Previous work has established that RNNs with an unbounded activation function have the capacity to count exactly. However, it has also been shown that RNNs are challenging to train effectively and generally do not learn exact counting behaviour. In this paper, we focus on this problem by studying the simplest possible RNN, a linear single-cell network. We conduct a theoretical analysis of linear RNNs and identify conditions for the models to exhibit exact counting behaviour. We provide a formal proof that these conditions are necessary and sufficient. We also conduct an empirical analysis using tasks involving a Dyck-1-like Balanced Bracket language under two different settings. We observe that linear RNNs generally do not meet the necessary and sufficient conditions for counting behaviour when trained with the standard approach. We investigate how varying the length of training sequences and utilising different target classes impacts model behaviour during training and the ability of linear RNN models to effectively approximate the indicator conditions.

The field of visual question answering (VQA) has recently seen a surge in research focused on providing explanations for predicted answers. However, current systems mostly rely on separate models to predict answers and generate explanations, leading to less grounded and frequently inconsistent results. To address this, we propose a multitask learning approach towards a Unified Model for Answer and Explanation generation (UMAE). Our approach involves the addition of artificial prompt tokens to training data and fine-tuning a multimodal encoder-decoder model on a variety of VQA-related tasks. In our experiments, UMAE models surpass the prior state-of-the-art answer accuracy on A-OKVQA by 10 15%, show competitive results on OK-VQA, achieve new state-of-the-art explanation scores on A-OKVQA and VCR, and demonstrate promising out-of-domain performance on VQA-X.