The Boden-Hu conjecture holds precisely up to rank eight

Consider moduli schemes of vector bundles over a smooth projective curve endowed with parabolic structures over a marked point. Boden and Hu observed that a slight variation of the weights leads to a desingularisation of the moduli scheme, and they conjectured that one can always obtain a small resolution this way. The present text proves this conjecture in some cases (including all bundles of rank up to eight) and gives counterexamples in all other cases (in particular in every rank beyond eight). The main tool is a generalisation of Ext-groups involving more than two quasiparabolic bundles.Comment: 17 page

The fiscal cost of weak governance: Evidence from teacher absence in India.

The relative return to strategies that augment inputs versus those that reduce inefficiencies remains a key open question for education policy in low-income countries. Using a new nationally-representative panel dataset of schools across 1297 villages in India, we show that the large public investments in education over the past decade have led to substantial improvements in input-based measures of school quality, but only a modest reduction in inefficiency as measured by teacher absence. In our data, 23.6% of teachers were absent during unannounced school visits, and we estimate that the salary cost of unauthorized teacher absence is $1.5 billion/year. We find two robust correlations in the nationally-representative panel data that corroborate findings from smaller-scale experiments. First, reductions in student-teacher ratios are correlated with increased teacher absence. Second, increases in the frequency of school monitoring are strongly correlated with lower teacher absence. Using these results, we show that reducing inefficiencies by increasing the frequency of monitoring could be over ten times more cost effective at increasing the effective student-teacher ratio than hiring more teachers. Thus, policies that decrease the inefficiency of public education spending are likely to yield substantially higher marginal returns than those that augment inputs

Learning to Learn to Disambiguate: Meta-Learning for Few-Shot Word Sense Disambiguation

The success of deep learning methods hinges on the availability of large training datasets annotated for the task of interest. In contrast to human intelligence, these methods lack versatility and struggle to learn and adapt quickly to new tasks, where labeled data is scarce. Meta-learning aims to solve this problem by training a model on a large number of few-shot tasks, with an objective to learn new tasks quickly from a small number of examples. In this paper, we propose a meta-learning framework for few-shot word sense disambiguation (WSD), where the goal is to learn to disambiguate unseen words from only a few labeled instances. Meta-learning approaches have so far been typically tested in an $N$-way, $K$-shot classification setting where each task has $N$ classes with $K$ examples per class. Owing to its nature, WSD deviates from this controlled setup and requires the models to handle a large number of highly unbalanced classes. We extend several popular meta-learning approaches to this scenario, and analyze their strengths and weaknesses in this new challenging setting.Comment: Added additional experiment