India is a diverse society with unique challenges in developing AI systems, including linguistic diversity, oral traditions, data accessibility, and scalability. Existing foundation models are primarily trained on English, limiting their effectiveness for India's population. Indic languages comprise only 1 percent of Common Crawl corpora despite India representing 18 percent of the global population, leading to linguistic biases. Thousands of regional languages, dialects, and code mixing create additional representation challenges due to sparse training data. We introduce Krutrim LLM, a 2 trillion token multilingual model designed for India's linguistic landscape. It incorporates the largest known Indic dataset, mitigating data scarcity and ensuring balanced performance across dialects. Krutrim outperforms or matches state-of-the-art models on Indic benchmarks while maintaining competitive English performance. Despite being significantly smaller in training flops, Krutrim LLM matches or exceeds models like LLAMA-2 on 10 out of 16 tasks, with an average score of 0.57 versus 0.55. This evidences Krutrim's flexible multilingual fluency across diverse linguistic contexts. Krutrim is integrated with real-time search to improve factual accuracy in conversational AI applications. This enhances accessibility for over 1 billion users worldwide. Through intentional design choices addressing data imbalances, Krutrim LLM signifies meaningful progress in building ethical, globally representative AI models.

Invertible convolutions have been an essential element for building expressive normalizing flow-based generative models since their introduction in Glow. Several attempts have been made to design invertible $k \times k$ convolutions that are efficient in training and sampling passes. Though these attempts have improved the expressivity and sampling efficiency, they severely lagged behind Glow which used only $1 \times 1$ convolutions in terms of sampling time. Also, many of the approaches mask a large number of parameters of the underlying convolution, resulting in lower expressivity on a fixed run-time budget. We propose a $k \times k$ convolutional layer and Deep Normalizing Flow architecture which i.) has a fast parallel inversion algorithm with running time O$(n k^2)$ ($n$ is height and width of the input image and k is kernel size), ii.) masks the minimal amount of learnable parameters in a layer. iii.) gives better forward pass and sampling times comparable to other $k \times k$ convolution-based models on real-world benchmarks. We provide an implementation of the proposed parallel algorithm for sampling using our invertible convolutions on GPUs. Benchmarks on CIFAR-10, ImageNet, and CelebA datasets show comparable performance to previous works regarding bits per dimension while significantly improving the sampling time.