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.

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires matrix storage, inversion, and multiplication or Monte Carlo estimation, none of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we consider the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems.

Most applications of machine learning to classification assume a closed set of balanced classes. This is at odds with the real world, where class occurrence statistics often follow a long-tailed power-law distribution and it is unlikely that all classes are seen in a single sample. Nonparametric Bayesian models naturally capture this phenomenon, but have significant practical barriers to widespread adoption, namely implementation complexity and computational inefficiency. To address this, we present a method for extracting the inductive bias from a nonparametric Bayesian model and transferring it to an artificial neural network. By simulating data with a nonparametric Bayesian prior, we can metalearn a sequence model that performs inference over an unlimited set of classes. After training, this "neural circuit" has distilled the corresponding inductive bias and can successfully perform sequential inference over an open set of classes. Our experimental results show that the metalearned neural circuit achieves comparable or better performance than particle filter-based methods for inference in these models while being faster and simpler to use than methods that explicitly incorporate Bayesian nonparametric inference.