Andrea Asperti

Andrea Asperti, Marco Del Brutto

MicroRacer is a simple, open source environment inspired by car racing especially meant for the didactics of Deep Reinforcement Learning. The complexity of the environment has been explicitly calibrated to allow users to experiment with many different methods, networks and hyperparameters settings without requiring sophisticated software or the need of exceedingly long training times. Baseline agents for major learning algorithms such as DDPG, PPO, SAC, TD2 and DSAC are provided too, along with a preliminary comparison in terms of training time and performance.

Andrea Asperti, Fabio Merizzi, Alberto Paparella et al.

In recent years traditional numerical methods for accurate weather prediction have been increasingly challenged by deep learning methods. Numerous historical datasets used for short and medium-range weather forecasts are typically organized into a regular spatial grid structure. This arrangement closely resembles images: each weather variable can be visualized as a map or, when considering the temporal axis, as a video. Several classes of generative models, comprising Generative Adversarial Networks, Variational Autoencoders, or the recent Denoising Diffusion Models have largely proved their applicability to the next-frame prediction problem, and is thus natural to test their performance on the weather prediction benchmarks. Diffusion models are particularly appealing in this context, due to the intrinsically probabilistic nature of weather forecasting: what we are really interested to model is the probability distribution of weather indicators, whose expected value is the most likely prediction. In our study, we focus on a specific subset of the ERA-5 dataset, which includes hourly data pertaining to Central Europe from the years 2016 to 2021. Within this context, we examine the efficacy of diffusion models in handling the task of precipitation nowcasting. Our work is conducted in comparison to the performance of well-established U-Net models, as documented in the existing literature. Our proposed approach of Generative Ensemble Diffusion (GED) utilizes a diffusion model to generate a set of possible weather scenarios which are then amalgamated into a probable prediction via the use of a post-processing network. This approach, in comparison to recent deep learning models, substantially outperformed them in terms of overall performance.

Andrea Asperti, Valerio Tonelli

Different encodings of datapoints in the latent space of latent-vector generative models may result in more or less effective and disentangled characterizations of the different explanatory factors of variation behind the data. Many works have been recently devoted to the explorationof the latent space of specific models, mostly focused on the study of how features are disentangled and of how trajectories producing desired alterations of data in the visible space can be found. In this work we address the more general problem of comparing the latent spaces of different models, looking for transformations between them. We confined the investigation to the familiar and largely investigated case of generative models for the data manifold of human faces. The surprising, preliminary result reported in this article is that (provided models have not been taught or explicitly conceived to act differently) a simple linear mapping is enough to pass from a latent space to another while preserving most of the information.

Andrea Asperti, Davide Evangelista, Samuele Marro et al.

Denoising Diffusion models are gaining increasing popularity in the field of generative modeling for several reasons, including the simple and stable training, the excellent generative quality, and the solid probabilistic foundation. In this article, we address the problem of {\em embedding} an image into the latent space of Denoising Diffusion Models, that is finding a suitable ``noisy'' image whose denoising results in the original image. We particularly focus on Denoising Diffusion Implicit Models due to the deterministic nature of their reverse diffusion process. As a side result of our investigation, we gain a deeper insight into the structure of the latent space of diffusion models, opening interesting perspectives on its exploration, the definition of semantic trajectories, and the manipulation/conditioning of encodings for editing purposes. A particularly interesting property highlighted by our research, which is also characteristic of this class of generative models, is the independence of the latent representation from the networks implementing the reverse diffusion process. In other words, a common seed passed to different networks (each trained on the same dataset), eventually results in identical images.

Andrea Asperti, Gabriele Colasuonno, Antonio Guerra

Accurately modeling the effects of illumination and shadows during head rotation is critical in computer vision for enhancing image realism and reducing artifacts. This study delves into the latent space of denoising diffusion models to identify compelling trajectories that can express continuous head rotation under varying lighting conditions. A key contribution of our work is the generation of additional labels from the CelebA dataset,categorizing images into three groups based on prevalent illumination direction: left, center, and right. These labels play a crucial role in our approach, enabling more precise manipulations and improved handling of lighting variations. Leveraging a recent embedding technique for Denoising Diffusion Implicit Models (DDIM), our method achieves noteworthy manipulations, encompassing a wide rotation angle of $\pm 30$ degrees, while preserving individual distinct characteristics even under challenging illumination conditions. Our methodology involves computing trajectories that approximate clouds of latent representations of dataset samples with different yaw rotations through linear regression. Specific trajectories are obtained by analyzing subsets of data that share significant attributes with the source image, including light direction. Notably, our approach does not require any specific training of the generative model for the task of rotation; we merely compute and follow specific trajectories in the latent space of a pre-trained face generation model. This article showcases the potential of our approach and its current limitations through a qualitative discussion of notable examples. This study contributes to the ongoing advancements in representation learning and the semantic investigation of the latent space of generative models.

Fabio Merizzi, Andrea Asperti, Stefano Colamonaco

The Copernicus Regional Reanalysis for Europe, CERRA, is a high-resolution regional reanalysis dataset for the European domain. In recent years it has shown significant utility across various climate-related tasks, ranging from forecasting and climate change research to renewable energy prediction, resource management, air quality risk assessment, and the forecasting of rare events, among others. Unfortunately, the availability of CERRA is lagging two years behind the current date, due to constraints in acquiring the requisite external data and the intensive computational demands inherent in its generation. As a solution, this paper introduces a novel method using diffusion models to approximate CERRA downscaling in a data-driven manner, without additional informations. By leveraging the lower resolution ERA5 dataset, which provides boundary conditions for CERRA, we approach this as a super-resolution task. Focusing on wind speed around Italy, our model, trained on existing CERRA data, shows promising results, closely mirroring original CERRA data. Validation with in-situ observations further confirms the model's accuracy in approximating ground measurements.

Andrea Asperti, Salvatore Fiorilla, Simone Nardi et al.

Person re-identification (ReId), a crucial task in surveillance, involves matching individuals across different camera views. The advent of Deep Learning, especially supervised techniques like Convolutional Neural Networks and Attention Mechanisms, has significantly enhanced person Re-ID. However, the success of supervised approaches hinges on vast amounts of annotated data, posing scalability challenges in data labeling and computational costs. To address these limitations, recent research has shifted towards unsupervised person re-identification. Leveraging abundant unlabeled data, unsupervised methods aim to overcome the need for pairwise labelled data. Although traditionally trailing behind supervised approaches, unsupervised techniques have shown promising developments in recent years, signalling a narrowing performance gap. Motivated by this evolving landscape, our survey pursues two primary objectives. First, we review and categorize significant publications in supervised person re-identification, providing an in-depth overview of the current state-of-the-art and emphasizing little room for further improvement in this domain. Second, we explore the latest advancements in unsupervised person re-identification over the past three years, offering insights into emerging trends and shedding light on the potential convergence of performance between supervised and unsupervised paradigms. This dual-focus survey aims to contribute to the evolving narrative of person re-identification, capturing both the mature landscape of supervised techniques and the promising outcomes in the realm of unsupervised learning.

Andrea Asperti, Franky George, Tiberio Marras et al.

In recent years, advancements in generative artificial intelligence have led to the development of sophisticated tools capable of mimicking diverse artistic styles, opening new possibilities for digital creativity and artistic expression. This paper presents a critical assessment of the style replication capabilities of contemporary generative models, evaluating their strengths and limitations across multiple dimensions. We examine how effectively these models reproduce traditional artistic styles while maintaining structural integrity and compositional balance in the generated images. The analysis is based on a new large dataset of AI-generated works imitating artistic styles of the past, holding potential for a wide range of applications: the "AI-pastiche" dataset. The study is supported by extensive user surveys, collecting diverse opinions on the dataset and investigation both technical and aesthetic challenges, including the ability to generate outputs that are realistic and visually convincing, the versatility of models in handling a wide range of artistic styles, and the extent to which they adhere to the content and stylistic specifications outlined in prompts. This paper aims to provide a comprehensive overview of the current state of generative tools in style replication, offering insights into their technical and artistic limitations, potential advancements in model design and training methodologies, and emerging opportunities for enhancing digital artistry, human-AI collaboration, and the broader creative landscape.

Andrea Asperti, Leonardo Dessì, Maria Chiara Tonetti et al.

CLIP has emerged as a powerful multimodal model capable of connecting images and text through joint embeddings, but to what extent does it 'see' the same way humans do - especially when interpreting artworks? In this paper, we investigate CLIP's ability to extract high-level semantic and stylistic information from paintings, including both human-created and AI-generated imagery. We evaluate its perception across multiple dimensions: content, scene understanding, artistic style, historical period, and the presence of visual deformations or artifacts. By designing targeted probing tasks and comparing CLIP's responses to human annotations and expert benchmarks, we explore its alignment with human perceptual and contextual understanding. Our findings reveal both strengths and limitations in CLIP's visual representations, particularly in relation to aesthetic cues and artistic intent. We further discuss the implications of these insights for using CLIP as a guidance mechanism during generative processes, such as style transfer or prompt-based image synthesis. Our work highlights the need for deeper interpretability in multimodal systems, especially when applied to creative domains where nuance and subjectivity play a central role.

Andrea Asperti, Alberto Naibo, Claudio Sacerdoti Coen

Large Language Models (LLMs) have shown remarkable abilities in structured reasoning and symbolic tasks, with coding emerging as a particular area of strength. This success has sparked growing interest in applying LLMs to mathematics, both in informal problem-solving and formal theorem proving. However, progress in formal mathematics has proven to be significantly more difficult, despite surface-level similarities between programming and proof construction. This discrepancy raises important questions about how LLMs ``reason'', how they are supervised, and whether they internally track a notion of computational or deductive state. In this article, we address the state-of-the-art of the discipline, focusing on recent models and benchmarks, and explore three central issues at the intersection of machine learning and mathematical cognition: (i) the trade-offs between formal and informal mathematics as training domains; (ii) the deeper reasons why proof generation remains more brittle than code synthesis; (iii) and the question of whether LLMs represent, or merely mimic, a notion of evolving logical state. Our goal is not to draw hard boundaries, but to identify where the current limits lie, and how they might be extended.

Andrea Asperti, Ali Aydogdu, Angelo Greco et al.

Sea Surface Temperature (SST) reconstructions from satellite images affected by cloud gaps have been extensively documented in the past three decades. Here we describe several Machine Learning models to fill the cloud-occluded areas starting from MODIS Aqua nighttime L3 images. To tackle this challenge, we employed a type of Convolutional Neural Network model (U-net) to reconstruct cloud-covered portions of satellite imagery while preserving the integrity of observed values in cloud-free areas. We demonstrate the outstanding precision of U-net with respect to available products done using OI interpolation algorithms. Our best-performing architecture show 50% lower root mean square errors over established gap-filling methods.

X. Angelo Huang, Emanuele La Malfa, Samuele Marro et al.

Theory of Mind (ToM) can be used to assess the capabilities of Large Language Models (LLMs) in complex scenarios where social reasoning is required. While the research community has proposed many ToM benchmarks, their hardness varies greatly, and their complexity is not well defined. This work proposes a framework inspired by cognitive load theory to measure the complexity of ToM tasks. We quantify a problem's complexity as the number of states necessary to solve it correctly. Our complexity measure also accounts for spurious states of a ToM problem designed to make it apparently harder. We use our method to assess the complexity of five widely adopted ToM benchmarks. On top of this framework, we design a prompting technique that augments the information available to a model with a description of how the environment changes with the agents' interactions. We name this technique Discrete World Models (DWM) and show how it elicits superior performance on ToM tasks.

Andrea Asperti, Laura Bugo, Daniele Filippini

In this article we introduce the notion of Split Variational Autoencoder (SVAE), whose output $\hat{x}$ is obtained as a weighted sum $σ\odot \hat{x_1} + (1-σ) \odot \hat{x_2}$ of two generated images $\hat{x_1},\hat{x_2}$, and $σ$ is a {\em learned} compositional map. The composing images $\hat{x_1},\hat{x_2}$, as well as the $σ$-map are automatically synthesized by the model. The network is trained as a usual Variational Autoencoder with a negative loglikelihood loss between training and reconstructed images. No additional loss is required for $\hat{x_1},\hat{x_2}$ or $σ$, neither any form of human tuning. The decomposition is nondeterministic, but follows two main schemes, that we may roughly categorize as either \say{syntactic} or \say{semantic}. In the first case, the map tends to exploit the strong correlation between adjacent pixels, splitting the image in two complementary high frequency sub-images. In the second case, the map typically focuses on the contours of objects, splitting the image in interesting variations of its content, with more marked and distinctive features. In this case, according to empirical observations, the Fréchet Inception Distance (FID) of $\hat{x_1}$ and $\hat{x_2}$ is usually lower (hence better) than that of $\hat{x}$, that clearly suffers from being the average of the former. In a sense, a SVAE forces the Variational Autoencoder to make choices, in contrast with its intrinsic tendency to {\em average} between alternatives with the aim to minimize the reconstruction loss towards a specific sample. According to the FID metric, our technique, tested on typical datasets such as Mnist, Cifar10 and CelebA, allows us to outperform all previous purely variational architectures (not relying on normalization flows).

Andrea Asperti, Davide Evangelista, Moreno Marzolla

The term GreenAI refers to a novel approach to Deep Learning, that is more aware of the ecological impact and the computational efficiency of its methods. The promoters of GreenAI suggested the use of Floating Point Operations (FLOPs) as a measure of the computational cost of Neural Networks; however, that measure does not correlate well with the energy consumption of hardware equipped with massively parallel processing units like GPUs or TPUs. In this article, we propose a simple refinement of the formula used to compute floating point operations for convolutional layers, called α-FLOPs, explaining and correcting the traditional discrepancy with respect to different layers, and closer to reality. The notion of α-FLOPs relies on the crucial insight that, in case of inputs with multiple dimensions, there is no reason to believe that the speedup offered by parallelism will be uniform along all different axes.

Andrea Asperti, Stefano Dal Bianco

We provide a syllabification algorithm for the Divine Comedy using techniques from probabilistic and constraint programming. We particularly focus on the synalephe, addressed in terms of the "propensity" of a word to take part in a synalephe with adjacent words. We jointly provide an online vocabulary containing, for each word, information about its syllabification, the location of the tonic accent, and the aforementioned synalephe propensity, on the left and right sides. The algorithm is intrinsically nondeterministic, producing different possible syllabifications for each verse, with different likelihoods; metric constraints relative to accents on the 10th, 4th and 6th syllables are used to further reduce the solution space. The most likely syllabification is hence returned as output. We believe that this work could be a major milestone for a lot of different investigations. From the point of view of digital humanities it opens new perspectives on computer assisted analysis of digital sources, comprising automated detection of anomalous and problematic cases, metric clustering of verses and their categorization, or more foundational investigations addressing e.g. the phonetic roles of consonants and vowels. From the point of view of text processing and deep learning, information about syllabification and the location of accents opens a wide range of exciting perspectives, from the possibility of automatic learning syllabification of words and verses, to the improvement of generative models, aware of metric issues, and more respectful of the expected musicality.

Andrea Asperti

In this article, we highlight what appears to be major issue of Variational Autoencoders, evinced from an extensive experimentation with different network architectures and datasets: the variance of generated data is significantly lower than that of training data. Since generative models are usually evaluated with metrics such as the Frechet Inception Distance (FID) that compare the distributions of (features of) real versus generated images, the variance loss typically results in degraded scores. This problem is particularly relevant in a two stage setting, where we use a second VAE to sample in the latent space of the first VAE. The minor variance creates a mismatch between the actual distribution of latent variables and those generated by the second VAE, that hinders the beneficial effects of the second stage. Renormalizing the output of the second VAE towards the expected normal spherical distribution, we obtain a sudden burst in the quality of generated samples, as also testified in terms of FID.

Andrea Asperti, Matteo Trentin

In the loss function of Variational Autoencoders there is a well known tension between two components: the reconstruction loss, improving the quality of the resulting images, and the Kullback-Leibler divergence, acting as a regularizer of the latent space. Correctly balancing these two components is a delicate issue, easily resulting in poor generative behaviours. In a recent work, Dai and Wipf obtained a sensible improvement by allowing the network to learn the balancing factor during training, according to a suitable loss function. In this article, we show that learning can be replaced by a simple deterministic computation, helping to understand the underlying mechanism, and resulting in a faster and more accurate behaviour. On typical datasets such as Cifar and Celeba, our technique sensibly outperforms all previous VAE architectures.

Andrea Asperti

Working in high-dimensional latent spaces, the internal encoding of data in Variational Autoencoders becomes naturally sparse. We discuss this known but controversial phenomenon sometimes refereed to as overpruning, to emphasize the under-use of the model capacity. In fact, it is an important form of self-regularization, with all the typical benefits associated with sparsity: it forces the model to focus on the really important features, highly reducing the risk of overfitting. Especially, it is a major methodological guide for the correct tuning of the model capacity, progressively augmenting it to attain sparsity, or conversely reducing the dimension of the network removing links to zeroed out neurons. The degree of sparsity crucially depends on the network architecture: for instance, convolutional networks typically show less sparsity, likely due to the tighter relation of features to different spatial regions of the input.

Andrea Asperti, Daniele Cortesi, Francesco Sovrano

Rogue is a famous dungeon-crawling video-game of the 80ies, the ancestor of its gender. Rogue-like games are known for the necessity to explore partially observable and always different randomly-generated labyrinths, preventing any form of level replay. As such, they serve as a very natural and challenging task for reinforcement learning, requiring the acquisition of complex, non-reactive behaviors involving memory and planning. In this article we show how, exploiting a version of A3C partitioned on different situations, the agent is able to reach the stairs and descend to the next level in 98% of cases.

Andrea Asperti, Claudio Mastronardo

The lack, due to privacy concerns, of large public databases of medical pathologies is a well-known and major problem, substantially hindering the application of deep learning techniques in this field. In this article, we investigate the possibility to supply to the deficiency in the number of data by means of data augmentation techniques, working on the recent Kvasir dataset of endoscopical images of gastrointestinal diseases. The dataset comprises 4,000 colored images labeled and verified by medical endoscopists, covering a few common pathologies at different anatomical landmarks: Z-line, pylorus and cecum. We show how the application of data augmentation techniques allows to achieve sensible improvements of the classification with respect to previous approaches, both in terms of precision and recall.

Andrea Asperti, Wilmer Ricciotti

This article describes a prototype implementation of a web interface for the Matita proof assistant. The interface supports all basic functionalities of the local Gtk interface, but takes advantage of the markup to enrich the document with several kinds of annotations or active elements. Annotations may have both a presentational/hypertextual nature, aimed to improve the quality of the proof script as a human readable document, or a more semantic nature, aimed to help the system in its processing of the script. The latter kind comprises information automatically generated by the proof assistant during previous compilations, and stored to improve the performance of re-executing expensive operations like disambiguation or automation.

Andrea Asperti, Wilmer Ricciotti, Claudio Sacerdoti Coen et al.

The paper describes the refinement algorithm for the Calculus of (Co)Inductive Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement algorithm is in charge of giving a meaning to the terms, types and proof terms directly written by the user or generated by using tactics, decision procedures or general automation. The terms are written in an "external syntax" meant to be user friendly that allows omission of information, untyped binders and a certain liberal use of user defined sub-typing. The refiner modifies the terms to obtain related well typed terms in the internal syntax understood by the kernel of the ITP. In particular, it acts as a type inference algorithm when all the binders are untyped. The proposed algorithm is bi-directional: given a term in external syntax and a type expected for the term, it propagates as much typing information as possible towards the leaves of the term. Traditional mono-directional algorithms, instead, proceed in a bottom-up way by inferring the type of a sub-term and comparing (unifying) it with the type expected by its context only at the end. We propose some novel bi-directional rules for CIC that are particularly effective. Among the benefits of bi-directionality we have better error message reporting and better inference of dependent types. Moreover, thanks to bi-directionality, the coercion system for sub-typing is more effective and type inference generates simpler unification problems that are more likely to be solved by the inherently incomplete higher order unification algorithms implemented. Finally we introduce in the external syntax the notion of vector of placeholders that enables to omit at once an arbitrary number of arguments. Vectors of placeholders allow a trivial implementation of implicit arguments and greatly simplify the implementation of primitive and simple tactics.