Related papers: A Universal Kernel for Learning Regular Languages
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…
Learning a kernel matrix from relative comparison human feedback is an important problem with applications in collaborative filtering, object retrieval, and search. For learning a kernel over a large number of objects, existing methods face…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
We settle the equivalence between the problem of hitting a polyhedral set by the orbit of a linear map and the intersection of a regular language and a language of permutations of binary words (the permutation filter realizability problem).…
Are large language models (LLMs) sensitive to the distinction between humanly possible and impossible languages? This question was recently used in a broader debate on whether LLMs and humans share the same innate learning biases. Previous…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…
In order to achieve deep natural language understanding, syntactic constituent parsing is a vital step, highly demanded by many artificial intelligence systems to process both text and speech. One of the most recent proposals is the use of…
We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e.…
Equational reasoning is one of the key features of pure functional languages such as Haskell. To date, however, such reasoning always took place externally to Haskell, either manually on paper, or mechanised in a theorem prover. This…
$C^*$-algebra-valued kernels could pave the way for the next generation of kernel machines. To further our fundamental understanding of learning with $C^*$-algebraic kernels, we propose a new class of positive definite kernels based on the…
The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.
Despite the well-developed cut-edge representation learning for language, most language representation models usually focus on specific level of linguistic unit, which cause great inconvenience when being confronted with handling multiple…
Ad hoc parsers are everywhere: they appear any time a string is split, looped over, interpreted, transformed, or otherwise processed. Every ad hoc parser gives rise to a language: the possibly infinite set of input strings that the program…
Natural languages are complexly structured entities. They exhibit characterising regularities that can be exploited to link them one another. In this work, I compare two morphological aspects of languages: Written Patterns and Sentence…
Distributed word embeddings have shown superior performances in numerous Natural Language Processing (NLP) tasks. However, their performances vary significantly across different tasks, implying that the word embeddings learnt by those…
We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…