Measuring Sharpness in Grokking

Neural networks sometimes exhibit grokking, a phenomenon where perfect or near-perfect performance is achieved on a validation set well after the same performance has been obtained on the corresponding training set. In this workshop paper, we introduce a robust technique for measuring grokking, based on fitting an appropriate functional form. We then use this to investigate the sharpness of transitions in training and validation accuracy under two settings. The first setting is the theoretical framework developed by Levi et al. (2023) where closed form expressions are readily accessible. The second setting is a two-layer MLP trained to predict the parity of bits, with grokking induced by the concealment strategy of Miller et al. (2023). We find that trends between relative grokking gap and grokking sharpness are similar in both settings when using absolute and relative measures of sharpness. Reflecting on this, we make progress toward explaining some trends and identify the need for further study to untangle the various mechanisms which influence the sharpness of grokking.

Grokking Beyond Neural Networks: An Empirical Exploration with Model Complexity

In some settings neural networks exhibit a phenomenon known as grokking, where they achieve perfect or near-perfect accuracy on the validation set long after the same performance has been achieved on the training set. In this paper, we discover that grokking is not limited to neural networks but occurs in other settings such as Gaussian process (GP) classification, GP regression and linear regression. We also uncover a mechanism by which to induce grokking on algorithmic datasets via the addition of dimensions containing spurious information. The presence of the phenomenon in non-neural architectures provides evidence that grokking is not specific to SGD or weight norm regularisation. Instead, grokking may be possible in any setting where solution search is guided by complexity and error. Based on this insight and further trends we see in the training trajectories of a Bayesian neural network (BNN) and GP regression model, we make progress towards a more general theory of grokking. Specifically, we hypothesise that the phenomenon is governed by the accessibility of certain regions in the error and complexity landscapes.

Adversarial Fine-Tuning of Language Models: An Iterative Optimisation Approach for the Generation and Detection of Problematic Content

In this paper, we tackle the emerging challenge of unintended harmful content generation in Large Language Models (LLMs) with a novel dual-stage optimisation technique using adversarial fine-tuning. Our two-pronged approach employs an adversarial model, fine-tuned to generate potentially harmful prompts, and a judge model, iteratively optimised to discern these prompts. In this adversarial cycle, the two models seek to outperform each other in the prompting phase, generating a dataset of rich examples which are then used for fine-tuning. This iterative application of prompting and fine-tuning allows continuous refinement and improved performance. The performance of our approach is evaluated through classification accuracy on a dataset consisting of problematic prompts not detected by GPT-4, as well as a selection of contentious but unproblematic prompts. We show considerable increase in classification accuracy of the judge model on this challenging dataset as it undergoes the optimisation process. Furthermore, we show that a rudimentary model \texttt{ada} can achieve 13\% higher accuracy on the hold-out test set than GPT-4 after only a few rounds of this process, and that this fine-tuning improves performance in parallel tasks such as toxic comment identification.

Steering Language Generation: Harnessing Contrastive Expert Guidance and Negative Prompting for Coherent and Diverse Synthetic Data Generation

Large Language Models (LLMs) hold immense potential to generate synthetic data of high quality and utility, which has numerous applications from downstream model training to practical data utilisation. However, contemporary models, despite their impressive capacities, consistently struggle to produce both coherent and diverse data. To address the coherency issue, we introduce contrastive expert guidance, where the difference between the logit distributions of fine-tuned and base language models is emphasised to ensure domain adherence. In order to ensure diversity, we utilise existing real and synthetic examples as negative prompts to the model. We deem this dual-pronged approach to logit reshaping as STEER: Semantic Text Enhancement via Embedding Repositioning. STEER operates at inference-time and systematically guides the LLMs to strike a balance between adherence to the data distribution (ensuring semantic fidelity) and deviation from prior synthetic examples or existing real datasets (ensuring diversity and authenticity). This delicate balancing act is achieved by dynamically moving towards or away from chosen representations in the latent space. STEER demonstrates improved performance over previous synthetic data generation techniques, exhibiting better balance between data diversity and coherency across three distinct tasks: hypothesis generation, toxic and non-toxic comment generation, and commonsense reasoning task generation. We demonstrate how STEER allows for fine-tuned control over the diversity-coherency trade-off via its hyperparameters, highlighting its versatility.

Rice paddy disease classifications using CNNs

Rice is a staple food in the world's diet, and yet huge percentages of crop yields are lost each year to disease. To combat this problem, people have been searching for ways to automate disease diagnosis. Here, we extend on previous modelling work by analysing how disease-classification accuracy is sensitive to both model architecture and common computer vision techniques. In doing so, we maximise accuracy whilst working in the constraints of smaller model sizes, minimum GPUs and shorter training times. Whilst previous state-of-the-art models had 93% accuracy only predicting 5 diseases, we improve this to 98.7% using 10 disease classes.

Eigenvalue initialisation and regularisation for Koopman autoencoders

Regularising the parameter matrices of neural networks is ubiquitous in training deep models. Typical regularisation approaches suggest initialising weights using small random values, and to penalise weights to promote sparsity. However, these widely used techniques may be less effective in certain scenarios. Here, we study the Koopman autoencoder model which includes an encoder, a Koopman operator layer, and a decoder. These models have been designed and dedicated to tackle physics-related problems with interpretable dynamics and an ability to incorporate physics-related constraints. However, the majority of existing work employs standard regularisation practices. In our work, we take a step toward augmenting Koopman autoencoders with initialisation and penalty schemes tailored for physics-related settings. Specifically, we propose the "eigeninit" initialisation scheme that samples initial Koopman operators from specific eigenvalue distributions. In addition, we suggest the "eigenloss" penalty scheme that penalises the eigenvalues of the Koopman operator during training. We demonstrate the utility of these schemes on two synthetic data sets: a driven pendulum and flow past a cylinder; and two real-world problems: ocean surface temperatures and cyclone wind fields. We find on these datasets that eigenloss and eigeninit improves the convergence rate by up to a factor of 5, and that they reduce the cumulative long-term prediction error by up to a factor of 3. Such a finding points to the utility of incorporating similar schemes as an inductive bias in other physics-related deep learning approaches.