Although much research has been done on proposing new models or loss functions to improve the generalisation of artificial neural networks (ANNs), less attention has been directed to the impact of the training data on generalisation. In this work, we start from approximating the interaction between samples, i.e. how learning one sample would modify the model's prediction on other samples. Through analysing the terms involved in weight updates in supervised learning, we find that labels influence the interaction between samples. Therefore, we propose the labelled pseudo Neural Tangent Kernel (lpNTK) which takes label information into consideration when measuring the interactions between samples. We first prove that lpNTK asymptotically converges to the empirical neural tangent kernel in terms of the Frobenius norm under certain assumptions. Secondly, we illustrate how lpNTK helps to understand learning phenomena identified in previous work, specifically the learning difficulty of samples and forgetting events during learning. Moreover, we also show that using lpNTK to identify and remove poisoning training samples does not hurt the generalisation performance of ANNs.

Henry Conklin, Bailin Wang, Kenny Smith, Ivan Titov. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.

Language is culturally transmitted. Iterated learning, the process by which the output of one individual's learning becomes the input to other individuals' learning, provides a framework for investigating the cultural evolution of linguistic structure. We present two models, based upon the iterated learning framework, which show that the poverty of the stimulus available to language learners leads to the emergence of linguistic structure. Compositionality is language's adaptation to stimulus poverty.

Human language is learned, symbolic and exhibits syntactic structure, a set of properties which make it unique among naturally-occurring communication systems. How did human language come to be as it is? Language is culturally transmitted and cultural processes may have played a role in shaping language. However, it has been suggested that the cultural transmission oflanguage is constrained by some language-specific innate endowment. The primary objective of the research outlined in this paper is to investigate how such an endowment would influence the acquisition of langage and the dynamics of the repeated cultural transmission of language. To this end, a new connectionist model of the cultural evolution of communication is presented. In this model an individual's innate endowment is considered to be a learning rule with an associated learning bias. The model allows manipulations to be made to this learning apparatus andthe impact of such manipulations on the processes of language acquisition and language evolution to be explored. These investigations reveal that an innate endowment consisting of an ability to read the communicative intentions of others and a bias towards acquiring one-to-one mappings between meanings and signals results in the emergence, through purely cultural processes, of optimal communication. It has previously been suggested that humans possess just such an innate endowment. Properties of human language may therefore best be explained in terms of cultural evolution on an innate substrate.