Notes

Ad-Hoc Teamwork (AHT) in Reinforcement Learning Problem Setting & Motivation Ad-hoc teamwork concerns agents that must cooperate effectively with previously unknown teammates without any prior coordination, communication protocol, or shared learning history. This is the multi-agent analogue of zero-shot generalization: the agent is dropped into a team and must immediately contribute productively. The setting departs from self-play / centralized training in that the partner distribution at test time is exogenous and possibly non-stationary. ...

Zero Knowledge Proofs Motivation & Foundational Context ZKPs sit at the intersection of Complexity Theory, Cryptography, and Interactive Proof Systems. The core question: can you convince someone you know something without revealing what you know? This has profound implications for privacy-preserving authentication, blockchain protocols, and verifiable computation. Interactive Proof Systems Interactive Theorem Provers The Classical Model An interactive proof system involves two parties exchanging messages: Prover (P): Computationally unbounded; claims a statement is true. Verifier (V): Probabilistic polynomial-time (PPT); decides accept/reject. “An interactive proof system for a language $L$ is a protocol $(P, V)$ such that completeness and soundness hold.” ~ Goldwasser, Micali, Rackoff (1985) ...

Universal Composability (UC) Framework Motivation: The Composition Problem The fundamental issue UC addresses: protocols proven secure in isolation can fail catastrophically when run concurrently with other protocols. Classical security definitions (e.g., standalone simulation-based security) do not guarantee that security properties are preserved under arbitrary composition. Real-world systems always run multiple protocols simultaneously, sharing state, keys, randomness, and communication channels. The Composition Problem A protocol $\pi$ proven secure in a standalone setting may become insecure when executed concurrently with arbitrary protocols $\pi_1, \dots, \pi_n$, even if each $\pi_i$ is itself secure in isolation. ...

Process Calculus and Session Types (Honda, Yoshida, Carbone) Historical Lineage and Motivation The process calculus literature on session types originates from the fundamental insight that communication itself can be typed. Just as data types codify the structure of data, session types codify the structure of communication and make it available to programming tools. The key intellectual trajectory runs: Milner et al. (1992): The π-calculus — a calculus of mobile processes with name-passing and channel mobility. Honda (1993): “Types for Dyadic Interaction” at CONCUR'93 — the first session type system. Takeuchi, Honda & Kubo (1994): An interaction-based language with typing at PARLE'94. Honda, Vasconcelos & Kubo (1998): The canonical binary session type system at ESOP'98 (awarded ETAPS Test-of-Time Award, 2019). Honda, Yoshida & Carbone (2008/2016): Multiparty Asynchronous Session Types (MPST) at POPL'08, journal version in JACM 2016. The driving application domain is structured communication-centred programming: web services, business protocols, parallel scientific computing, multi-core programming. The thing you have to remember is that session types are not just about preventing type mismatches on messages — they statically enforce the entire conversational protocol. ...

NOTE: this is an old set of note, and it is of quite bad quality, it should be completely rewritten. $$ F(x) = \int _{-\infty}^{x} f(t) \, dt $$ A volte la densità non è definita, mentre la funzione cumulativa lo è , per questo spesso cominciamo a definire partendo dalla definizione. $$ F_{X}(x) = \mathbb{P}(X \leq x) = \int_{-\infty}^{x} f_{X}(z) \, dz $$Generalized inverse This is known as the universality of the uniform, every invertible CDF can be written with respect to the uniform distribution. ...

Questo è stato creato da 1948 Shannon in (Shannon 1948). Questa nozione è basata sulla nozione di probabilità, perché le cose rare sono più informative rispetto a qualcosa che accade spesso. Introduction to Entropy The Shannon Information Content $$ h(x = a_{i}) = \log_{2}\frac{1}{P(x = a_{i})} $$ We will see that the entropy is a weighted average of the information, so the expected information content in a distribution. Kolmogorov complexity è un modo diverso per definire la complessità. Legato è Neural Networks#Kullback-Leibler Divergence. ...

These notes cover the core concepts of the Information Bottleneck method, widely used in machine learning and theoretical neuroscience. We start by defining the fundamental tension in learning and representation. Learning Design Goals Compression: The representation should be as simple as possible (Occam’s Razor). Relevance: The representation must retain enough information to predict the target variable accurately. Generalization: The system should perform well on unseen data, which is often a function of finding the right balance between the first two. Invariance: The representation should ignore “nuisance variables” (noise) present in the input that do not correlate with the output. ...

Log Linear Models can be considered the most basic model used in natural languages. The main idea is to try to model the correlations of our data, or how the posterior $p(y \mid x)$ varies, where $x$ is our single data point features and $y$ are the labels of interest. This is a form of generalization because contextualized events (x, y) with similar descriptions tend to have similar probabilities. These kinds of models are so common that it has been discovered in many fields (and thus assuming different names): some of the most famous are Gibbs distributions, undirected graphical models, Markov Random Fields or Conditional Random Fields, exponential models, and (regularized) maximum entropy models. Special cases include logistic regression and Boltzmann machines. ...

2.1 Elementi di base 2.1.1 Definizione e caratteristiche Tutto è un insieme (su questo si basa la maggior parte della matematica) Efficace nella descrizione degli oggetti (infiniti è ez), ma non è efficiente nel calcolo in quanto non dà nessun indizio sul’implementazione in memoria o sul modo per calcolarlo, c’è solo una associazione Si può concludere che per l’informatico non serve a molto questa teoria, ma è la base per la matematica. ...

pWith confidential computing we want to guarantee confidentiality and integrity of a user’s computation running on a remote (cloud) system, including: The program Its inputs and outputs Intermediate state, control flow, etc. Even if do not trust the cloud provider! Usually it is easy to guarantee that kind of privacy if you are storing or communicating using encryption methods (see Asymmetric Cryptography, Block Ciphers), but it’s difficult to do so if the program is running. ...