Diffusion models have emerged as a powerful paradigm for generation, obtaining strong performance in various domains with continuous-valued inputs. Despite the promises of fully non-autoregressive text generation, applying diffusion models to natural language remains challenging due to its discrete nature. In this work, we propose Text-to-text Self-conditioned Simplex Diffusion (TESS), a text diffusion model that is fully non-autoregressive, employs a new form of self-conditioning, and applies the diffusion process on the logit simplex space rather than the typical learned embedding space. Through extensive experiments on natural language understanding and generation tasks including summarization, text simplification, paraphrase generation, and question generation, we demonstrate that TESS outperforms state-of-the-art non-autoregressive models and is competitive with pretrained autoregressive sequence-to-sequence models.

Despite the progress made in recent years in addressing natural language understanding (NLU) challenges, the majority of this progress remains to be concentrated on resource-rich languages like English. This work focuses on Persian language, one of the widely spoken languages in the world, and yet there are few NLU datasets available for this rich language. The availability of high-quality evaluation datasets is a necessity for reliable assessment of the progress on different NLU tasks and domains. We introduce ParsiNLU, the first benchmark in Persian language that includes a range of high-level tasks -- Reading Comprehension, Textual Entailment, etc. These datasets are collected in a multitude of ways, often involving manual annotations by native speakers. This results in over 14.5$k$ new instances across 6 distinct NLU tasks. Besides, we present the first results on state-of-the-art monolingual and multi-lingual pre-trained language-models on this benchmark and compare them with human performance, which provides valuable insights into our ability to tackle natural language understanding challenges in Persian. We hope ParsiNLU fosters further research and advances in Persian language understanding.

We consider the class of convex minimization problems, composed of a self-concordant function, such as the logdet metric, a convex data fidelity term h(.) and, a regularizing — possibly non-smooth — function g(.). This type of problems have recently attracted a great deal of interest, mainly due to their omnipresence in top-notch applications. Under this locally Lipschitz continuous gradient setting, we analyze the convergence behavior of proximal Newton schemes with the added twist of a probable presence of inexact evaluations. We prove attractive convergence rate guarantees and enhance state-of-the-art optimization schemes to accommodate such developments. Experimental results on sparse covariance estimation show the merits of our algorithm, both in terms of recovery efficiency and complexity.

We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This type of problems have recently attracted a great deal of interest, mainly due to their omnipresence in top-notch applications. Under this \emph{locally} Lipschitz continuous gradient setting, we analyze the convergence behavior of proximal Newton schemes with the added twist of a probable presence of inexact evaluations. We prove attractive convergence rate guarantees and enhance state-of-the-art optimization schemes to accommodate such developments. Experimental results on sparse covariance estimation show the merits of our algorithm, both in terms of recovery efficiency and complexity.