Compressing Transformer Language Models via Matrix Product Operator Decomposition: A Case Study on PicoGPT

• URL: http://arxiv.org/abs/2603.28534v1
• Date: Mon, 30 Mar 2026 14:57:47 GMT
• Title: Compressing Transformer Language Models via Matrix Product Operator Decomposition: A Case Study on PicoGPT
• Abstract summary: Transformer-based language models achieve strong performance across NLP tasks, but their quadratic parameter scaling with hidden dimension makes deployment on resource-constrained hardware expensive.<n>We study Matrix Product Operator decomposition as a principled compression method for transformers.<n>MPO factorises weight matrices into chains of low-rank cores, with approximation quality controlled by the bond dimension chi.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Transformer-based language models achieve strong performance across NLP tasks, but their quadratic parameter scaling with hidden dimension makes deployment on resource-constrained hardware expensive. We study Matrix Product Operator (MPO) decomposition as a principled compression method for transformers. MPO factorises weight matrices into chains of low-rank cores, with approximation quality controlled by the bond dimension chi. We replace every nn.Linear layer in PicoGPT, a GPT-2-style character-level language model with about 1M parameters, with an MPOLinear module parameterised as an MPO chain. Cores are initialised either by TT-SVD from pretrained dense weights or from random initialisation, and trained using standard PyTorch autograd without a custom backward pass. We derive balanced factorisation schemes for the five distinct weight shapes in PicoGPT and evaluate bond dimensions chi in {4, 8, 16, 32} on Tiny Shakespeare. MPO compression achieves up to 13x compression per transformer block at chi = 4. At chi = 16, the model uses 191,872 parameters instead of 1,020,224 while retaining 97.7% of baseline token accuracy (51.6% vs 52.8%). Reconstruction error follows the expected trend and is lower for three-site than two-site factorisations at the same bond dimension. The chi = 8 model gives the best accuracy per parameter, exceeding the dense baseline by 2.7x on this metric. These results show that MPO parameterisation is a practical and theoretically grounded alternative to low-rank methods and unstructured pruning for transformer compression.

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