Lecturer: Osvaldo Simeone (Northeastern University London)
This mini-course starts by exploring two frontier directions in the design of AI systems that are computationally efficient: neuromorphic computing and quantum machine learning. The course concludes with a rigorous treatment of calibration methods that provide formal statistical guarantees on the behaviour of AI models in practice. The material is drawn from the lecturer's recent research and monographs, offering a unified perspective that bridges theory and emerging applications.
The rapid growth of AI has brought unprecedented capabilities but also escalating energy demands. This first part examines neuromorphic computing as a principled response to that challenge, revisiting brain-inspired design ideas in the light of modern deep learning architectures.
Drawing on the paper Modern Neuromorphic AI: From Intra-Token to Inter-Token Processing (arXiv:2601.00245), the lectures explore how concepts such as discrete and sparse activations, recurrent dynamics, and non-linear feedback — long central to spiking neural networks (SNNs) — reappear in contemporary architectures including state-space models and transformers. A key organising lens is the distinction between intra-token processing (transformations across the channels of a single input vector) and inter-token processing (transformations across a sequence of vectors).
The second part of this block turns to communication systems as a compelling application domain. Based on the paper Neuromorphic Wireless Cognition (arXiv:2206.06047, Chen, Skatchkovsky & Simeone, IEEE Trans. Cognitive Commun. Netw., 2023), the lectures present an end-to-end design for neuromorphic wireless IoT systems.
Topics covered: Spiking neural networks and biologically inspired computing · Connections between SNNs, state-space models, and transformer architectures · Intra-token vs. inter-token processing · Event-driven semantic communications · End-to-end neuromorphic system design for wireless IoT
The second part introduces quantum machine learning (QML) from an engineer's perspective, with an emphasis on statistical foundations and learning-theoretic analysis. Lectures follow in part the monograph An Introduction to Quantum Machine Learning for Engineers (arXiv:2205.09510) and the textbook Classical and Quantum Information Theory (Cambridge University Press).
The material is self-contained, starting from quantum states, operations, and measurements before building up to parametrised quantum circuits (PQCs). A particular focus is placed on fundamental statistical tasks in the quantum setting: binary hypothesis testing and classification, quantum state discrimination, and learning from data when measurements are destructive and irreversible.
Topics covered: Quantum states, operations, and measurements · Parametrised quantum circuits (PQCs) · Binary quantum classification and hypothesis testing · Quantum generative and discriminative models · Learning-theoretic analysis: copy complexity and generalisation in QML · The variational quantum eigensolver
The final part addresses one of the most pressing practical challenges in deploying AI: ensuring that model outputs come with rigorous, interpretable reliability guarantees. Based on the survey Conformal Calibration (arXiv:2504.09310, Simeone, Park & Zecchin, 2025), the lectures review conformal calibration — a collection of computationally lightweight, statistically rigorous tools that operate on top of any pre-trained model without requiring retraining.
Topics covered: Limitations of the train-and-deploy paradigm · Conformal prediction and uncertainty quantification · Prediction sets with formal coverage guarantees · Statistically valid hyperparameter selection · Online monitoring and adaptive calibration · Applications to communication systems and beyond
The fourth part develops a rigorous, modern treatment of statistical hypothesis testing, with an emphasis on the principles that underlie both classical and emerging approaches. The central question is how to quantify evidence against a null hypothesis in a way that is statistically valid, interpretable, and computationally tractable.
The first block covers the foundations of p-value construction, introducing p-values as measures of evidence and examining their strengths and limitations. A general recipe for constructing valid p-values under composite nulls is presented: rank p-values for the exchangeability null, sign-flip p-values for the symmetry null, Hoeffding p-values for bounded means, and permutation p-values under group-invariance nulls.
The second block introduces e-values as an alternative and often more powerful currency for expressing statistical evidence. The lectures establish key properties: post-hoc validity, multiplicative combination across independent experiments, and robustness to optional stopping. The connection to sequential inference is made precise through e-processes and Ville's inequality.
Topics covered: p-values as measures of evidence: construction, calibration, and limitations · Rank, sign-flip, Hoeffding, and permutation p-values · e-values: definition, properties, and comparison with p-values · e-processes
A background in probability, linear algebra, and basic machine learning is assumed. No prior knowledge of quantum mechanics or neuromorphic hardware is required; all necessary concepts will be developed from first principles during the course.