Pre-training a language model equips it with a broad understanding of the world, while fine- tuning refines it into a helpful assistant. However, fine-tuning does not exclusively enhance task- specific behaviors but also suppresses some of the beneficial variability from pre-training. This reduction in diversity is partly due to the optimization process, which theoretically decreases model entropy in exchange for task performance. To counteract this, we introduce hindsight merging, a technique that combines a fine-tuned model with a previous training checkpoint using linear interpolation to restore entropy and improve performance. Hindsight-merged models retain strong instruction-following capabilities and alignment while displaying increased diversity present in the base model. Additionally, this results in improved inference scaling, achieving a consistent 20-50% increase in pass@10 relative to the instruction tuned model across a coding benchmark and series of models. Our findings suggest that hindsight merging is an effective strategy for generating diverse generations that follow instructions.

Counterfactual explanations (CEs) are a practical tool for demonstrating why machine learning classifiers make particular decisions. For CEs to be useful, it is important that they are easy for users to interpret. Existing methods for generating interpretable CEs rely on auxiliary generative models, which may not be suitable for complex datasets, and incur engineering overhead. We introduce a simple and fast method for generating interpretable CEs in a white-box setting without an auxiliary model, by using the predictive uncertainty of the classifier. Our experiments show that our proposed algorithm generates more interpretable CEs, according to IM1 scores (Van Looveren et al., 2019), than existing methods. Additionally, our approach allows us to estimate the uncertainty of a CE, which may be important in safety-critical applications, such as those in the medical domain.

Reliable yet efficient evaluation of generalisation performance of a proposed architecture is crucial to the success of neural architecture search (NAS). Traditional approaches face a variety of limitations: training each architecture to completion is prohibitively expensive, early stopped validation accuracy may correlate poorly with fully trained performance, and model-based estimators require large training sets. We instead propose to estimate the final test performance based on a simple measure of training speed. Our estimator is theoretically motivated by the connection between generalisation and training speed, and is also inspired by the reformulation of a PAC-Bayes bound under the Bayesian setting. Our model-free estimator is simple, efficient, and cheap to implement, and does not require hyperparameter-tuning or surrogate training before deployment. We demonstrate on various NAS search spaces that our estimator consistently outperforms other alternatives in achieving better correlation with the true test performance rankings. We further show that our estimator can be easily incorporated into both query-based and one-shot NAS methods to improve the speed or quality of the search.

We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model's training speed can be used to estimate its marginal likelihood. Second, that this measure, under certain conditions, predicts the relative weighting of models in linear model combinations trained to minimize a regression loss. We verify our results in model selection tasks for linear models and for the infinite-width limit of deep neural networks. We further provide encouraging empirical evidence that the intuition developed in these settings also holds for deep neural networks trained with stochastic gradient descent. Our results suggest a promising new direction towards explaining why neural networks trained with stochastic gradient descent are biased towards functions that generalize well.