Aldo Glielmo

Aldo Glielmo, Iuri Macocco, Diego Doimo et al.

DADApy is a python software package for analysing and characterising high-dimensional data manifolds. It provides methods for estimating the intrinsic dimension and the probability density, for performing density-based clustering and for comparing different distance metrics. We review the main functionalities of the package and exemplify its usage in toy cases and in a real-world application. DADApy is freely available under the open-source Apache 2.0 license.

Antonio Di Noia, Iuri Macocco, Aldo Glielmo et al. · eth-zurich

The Intrinsic Dimension (ID) is a key concept in unsupervised learning and feature selection, as it is a lower bound to the number of variables which are necessary to describe a system. However, in almost any real-world dataset the ID depends on the scale at which the data are analysed. Quite typically at a small scale, the ID is very large, as the data are affected by measurement errors. At large scale, the ID can also appear erroneously large, due to the curvature and the topology of the manifold containing the data. In this work, we introduce an automatic protocol to select the sweet spot, namely the correct range of scales in which the ID is meaningful and useful. This protocol is based on imposing that for distances smaller than the correct scale the density of the data is constant. In the presented framework, to estimate the density it is necessary to know the ID, therefore, this condition is imposed self-consistently. We illustrate the usefulness and robustness of this procedure to noise by benchmarks on artificial and real-world datasets.

Iuri Macocco, Aldo Glielmo, Jacopo Grilli et al.

Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods are designed for continuous spaces, and their use for discrete spaces can lead to errors and biases. In this letter we introduce an algorithm to infer the intrinsic dimension (ID) of datasets embedded in discrete spaces. We demonstrate its accuracy on benchmark datasets, and we apply it to analyze a metagenomic dataset for species fingerprinting, finding a surprisingly small ID, of order 2. This suggests that evolutive pressure acts on a low-dimensional manifold despite the high-dimensionality of sequences' space.

Aldo Glielmo, Marco Favorito, Debmallya Chanda et al.

Calibrating agent-based models (ABMs) in economics and finance typically involves a derivative-free search in a very large parameter space. In this work, we benchmark a number of search methods in the calibration of a well-known macroeconomic ABM on real data, and further assess the performance of "mixed strategies" made by combining different methods. We find that methods based on random-forest surrogates are particularly efficient, and that combining search methods generally increases performance since the biases of any single method are mitigated. Moving from these observations, we propose a reinforcement learning (RL) scheme to automatically select and combine search methods on-the-fly during a calibration run. The RL agent keeps exploiting a specific method only as long as this keeps performing well, but explores new strategies when the specific method reaches a performance plateau. The resulting RL search scheme outperforms any other method or method combination tested, and does not rely on any prior information or trial and error procedure.

Matteo Carli, Alex Rodriguez, Alessandro Laio et al.

We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences between neighbouring data points. Subsequently, such differences are integrated, weighted by their associated uncertainties, using a maximum-likelihood formulation. This procedure can be seen as an extension to a multidimensional setting of the thermodynamic integration, a technique developed in statistical physics. The method leverages the manifold hypothesis, estimating quantities within the intrinsic data manifold without defining an explicit coordinate map. It does not rely on any binning or space partitioning, but rather on the construction of a neighbourhood graph based on an adaptive bandwidth selection procedure. BMTI mitigates the limitations commonly associated with traditional nonparametric density estimators, effectively reconstructing smooth profiles even in high-dimensional embedding spaces. The method is tested on a variety of complex synthetic high-dimensional datasets, where it is shown to outperform traditional estimators, and is benchmarked on realistic datasets from the chemical physics literature.

Simone Brusatin, Tommaso Padoan, Andrea Coletta et al.

Agent-based models (ABMs) are simulation models used in economics to overcome some of the limitations of traditional frameworks based on general equilibrium assumptions. However, agents within an ABM follow predetermined 'bounded rational' behavioural rules which can be cumbersome to design and difficult to justify. Here we leverage multi-agent reinforcement learning (RL) to expand the capabilities of ABMs with the introduction of 'fully rational' agents that learn their policy by interacting with the environment and maximising a reward function. Specifically, we propose a 'Rational macro ABM' (R-MABM) framework by extending a paradigmatic macro ABM from the economic literature. We show that gradually substituting ABM firms in the model with RL agents, trained to maximise profits, allows for studying the impact of rationality on the economy. We find that RL agents spontaneously learn three distinct strategies for maximising profits, with the optimal strategy depending on the level of market competition and rationality. We also find that RL agents with independent policies, and without the ability to communicate with each other, spontaneously learn to segregate into different strategic groups, thus increasing market power and overall profits. Finally, we find that a higher number of rational (RL) agents in the economy always improves the macroeconomic environment as measured by total output. Depending on the specific rational policy, this can come at the cost of higher instability. Our R-MABM framework allows for stable multi-agent learning, is available in open source, and represents a principled and robust direction to extend economic simulators.

Tiziano Balaconi, Aldo Glielmo, Marco Taboga

We introduce GasRL, a simulator that couples a calibrated representation of the natural gas market with a model of storage-operator policies trained with deep reinforcement learning (RL). We use it to analyse how optimal stockpile management affects equilibrium prices and the dynamics of demand and supply. We test various RL algorithms and find that Soft Actor Critic (SAC) exhibits superior performance in the GasRL environment: multiple objectives of storage operators - including profitability, robust market clearing and price stabilisation - are successfully achieved. Moreover, the equilibrium price dynamics induced by SAC-derived optimal policies have characteristics, such as volatility and seasonality, that closely match those of real-world prices. Remarkably, this adherence to the historical distribution of prices is obtained without explicitly calibrating the model to price data. We show how the simulator can be used to assess the effects of EU-mandated minimum storage thresholds. We find that such thresholds have a positive effect on market resilience against unanticipated shifts in the distribution of supply shocks. For example, with unusually large shocks, market disruptions are averted more often if a threshold is in place.

Claudia Biancotti, Carolina Camassa, Andrea Coletta et al.

Advancements in large language models (LLMs) have renewed concerns about AI alignment - the consistency between human and AI goals and values. As various jurisdictions enact legislation on AI safety, the concept of alignment must be defined and measured across different domains. This paper proposes an experimental framework to assess whether LLMs adhere to ethical and legal standards in the relatively unexplored context of finance. We prompt twelve LLMs to impersonate the CEO of a financial institution and test their willingness to misuse customer assets to repay outstanding corporate debt. Beginning with a baseline configuration, we adjust preferences, incentives and constraints, analyzing the impact of each adjustment with logistic regression. Our findings reveal significant heterogeneity in the baseline propensity for unethical behavior of LLMs. Factors such as risk aversion, profit expectations, and regulatory environment consistently influence misalignment in ways predicted by economic theory, although the magnitude of these effects varies across LLMs. This paper highlights both the benefits and limitations of simulation-based, ex post safety testing. While it can inform financial authorities and institutions aiming to ensure LLM safety, there is a clear trade-off between generality and cost.

Federico Gabriele, Aldo Glielmo, Marco Taboga

Current macroeconomic models with agent heterogeneity can be broadly divided into two main groups. Heterogeneous-agent general equilibrium (GE) models, such as those based on Heterogeneous Agents New Keynesian (HANK) or Krusell-Smith (KS) approaches, rely on GE and 'rational expectations', somewhat unrealistic assumptions that make the models very computationally cumbersome, which in turn limits the amount of heterogeneity that can be modelled. In contrast, agent-based models (ABMs) can flexibly encompass a large number of arbitrarily heterogeneous agents, but typically require the specification of explicit behavioural rules, which can lead to a lengthy trial-and-error model-development process. To address these limitations, we introduce MARL-BC, a framework that integrates deep multi-agent reinforcement learning (MARL) with Real Business Cycle (RBC) models. We demonstrate that MARL-BC can: (1) recover textbook RBC results when using a single agent; (2) recover the results of the mean-field KS model using a large number of identical agents; and (3) effectively simulate rich heterogeneity among agents, a hard task for traditional GE approaches. Our framework can be thought of as an ABM if used with a variety of heterogeneous interacting agents, and can reproduce GE results in limit cases. As such, it is a step towards a synthesis of these often opposed modelling paradigms.

Matteo Tusoni, Giuseppe Masi, Andrea Coletta et al.

Exploring causal relationships in stochastic time series is a challenging yet crucial task with a vast range of applications, including finance, economics, neuroscience, and climate science. Many algorithms for Causal Discovery (CD) have been proposed, but they often exhibit a high sensitivity to noise, resulting in misleading causal inferences when applied to real data. In this paper, we observe that the frequency spectra of typical real-world time series follow a power-law distribution, notably due to an inherent self-organizing behavior. Leveraging this insight, we build a robust CD method based on the extraction of power -law spectral features that amplify genuine causal signals. Our method consistently outperforms state-of-the-art alternatives on both synthetic benchmarks and real-world datasets with known causal structures, demonstrating its robustness and practical relevance.

Charles Camboulin, Diego Doimo, Aldo Glielmo

This work presents an analysis of the hidden representations of Variational Autoencoders (VAEs) using the Intrinsic Dimension (ID) and the Information Imbalance (II). We show that VAEs undergo a transition in behaviour once the bottleneck size is larger than the ID of the data, manifesting in a double hunchback ID profile and a qualitative shift in information processing as captured by the II. Our results also highlight two distinct training phases for architectures with sufficiently large bottleneck sizes, consisting of a rapid fit and a slower generalisation, as assessed by a differentiated behaviour of ID, II, and KL loss. These insights demonstrate that II and ID could be valuable tools for aiding architecture search, for diagnosing underfitting in VAEs, and, more broadly, they contribute to advancing a unified understanding of deep generative models through geometric analysis.

Diego Doimo, Aldo Glielmo, Sebastian Goldt et al.

Deep neural networks (DNNs) defy the classical bias-variance trade-off: adding parameters to a DNN that interpolates its training data will typically improve its generalization performance. Explaining the mechanism behind this ``benign overfitting'' in deep networks remains an outstanding challenge. Here, we study the last hidden layer representations of various state-of-the-art convolutional neural networks and find that if the last hidden representation is wide enough, its neurons tend to split into groups that carry identical information, and differ from each other only by statistically independent noise. The number of such groups increases linearly with the width of the layer, but only if the width is above a critical value. We show that redundant neurons appear only when the training process reaches interpolation and the training error is zero.

Aldo Glielmo, Claudio Zeni, Bingqing Cheng et al.

Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using subsets of these features. Using the fewest features but still retaining sufficient information about the system is crucial in many statistical learning approaches, particularly when data are sparse. We introduce a statistical test that can assess the relative information retained when using two different distance measures, and determine if they are equivalent, independent, or if one is more informative than the other. This in turn allows finding the most informative distance measure out of a pool of candidates. The approach is applied to find the most relevant policy variables for controlling the Covid-19 epidemic and to find compact yet informative representations of atomic structures, but its potential applications are wide ranging in many branches of science.

Diego Doimo, Aldo Glielmo, Alessio Ansuini et al.

Deep convolutional networks (DCNs) learn meaningful representations where data that share the same abstract characteristics are positioned closer and closer. Understanding these representations and how they are generated is of unquestioned practical and theoretical interest. In this work we study the evolution of the probability density of the ImageNet dataset across the hidden layers in some state-of-the-art DCNs. We find that the initial layers generate a unimodal probability density getting rid of any structure irrelevant for classification. In subsequent layers density peaks arise in a hierarchical fashion that mirrors the semantic hierarchy of the concepts. Density peaks corresponding to single categories appear only close to the output and via a very sharp transition which resembles the nucleation process of a heterogeneous liquid. This process leaves a footprint in the probability density of the output layer where the topography of the peaks allows reconstructing the semantic relationships of the categories.

Mihai Cucuringu, Peter Davies, Aldo Glielmo et al.

We introduce a principled and theoretically sound spectral method for $k$-way clustering in signed graphs, where the affinity measure between nodes takes either positive or negative values. Our approach is motivated by social balance theory, where the task of clustering aims to decompose the network into disjoint groups, such that individuals within the same group are connected by as many positive edges as possible, while individuals from different groups are connected by as many negative edges as possible. Our algorithm relies on a generalized eigenproblem formulation inspired by recent work on constrained clustering. We provide theoretical guarantees for our approach in the setting of a signed stochastic block model, by leveraging tools from matrix perturbation theory and random matrix theory. An extensive set of numerical experiments on both synthetic and real data shows that our approach compares favorably with state-of-the-art methods for signed clustering, especially for large number of clusters and sparse measurement graphs.