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Out-of-distribution generalization capabilities of sequence-to-sequence models can be studied from the lens of two crucial forms of generalization: length generalization -- the ability to generalize to longer sequences than ones seen during…
This paper discusses a restriction of quantum theory, in which very complex states would be excluded. The toy theory is phrased in the language of the circuit model for quantum computing, its key ingredient being a limitation on the number…
Compositional, structured models are appealing because they explicitly decompose problems and provide interpretable intermediate outputs that give confidence that the model is not simply latching onto data artifacts. Learning these models…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigid, but we prove that it is neither equivalent to the axiom…
Although living organisms are affected by many interrelated and unidentified variables, this complexity does not automatically impose a fundamental limitation on statistical inference. Nor need one invoke such complexity as an explanation…
Large-language models (LLMs) can support a wide range of applications like conversational agents, creative writing or general query answering. However, they are ill-suited for query answering in high-stake domains like medicine because they…
We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…
We consider the problem of formalizing the familiar notion of widening in abstract interpretation in higher-order logic. It turns out that many axioms of widening (e.g. widening sequences are ascending) are not useful for proving…
Search systems are often focused on providing relevant results for the "now", assuming both corpora and user needs that focus on the present. However, many corpora today reflect significant longitudinal collections ranging from 20 years of…
Identifying the relations that exist between words (or entities) is important for various natural language processing tasks such as, relational search, noun-modifier classification and analogy detection. A popular approach to represent the…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
Either fibered knots supporting the tight contact structure are unique in their smooth concordance class or there exists a fibered counterexample to the Slice-Ribbon Conjecture.
Recombining known primitive concepts into larger novel combinations is a quintessentially human cognitive capability. Whether large neural models in NLP can acquire this ability while learning from data is an open question. In this paper,…
The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…
Composing basic skills from simple tasks to accomplish composite tasks is crucial for modern intelligent systems. We investigate the in-context composition ability of language models to perform composite tasks that combine basic skills…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
Conjunctive queries select and are expected to return certain tuples from a relational database. We study the potentially easier problem of counting all selected tuples, rather than enumerating them. In particular, we are interested in the…
One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research…
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…