arXiv subjects

Giulia Luise

Publications and source records attributed to Giulia Luise.

16 recordsLinked to original sources

arXiv2025

Accurate Chemistry Collection: Coupled cluster atomization energies for broad chemical space

Accurate thermochemical data with sub-chemical accuracy (within 1 kcal mol$^{-1}$ of the empirical ground truth) are essential for advancing computational chemistry methods. However, existing datasets that reach this level of accuracy remain limited in size or scope. This hinders the development of data-driven methods with predictive accuracy across the broad chemical space of closed-shell, neutral molecules. Here we present Microsoft Research Accurate Chemistry Collection (MSR-ACC) and its first release, MSR-ACC/TAE25, comprising 73,040 total atomization energies at the CCSD(T)/CBS level obtained with the W1-F12 thermochemical protocol. The dataset is constructed to exhaustively cover the chemical space of closed-shell, charge-neutral, covalently bound equilibrium molecular structures containing up to 5 non-hydrogen atoms drawn from elements up to argon and lacking significant multireference character. The dataset and its canonical train and validation splits are openly available on Zenodo in the QCSchema format under the CDLA Permissive 2.0 license. This first release of MSR-ACC enables data-driven approaches for developing predictive computational chemistry methods with unprecedented accuracy and scope.

physics.chem-ph↗

arXiv2025

Accurate and scalable exchange-correlation with deep learning

Density Functional Theory (DFT) underpins much of modern computational chemistry and materials science. Yet, the reliability of DFT-derived predictions of experimentally measurable properties remains fundamentally limited by the need to approximate the unknown exchange-correlation (XC) functional. The traditional paradigm for improving accuracy has relied on increasingly elaborate hand-crafted functional forms. This approach has led to a longstanding trade-off between computational efficiency and accuracy, which remains insufficient for reliable predictive modelling of laboratory experiments. Here we introduce Skala, a deep learning-based XC functional that surpasses state-of-the-art hybrid functionals in accuracy across the main-group chemistry benchmark set GMTKN55 with an error of 2.8 kcal/mol, while retaining the lower computational cost characteristic of semi-local DFT. This demonstrated departure from the historical trade-off between accuracy and efficiency is enabled by learning non-local representations of electronic structure directly from data, bypassing the need for increasingly costly hand-engineered features. Leveraging an unprecedented volume of high-accuracy reference data from wavefunction-based methods, we establish that modern deep learning enables systematically improvable neural exchange-correlation models as training datasets expand, positioning first-principles simulations to become progressively more predictive.

physics.chem-ph↗

arXiv2023

Bag of Policies for Distributional Deep Exploration

Efficient exploration in complex environments remains a major challenge for reinforcement learning (RL). Compared to previous Thompson sampling-inspired mechanisms that enable temporally extended exploration, i.e., deep exploration, we focus on deep exploration in distributional RL. We develop here a general purpose approach, Bag of Policies (BoP), that can be built on top of any return distribution estimator by maintaining a population of its copies. BoP consists of an ensemble of multiple heads that are updated independently. During training, each episode is controlled by only one of the heads and the collected state-action pairs are used to update all heads off-policy, leading to distinct learning signals for each head which diversify learning and behaviour. To test whether optimistic ensemble method can improve on distributional RL as did on scalar RL, by e.g. Bootstrapped DQN, we implement the BoP approach with a population of distributional actor-critics using Bayesian Distributional Policy Gradients (BDPG). The population thus approximates a posterior distribution of return distributions along with a posterior distribution of policies. Another benefit of building upon BDPG is that it allows to analyze global posterior uncertainty along with local curiosity bonus simultaneously for exploration. As BDPG is already an optimistic method, this pairing helps to investigate if optimism is accumulatable in distributional RL. Overall BoP results in greater robustness and speed during learning as demonstrated by our experimental results on ALE Atari games.

cs.LG↗

arXiv2023

On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology

Message Passing Neural Networks (MPNNs) are instances of Graph Neural Networks that leverage the graph to send messages over the edges. This inductive bias leads to a phenomenon known as over-squashing, where a node feature is insensitive to information contained at distant nodes. Despite recent methods introduced to mitigate this issue, an understanding of the causes for over-squashing and of possible solutions are lacking. In this theoretical work, we prove that: (i) Neural network width can mitigate over-squashing, but at the cost of making the whole network more sensitive; (ii) Conversely, depth cannot help mitigate over-squashing: increasing the number of layers leads to over-squashing being dominated by vanishing gradients; (iii) The graph topology plays the greatest role, since over-squashing occurs between nodes at high commute (access) time. Our analysis provides a unified framework to study different recent methods introduced to cope with over-squashing and serves as a justification for a class of methods that fall under graph rewiring.

cs.LG↗

arXiv2022

Schedule-Robust Online Continual Learning

A continual learning (CL) algorithm learns from a non-stationary data stream. The non-stationarity is modeled by some schedule that determines how data is presented over time. Most current methods make strong assumptions on the schedule and have unpredictable performance when such requirements are not met. A key challenge in CL is thus to design methods robust against arbitrary schedules over the same underlying data, since in real-world scenarios schedules are often unknown and dynamic. In this work, we introduce the notion of schedule-robustness for CL and a novel approach satisfying this desirable property in the challenging online class-incremental setting. We also present a new perspective on CL, as the process of learning a schedule-robust predictor, followed by adapting the predictor using only replay data. Empirically, we demonstrate that our approach outperforms existing methods on CL benchmarks for image classification by a large margin.

cs.LG↗

arXiv2022

Meta Optimal Transport

We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and information present from past problems to rapidly predict and solve new problems. Otherwise, standard methods ignore the knowledge of the past solutions and suboptimally re-solve each problem from scratch. We instantiate Meta OT models in discrete and continuous settings between grayscale images, spherical data, classification labels, and color palettes and use them to improve the computational time of standard OT solvers. Our source code is available at http://github.com/facebookresearch/meta-ot

cs.LG↗

arXiv2022

Heterogeneous manifolds for curvature-aware graph embedding

Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space matches that of the graph. Euclidean spaces are often a poor choice for many types of real-world graphs, where hierarchical structure and a power-law degree distribution are linked to negative curvature. In this regard, it has recently been shown that hyperbolic spaces and more general manifolds, such as products of constant-curvature spaces and matrix manifolds, are advantageous to approximately match nodes pairwise distances. However, all these classes of manifolds are homogeneous, implying that the curvature distribution is the same at each point, making them unsuited to match the local curvature (and related structural properties) of the graph. In this paper, we study graph embeddings in a broader class of heterogeneous rotationally-symmetric manifolds. By adding a single extra radial dimension to any given existing homogeneous model, we can both account for heterogeneous curvature distributions on graphs and pairwise distances. We evaluate our approach on reconstruction tasks on synthetic and real datasets and show its potential in better preservation of high-order structures and heterogeneous random graphs generation.

stat.ML↗

arXiv2021

Enabling risk-aware Reinforcement Learning for medical interventions through uncertainty decomposition

Reinforcement Learning (RL) is emerging as tool for tackling complex control and decision-making problems. However, in high-risk environments such as healthcare, manufacturing, automotive or aerospace, it is often challenging to bridge the gap between an apparently optimal policy learnt by an agent and its real-world deployment, due to the uncertainties and risk associated with it. Broadly speaking RL agents face two kinds of uncertainty, 1. aleatoric uncertainty, which reflects randomness or noise in the dynamics of the world, and 2. epistemic uncertainty, which reflects the bounded knowledge of the agent due to model limitations and finite amount of information/data the agent has acquired about the world. These two types of uncertainty carry fundamentally different implications for the evaluation of performance and the level of risk or trust. Yet these aleatoric and epistemic uncertainties are generally confounded as standard and even distributional RL is agnostic to this difference. Here we propose how a distributional approach (UA-DQN) can be recast to render uncertainties by decomposing the net effects of each uncertainty. We demonstrate the operation of this method in grid world examples to build intuition and then show a proof of concept application for an RL agent operating as a clinical decision support system in critical care

cs.AI↗

arXiv2021

Aligning Time Series on Incomparable Spaces

Dynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces. In this work, we consider a setting in which time series live on different spaces without a sensible ground metric, causing DTW to become ill-defined. To alleviate this, we propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces that avoids the comparability requirement by instead considering intra-relational geometry. We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces. We further propose a smoothed version of GDTW as a differentiable loss and assess its properties in a variety of settings, including barycentric averaging, generative modeling and imitation learning.

cs.LG↗

arXiv2021

The Wasserstein Proximal Gradient Algorithm

Wasserstein gradient flows are continuous time dynamics that define curves of steepest descent to minimize an objective function over the space of probability measures (i.e., the Wasserstein space). This objective is typically a divergence w.r.t. a fixed target distribution. In recent years, these continuous time dynamics have been used to study the convergence of machine learning algorithms aiming at approximating a probability distribution. However, the discrete-time behavior of these algorithms might differ from the continuous time dynamics. Besides, although discretized gradient flows have been proposed in the literature, little is known about their minimization power. In this work, we propose a Forward Backward (FB) discretization scheme that can tackle the case where the objective function is the sum of a smooth and a nonsmooth geodesically convex terms. Using techniques from convex optimization and optimal transport, we analyze the FB scheme as a minimization algorithm on the Wasserstein space. More precisely, we show under mild assumptions that the FB scheme has convergence guarantees similar to the proximal gradient algorithm in Euclidean spaces.

math.OC↗

arXiv2021

A Non-Asymptotic Analysis for Stein Variational Gradient Descent

We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises a set of particles to approximate a target probability distribution $π\propto e^{-V}$ on $\mathbb{R}^d$. In the population limit, SVGD performs gradient descent in the space of probability distributions on the KL divergence with respect to $π$, where the gradient is smoothed through a kernel integral operator. In this paper, we provide a novel finite time analysis for the SVGD algorithm. We provide a descent lemma establishing that the algorithm decreases the objective at each iteration, and rates of convergence for the average Stein Fisher divergence (also referred to as Kernel Stein Discrepancy). We also provide a convergence result of the finite particle system corresponding to the practical implementation of SVGD to its population version.

stat.ML↗

arXiv2020

Generalization Properties of Optimal Transport GANs with Latent Distribution Learning

The Generative Adversarial Networks (GAN) framework is a well-established paradigm for probability matching and realistic sample generation. While recent attention has been devoted to studying the theoretical properties of such models, a full theoretical understanding of the main building blocks is still missing. Focusing on generative models with Optimal Transport metrics as discriminators, in this work we study how the interplay between the latent distribution and the complexity of the pushforward map (generator) affects performance, from both statistical and modelling perspectives. Motivated by our analysis, we advocate learning the latent distribution as well as the pushforward map within the GAN paradigm. We prove that this can lead to significant advantages in terms of sample complexity.

stat.ML↗

arXiv2019

Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm

We present a novel algorithm to estimate the barycenter of arbitrary probability distributions with respect to the Sinkhorn divergence. Based on a Frank-Wolfe optimization strategy, our approach proceeds by populating the support of the barycenter incrementally, without requiring any pre-allocation. We consider discrete as well as continuous distributions, proving convergence rates of the proposed algorithm in both settings. Key elements of our analysis are a new result showing that the Sinkhorn divergence on compact domains has Lipschitz continuous gradient with respect to the Total Variation and a characterization of the sample complexity of Sinkhorn potentials. Experiments validate the effectiveness of our method in practice.

stat.ML↗

arXiv2019

Contraction and regularizing properties of heat flows in metric measure spaces

We illustrate some novel contraction and regularizing properties of the Heat flow in metric-measure spaces that emphasize an interplay between Hellinger-Kakutani, Kantorovich-Wasserstein and Hellinger-Kantorvich distances. Contraction properties of Hellinger-Kakutani distances and general Csiszár divergences hold in arbitrary metric-measure spaces and do not require assumptions on the linearity of the flow. When weaker transport distances are involved, we will show that contraction and regularizing effects rely on the dual formulations of the distances and are strictly related to lower Ricci curvature bounds in the setting of $RCD(K,\infty)$ metric measure spaces.

math.AP↗

arXiv2019

Leveraging Low-Rank Relations Between Surrogate Tasks in Structured Prediction

We study the interplay between surrogate methods for structured prediction and techniques from multitask learning designed to leverage relationships between surrogate outputs. We propose an efficient algorithm based on trace norm regularization which, differently from previous methods, does not require explicit knowledge of the coding/decoding functions of the surrogate framework. As a result, our algorithm can be applied to the broad class of problems in which the surrogate space is large or even infinite dimensional. We study excess risk bounds for trace norm regularized structured prediction, implying the consistency and learning rates for our estimator. We also identify relevant regimes in which our approach can enjoy better generalization performance than previous methods. Numerical experiments on ranking problems indicate that enforcing low-rank relations among surrogate outputs may indeed provide a significant advantage in practice.

cs.LG↗

arXiv2018

Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance

Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version that is less accurate but easy to differentiate. In this work we characterize the differential properties of the original Sinkhorn distance, proving that it enjoys the same smoothness as its regularized version and we explicitly provide an efficient algorithm to compute its gradient. We show that this result benefits both theory and applications: on one hand, high order smoothness confers statistical guarantees to learning with Wasserstein approximations. On the other hand, the gradient formula allows us to efficiently solve learning and optimization problems in practice. Promising preliminary experiments complement our analysis.

stat.ML↗