Stéphane Bressan

Fangyi Zhu, Lok You Tan, See-Kiong Ng et al.

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.

Fangyi Zhu, See-Kiong Ng, Stéphane Bressan

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.

Saumya Shah, Zi-Yu Khoo, Abel Yang et al.

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.

Félix Chavelli, Zi-Yu Khoo, Dawen Wu et al.

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.

Pratik Karmakar, Mikaël Monet, Pierre Senellart et al.

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.

Zi-Yu Khoo, Delong Zhang, Stéphane Bressan

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.

Zi-Yu Khoo, Abel Yang, Jonathan Sze Choong Low et al.

Can a machine or algorithm discover or learn Kepler's first law from astronomical sightings alone? We emulate Johannes Kepler's discovery of the equation of the orbit of Mars with the Rudolphine tables using AI Feynman, a physics-inspired tool for symbolic regression.

Zi-Yu Khoo, Gokul Rajiv, Abel Yang et al.

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.

Zi-Yu Khoo, Jonathan Sze Choong Low, Stéphane Bressan

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.

Zi-Yu Khoo, Dawen Wu, Jonathan Sze Choong Low et al.

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.

Debabrota Basu, Pierre Senellart, Stéphane Bressan

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.