arXiv subjects

Jean-Charles Delvenne

Publications and source records attributed to Jean-Charles Delvenne.

At least 19 recordsLinked to original sources

arXiv2026

Random Wavelet Features for Graph Kernel Machines

Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design node embeddings whose dot products capture meaningful notions of node similarity induced by the graph. Graph kernels offer a principled way to define such similarities, but their direct computation is often prohibitive for large networks. Inspired by random feature methods for kernel approximation in Euclidean spaces, we introduce randomized spectral node embeddings whose dot products estimate a low-rank approximation of any specific graph kernel. We provide theoretical and empirical results showing that our embeddings achieve more accurate kernel approximations than existing methods, particularly for spectrally localized kernels. These results demonstrate the effectiveness of randomized spectral constructions for scalable and principled graph representation learning.

cs.LG↗

arXiv2025

Thermodynamic Geometric Constraint on the Spectrum of Markov Rate Matrices

The spectrum of Markov generators encodes physical information beyond simple decay and oscillation, which reflects irreversibility and governs the structure of correlation functions. In this work, we prove an ellipse theorem that provides a universal thermodynamic geometric constraint on the spectrum of Markov rate matrices. The theorem states that all eigenvalues lie within a specific ellipse in the complex plane. In particular, the imaginary parts of the spectrum, which indicate oscillatory modes, are bounded by the maximum thermodynamic force associated with individual transitions. This spectral bound further constrains the initial short-time behavior of correlation functions between two arbitrary observables. Finally, we compare our result with a previously proposed conjecture, which remains an open problem and warrants further investigation.

cond-mat.stat-mech↗

arXiv2025

Analog and Symbolic Computation through the Koopman Framework

We develop a Koopman operator framework for studying the {computational properties} of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ``Koopman halting problem that is recursively enumerable in general. For symbolic systems, such as those defined on Cantor space, this operator formulation captures the reachability between clopen sets, while for equicontinuous systems we prove that the Koopman halting problem is decidable. Our framework demonstrates that absorbing (halting) states {in finite automata} correspond to Koopman eigenfunctions with eigenvalue one, while cycles in the transition graph impose algebraic constraints on spectral properties. These results provide a unifying perspective on computation in symbolic and analog systems, showing how computational universality is reflected in operator spectra, invariant subspaces, and algebraic structures. Beyond symbolic dynamics, this operator-theoretic lens opens pathways to analyze {computational power of} a broader class of dynamical systems, including polynomial and analog models, and suggests that computational hardness may admit dynamical signatures in terms of Koopman spectral structure.

math-ph↗

arXiv2025

Noise-dissipation relation for nonlinear electronic circuits

An extension of fluctuation-dissipation theorem is used to derive a "speed limit" theorem for nonlinear electronic devices. This speed limit provides a lower bound on the dissipation that is incurred when transferring a given amount of electric charge in a certain amount of time with a certain noise level (average variance of the current). This bound, which implies a high energy dissipation for fast, low-noise operations (such as switching a bit in a digital memory), brings together recent results of stochastic thermodynamics into a form that is usable for practical nonlinear electronic circuits, as we illustrate on a switching circuit made of an nMOS pass gate in a state-of-the-art industrial technology.

cond-mat.stat-mech↗

arXiv2025

Theoretical Barriers in Bellman-Based Reinforcement Learning

Reinforcement Learning algorithms designed for high-dimensional spaces often enforce the Bellman equation on a sampled subset of states, relying on generalization to propagate knowledge across the state space. In this paper, we identify and formalize a fundamental limitation of this common approach. Specifically, we construct counterexample problems with a simple structure that this approach fails to exploit. Our findings reveal that such algorithms can neglect critical information about the problems, leading to inefficiencies. Furthermore, we extend this negative result to another approach from the literature: Hindsight Experience Replay learning state-to-state reachability.

cs.LG↗

arXiv2024

Predicting State Transitions in Autonomous Nonlinear Bistable Systems with Hidden Stochasticity

Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these transitions are failures, usually simulated in a Monte-Carlo fashion at a high CPU-time price. Existing closed-form formulas, relying on near-stable-steady-state approximations of the nonlinear system dynamics to estimate the mean transition time, have turned out inaccurate. Our contribution is twofold. From a unidimensional stochastic model of overdamped autonomous systems, we propose an extended Eyring-Kramers analytical formula accounting for both nonlinear drift and state-dependent white noise variance, rigorously derived from Itô stochastic calculus. We also adapt it to practical system engineering situations where the intrinsic noise sources are hidden and can only be inferred from the fluctuations of observables measured in steady states. First numerical trials on an industrial electronic case study suggest that our approximate prediction formula achieve remarkable accuracy, outperforming previous non-Monte-Carlo approaches.

cond-mat.stat-mech↗

arXiv2024

Moments of Entropy Production in Dissipative Devices

We characterize the possible moments of entropy production for general overdamped Markovian systems. We find a general formulation of the problem, and derive a new necessary condition between the second and third moment. We determine all possible first, second and third moments of entropy production for a white noise process. As a consequence, we obtain a lower bound for the skewness of the current fluctuations in dissipative devices such as transistors, thereby demonstrating that the Gaussianity assumption widely used in electronic engineering is thermodynamically inconsistent.

cond-mat.stat-mech↗

arXiv2024

Ellipsoidal embeddings of graphs

Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis tools are based on the algebraic representation of graphs via matrices such as the graph Laplacian, or on associated graph embeddings. Such embeddings associate to each node a set of coordinates in a vector space, a representation which can then be employed for learning tasks such as the classification or alignment of the nodes of the graph. As the geometric picture provided by embedding methods enables the use of a multitude of methods developed for vector space data, embeddings have thus gained interest both from a theoretical as well as a practical perspective. Inspired by trace-optimization problems, often encountered in the analysis of graph-based data, here we present a method to derive ellipsoidal embeddings of the nodes of a graph, in which each node is assigned a set of coordinates on the surface of a hyperellipsoid. Our method may be seen as an alternative to popular spectral embedding techniques, to which it shares certain similarities we discuss. To illustrate the utility of the embedding we conduct a case study in which we analyse synthetic and real world networks with modular structure, and compare the results obtained with known methods in the literature.

cs.SI↗

arXiv2024

Variability-Aware Noise-Induced Dynamic Instability of Ultra-Low-Voltage SRAM Bitcells

Stability of ultra-low-voltage SRAM bitcells in retention mode is threatened by two types of uncertainty: process variability and intrinsic noise. While variability dominates the failure probability, noise-induced bit flips in weakened bitcells lead to dynamic instability. We study both effects jointly in a unified SPICE simulation framework. Starting from a synthetic representation of process variations introduced in a previous work, we identify the cases of poor noise immunity that require thorough noise analyses. Relying on a rigorous and systematic methodology, we simulate them in the time domain so as to emulate a true data retention operation. Short times to failure, unacceptable for a practical ultra-low-power memory system application, are recorded. The transient bit-flip mechanism is analysed and a dynamic failure criterion involving the unstable point is established. We conclude that, beyond static variability, the dynamic noise inflates defectiveness among SRAM bitcells. We also discuss the limits of existing analytical formulas from the literature, which rely on a linear near-equilibrium approximation of the SRAM dynamics to, inaccurately, predict the mean time to failure.

cs.AR↗

arXiv2024

Stochastic Nonlinear Dynamical Modelling of SRAM Bitcells in Retention Mode

SRAM bitcells in retention mode behave as autonomous stochastic nonlinear dynamical systems. From observation of variability-aware transient noise simulations, we provide an unidimensional model, fully characterizable by conventional deterministic SPICE simulations, insightfully explaining the mechanism of intrinsic noise-induced bit flips. The proposed model is exploited to, first, explain the reported inaccuracy of existing closed-form near-equilibrium formulas aimed at predicting the mean time to failure and, secondly, to propose a closer estimate attractive in terms of CPU time.

cs.AR↗

arXiv2023

Efficiency Separation between RL Methods: Model-Free, Model-Based and Goal-Conditioned

We prove a fundamental limitation on the efficiency of a wide class of Reinforcement Learning (RL) algorithms. This limitation applies to model-free RL methods as well as a broad range of model-based methods, such as planning with tree search. Under an abstract definition of this class, we provide a family of RL problems for which these methods suffer a lower bound exponential in the horizon for their interactions with the environment to find an optimal behavior. However, there exists a method, not tailored to this specific family of problems, which can efficiently solve the problems in the family. In contrast, our limitation does not apply to several types of methods proposed in the literature, for instance, goal-conditioned methods or other algorithms that construct an inverse dynamics model.

cs.LG↗

arXiv2023

The non-Landauer Bound for the Dissipation of Bit Writing Operation

We propose a novel bound on the mimimum dissipation required in any circumstances to transfer a certain amount of charge through any resistive device. We illustrate it on the task of writing a logical 1 (encoded as a prescribed voltage) into a capacitance, through various linear or nonlinear devices. We show that, even though the celebrated Landauer bound (which only applies to bit erasure) does not apply here, one can still formulate a "non- Landauer" lower bound on dissipation, that crucially depends on the time budget to perform the operation, as well as the average conductance of the driving device. We compare our bound with empirical results reported in the literature and realistic simulations of CMOS pass and transmission gates in decananometer technology. Our non-Landauer bound turns out to be a quantitative benchmark to assess the (non-)optimality of a writing operation.

cond-mat.stat-mech↗

arXiv2023

Bounding Variance and Skewness of Fluctuations in Nonlinear Mesoscopic Systems with Stochastic Thermodynamics

Fluctuations arising in nonlinear dissipative systems (diode, transistors, chemical reaction, etc.) subject to an external drive (voltage, chemical potential, etc.) are well known to elude any simple characterization such as the fluctuation-dissipation theorem (also called Johnson-Nyquist law, or Einstein's law in specific contexts). Using results from stochastic thermodynamics, we show that the variance of these fluctuations exceeds the variance predicted by a suitably extended version of Johnson-Nyquist's formula, by an amount that is controlled by the skewness (third moment) of the fluctuations. As a consequence, symmetric fluctuations necessarily obey the extended Johnson-Nyquist formula. This shows the physical inconsistency of Gaussian approximation for the noise arising in some nonlinear models, such as MOS transistors or chemical reactions. More generally, this suggests the need for a stochastic nonlinear systems theory that is compatible with the teachings of thermodynamics.

cond-mat.stat-mech↗

arXiv2022

PAC-learning gains of Turing machines over circuits and neural networks

A caveat to many applications of the current Deep Learning approach is the need for large-scale data. One improvement suggested by Kolmogorov Complexity results is to apply the minimum description length principle with computationally universal models. We study the potential gains in sample efficiency that this approach can bring in principle. We use polynomial-time Turing machines to represent computationally universal models and Boolean circuits to represent Artificial Neural Networks (ANNs) acting on finite-precision digits. Our analysis unravels direct links between our question and Computational Complexity results. We provide lower and upper bounds on the potential gains in sample efficiency between the MDL applied with Turing machines instead of ANNs. Our bounds depend on the bit-size of the input of the Boolean function to be learned. Furthermore, we highlight close relationships between classical open problems in Circuit Complexity and the tightness of these.

cs.LG↗

arXiv2022

A model-based approach to meta-Reinforcement Learning: Transformers and tree search

Meta-learning is a line of research that develops the ability to leverage past experiences to efficiently solve new learning problems. Meta-Reinforcement Learning (meta-RL) methods demonstrate a capability to learn behaviors that efficiently acquire and exploit information in several meta-RL problems. In this context, the Alchemy benchmark has been proposed by Wang et al. [2021]. Alchemy features a rich structured latent space that is challenging for state-of-the-art model-free RL methods. These methods fail to learn to properly explore then exploit. We develop a model-based algorithm. We train a model whose principal block is a Transformer Encoder to fit the symbolic Alchemy environment dynamics. Then we define an online planner with the learned model using a tree search method. This algorithm significantly outperforms previously applied model-free RL methods on the symbolic Alchemy problem. Our results reveal the relevance of model-based approaches with online planning to perform exploration and exploitation successfully in meta-RL. Moreover, we show the efficiency of the Transformer architecture to learn complex dynamics that arise from latent spaces present in meta-RL problems.

cs.LG↗

arXiv2022

The Thermo-Kinetic Relations

Thermo-Kinetic relations bound thermodynamic quantities such as entropy production with statistics of dynamical observables. We introduce a Thermo-Kinetic Relation to bound the entropy production or the non-adiabatic (Hatano-Sasa, excess) entropy production for overdamped Markov jump processes, possibly with time-varying rates and non stationary distributions. For stationary cases, this bound is akin to a Thermodynamic Uncertainty Relation, only involving absolute fluctuations rather than the mean square, thereby offering a better lower bound far from equilibrium. For non-stationary cases, this bound generalises Classical Speed Limits, where the kinetic term is not necessarily the activity (number of jumps) but any trajectory observable of interest. As a consequence, in the task of driving a system from a given probability distribution to another, we find a trade-off between non-adiabatic entropy production and housekeeping entropy production: the latter can be increased in order to decrease the former, although to a limited extent. We also find constraints specific to constant-rate Markov processes. We illustrate our Thermo-Kinetic Relations on simple examples from biophysics and computing devices.

cond-mat.stat-mech↗

arXiv2022

Flow stability for dynamic community detection

Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in such systems is to extract a simplified view of their time-dependent network of interactions. Community detection in temporal networks usually relies on aggregation over time windows or consider sequences of different stationary epochs. For dynamics-based methods, attempts to generalize static-network methodologies also face the fundamental difficulty that a stationary state of the dynamics does not always exist. Here, we derive a method based on a dynamical process evolving on the temporal network. Our method allows dynamics that do not reach a steady state and uncovers two sets of communities for a given time interval that accounts for the ordering of edges in forward and backward time. We show that our method provides a natural way to disentangle the different dynamical scales present in a system with synthetic and real-world examples.

physics.soc-ph↗

arXiv2021

Positive semi-definite embedding for dimensionality reduction and out-of-sample extensions

In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding coordinates are the eigenvectors of a positive semi-definite kernel obtained as the solution of an infinite dimensional analogue of a semi-definite program. This embedding is adaptive and non-linear. We discuss this problem both with weak and strong smoothness assumptions about the learned kernel. A main feature of our approach is the existence of an out-of-sample extension formula of the embedding coordinates in both cases. This extrapolation formula yields an extension of the kernel matrix to a data-dependent Mercer kernel function. Our empirical results indicate that this embedding method is more robust with respect to the influence of outliers, compared with a spectral embedding method.

cs.LG↗