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While large language models (LLMs) like GPT-3 have achieved impressive results on multiple choice question answering (MCQA) tasks in the zero, one, and few-shot settings, they generally lag behind the MCQA state of the art (SOTA). MCQA tasks have traditionally been presented to LLMs like cloze tasks. An LLM is conditioned on a question (without the associated answer options) and its chosen option is the one assigned the highest probability after normalization (for length, etc.). A more natural prompting approach is to present the question and answer options to the LLM jointly and have it output the symbol (e.g., “A”) associated with its chosen answer option. This approach allows the model to explicitly compare answer options, reduces computational costs, and mitigates the effects of tokenization scheme and answer option representations on answer selection. For the natural approach to be effective, the LLM it is used with must be able to associate answer options with the symbols that represent them. The LLM needs what we term multiple choice symbol binding (MCSB) ability. This ability varies greatly by model. We show that a model with high MCSB ability performs much better with the natural approach than with the traditional approach across 20 diverse datasets and largely closes the gap with the SOTA, suggesting that the MCQA ability of LLMs has been previously underestimated. 

Integrating functions on discrete domains into neural networks is key to develop- ing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep learning architectures that rely on representations in high-dimensional vector spaces. In this work, we address both difficulties for set functions, which capture many important discrete problems. First, we develop a framework for extending set functions onto low-dimensional continuous domains, where many extensions are naturally defined. Our framework subsumes many well-known extensions as special cases. Second, to avoid undesirable low-dimensional neural network bottlenecks, we convert low-dimensional extensions into representations in high-dimensional spaces, taking inspiration from the success of semidefinite programs for combinatorial optimization. Empirically, we observe benefits of our extensions for unsupervised neural combinatorial optimization, in particular with high-dimensional representations. 

The generalization of representations learned via contrastive learning depends crucially on what features of the data are extracted. However, we observe that the contrastive loss does not always sufficiently guide which features are extracted, a behavior that can negatively impact the performance on downstream tasks via "shortcuts", i.e., by inadvertently suppressing important predictive features. We find that feature extraction is influenced by the difficulty of the so-called instance discrimination task (i.e., the task of discriminating pairs of similar points from pairs of dissimilar ones). Although harder pairs improve the representation of some features, the improvement comes at the cost of suppressing previously well-represented features. In response, we propose implicit feature modification (IFM), a method for altering positive and negative samples in order to guide contrastive models towards capturing a wider variety of predictive features. Empirically, we observe that IFM reduces feature suppression, and as a result, improves performance on vision and medical imaging tasks.