Peter Grindrod

Catherine F. Higham, Desmond J. Higham, Peter Grindrod

Generative artificial intelligence (AI) refers to algorithms that create synthetic but realistic output. Diffusion models currently offer state of the art performance in generative AI for images. They also form a key component in more general tools, including text-to-image generators and large language models. Diffusion models work by adding noise to the available training data and then learning how to reverse the process. The reverse operation may then be applied to new random data in order to produce new outputs. We provide a brief introduction to diffusion models for applied mathematicians and statisticians. Our key aims are (a) to present illustrative computational examples, (b) to give a careful derivation of the underlying mathematical formulas involved, and (c) to draw a connection with partial differential equation (PDE) diffusion models. We provide code for the computational experiments. We hope that this topic will be of interest to advanced undergraduate students and postgraduate students. Portions of the material may also provide useful motivational examples for those who teach courses in stochastic processes, inference, machine learning, PDEs or scientific computing.

Jumbly Grindrod, Peter Grindrod

We investigate how word meanings are represented in the transformer language models. Specifically, we focus on whether transformer models employ something analogous to a lexical store - where each word has an entry that contains semantic information. To do this, we extracted the token embedding space of RoBERTa-base and k-means clustered it into 200 clusters. In our first study, we then manually inspected the resultant clusters to consider whether they are sensitive to semantic information. In our second study, we tested whether the clusters are sensitive to five psycholinguistic measures: valence, concreteness, iconicity, taboo, and age of acquisition. Overall, our findings were very positive - there is a wide variety of semantic information encoded within the token embedding space. This serves to rule out certain "meaning eliminativist" hypotheses about how transformer LLMs process semantic information.