Large Language Models (LLMs) excel in linguistic tasks but struggle with mathematical reasoning, particularly in non- English languages like Hindi. This research aims to en- hance the mathematical reasoning skills of smaller, resource- efficient open-source LLMs in both Hindi and English. We evaluate models like OpenHathi 7B, LLaMA-2 7B, Wizard- Math 7B, Mistral 7B, LLeMMa 7B, MAmmoTH 7B, Gemini Pro, and GPT-4 using zero-shot, few-shot chain-of-thought (CoT) methods, and supervised fine-tuning. Our approach in- corporates curriculum learning, progressively training mod- els on increasingly difficult problems, a novel Decompo- sition Strategy to simplify complex arithmetic operations, and a Structured Solution Design that divides solutions into phases. Our experiments result in notable performance en- hancements. WizardMath 7B exceeds Gemini’s accuracy on English datasets by +6% and matches Gemini’s performance on Hindi datasets. Adopting a bilingual approach that com- bines English and Hindi samples achieves results comparable to individual language models, demonstrating the capability to learn mathematical reasoning in both languages. This re- search highlights the potential for improving mathematical reasoning in open-source LLMs.

Cryo-electron tomography (cryo-ET) is confronted with the intricate task of unveiling novel structures. General class discovery (GCD) seeks to identify new classes by learning a model that can pseudo-label unannotated (novel) instances solely using supervision from labeled (base) classes. While 2D GCD for image data has made strides, its 3D counterpart remains unexplored. Traditional methods encounter challenges due to model bias and limited feature transferability when clustering unlabeled 2D images into known and potentially novel categories based on labeled data. To address this limitation and extend GCD to 3D structures, we propose an innovative approach that harnesses a pretrained 2D transformer, enriched by an effective weight inflation strategy tailored for 3D adaptation, followed by a decoupled prototypical network. Incorporating the power of pretrained weight-inflated Transformers, we further integrate CLIP, a vision-language model to incorporate textual information. Our method synergizes a graph convolutional network with CLIP's frozen text encoder, preserving class neighborhood structure. In order to effectively represent unlabeled samples, we devise semantic distance distributions, by formulating a bipartite matching problem for category prototypes using a decoupled prototypical network. Empirical results unequivocally highlight our method's potential in unveiling hitherto unknown structures in cryo-ET. By bridging the gap between 2D GCD and the distinctive challenges of 3D cryo-ET data, our approach paves novel avenues for exploration and discovery in this domain.

We delve into Open Domain Generalization (ODG), marked by domain and category shifts between training's labeled source and testing's unlabeled target domains. Existing solutions to ODG face limitations due to constrained generalizations of traditional CNN backbones and errors in detecting target open samples in the absence of prior knowledge. Addressing these pitfalls, we introduce ODG-CLIP, harnessing the semantic prowess of the vision-language model, CLIP. Our framework brings forth three primary innovations: Firstly, distinct from prevailing paradigms, we conceptualize ODG as a multi-class classification challenge encompassing both known and novel categories. Central to our approach is modeling a unique prompt tailored for detecting unknown class samples, and to train this, we employ a readily accessible stable diffusion model, elegantly generating proxy images for the open class. Secondly, aiming for domain-tailored classification (prompt) weights while ensuring a balance of precision and simplicity, we devise a novel visual stylecentric prompt learning mechanism. Finally, we infuse images with class-discriminative knowledge derived from the prompt space to augment the fidelity of CLIP's visual embeddings. We introduce a novel objective to safeguard the continuity of this infused semantic intel across domains, especially for the shared classes. Through rigorous testing on diverse datasets, covering closed and open-set DG contexts, ODG-CLIP demonstrates clear supremacy, consistently outpacing peers with performance boosts between 8%-16%. Code will be available at https://github.com/mainaksingha01/ODG-CLIP.