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Stéphane Bressan

Publications and source records attributed to Stéphane Bressan.

17 recordsLinked to original sources
arXiv2025

Rediscovering the Lunar Equation of the Centre with AI Feynman via Embedded Physical Biases

This work explores using the physics-inspired AI Feynman symbolic regression algorithm to automatically rediscover a fundamental equation in astronomy -- the Equation of the Centre. Through the introduction of observational and inductive biases corresponding to the physical nature of the system through data preprocessing and search space restriction, AI Feynman was successful in recovering the first-order analytical form of this equation from lunar ephemerides data. However, this manual approach highlights a key limitation in its reliance on expert-driven coordinate system selection. We therefore propose an automated preprocessing extension to find the canonical coordinate system. Results demonstrate that targeted domain knowledge embedding enables symbolic regression to rediscover physical laws, but also highlight further challenges in constraining symbolic regression to derive physics equations when leveraging domain knowledge through tailored biases.

cs.LG↗
arXiv2024

Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems

The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state variables or result in overparameterized state spaces. Boyuan Chen and his co-authors proposed a neural network model that estimates the degrees of freedom and attempts to discover the state variables of a dynamical system. Despite its innovative approach, this baseline model lacks a connection to the physical principles governing the systems it analyzes, leading to unreliable state variables. This research proposes a method that leverages the physical characteristics of second-order Hamiltonian systems to constrain the baseline model. The proposed model outperforms the baseline model in identifying a minimal set of non-redundant and interpretable state variables.

cs.AI↗
arXiv2024

The Steepest Slope toward a Quantum Few-body Solution: Gradient Variational Methods for the Quantum Few-body Problem

Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation methods to tackle quantum few-body problems. In particular, variational methods have been proposed to ease numerical calculations and obtain precise solutions. One such method is the Stochastic Variational Method, which employs a stochastic search to determine the number and parameters of correlated Gaussian basis functions used to construct an ansatz of the wave function. Stochastic methods, however, face numerical and optimization challenges as the number of particles increases. We introduce a family of gradient variational methods that replace stochastic search with gradient optimization. We comparatively and empirically evaluate the performance of the baseline Stochastic Variational Method, several instances of the gradient variational method family, and some hybrid methods for selected few-body problems. We show that gradient and hybrid methods can be more efficient and effective than the Stochastic Variational Method. We discuss the role of singularities, oscillations, and gradient optimization strategies in the performance of the respective methods.

physics.comp-ph↗
arXiv2024

Separable Hamiltonian Neural Networks

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive separability of the Hamiltonian reduces the regression complexity and improves regression performance. We propose separable HNNs that embed additive separability within HNNs using observational, learning, and inductive biases. We show that the proposed models are more effective than the HNN at regressing the Hamiltonian and the vector field. Consequently, the proposed models predict the dynamics and conserve the total energy of the Hamiltonian system more accurately.

cs.LG↗
arXiv2024

Expected Shapley-Like Scores of Boolean Functions: Complexity and Applications to Probabilistic Databases

Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf values. In this work we adapt these Shapley-like scores to probabilistic settings, the objective being to compute their expected value. We show that the computations of expected Shapley values and of the expected values of Boolean functions are interreducible in polynomial time, thus obtaining the same tractability landscape. We investigate the specific tractable case where Boolean functions are represented as deterministic decomposable circuits, designing a polynomial-time algorithm for this setting. We present applications to probabilistic databases through database provenance, and an effective implementation of this algorithm within the ProvSQL system, which experimentally validates its feasibility over a standard benchmark.

cs.DB↗
arXiv2024

Supervised Training of Neural-Network Quantum States for the Next Nearest Neighbor Ising model

Different neural network architectures can be unsupervisedly or supervisedly trained to represent quantum states. We explore and compare different strategies for the supervised training of feed forward neural network quantum states. We empirically and comparatively evaluate the performance of feed forward neural network quantum states in different phases of matter for variants of the architecture, for different hyper-parameters, and for two different loss functions, to which we refer as \emph{mean-squared error} and \emph{overlap}, respectively. We consider the next-nearest neighbor Ising model for the diversity of its phases and focus on its paramagnetic, ferromagnetic, and pair-antiferromagnetic phases. We observe that the overlap loss function allows better training of the model across all phases, provided a rescaling of the neural network.

cond-mat.stat-mech↗
arXiv2023

A Comparative Evaluation of Additive Separability Tests for Physics-Informed Machine Learning

Many functions characterising physical systems are additively separable. This is the case, for instance, of mechanical Hamiltonian functions in physics, population growth equations in biology, and consumer preference and utility functions in economics. We consider the scenario in which a surrogate of a function is to be tested for additive separability. The detection that the surrogate is additively separable can be leveraged to improve further learning. Hence, it is beneficial to have the ability to test for such separability in surrogates. The mathematical approach is to test if the mixed partial derivative of the surrogate is zero; or empirically, lower than a threshold. We present and comparatively and empirically evaluate the eight methods to compute the mixed partial derivative of a surrogate function.

cs.LG↗
arXiv2023

Celestial Machine Learning: Discovering the Planarity, Heliocentricity, and Orbital Equation of Mars with AI Feynman

Can a machine or algorithm discover or learn the elliptical orbit of Mars from astronomical sightings alone? Johannes Kepler required two paradigm shifts to discover his First Law regarding the elliptical orbit of Mars. Firstly, a shift from the geocentric to the heliocentric frame of reference. Secondly, the reduction of the orbit of Mars from a three- to a two-dimensional space. We extend AI Feynman, a physics-inspired tool for symbolic regression, to discover the heliocentricity and planarity of Mars' orbit and emulate his discovery of Kepler's first law.

astro-ph.EP↗
arXiv2023

What's Next? Predicting Hamiltonian Dynamics from Discrete Observations of a Vector Field

We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively evaluate the methods and observe that information that the system is Hamiltonian can be effectively informed, and that different methods strike different trade-offs between efficiency and effectiveness for different dynamical systems.

cs.LG↗
arXiv2023

Extending JumpProcess.jl for fast point process simulation with time-varying intensities

Point processes model the occurrence of a countable number of random points over some support. They can model diverse phenomena, such as chemical reactions, stock market transactions and social interactions. We show that JumpProcesses.jl is a fast, general-purpose library for simulating point processes. JumpProcesses.jl was first developed for simulating jump processes via stochastic simulation algorithms (SSAs) (including Doob's method, Gillespie's methods, and Kinetic Monte Carlo methods). Historically, jump processes have been developed in the context of dynamical systems to describe dynamics with discrete jumps. In contrast, the development of point processes has been more focused on describing the occurrence of random events. In this paper, we bridge the gap between the treatment of point and jump process simulation. The algorithms previously included in JumpProcesses.jl can be mapped to three general methods developed in statistics for simulating evolutionary point processes. Our comparative exercise revealed that the library initially lacked an efficient algorithm for simulating processes with variable intensity rates. We, therefore, extended JumpProcesses.jl with a new simulation algorithm, Coevolve, that enables the rapid simulation of processes with locally-bounded variable intensity rates. It is now possible to efficiently simulate any point process on the real line with a non-negative, left-continuous, history-adapted and locally bounded intensity rate coupled or not with differential equations. This extension significantly improves the computational performance of JumpProcesses.jl when simulating such processes, enabling it to become one of the few readily available, fast, general-purpose libraries for simulating evolutionary point processes.

stat.CO↗
arXiv2023

Confidential Truth Finding with Multi-Party Computation (Extended Version)

Federated knowledge discovery and data mining are challenged to assess the trustworthiness of data originating from autonomous sources while protecting confidentiality and privacy. Truth-finding algorithms help corroborate data from disagreeing sources. For each query it receives, a truth-finding algorithm predicts a truth value of the answer, possibly updating the trustworthiness factor of each source. Few works, however, address the issues of confidentiality and privacy. We devise and present a secure secret-sharing-based multi-party computation protocol for pseudo-equality tests that are used in truth-finding algorithms to compute additions depending on a condition. The protocol guarantees confidentiality of the data and privacy of the sources. We also present variants of truth-finding algorithms that would make the computation faster when executed using secure multi-party computation. We empirically evaluate the performance of the proposed protocol on two state-of-the-art truth-finding algorithms, Cosine, and 3-Estimates, and compare them with that of the baseline plain algorithms. The results confirm that the secret-sharing-based secure multi-party algorithms are as accurate as the corresponding baselines but for proposed numerical approximations that significantly reduce the efficiency loss incurred.

cs.CR↗
arXiv2023

COOL, a Context Outlooker, and its Application to Question Answering and other Natural Language Processing Tasks

Vision outlooker improves the performance of vision transformers, which implements a self-attention mechanism by adding an outlook attention, a form of local attention. In natural language processing, as has been the case in computer vision and other domains, transformer-based models constitute the state-of-the-art for most processing tasks. In this domain, too, many authors have argued and demonstrated the importance of local context. We present an outlook attention mechanism, COOL, for natural language processing. COOL, added on top of the self-attention layers of a transformer-based model, encodes local syntactic context considering word proximity and more pair-wise constraints than dynamic convolution used by existing approaches. A comparative empirical performance evaluation of an implementation of COOL with different transformer-based models confirms the opportunity for improvement over a baseline using the original models alone for various natural language processing tasks, including question answering. The proposed approach achieves competitive performance with existing state-of-the-art methods on some tasks.

cs.CL↗
arXiv2022

Syntax-informed Question Answering with Heterogeneous Graph Transformer

Large neural language models are steadily contributing state-of-the-art performance to question answering and other natural language and information processing tasks. These models are expensive to train. We propose to evaluate whether such pre-trained models can benefit from the addition of explicit linguistics information without requiring retraining from scratch. We present a linguistics-informed question answering approach that extends and fine-tunes a pre-trained transformer-based neural language model with symbolic knowledge encoded with a heterogeneous graph transformer. We illustrate the approach by the addition of syntactic information in the form of dependency and constituency graphic structures connecting tokens and virtual vertices. A comparative empirical performance evaluation with BERT as its baseline and with Stanford Question Answering Dataset demonstrates the competitiveness of the proposed approach. We argue, in conclusion and in the light of further results of preliminary experiments, that the approach is extensible to further linguistics information including semantics and pragmatics.

cs.CL↗
arXiv2020

$ε$-net Induced Lazy Witness Complexes on Graphs

Computation of persistent homology of simplicial representations such as the Rips and the Cěch complexes do not efficiently scale to large point clouds. It is, therefore, meaningful to devise approximate representations and evaluate the trade-off between their efficiency and effectiveness. The lazy witness complex economically defines such a representation using only a few selected points, called landmarks. Topological data analysis traditionally considers a point cloud in a Euclidean space. In many situations, however, data is available in the form of a weighted graph. A graph along with the geodesic distance defines a metric space. This metric space of a graph is amenable to topological data analysis. We discuss the computation of persistent homologies on a weighted graph. We present a lazy witness complex approach leveraging the notion of $ε$-net that we adapt to weighted graphs and their geodesic distance to select landmarks. We show that the value of the $ε$ parameter of the $ε$-net provides control on the trade-off between choice and number of landmarks and the quality of the approximate simplicial representation. We present three algorithms for constructing an $ε$-net of a graph. We comparatively and empirically evaluate the efficiency and effectiveness of the choice of landmarks that they induce for the topological data analysis of different real-world graphs.

cs.CG↗
arXiv2019

BelMan: Bayesian Bandits on the Belief--Reward Manifold

We propose a generic, Bayesian, information geometric approach to the exploration--exploitation trade-off in multi-armed bandit problems. Our approach, BelMan, uniformly supports pure exploration, exploration--exploitation, and two-phase bandit problems. The knowledge on bandit arms and their reward distributions is summarised by the barycentre of the joint distributions of beliefs and rewards of the arms, the \emph{pseudobelief-reward}, within the beliefs-rewards manifold. BelMan alternates \emph{information projection} and \emph{reverse information projection}, i.e., projection of the pseudobelief-reward onto beliefs-rewards to choose the arm to play, and projection of the resulting beliefs-rewards onto the pseudobelief-reward. It introduces a mechanism that infuses an exploitative bias by means of a \emph{focal distribution}, i.e., a reward distribution that gradually concentrates on higher rewards. Comparative performance evaluation with state-of-the-art algorithms shows that BelMan is not only competitive but can also outperform other approaches in specific setups, for instance involving many arms and continuous rewards.

cs.LG↗
arXiv2019

Topological Data Analysis with $ε$-net Induced Lazy Witness Complex

Topological data analysis computes and analyses topological features of the point clouds by constructing and studying a simplicial representation of the underlying topological structure. The enthusiasm that followed the initial successes of topological data analysis was curbed by the computational cost of constructing such simplicial representations. The lazy witness complex is a computationally feasible approximation of the underlying topological structure of a point cloud. It is built in reference to a subset of points, called landmarks, rather than considering all the points as in the Čech and Vietoris-Rips complexes. The choice and the number of landmarks dictate the effectiveness and efficiency of the approximation. We adopt the notion of $ε$-cover to define $ε$-net. We prove that $ε$-net, as a choice of landmarks, is an $ε$-approximate representation of the point cloud and the induced lazy witness complex is a $3$-approximation of the induced Vietoris-Rips complex. Furthermore, we propose three algorithms to construct $ε$-net landmarks. We establish the relationship of these algorithms with the existing landmark selection algorithms. We empirically validate our theoretical claims. We empirically and comparatively evaluate the effectiveness, efficiency, and stability of the proposed algorithms on synthetic and real datasets.

cs.CG↗