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.

AstroLLaMA: Towards Specialized Foundation Models in Astronomy

Large language models excel in many human-language tasks but often falter in highly specialized domains like scholarly astronomy. To bridge this gap, we introduce AstroLLaMA, a 7-billion-parameter model fine-tuned from LLaMA-2 using over 300,000 astronomy abstracts from arXiv. Optimized for traditional causal language modeling, AstroLLaMA achieves a 30% lower perplexity than Llama-2, showing marked domain adaptation. Our model generates more insightful and scientifically relevant text completions and embedding extraction than state-of-the-arts foundation models despite having significantly fewer parameters. AstroLLaMA serves as a robust, domain-specific model with broad fine-tuning potential. Its public release aims to spur astronomy-focused research, including automatic paper summarization and conversational agent development.

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.

q-Paths: Generalizing the Geometric Annealing Path using Power Means

Many common machine learning methods involve the geometric annealing path, a sequence of intermediate densities between two distributions of interest constructed using the geometric average. While alternatives such as the moment-averaging path have demonstrated performance gains in some settings, their practical applicability remains limited by exponential family endpoint assumptions and a lack of closed form energy function. In this work, we introduce $q$-paths, a family of paths which is derived from a generalized notion of the mean, includes the geometric and arithmetic mixtures as special cases, and admits a simple closed form involving the deformed logarithm function from nonextensive thermodynamics. Following previous analysis of the geometric path, we interpret our $q$-paths as corresponding to a $q$-exponential family of distributions, and provide a variational representation of intermediate densities as minimizing a mixture of $\alpha$-divergences to the endpoints. We show that small deviations away from the geometric path yield empirical gains for Bayesian inference using Sequential Monte Carlo and generative model evaluation using Annealed Importance Sampling.

Annealed Importance Sampling with q-Paths

Annealed importance sampling (AIS) is the gold standard for estimating partition functions or marginal likelihoods, corresponding to importance sampling over a path of distributions between a tractable base and an unnormalized target. While AIS yields an unbiased estimator for any path, existing literature has been primarily limited to the geometric mixture or moment-averaged paths associated with the exponential family and KL divergence. We explore AIS using $q$-paths, which include the geometric path as a special case and are related to the homogeneous power mean, deformed exponential family, and $\alpha$-divergence.

Learning Attribute-Based and Relationship-Based Access Control Policies with Unknown Values

Attribute-Based Access Control (ABAC) and Relationship-based access control (ReBAC) provide a high level of expressiveness and flexibility that promote security and information sharing, by allowing policies to be expressed in terms of attributes of and chains of relationships between entities. Algorithms for learning ABAC and ReBAC policies from legacy access control information have the potential to significantly reduce the cost of migration to ABAC or ReBAC. This paper presents the first algorithms for mining ABAC and ReBAC policies from access control lists (ACLs) and incomplete information about entities, where the values of some attributes of some entities are unknown. We show that the core of this problem can be viewed as learning a concise three-valued logic formula from a set of labeled feature vectors containing unknowns, and we give the first algorithm (to the best of our knowledge) for that problem.