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A subclass of nondeterministic Finite Automata generated by means of regular Grammars (GFAs, for short) is introduced. A process algebra is proposed, whose semantics maps a term to a GFA. We prove a representability theorem: for each GFA…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
Weighted automata is a basic tool for specification in quantitative verification, which allows to express quantitative features of analysed systems such as resource consumption. Quantitative specification can be assisted by automata…
A cohesive power of a structure is an effective analog of the classical ultrapower of a structure. We start with a computable structure, and consider its countable ultrapower over a cohesive set of natural numbers. A cohesive set is an…
Probabilistic programming languages and modeling toolkits are two modular ways to build and reuse stochastic models and inference procedures. Combining strengths of both, we express models and inference as generalized coroutines in the same…
A deterministic finite-state automaton (FSA) is an abstract sequential machine that reads the symbols comprising an input word one at a time. An FSA is symmetric if its output is independent of the order in which the input symbols are read,…
This paper presents ReasonFormer, a unified reasoning framework for mirroring the modular and compositional reasoning process of humans in complex decision-making. Inspired by dual-process theory in cognitive science, the representation…
In this note, we provide some categorical perspectives on the relativization construction arising from quantum measurement theory in the presence of symmetries and occupying a central place in the operational approach to quantum reference…
Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier…
Natural language is characterized by compositionality: the meaning of a complex expression is constructed from the meanings of its constituent parts. To facilitate the evaluation of the compositional abilities of language processing…
Designers of statistical machine translation (SMT) systems have begun to employ tree-structured translation models. Systems involving tree-structured translation models tend to be complex. This article aims to reduce the conceptual…
The web-scale of pretraining data has created an important evaluation challenge: to disentangle linguistic competence on cases well-represented in pretraining data from generalization to out-of-domain language, specifically the dynamic,…
In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…
Binary multirelations can model alternating nondeterminism, for instance, in games or nondeterministically evolving systems interacting with an environment. Such systems can show partial or total functional behaviour at both levels of…
We propose an alternative and unifying framework for decision-making that, by using quantum mechanics, provides more generalised cognitive and decision models with the ability to represent more information than classical models. This…
We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or $\epsilon$-transitions. Our approach employs monads with a parametrized fixpoint operator $\dagger$ to give a semantics to…
Compositional generalization allows efficient learning and human-like inductive biases. Since most research investigating compositional generalization in NLP is done on English, important questions remain underexplored. Do the necessary…
We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…
Compositional generalization-the systematic combination of known components into novel structures-remains a core challenge in cognitive science and machine learning. Although transformer-based large language models can exhibit strong…