Related papers: Fixed-point Characterization of Compositionality P…
We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete…
Humans are able to perform a myriad of sophisticated tasks by drawing upon skills acquired through prior experience. For autonomous agents to have this capability, they must be able to extract reusable skills from past experience that can…
We study composition operators on spaces of holomorphic Lipschitz functions defined on the open unit ball of a complex Banach space. Our approach is based on the linearization of the symbol through the holomorphic Lipschitz-free spaces,…
Programs that combine I/O and countable probabilistic choice, modulo either bisimilarity or trace equivalence, can be seen as describing a probabilistic strategy. For well-founded programs, we might expect to axiomatize bisimilarity via a…
In a multi-modeling based approach, the system under development is described by several models that represent various perspectives and concerns. Obviously, these partial representations are less complex than the global model, but they need…
Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…
A core aspect of compositionality, systematicity is a desirable property in ML models as it enables strong generalization to novel contexts. This has led to numerous studies proposing benchmarks to assess systematic generalization, as well…
Humans leverage compositionality to efficiently learn new concepts, understanding how familiar parts can combine together to form novel objects. In contrast, popular computer vision models struggle to make the same types of inferences,…
Consonance is related to the perception of pleasantness arising from a combination of sounds and has been approached quantitatively using mathematical relations, physics, information theory, and psychoacoustics. Tonal consonance is present…
Hybrid Communicating Sequential Processes (HCSP) is a powerful formal modeling language for hybrid systems, which is an extension of CSP by introducing differential equations for modeling continuous evolution and interrupts for modeling…
We describe a procedure based on the iteration of an initial function by an appropriated operator, acting on continuous functions, in order to get a fixed point. This fixed point will be a calibrated subaction for the doubling map on the…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which…
We develop operators for construction of proposals in probabilistic programs, which we refer to as inference combinators. Inference combinators define a grammar over importance samplers that compose primitive operations such as application…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
Prompts have been shown to be an effective method to adapt a frozen Pretrained Language Model (PLM) to perform well on downstream tasks. Prompts can be represented by a human-engineered word sequence or by a learned continuous embedding. In…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
We consider the stability and the input-output analysis problems of a class of large-scale hybrid systems composed of continuous dynamics coupled with discrete dynamics defined over finite alphabets, e.g., deterministic finite state…
This paper studies the behaviour of iterates of weighted composition operators acting on spaces of analytic functions, with particular emphasis on the Hardy space $H^2$. Questions relating to uniform, strong and weak convergence are…
Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also…
A key property for systems subject to uncertainty in their operating environment is robustness, ensuring that unmodelled, but bounded, disturbances have only a proportionally bounded effect upon the behaviours of the system. Inspired by…