On the Relationship Between Representation Geometry and Generalization in Deep Neural Networks

We investigate the relationship between representation geometry and neural network performance. Analyzing 52 pretrained ImageNet models across 13 architecture families, we show that effective dimension -- an unsupervised geometric metric -- strongly predicts accuracy. Output effective dimension achieves partial r=0.75 ($p < 10^(-10)$) after controlling for model capacity, while total compression achieves partial r=-0.72. These findings replicate across ImageNet and CIFAR-10, and generalize to NLP: effective dimension predicts performance for 8 encoder models on SST-2/MNLI and 15 decoder-only LLMs on AG News (r=0.69, p=0.004), while model size does not (r=0.07). We establish bidirectional causality: degrading geometry via noise causes accuracy loss (r=-0.94, $p < 10^(-9)$), while improving geometry via PCA maintains accuracy across architectures (-0.03pp at 95% variance). This relationship is noise-type agnostic -- Gaussian, Uniform, Dropout, and Salt-and-pepper noise all show $|r| > 0.90$. These results establish that effective dimension provides domain-agnostic predictive and causal information about neural network performance, computed entirely without labels.

Can maiBERT Speak for Maithili?

Natural Language Understanding (NLU) for low-resource languages remains a major challenge in NLP due to the scarcity of high-quality data and language-specific models. Maithili, despite being spoken by millions, lacks adequate computational resources, limiting its inclusion in digital and AI-driven applications. To address this gap, we introducemaiBERT, a BERT-based language model pre-trained specifically for Maithili using the Masked Language Modeling (MLM) technique. Our model is trained on a newly constructed Maithili corpus and evaluated through a news classification task. In our experiments, maiBERT achieved an accuracy of 87.02%, outperforming existing regional models like NepBERTa and HindiBERT, with a 0.13% overall accuracy gain and 5-7% improvement across various classes. We have open-sourced maiBERT on Hugging Face enabling further fine-tuning for downstream tasks such as sentiment analysis and Named Entity Recognition (NER).