Decompose, Mix, Adapt: A Unified Framework for Parameter-Efficient Neural Network Recombination and Compression

Adapting large pretrained models to diverse tasks is now routine, yet the two dominant strategies of parameter-efficient fine-tuning (PEFT) and low-rank compression are typically composed in sequence. This decoupled practice first compresses and then fine-tunes adapters, potentially misaligning the compressed subspace with downstream objectives and squandering a global parameter budget. To overcome this limitation, we introduce JACTUS (Joint Adaptation and Compression with a Task-aware Union of Subspaces), a single framework that unifies compression and adaptation. From a small calibration set, JACTUS estimates input and pre-activation gradient covariances, forms their orthogonal union with the pretrained weight subspace, performs a projected low-rank approximation inside this union, allocates rank globally by marginal gain per parameter, and trains only a compact core matrix. This explicitly mitigates the potential misalignment between the compressed subspace and downstream objectives by coupling the directions preserved for compression with those required for adaptation, yielding a deployable low-rank model that avoids retaining full frozen weights while enabling fast and robust tuning. On vision, JACTUS attains an average 89.2% accuracy on ViT-Base across eight datasets at 80% retained parameters, surpassing strong 100% PEFT baselines (e.g., DoRA 87.9%). On language, JACTUS achieves an 80.9% average on Llama2-7B commonsense QA at the same 80% retained-parameter budget, outperforming 100% PEFT (e.g., DoRA 79.7%) and exceeding prior compress-then-finetune pipelines under the same ratained-parameter budget. We will release code.

Lossless compression can reduce the storage and movement of model weights without changing their floating-point values, but repeated statistical analysis and code construction add computational overhead. We study whether the statistical structure of exponents can be prepared once and reused. For this, we introduce NeuralZip, which groups chunks with similar exponent distributions, shares Huffman codes, and selectively represents recurring exponent tuples using packed exponents, thereby achieving additional moderate compression ratios. A setup chooses these representations before subsequent encodings, while every encoding still processes the current tensor values. In floating-point model checkpoints, post-setup compression is 1.81-21.33$\times$ faster than the baselines and achieves exact bit-to-bit reconstruction. We show that this setup can be precomputed and transferred from another compatible architecture, preserving similar compression ratios and avoiding the need to amortize setup costs. Therefore, compression adaptation is transferable and reusable. Training checkpoints demonstrate continued reuse as the weights evolve. Finally, GPU experiments reduce active memory usage by up to 27.5$\%$ while reproducing the logits exactly.

Memory constraints remain a critical bottleneck in the deployment of large-scale AI models. Parameter sharing across network depth reduces model storage, but repeatedly applying an identical transformation limits flexibility across layers. Inspired by time--memory trade-offs in classical algorithms, we introduce the Linear Reusable Neural Bases (LRNB) architecture, an RNN-based framework that improves parameter efficiency through parameter reuse at the neuron level. Each feedforward residual module is represented as a linear combination of shared neural bases, with depth-specific learnable coefficients and optional shifts providing flexibility across layers. This formulation reduces parameter redundancy across depth and enables the construction of wider and deeper networks within a fixed parameter budget. We further provide a geometric interpretation of the neural bases from a vector-field perspective and extend the framework to linear projection modules. Experiments demonstrate that the LRNB architecture achieves comparable or lower final training loss than independently parameterized baselines while using fewer parameters and maintaining stable training dynamics. These findings support neuron-level reuse as a practical approach to parameter-efficient network design.