Structured pruning is a widely used technique for reducing the size of pre-trained language models (PLMs), but current methods often overlook the potential of compressing the hidden dimension d in PLMs, a dimension critical to model size and efficiency. This paper introduces a novel structured pruning approach, Structured Pruning with PCA Projection ( SP³), targeting the effective reduction of d by projecting features into a space defined by principal components before masking. Extensive experiments on benchmarks (GLUE and SQuAD) show that can reduce d by 70%, compress 94% of the BERT_base model, and maintain over 96% accuracy and outperform other methods that compress d by 6% in accuracy at the same compression ratio. SP³ has also proven effective with other models, including OPT and Llama.Our data and code are available at https://github.com/hyx1999/SP3

Math word problems (MWP) involving advanced operators such as linear equation solver cannot be easily tackled by earlier MWP methods, because the existing generation methods suffer from repeated sub-expression generation and deductive methods are restricted to dealing with binary operations. This paper propose a new multivariate directed acyclic graph (mDAG) as an alternative to the generation methods’ binary expression tree or the deductive methods’ binary directed acyclic graph. Then to produce the topological ordering of mDAG, we propose a generation-based deductive (GeDe) model, which equips a generation model with a re-encoder to keep the deductive property but avoid the expensive enumeration of the deductive methods. GeDe performs well on math problems with many operators on the widely used benchmarks as well as solving multivariate operators on our own CMWPA benchmark. Our code is available at https://github.com/hyx1999/GeDe