The increased availability of data and computing resources has enabled researchers to successfully adopt machine learning (ML) techniques and make significant contributions in several engineering areas. ML and in particular deep learning (DL) algorithms have shown to perform better in tasks where a physical bottom-up description of the phenomenon is lacking and/or is mathematically intractable. Indeed, they take advantage of the observations of natural phenomena to automatically acquire knowledge and learn internal relations. Despite the historical model-based mindset, communications engineering recently started shifting the focus towards top-down data-driven learning models, especially in domains such as channel modeling and physical layer design, where in most of the cases no general optimal strategies are known. In this thesis, we aim at solving some fundamental open challenges in physical layer communications exploiting new DL paradigms. In particular, we mathematically formulate, under ML terms, classic problems such as channel capacity and optimal coding-decoding schemes, for any arbitrary communication medium. We design and develop the architecture, algorithm and code necessary to train the equivalent DL model, and finally, we propose novel solutions to long-standing problems in the field.

Ranking data are frequently obtained nowadays but there are still scarce methods for treating these data when temporally observed. The present paper contributes to this topic by proposing and developing novel models for handling time series of ranking data. We introduce a class of time-varying ranking models inspired by the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models. More specifically, the temporal dynamics are defined by the conditional distribution of the current ranking given the past rankings, which are assumed to follow a Mallows distribution, which implicitly depends on a distance. Then, autoregressive and feedback components are incorporated into the model through the conditional expectation of the associated distances. Theoretical properties of our ranking GARCH models such as stationarity and ergodicity are established. The estimation of parameters is performed via maximum likelihood estimation when data is fully observed. We develop a Monte Carlo Expectation-Maximisation algorithm to deal with cases involving missing data. Monte Carlo simulation studies are presented to study the performance of the proposed estimators under both non-missing and missing data scenarios. A real data application about the weekly ranking of professional tennis players from 2015 to 2019 is presented under our proposed ranking GARCH models.

The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating a conditional mean, this can be achieved by producing a predictive interval for the output, or to even learn a model of the conditional probability $p(y|x)$ of an output $y$ given input features $x$. While this can be done under parametric assumptions with, e.g. generalized linear model, these are typically too strong, and non-parametric models offer flexible alternatives. In particular, for scalar outputs, learning directly a model of the conditional cumulative distribution function of $y$ given $x$ can lead to more precise probabilistic estimates, and the use of proper scoring rules such as the weighted interval score (WIS) and the continuous ranked probability score (CRPS) lead to better coverage and calibration properties. This paper introduces novel algorithms for learning probabilistic regression trees for the WIS or CRPS loss functions. These algorithms are made computationally efficient thanks to an appropriate use of known data structures - namely min-max heaps, weight-balanced binary trees and Fenwick trees. Through numerical experiments, we demonstrate that the performance of our methods is competitive with alternative approaches. Additionally, our methods benefit from the inherent interpretability and explainability of trees. As a by-product, we show how our trees can be used in the context of conformal prediction and explain why they are particularly well-suited for achieving group-conditional coverage guarantees.

This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D2PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the probabilistic extensions of Canonical Correlation Analysis (CCA), D2PCCA captures nonlinear latent dynamics and supports enhancements such as KL annealing for improved convergence and normalizing flows for a more flexible posterior approximation. D2PCCA naturally extends to multiple observed variables, making it a versatile tool for encoding prior knowledge about sequential datasets and providing a probabilistic understanding of the system's dynamics. Experimental validation on real financial datasets demonstrates the effectiveness of D2PCCA and its extensions in capturing latent dynamics.

In cooperative multi-agent reinforcement learning (MARL), learning effective policies is challenging when global rewards are sparse and delayed. This difficulty arises from the need to assign credit across both agents and time steps, a problem that existing methods often fail to address in episodic, long-horizon tasks. We propose Temporal-Agent Reward Redistribution $TAR^2$, a novel approach that decomposes sparse global rewards into agent-specific, time-step-specific components, thereby providing more frequent and accurate feedback for policy learning. Theoretically, we show that $TAR^2$ (i) aligns with potential-based reward shaping, preserving the same optimal policies as the original environment, and (ii) maintains policy gradient update directions identical to those under the original sparse reward, ensuring unbiased credit signals. Empirical results on two challenging benchmarks, SMACLite and Google Research Football, demonstrate that $TAR^2$ significantly stabilizes and accelerates convergence, outperforming strong baselines like AREL and STAS in both learning speed and final performance. These findings establish $TAR^2$ as a principled and practical solution for agent-temporal credit assignment in sparse-reward multi-agent systems.

Spin systems form an important class of undirected graphical models. For two Gibbs distributions $\mu$ and $\nu$ induced by two spin systems on the same graph $G = (V, E)$, we study the problem of approximating the total variation distance $d_{TV}(\mu,\nu)$ with an $\epsilon$-relative error. We propose a new reduction that connects the problem of approximating the TV-distance to sampling and approximate counting. Our applications include the hardcore model and the antiferromagnetic Ising model in the uniqueness regime, the ferromagnetic Ising model, and the general Ising model satisfying the spectral condition. Additionally, we explore the computational complexity of approximating the total variation distance $d_{TV}(\mu_S,\nu_S)$ between two marginal distributions on an arbitrary subset $S \subseteq V$. We prove that this problem remains hard even when both $\mu$ and $\nu$ admit polynomial-time sampling and approximate counting algorithms.

Learning informative representations of phylogenetic tree structures is essential for analyzing evolutionary relationships. Classical distance-based methods have been widely used to project phylogenetic trees into Euclidean space, but they are often sensitive to the choice of distance metric and may lack sufficient resolution. In this paper, we introduce phylogenetic variational autoencoders (PhyloVAEs), an unsupervised learning framework designed for representation learning and generative modeling of tree topologies. Leveraging an efficient encoding mechanism inspired by autoregressive tree topology generation, we develop a deep latent-variable generative model that facilitates fast, parallelized topology generation. Phylo-VAE combines this generative model with a collaborative inference model based on learnable topological features, allowing for high-resolution representations of phylogenetic tree samples. Extensive experiments demonstrate PhyloVAE's robust representation learning capabilities and fast generation of phylogenetic tree topologies. Phylogenetic trees are the foundational structure for describing the evolutionary processes among individuals or groups of biological entities. Reconstructing these trees based on collected biological sequences (e.g., DNA, RNA, protein) from observed species, also known as phylogenetic inference (Felsenstein, 2004), is an essential discipline of computational biology (Fitch, 1971; Felsenstein, 1981; Yang & Rannala, 1997; Ronquist et al., 2012). Large collections of trees obtained from these approaches (e.g., posterior samples from MCMC runs (Ronquist et al., 2012)), however, are often difficult to summarize or visualize due to the discrete and non-Euclidean nature of the tree topology space The classical approach to visualize and analyze distributions of phylogenetic trees is to calculate pairwise distances between the trees and project them into a plane using multidimensional scaling (MDS) (Amenta & Klingner, 2002; Hillis et al., 2005; Jombart et al., 2017). However, these approaches have the shortcoming that one can not map an arbitrary point in the visualization to a tree, and therefore do not form an actual visualization of the relevant tree space.

This position paper argues that AI agents should be regulated based on the sequence of actions they autonomously take. AI agents with long-term planning and strategic capabilities can pose significant risks of human extinction and irreversible global catastrophes. While existing regulations often focus on computational scale as a proxy for potential harm, we contend that such measures are insufficient for assessing the risks posed by AI agents whose capabilities arise primarily from inference-time computation. To support our position, we discuss relevant regulations and recommendations from AI scientists regarding existential risks, as well as the advantages of action sequences over existing impact measures that require observing environmental states.

The humanoid robot (Unitree G1) demonstrates diverse agile whole-body skills, showcasing the control policies' agility: (a) Cristiano Ronaldo's signature celebration involving a jump with a 180-degree mid-air rotation; (b) LeBron James's "Silencer" celebration involving single-leg balancing; and (c) Kobe Bryant's famous fadeaway jump shot involving single-leg jumping and landing; (d) 1.5m-forward jumping; (e) Leg stretching; (f) 1.3m-side jumping. Abstract -- Humanoid robots hold the potential for unparalleled versatility for performing human-like, whole-body skills. However, achieving agile and coordinated whole-body motions remains a significant challenge due to the dynamics mismatch between simulation and the real world. Existing approaches, such as system identification (SysID) and domain randomization (DR) methods, often rely on labor-intensive parameter tuning or result in overly conservative policies that sacrifice agility. In this paper, we present ASAP (Aligning Simulation and Real Physics), a two-stage framework designed to tackle the dynamics mismatch and enable agile humanoid whole-body skills. Then ASAP fine-tunes pre-trained policies with the delta action model integrated into the simulator to align effectively with real-world dynamics. We evaluate ASAP across three transfer scenarios--IsaacGym to IsaacSim, IsaacGym to Genesis, and IsaacGym to the real-world Unitree G1 humanoid robot. Our approach significantly improves agility and whole-body coordination across various dynamic motions, reducing tracking error compared to SysID, DR, and delta dynamics learning baselines. ASAP enables highly agile motions that were previously difficult to achieve, demonstrating the potential of delta action learning in bridging simulation and real-world dynamics. These results suggest a promising sim-to-real direction for developing more expressive and agile humanoids. I NTRODUCTION For decades, we have envisioned humanoid robots achieving or even surpassing human-level agility. However, most prior work [46, 74, 47, 73, 107, 19, 95, 50] has primarily focused on locomotion, treating the legs as a means of mobility. Recent studies [10, 25, 24, 26, 32] have introduced whole-body expressiveness in humanoid robots, but these efforts have primarily focused on upper-body motions and have yet to achieve the agility seen in human movement.

Digital twins have been actively explored in many engineering applications, such as manufacturing and autonomous systems. However, model discrepancy is ubiquitous in most digital twin models and has significant impacts on the performance of using those models. In recent years, data-driven modeling techniques have been demonstrated promising in characterizing the model discrepancy in existing models, while the training data for the learning of model discrepancy is often obtained in an empirical way and an active approach of gathering informative data can potentially benefit the learning of model discrepancy. On the other hand, Bayesian experimental design (BED) provides a systematic approach to gathering the most informative data, but its performance is often negatively impacted by the model discrepancy. In this work, we build on sequential BED and propose an efficient approach to iteratively learn the model discrepancy based on the data from the BED. The performance of the proposed method is validated by a classical numerical example governed by a convection-diffusion equation, for which full BED is still feasible. The proposed method is then further studied in the same numerical example with a high-dimensional model discrepancy, which serves as a demonstration for the scenarios where full BED is not practical anymore. An ensemble-based approximation of information gain is further utilized to assess the data informativeness and to enhance learning model discrepancy. The results show that the proposed method is efficient and robust to the active learning of high-dimensional model discrepancy, using data suggested by the sequential BED. We also demonstrate that the proposed method is compatible with both classical numerical solvers and modern auto-differentiable solvers.