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Human language is full of compositional syntactic structures, and although neural networks have contributed to groundbreaking improvements in computer systems that process language, widely-used neural network architectures still exhibit…
Computation is classically studied in terms of automata, formal languages and algorithms; yet, the relation between neural dynamics and symbolic representations and operations is still unclear in traditional eliminative connectionism.…
Understanding the mental state of other people is an important skill for intelligent agents and robots to operate within social environments. However, the mental processes involved in `mind-reading' are complex. One explanation of such…
Building machines that can understand text like humans is an AI-complete problem. A great deal of research has already gone into this, with astounding results, allowing everyday people to discuss with their telephones, or have their reading…
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these…
The unprecedented surge in video data production in recent years necessitates efficient tools to extract meaningful frames from videos for downstream tasks. Long-term temporal reasoning is a key desideratum for frame retrieval systems.…
Large language models (LLMs) have demonstrated strong performance on formal language tasks, yet whether this reflects genuine symbolic reasoning or pattern matching on familiar constructions remains unclear. We introduce a benchmark for…
The hard problem in artificial intelligence asks how the shuffling of syntactical symbols in a program can lead to systems which experience semantics and qualia. We address this question in three stages. First, we introduce a new class of…
Computational modelling offers a powerful tool for formalising psychological theories, making them more transparent, testable, and applicable in digital contexts. Yet, the question often remains: how should one computationally model a…
We present here three different approaches to the problem of modeling mathematically the concept of a non-deterministic mechanism. Each of these three approaches leads to a mathematical definition. We then show that all the three…
Deterministic models are approximations of reality that are easy to interpret and often easier to build than stochastic alternatives. Unfortunately, as nature is capricious, observational data can never be fully explained by deterministic…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
Recurrent Neural Networks are an effective and prevalent tool used to model sequential data such as natural language text. However, their deep nature and massive number of parameters pose a challenge for those intending to study precisely…
We investigate families of infinite automata for context-sensitive languages. An infinite automaton is an infinite labeled graph with two sets of initial and final vertices. Its language is the set of all words labelling a path from an…
This paper develops a free energy theory from physics including the variational principles for automata and languages and also provides algorithms to compute the energy as well as efficient algorithms for estimating the nondeterminism in a…
Exclusive nondeterministic finite automata (XNFA) are nondeterministic finite automata with a special acceptance condition. An input is accepted if there is exactly one accepting path in its computation tree. If there are none or more than…
An iterated uniform finite-state transducer (IUFST) runs the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The IUFST accepts the input…
We examine questions involving nondeterministic finite automata where all states are final, initial, or both initial and final. First, we prove hardness results for the nonuniversality and inequivalence problems for these NFAs. Next, we…
We introduce and study the repetitive variants of the deterministic and the nondeterministic finite automaton with translucent words (DFAwtw and NFAwtw). On seeing the right sentinel, a repetitive NFAwtw need not halt immediately, accepting…
We introduce a neural network architecture and a learning algorithm to produce factorized symbolic representations. We propose to learn these concepts by observing consecutive frames, letting all the components of the hidden representation…