any utility function, with its complexity depending on the number of exponentials.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Large deviations for configurations generated by Gibbs distributions with energy functionals consisting of singular interaction and weakly confining potentials

We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% β_n$ and an energy functional consisting of a (possibly singular) interaction potential and a (possibly weakly) confining potential. Under fairly general assumptions on the potentials, we use a common framework to establish LDPs both with speeds $β_n/n \rightarrow \infty$, in which case the rate function is expressed in terms of a functional involving the potentials, and with speed $β_n =n$, when the rate function contains an additional entropic term. Such LDPs are motivated by questions arising in random matrix theory, sampling, simulated annealing and asymptotic convex geometry. Our approach, which uses the weak convergence method developed by Dupuis and Ellis, establishes LDPs with respect to stronger Wasserstein-type topologies. Our results address several interesting examples not covered by previous works, including the case of a weakly confining potential, which allows for rate functions with minimizers that do not have compact support, thus resolving several open questions raised in a work of Chafa\"ı et al.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Training Generative Networks with general Optimal Transport distances

We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs, where the Euclidean distance is ${\it implicitly}$ used, this new method allows to ${\it explicitly}$ use ${\it any}$ transportation cost function that can be chosen to match the problem at hand. For example, it allows to use the squared distance as a transportation cost function, giving rise to the Wasserstein-2 metric for probability distributions, which results in fast and stable gradient descends. It also allows to use image centered distances, like the structure similarity index, with notable differences in the results.

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preprint2019arXiv

A Fenchel-Moreau-Rockafellar type theorem on the Kantorovich-Wasserstein space with Applications in Partially Observable Markov Decision Processes

By using the fact that the space of all probability measures with finite support can be somehow completed in two different fashions, one generating the Arens-Eells space and another generating the Kantorovich-Wasserstein (Wasserstein-1) space, and by exploiting the duality relationship between the Arens-Eells space with the space of Lipschitz functions, we provide a dual representation of Fenchel-Moreau-Rockafellar type for proper convex functionals on Wasserstein-1. We retrieve dual transportation inequalities as a Corollary and we provide examples where the theorem can be used to easily prove dual expressions like the celebrated Donsker-Varadhan variational formula. Finally our result allows to write convex functions as the supremum over all linear functions that are generated by roots of its conjugate dual, something that we apply to the field of Partially observable Markov decision processes (POMDPs) to approximate the value function of a given POMDP by iterating level sets. This extends the method used in Smallwood 1973 for finite state spaces to the case were the state space is a Polish metric space.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Gradient flow structure for McKean-Vlasov equations on discrete spaces

In this work, we show that a family of non-linear mean-field equations on discrete spaces can be viewed as a gradient flow of a natural free energy functional with respect to a certain metric structure we make explicit. We also prove that this gradient flow structure arises as the limit of the gradient flow structures of a natural sequence of N-particle dynamics, as N goes to infinity.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Relations between $\mathcal{L}^p$- and Pointwise Convergence of Families of Functions Indexed by the Unit Interval

We construct a variety of mappings of the unit interval into $\mathcal{L}^p([0,1])$ to generalize classical examples of $\mathcal{L}^p$-convergence of sequences of functions with simultaneous pointwise divergence. By establishing relations between the regularity of the functions in the image of the mappings and the topology of $[0,1]$, we obtain examples which are $\mathcal{L}^p$-continuous but exhibit discontinuity in a pointwise sense to different degrees. We conclude by proving an Egorov-type theorem, namely that if almost every function in the image is continuous, then we can remove a set of arbitrarily small measure from the index set $[0,1]$ and establish pointwise limits for all functions in the remaining image.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Wasserstein gradient flows from large deviations of thermodynamic limits

We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle system on one hand and as a Wasserstein gradient flow on the other. We write the rate functional, that characterizes the large deviations from the hydrodynamic limit, in a way that the free energy appears explicitly. Next we use this formulation via the contraction principle to prove that the discreet time rate functional is asymptotically equivalent in the Gamma-convergence sense to the functional derived from the Wasserstein gradient discretization scheme.

0 citations0 reviewsNo code linkedOpen access