arXiv subjects

Davide Gabrielli

Publications and source records attributed to Davide Gabrielli.

At least 19 recordsLinked to original sources

arXiv2026

Beyond Binary Rewards: A Comparative Study of Reward Design for Reinforcement Unlearning

Machine unlearning seeks to selectively remove specific knowledge from trained language models without full retraining, a growing necessity under privacy regulations such as GDPR and the EU AI Act. Recent work has reformulated unlearning as a Reinforcement Learning with Verifiable Rewards (RLVR) problem, where models are optimized against verifiable rewards computed directly from their outputs. However, existing methods rely on sparse binary rewards that provide minimal learning signal, indicating only whether forbidden content was avoided, and limiting convergence speed. In this paper, we study how reward design affects unlearning efficiency within the Reinforcement Unlearning (RUL) framework. We introduce a principled reward decomposition framework that decouples verifiability from sparsity, and propose two new reward functions: an exponential reward that provides graded penalties based on the count of forbidden-concept occurrences, and a PageRank inspired reward that weights penalties by semantic importance. We conduct experiments on the Real World Knowledge Unlearning (RWKU) benchmark, demonstrating that both rewards consistently outperform the binary setting, while reaching similar forgetting performance up to $3\times$ faster and preserving general model utility. Our results show that reward design is a key driver of unlearning efficiency offering a practical path toward scalable and efficient machine unlearning.

cs.LG↗

arXiv2026

The Invariant Measure of Multiscale Markov Chains via Fast Arborescence Factorization

We consider a family of continuous-time Markov chains with finite strongly connected transition graph and rates $\left(r_N\right)_{N>0}$ depending on a parameter $N$, so that, when $N$ is large, transitions may happen on different time scales. Under suitable general assumptions on the asymptotic behavior of the rates, we give a recursive characterization of the limiting invariant measure. The recursion is encoded in a forest structure equivalent to the one recently developed in the analysis of dynamical aspects of metastability \cite{BL,LX}. Our proof is based on a combinatorial representation of the invariant measure, given by the Markov chain tree theorem. Basic steps are the reduction of the chain by a trace process, the introduction of an effective dynamics, and a careful analysis of the set of relevant arborescences in the expansion. In particular we use a factorization of fast arborescences. As a byproduct we obtain properties of the arborescences of generalized star-delta reductions of weighted digraphs.

math.PR↗

arXiv2026

Slot decomposition of continuous Box-Ball Systems

We study a piecewise constant function $\eta:\mathbb R\to\{-1,1\}$ with a finite number of discontinuities in any interval. We assume that the associated walk $\xi:\mathbb R\to\mathbb R$ satisfying $\xi'(x)=\eta(x)$, pinned by $\xi(0)=0$, has finite length excursions over past minima. This is the continuous generalization of an initial ball configuration in the discrete Box Ball System introduced by Takahashi and Satsuma, where solitons of integer sizes $k\ge1$ are identified. We extend the slot decomposition developed by Ferrari, Nguyen, Rolla and Wang in the discrete setting to the continuous case. Each soliton of $\xi$ is represented by a point in two dimensional space, one coordinate for position and the other for the soliton height, mapping $\xi$ to a point configuration. We consider a distribution on walks given by a product measure on the decomposition of the path into excursions over past minima. Excursions are distributed as products of their solitons weights, which are determined by the soliton heights. We show that when the weight function is in $L^1$ the slot decomposition of $\xi$ is a Poisson process. This extends to the continuous case an approach of Ferrari and Gabrielli. As an example, we compute the intensity measure of the Poisson process associated to the asymmetric telegraph process introduced by Kac. In a forthcoming paper we discuss the dynamic properties.

math.PR↗

arXiv2026

A Multi-Agent Framework for Interpreting Multivariate Physiological Time Series

Continuous physiological monitoring is central to emergency care, yet deploying trustworthy AI is challenging. While LLMs can translate complex physiological signals into clinical narratives, it is unclear how agentic systems perform relative to zero-shot inference. To address these questions, we present Vivaldi, a role-structured multi-agent system that explains multivariate physiological time series. Due to regulatory constraints that preclude live deployment, we instantiate Vivaldi in a controlled, clinical pilot to a small, highly qualified cohort of emergency medicine experts, whose evaluations reveal a context-dependent picture that contrasts with prevailing assumptions that agentic reasoning uniformly improves performance. Our experiments show that agentic pipelines substantially benefit non-thinking and medically fine-tuned models, improving expert-rated explanation justification and relevance by +6.9 and +9.7 points, respectively. Contrarily, for thinking models, agentic orchestration often degrades explanation quality, including a 14-point drop in relevance, while improving diagnostic precision (ESI F1 +3.6). We also find that explicit tool-based computation is decisive for codifiable clinical metrics, whereas subjective targets, such as pain scores and length of stay, show limited or inconsistent changes. Expert evaluation further indicates that gains in clinical utility depend on visualization conventions, with medically specialized models achieving the most favorable trade-offs between utility and clarity. Together, these findings show that the value of agentic AI lies in the selective externalization of computation and structure rather than in maximal reasoning complexity, and highlight concrete design trade-offs and learned lessons, broadly applicable to explainable AI in safety-critical healthcare settings.

cs.LG↗

arXiv2026

Large deviations and the matrix product ansatz

We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and columns labeled by a finite or countable set $B$. We prove for such kind of measures large deviations principles for several empirical measures. Our approach is based on a simultaneous combination of an enlargement of the state space to sequences on $A\times B$ and a spectral conjugation that produces a stochastic matrix, as discussed in \cite{GI1}. As a result we describe the measures as hidden Markov measures and can deduce the large deviations results by contraction from the corresponding ones for the enlarged Markov chain. The measure on the enlarged state space is a Markov bridge. The invariant measures of several non equilibrium models of interacting particle systems can be represented by the so called {\it Matrix Product Ansatz} that corresponds to measures of the type that we consider and with matrices labeled by $B$ that is typically countable infinite. The large deviations behavior is different in the cases with $B$ finite or countable. In the finite case we give a variational formula for both the algebraic and the spatial empirical measures, that can be solved in special cases. For the infinite case, we illustrate the method through an example that is the invariant measure of the boundary driven TASEP model in a special regime. We recover in this way the celebrated results in \cite{Der4,Derr7}, and in particular we obtain a variational representation of the rate function similar to that in \cite{Bryc}. Our approach is general and can in principle be applied to any measure represented by the matrix product ansatz with matrices having positive entries.

math.PR↗

arXiv2025

Inverse Language Modeling towards Robust and Grounded LLMs

The current landscape of defensive mechanisms for LLMs is fragmented and underdeveloped, unlike prior work on classifiers. To further promote adversarial robustness in LLMs, we propose Inverse Language Modeling (ILM), a unified framework that simultaneously 1) improves the robustness of LLMs to input perturbations, and, at the same time, 2) enables native grounding by inverting model outputs to identify potentially toxic or unsafe input triggers. ILM transforms LLMs from static generators into analyzable and robust systems, potentially helping RED teaming. ILM can lay the foundation for next-generation LLMs that are not only robust and grounded but also fundamentally more controllable and trustworthy. The code is publicly available at github.com/davegabe/pag-llm.

cs.CL↗

arXiv2025

Mixtures, Markov bridges and the matrix product ansatz

We give a probabilistic characterization of the set of measures that can be represented by the matrix product ansatz. By suitably enlarging the state space, we show that a probability measure can be described in terms of non negative matrices by the {\it Matrix Product Ansatz}, if and only if it can be written as a mixture of inhomogeneous product measures where the mixing law is a Markov bridge. We give a constructive procedure to identify such probabilistic features. We illustrate the result by examples and show that existing probabilistic representations of the invariant measures of non equilibrium interacting particle systems can be obtained from the matrix product ansatz by this general procedure.

math.PR↗

arXiv2025

On the equivalence and optimality of transformations of diffusive systems

In this paper we introduce, inspired by Clausius and developing the ideas of \cite{pre}, the concept of equivalence of transformations in non equilibrium theory of diffusive systems within the framework of macroscopic fluctuation theory. Besides providing a new proof of a formula derived in \cite{mft,qc}, which is the basis of the equivalence, we show that equivalent quasistatic transformations can be distinguished in finite terms, by the renormalized work introduced in \cite{45,46,mft,qc}. This allows us to tackle the problem of determining the optimal quasistatic transformation among the equivalent ones.

cond-mat.stat-mech↗

arXiv2025

AI on the Pulse: Real-Time Health Anomaly Detection with Wearable and Ambient Intelligence

We introduce AI on the Pulse, a real-world-ready anomaly detection system that continuously monitors patients using a fusion of wearable sensors, ambient intelligence, and advanced AI models. Powered by UniTS, a state-of-the-art (SoTA) universal time-series model, our framework autonomously learns each patient's unique physiological and behavioral patterns, detecting subtle deviations that signal potential health risks. Unlike classification methods that require impractical, continuous labeling in real-world scenarios, our approach uses anomaly detection to provide real-time, personalized alerts for reactive home-care interventions. Our approach outperforms 12 SoTA anomaly detection methods, demonstrating robustness across both high-fidelity medical devices (ECG) and consumer wearables, with a ~ 22% improvement in F1 score. However, the true impact of AI on the Pulse lies in @HOME, where it has been successfully deployed for continuous, real-world patient monitoring. By operating with non-invasive, lightweight devices like smartwatches, our system proves that high-quality health monitoring is possible without clinical-grade equipment. Beyond detection, we enhance interpretability by integrating LLMs, translating anomaly scores into clinically meaningful insights for healthcare professionals.

cs.LG↗

arXiv2025

Freidlin-Wentzell solutions of discrete Hamilton Jacobi equations

We consider a sequence of finite irreducible Markov chains with exponentially small transition rates: the transition graph is a fixed, finite, strongly connected directed graph; the transition rates decay exponentially on a paramenter N with a given rate that varies from edge to edge. The stationary equation uniquely identifies the invariant measure for each N, but at exponential scale in the limit as N goes to infinity reduces to a discrete equation for the large deviation rate functional of the invariant measure, that in general has not an unique solution. In analogy with the continuous case of diffusions, we call such equation a discrete Hamilton-Jacobi equation. Likewise in the continuous case we introduce a notion of viscosity supersolutions and viscosity subsolutions and give a detailed geometric characterization of the solutions in terms of special faces of the polyedron of Lipschitz functions on the transition graph. This parallels the weak KAM theory in a purely discrete setting. We identify also a special vanishing viscosity solution obtained in the limit from the combinatorial representation of the invariant measure given by the matrix tree theorem. The result gives a selection principle on the set of solutions to the discrete Hamilton-Jacobi equation obtained by the Freidlin and Wentzell minimal arborescences construction; this enlightens and parallels what happens in the continuous setting.

math.PR↗

arXiv2024

Current fluctuations for the boundary-driven zero-range process on graphs: microscopic versus macroscopic approach and a theory of non-reversible resistor-like networks

We compute the joint large deviation rate functional in the limit of large time for the current flowing through the edges of a finite graph on which a boundary-driven system of stochastic particles evolves with zero-range dynamics.This generalizes one-dimensional results previously obtained with different approaches; our alternative techniques illuminate various connections and complementary perspectives. In particular, we here use a variational approach to derive the rate functional by contraction from a level 2.5 large deviation rate functional. We perform an exact minimization and finally obtain the rate functional as a variational problem involving a superposition of cost functions for each edge. The contributions from different edges are not independent since they are related by the values of a potential function on the nodes of the graph. The rate functional on the graph is a microscopic version of the continuous rate functional predicted by the macroscopic fluctuation theory, and we indeed show a convergence in the scaling limit. If we split the graph into two connected regions by a cutset and are interested just in the current flowing through the cutset, we find that the result is the same as that of an effective system composed of only one effective edge (as happens at macroscopic level and is expected also for other models). The characteristics of this effective edge are related to the ``capacities'' of the graph and can be obtained by a reduction using elementary transformations as in electrical networks; specifically, we treat components in parallel, in series, and in $N$-star configurations (reduced to effective complete $N$-graphs). Our reduction procedure is directly related to the reduction to the trace process and, since the dynamics is in general not reversible, it is also closely connected to the theory of non-reversible electrical networks.

cond-mat.stat-mech↗

arXiv2024

Seamless Monitoring of Stress Levels Leveraging a Universal Model for Time Sequences

Monitoring the stress level in patients with neurodegenerative diseases can help manage symptoms, improve patient's quality of life, and provide insight into disease progression. In the literature, ECG, actigraphy, speech, voice, and facial analysis have proven effective at detecting patients' emotions. On the other hand, these tools are invasive and do not integrate smoothly into the patient's daily life. HRV has also been proven to effectively indicate stress conditions, especially in combination with other signals. However, when HRV is derived from less invasive devices than the ECG, like wristbands and smartwatches, the quality of measurements significantly degrades. This paper presents a methodology for stress detection from a wristband based on a universal model for time series, UniTS, which we finetuned for the task and equipped with explainability features. We cast the problem as anomaly detection rather than classification to favor model adaptation to individual patients and allow the clinician to maintain greater control over the system's predictions. We demonstrate that our proposed model considerably surpasses 12 top-performing methods on three benchmark datasets. Furthermore, unlike other state-of-the-art systems, UniTS enables seamless monitoring, as it shows comparable performance when using signals from invasive or lightweight devices.

cs.LG↗

arXiv2024

Hidden temperature in the KMP model

In the Kipnis Marchioro Presutti (KMP) model a positive energy $ζ_i$ is associated with each vertex $i$ of a finite graph with a boundary. When a Poisson clock rings at an edge $ij$ with energies $ζ_i,ζ_j$, those values are substituted by $U(ζ_i+ζ_j)$ and $(1-U)(ζ_i+ζ_j)$, respectively, where $U$ is a uniform random variable in $(0,1)$. A value $T_j\ge 0$ is fixed at each boundary vertex $j$. The dynamics is defined in such way that the resulting Markov process $ζ(t)$, satisfies that $ζ_j(t)$ is exponential with mean $T_j$, for each boundary vertex $j$, for all $t$. We show that the invariant measure is the distribution of a vector $ζ$ with coordinates $ζ_i=T_i X_i$, where $X_i$ are iid exponential$(1)$ random variables, the law of $T$ is the invariant measure for an opinion random averaging/gossip model with the same boundary conditions of $ζ$, and the vectors $X$ and $T$ are independent. The result confirms a conjecture based on the large deviations of the model. When the graph is one-dimensional, we bound the correlations of the invariant measure and perform the hydrostatic limit. We show that the empirical measure of a configuration chosen with the invariant measure converges to the linear interpolation of the boundary values.

math.PR↗

arXiv2024

Solvable stationary non equilibrium states

We consider the one dimensional boundary driven harmonic model and its continuous version, both introduced in \cite{FGK}. By combining duality and integrability the authors of \cite{FG} obtained the invariant measures in a combinatorial representation. Here we give an integral representation of the invariant measures which turns out to be a convex combination of inhomogeneous product of geometric distributions for the discrete model and a convex combination of inhomogeneous product of exponential distributions for the continuous one. The mean values of the geometric and of the exponential variables are distributed according to the order statistics of i.i.d. uniform random variables on a suitable interval fixed by the boundary sources. The result is obtained solving exactly the stationary condition written in terms of the joint generating function. The method has an interest in itself and can be generalized to study other models. We briefly discuss some applications.

math.PR↗

arXiv2023

On a class of solvable stationary non equilibrium states for mass exchange models

We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of reversible models for which the product invariant measure is known and the gradient condition is satisfied so that we can explicitly compute the transport coefficients associated to the diffusive hydrodynamic rescaling. Based on the Macroscopic Fluctuation Theory \cite{mft} we have that the large deviations rate functional for a stationary non equilibrium state can be computed solving a Hamilton-Jacobi equation depending only on the transport coefficients and the details of the boundary sources. Thus, we are able to identify a class of models having transport coefficients for which the Hamilton-Jacobi equation can indeed be solved. We give a complete characterization in the case of generalized zero range models and discuss several other cases. For the generalized zero range models we identify a class of discrete models that, modulo trivial extensions, coincides with the class discussed in \cite{FG} and a class of continuous dynamics that coincides with the class in \cite{FFG}. Along the discussion we obtain a complete characterization of reversible misanthrope processes solving the discrete equations in \cite{CC}.

cond-mat.stat-mech↗

arXiv2022

Large deviations for diffusions: Donsker-Varadhan meet Freidlin-Wentzell

We consider a diffusion process on $\mathbb R^n$ and prove a large deviation principle for the empirical process in the joint limit in which the time window diverges and the noise vanishes. The corresponding rate function is given by the expectation of the Freidlin-Wentzell functional per unit of time. As an application of this result, we obtain a variational representation of the rate function for the Gallavotti-Cohen observable in the small noise and large time limits.

math.PR↗

arXiv2021

Concurrent Donsker-Varadhan and hydrodynamical large deviations

We consider the weakly asymmetric exclusion process on the $d$-dimensional torus. We prove a large deviations principle for the time averaged empirical density and current in the joint limit in which both the time interval and the number of particles diverge. This result is obtained both by analyzing the variational convergence, as the number of particles diverges, of the Donsker-Varadhan functional for the empirical process and by considering the large time behavior of the hydrodynamical rate function. The large deviations asymptotic of the time averaged current is then deduced by contraction principle. The structure of the minimizers of this variational problem corresponds to the possible occurrence of dynamical phase transitions.

math.PR↗

arXiv2021

Hydrodynamic limit of an exclusion process with vorticity

We construct a non reversible exclusion process with Bernoulli product invariant measure and having, in the diffusive hydrodynamic scaling, a non symmetric diffusion matrix, that can be explicitly computed. The antisymmetric part does not affect the evolution of the density but it is relevant for the evolution of the current. Switching on a weak external field we obtain a symmetric mobility matrix that is related just to the symmetric part of the diffusion matrix by an Einstein relation. We argue that this fact is typical within a class of generalized gradient models. We consider for simplicity the model in dimension $d=2$, but a similar behavior can be also obtained in higher dimensions.

math.PR↗