Activation-Aware Weight Tensorization: A Calibration-Time Preconditioner for Tensor-Network LLM Compression

Alessandro Beatini, Marco Maronese, Emanuele Rodolà

Post-training tensor-network compression replaces Transformer linear layers with Tensor Train (TT) or Tree Tensor Network (TTN) operators, but standard decompositions minimize weight-space Frobenius error rather than functional error under the layer's activation distribution. We propose Activation-aware Weight Tensorization (AWT), a training-free calibration wrapper that preconditions each weight matrix with a diagonal activation-derived scale before an unchanged TT/TTN solver and deploys the result with only an input-side elementwise rescaling. Across Llama 3.1 8B, Ministral 8B, and Qwen2.5 7B, AWT consistently improves vanilla TT/TTN tensorization at 2-6 times compression: under single-operator replacement, AWT closes 12-35% of the WikiText perplexity gap to the dense baseline across the three model families and 2-6 times compression settings; while under multi-operator Llama suffix replacement it closes 27-60% across attention-group and all-seven-matrix settings. The gains also transfer to downstream HellaSwag and ARC-Challenge evaluations. We further show that diagonal preconditioning is a robustness-modularity tradeoff rather than a diagonal-covariance assumption: a dense…