LoRA Superposition across Pretrained Models

Low-rank adaptation (LoRA) attaches small low-rank matrices to a frozen backbone, and public repositories host many LoRAs per backbone, each for a different concept or task. Combining several LoRAs in one generation forces a trade-off. Merging their weights into one update needs a single forward pass, but LoRAs trained for different concepts interfere and quality drops. Running each LoRA in its own forward pass (composite) preserves quality, but inference time grows linearly with the number of active LoRAs. We study a property of LoRA pools overlooked by prior multi-LoRA work. In real LoRA pools, the stacked low-rank factors need far fewer directions than their summed ranks. Using singular value decomposition, we find the minimal subspace that keeps 99% of the factor energy. On three diffusion pools, only 46% to 57% of the summed LoRA ranks is needed, and the subspace grows sub-linearly with pool size. A 48-LoRA sub-pool of LoRA-Hub on FLAN-T5 tasks shows comparable overlap (62%), while the diversity-curated LoRA-Retriever benchmark sits near the no-overlap baseline (96%), so pool composition rather than modality predicts where compression is large. We build on this overlap with LoRASpace, a training-free method that computes the subspace once per pool and reuses it in two inference modes, a static mode at merge cost and a dynamic mode for input-dependent routing. On the diffusion pools, static LoRASpace matches composite quality at merge cost, and dynamic LoRASpace is more than 6x faster than composite with six active LoRAs on a 17-LoRA pool, mainly because it runs one backbone pass instead of six. In an ablation, static variants at the same rank match LoRASpace, so the quality gain does not depend on the pool-wide basis. On the near-orthogonal LoRA-Retriever benchmark, compression is small and gains come from coupling with external retrieval.

How many of a neural network's parameters actually encode task-specific information? We investigate this question with LottaLoRA, a training paradigm in which every backbone weight is drawn at random and frozen; only low-rank LoRA adapters are trained. Across nine benchmarks spanning diverse architecture families from single-layer classifiers to 900M parameter Transformers low-rank adapters over frozen random backbones recover 96-100% of fully trained performance while training only 0.5-40% of the parameters. The task-specific signal therefore occupies a subspace orders of magnitude smaller than the full parameter count suggests. Three mechanistic findings underpin this result:(1) the frozen backbone is actively exploited when static the learned scaling~$β$ remains strictly positive across all architectures but when the scaffold is destabilized, the optimizer silences it and the LoRA factors absorb all task information; (2) the frozen backbone is preferable but interchangeable any random initialization works equally well, provided it remains fixed throughout training; and (3) the minimum LoRA rank at which performance saturates estimates the intrinsic dimensionality of the task, reminiscent of the number of components retained in Principal Component Analysis (PCA). The construction is formally analogous to Reservoir Computing unfolded along the depth axis of a feedforward network. Because the backbone is determined by a random seed alone, models can be distributed as adapters plus seed a footprint that grows with task complexity, not model size, so that storage and memory savings compound as architectures scale.

Adapting Vision Foundation Models (VFMs) to medical imaging via LoRA has become standard practice, yet model selection is guided almost entirely by downstream task metrics, treating backbones with similar performance as interchangeable. We investigate whether equal performance implies equal internal representational shift. We analyse four ViT-B/16 backbones, DINOv3, SigLIP2, MerMED-FM, and BiomedCLIP, pre-trained with different objectives (self-distillation vs. contrastive vision-language) and on different data domains (natural vs. medical images). We adapt each to brain tumour segmentation and evaluate on six datasets covering both segmentation and Alzheimer's disease classification. Using attention divergence, weight-change analysis, and activation patching, we find that the four models converge to similar segmentation performance (mean Dice 78-81%) through markedly different internal dynamics, yet diverge in cross-task transfer: segmentation adaptation improves Alzheimer's disease classification for DINOv3 but degrades it for the other three backbones. We reveal a dissociation between modification magnitude and causal importance: the most heavily modified layers are not the causally relevant ones, with early-to-mid layers identified as sufficient for segmentation recovery. Restricting LoRA to these layers matches or approaches full-layer segmentation while reducing classification degradation in the three affected backbones, providing a mechanistically grounded strategy that is more parameter-efficient and more robust than standard full-layer adaptation.