Amartya Roy

Anirbit Mukherjee, Amartya Roy

Deep Operator Networks are an increasingly popular paradigm for solving regression in infinite dimensions and hence solve families of PDEs in one shot. In this work, we aim to establish a first-of-its-kind data-dependent lowerbound on the size of DeepONets required for them to be able to reduce empirical error on noisy data. In particular, we show that for low training errors to be obtained on $n$ data points it is necessary that the common output dimension of the branch and the trunk net be scaling as $Ω\left ( \sqrt[\leftroot{-1}\uproot{-1}4]{n} \right )$. This inspires our experiments with DeepONets solving the advection-diffusion-reaction PDE, where we demonstrate the possibility that at a fixed model size, to leverage increase in this common output dimension and get monotonic lowering of training error, the size of the training data might necessarily need to scale at least quadratically with it.

Paramita Das, Amartya Roy, Ritabrata Chakraborty et al.

Although Wikipedia is the largest multilingual encyclopedia, it remains inherently incomplete. There is a significant disparity in the quality of content between high-resource languages (HRLs, e.g., English) and low-resource languages (LRLs, e.g., Hindi), with many LRL articles lacking adequate information. To bridge these content gaps, we propose a lightweight framework to enhance knowledge equity between English and Hindi. In case the English Wikipedia page is not up-to-date, our framework extracts relevant information from external resources readily available (such as English books) and adapts it to align with Wikipedia's distinctive style, including its \textit{neutral point of view} (NPOV) policy, using in-context learning capabilities of large language models. The adapted content is then machine-translated into Hindi for integration into the corresponding Wikipedia articles. On the other hand, if the English version is comprehensive and up-to-date, the framework directly transfers knowledge from English to Hindi. Our framework effectively generates new content for Hindi Wikipedia sections, enhancing Hindi Wikipedia articles respectively by 65% and 62% according to automatic and human judgment-based evaluations.