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Deep learning, despite its remarkable achievements, is still a young field. Like the early stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad-hoc design decisions, and the lack of a uniform and…
There has been much recent, exciting work on combining the complementary strengths of latent variable models and deep learning. Latent variable modeling makes it easy to explicitly specify model constraints through conditional independence…
A ``k-rule" is a sequence A=((A_n,B_n):n<omega) of pairwise disjoint sets B_n, each of cardinality at most k, where A_n is a subset of B_n. A set X of natural numbers (a ``real'') follows a rule A if for infinitely many n we have that the…
Recently, the separated fragment (SF) of first-order logic has been introduced. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. SF properly generalizes both the…
We study learning under regime variation, where the learner, its memory state, and the evaluative conditions may evolve over time. This paper is a foundational and structural contribution: its goal is to define the core learning-theoretic…
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The…
We derive finite-dimensional quantum mechanics from a single ontological principle, that \emph{existence is constituted by distinguishability}, together with two structural commitments: finite capacity $N$ (parametric input) and…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
This paper develops some mathematical models arising in behavioral sciences, particularly in psychology, which are formalized via general preferences with variable ordering structures. Our considerations are based on the recent variational…
Identifying causal relations is crucial for a variety of downstream tasks. In additional to observational data, background knowledge (BK), which could be attained from human expertise or experiments, is usually introduced for uncovering…
The primary goal of my Ph.D. study is to develop provably efficient and practical algorithms for data-driven sequential decision-making under uncertainty. My work focuses on reinforcement learning (RL), multi-armed bandits, and their…
A physical explanation for quantum bounds to nonlocality (Tsirelson's bound) is a fundamental problem that remains open, and one approach to explaining its origins is the so-called Exclusivity principle, relying on probabilistic assumptions…
Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Posibilistic logic is the most extended approach to handle uncertain and partially inconsistent information. Regarding normal forms, advances in possibilistic reasoning are mostly focused on clausal form. Yet, the encoding of real-world…
In the first part of this study, a convex-constrained penalized formulation was studied for a class of constant modulus (CM) problems. In particular, the error bound techniques were shown to play a vital role in providing exact penalization…
Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the…
Value independence is enormously beneficial for reasoning about software systems at scale. These benefits carry over into the world of formal verification. Reasoning about programs algebraically is a simple affair in a proof assistant,…
Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely.…
Causality has the potential to truly transform the way we solve a large number of real-world problems. Yet, so far, its potential largely remains to be unlocked as causality often requires crucial assumptions which cannot be tested in…