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We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
We investigate the merits of replication, and provide methods for optimal design (including replicates), with the goal of obtaining globally accurate emulation of noisy computer simulation experiments. We first show that replication can be…
Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…
Recently, deep architectures, such as recurrent and recursive neural networks have been successfully applied to various natural language processing tasks. Inspired by bidirectional recurrent neural networks which use representations that…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
When does a deterministic computational model define a probability distribution? What are its properties? This work formalises and settles this stochasticity problem for weighted automata, and its generalisation cost register automata…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
As reasoning modules, such as the chain-of-thought mechanism, are applied to large language models, they achieve strong performance on various tasks such as answering common-sense questions and solving math problems. The main challenge now…
We show that probabilistic computable functions, i.e., those functions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene's partial recursive…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
Prompt programming treats large language model prompts as software components with typed interfaces. Based on a literature survey of 15 recent works from 2023 to 2025, we observe a consistent trend: type systems are central to emerging…
Recurrent neural networks (RNNs) have shown promising performance for language modeling. However, traditional training of RNNs using back-propagation through time often suffers from overfitting. One reason for this is that stochastic…
Statistical language models are central to many applications that use semantics. Recurrent Neural Networks (RNN) are known to produce state of the art results for language modelling, outperforming their traditional n-gram counterparts in…
The organization of latent knowledge within large-scale models poses unique challenges when addressing overlapping representations and optimizing contextual accuracy. Conceptual redundancies embedded across layers often result in…
Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
Probabilistic language models are widely used in Information Retrieval (IR) to rank documents by the probability that they generate the query. However, the implementation of the probabilistic representations with programming languages that…
The lambda-calculus with de Bruijn indices assembles each alpha-class of lambda-terms in a unique term, using indices instead of variable names. Intersection types provide finitary type polymorphism and can characterise normalisable…
The latest research on Large Language Models (LLMs) has demonstrated significant advancement in the field of Natural Language Processing (NLP). However, despite this progress, there is still a lack of reliability in these models. This is…