This paper proposes a methodology for generating and perturbing detailed derivations of equations at scale, aided by a symbolic engine, to evaluate the generalisability of Transformers to out-of-distribution mathematical reasoning problems. Instantiating the framework in the context of sequence classification tasks, we compare the capabilities of GPT-4, GPT-3.5, and a canon of fine-tuned BERT models, exploring the relationship between specific operators and generalisation failure via the perturbation of reasoning aspects such as symmetry and variable surface forms. Surprisingly, our empirical evaluation reveals that the average in-distribution performance of fine-tuned models surpasses GPT-3.5, and rivals GPT-4. However, perturbations to input reasoning can reduce their performance by up to 80 F1 points. Overall, the results suggest that the in-distribution performance of smaller open-source models may potentially rival GPT by incorporating appropriately structured derivation dependencies during training, and highlight a shared weakness between BERT and GPT involving a relative inability to decode indirect references to mathematical entities. We release the full codebase, constructed datasets, and fine-tuned models to encourage future progress in the field.

In the last few years, there has been an increased interest in building multimodal (vision-language) models that are pretrained on larger but noisier datasets where the two modalities (e.g., image and text) loosely correspond to each other (e.g., Lu et al., 2019; Radford et al., 2021). Given a task (such as visual question answering), these models are then often fine-tuned on task-specific supervised datasets. (e.g., Lu et al., 2019; Chen et al.,2020; Tan and Bansal, 2019; Li et al., 2020a,b). In addition to the larger pretraining datasets, the transformer architecture (Vaswani et al., 2017) and in particular self-attention applied to two modalities are responsible for the impressive performance of the recent pretrained models on downstream tasks (Hendricks et al., 2021). In this tutorial, we focus on recent vision-language pretraining paradigms. Our goal is to first provide the background on image–language datasets, benchmarks, and modeling innovations before the multimodal pretraining area. Next we discuss the different family of models used for vision-language pretraining, highlighting their strengths and shortcomings. Finally, we discuss the limits of vision-language pretraining through statistical learning, and the need for alternative approaches such as causal representation learning.

The limits of applicability of vision-and language models are defined by the coverage of their training data. Tasks like vision question answering (VQA) often require commonsense and factual information beyond what can be learned from task-specific datasets. This paper investigates the injection of knowledge from general-purpose knowledge bases (KBs) into vision-and-language transformers. We use an auxiliary training objective that encourages the learned representations to align with graph embeddings of matching entities in a KB. We empirically study the relevance of various KBs to multiple tasks and benchmarks. The technique brings clear benefits to knowledge-demanding question answering tasks (OK-VQA, FVQA) by capturing semantic and relational knowledge absent from existing models. More surprisingly, the technique also benefits visual reasoning tasks (NLVR2, SNLI-VE). We perform probing experiments and show that the injection of additional knowledge regularizes the space of embeddings, which improves the representation of lexical and semantic similarities. The technique is model-agnostic and can expand the applicability of any vision-and-language transformer with minimal computational overhead.