While significant progress has been made in natural language processing (NLP), existing methods exhibit limitations in effectively interpreting and processing diverse mathematical modalities. Therefore, we introduce UniMath, a versatile and unified system designed for multimodal mathematical reasoning tasks. Tackling complex problem-solving in arithmetic, geometry, and table-based math, UniMath utilizes a fine-tuned T5 model augmented with a variational autoencoder (VAE)-based image tokenizer. By jointly training and evaluating the model on three diverse datasets - SVAMP, GeoQA, and TableMWP, UniMath achieves state-of-the-art performance. The model’s generalization ability is further demonstrated via fine-tuning on two additional datasets, MathQA and Geo-Proving. Through comprehensive evaluations, we showcase that joint training across diverse math tasks improves overall model performance and enhances its ability to generalize across different mathematical reasoning tasks. This pioneering approach provides a blueprint and inspires further efforts on unified mathematical reasoning with deep learning systems.

Current variational dialog models have employed pre-trained language models (PLMs) to parameterize the likelihood and posterior distributions. However, the Gaussian assumption made on the prior distribution is incompatible with these distributions, thus restricting the diversity of generated responses. These models also suffer from posterior collapse, i.e., the decoder tends to ignore latent variables and directly access information captured in the encoder through the cross-attention mechanism. In this work, we propose Dior-CVAE, a hierarchical conditional variational autoencoder (CVAE) with diffusion priors to address these challenges. We employ a diffusion model to increase the complexity of the prior distribution and its compatibility with the distributions produced by a PLM. Also, we propose memory dropout to the cross-attention mechanism, which actively encourages the use of latent variables for response generation. Overall, experiments across two commonly used open-domain dialog datasets show that our method can generate more diverse responses without large-scale dialog pre-training. Code is available at https://github.com/UKPLab/dior-cvae.