SAD-LoRA: Spectral Alignment for Low-Rank Knowledge Distillation

In the context of resource-constrained environments such as embedded systems, adapting reduced-size foundation models to downstream tasks has become increasingly popular. This has recently motivated the emerging setting of task-specific distillation, where a larger and a smaller version of the same foundation model are both adapted to the same downstream task, with the goal of transferring knowledge from the former to the latter. Recent work has demonstrated the benefits of using a larger version of the same foundation model to assist the adaptation of a smaller one. Typically, the larger model (teacher) is first adapted via fine-tuning or linear probing before its knowledge is distilled into the smaller model (student). While fine-tuning the teacher often increases its performance, recent work showed that probing it leads to better knowledge distillation to the student. Our findings show that this is mainly due to a mis-alignment in feature representation between the teacher and the student which occurs during the teacher's fine-tuning. Inspired by existing efforts to preserve previously learned knowledge, we first propose leveraging low-rank adaptation, resulting in better feature alignment and therefore better knowledge transfer. Drawing from this insight, we further enhance the feature alignment through a parameter-sharing strategy of the adapters between the two encoders during joint training. Our proposed method, SLAD, shows better feature alignment between the teacher and student, which results in increased performance for not only the student but also the teacher model, while being 2x faster to train than fine-tuning. Through extensive experiments on multiple classification and segmentation datasets, we demonstrate the improved accuracy and transfer efficiency of our method, achieving state-of-the-art performance in the task-specific distillation framework.

Fine-tuning large language models with LoRA requires choosing a rank r before training starts. Existing approaches either extract rank-1 components sequentially, freezing each component's error permanently into every subsequent residual, or optimize the full low-rank factorization jointly with guarantees that describe only the joint update, not individual rank-1 directions. We present AdaPaD (Adaptive Parallel Deflation), which trains all rank-1 components simultaneously: each worker refines its component against a deflation target built from the latest estimates of all predecessors, and as those estimates improve, the targets improve too. We call this property self-correction: deflation errors converge to zero over rounds rather than persisting as fixed residuals. On top of this backbone, AdaPaD adds advance learning (private pre-training before activation) and per-module dynamic rank discovery (importance-based growth until a shared budget is exhausted), making the rank distribution an output rather than an input. We prove that every component's error decays exponentially after a warm-up period, with a generalization bound that splits into a vanishing algorithmic term and an irreducible statistical floor. Empirically, AdaPaD is competitive with adaptive-rank LoRA baselines on GLUE with DeBERTaV3-base at matched parameter budgets, and competitive with fixed-rank LoRA on Qwen3-0.6B SQuAD/SQuAD v2 while deploying an adapter that is on average 30.7% smaller.

We study distillation for large language models under explicit compute constraints, with the goal of producing student models that are not only cheaper to train, but structurally efficient at inference time. While prior approaches to parameter-efficient distillation, such as LoRA, reduce adaptation cost, they leave the dense backbone unchanged and therefore fail to deliver meaningful inference savings. We propose Budgeted LoRA, a distillation framework that treats model compression as a structured compute allocation problem. Instead of using a fixed student architecture, we introduce a global compute budget that sets the final target fraction of dense computation retained. Under this constraint, the model redistributes capacity across dense and low-rank pathways via (i) module-level dense retention coefficients, (ii) adaptive low-rank allocation, and (iii) post-training compression that selectively removes, approximates, or preserves dense components. This formulation yields a family of students controlled by a single budget dial. Empirically, Budgeted LoRA matches standard LoRA perplexity at a moderate budget with a 1.74x compressed-module speedup; at an aggressive budget it achieves a 4.05x speedup with moderate perplexity degradation, and it preserves higher accuracy on function-style in-context learning probes. These results suggest that, under compute-constrained distillation, retaining behavior is less about matching perplexity or removing more parameters than it is about controlling how dense computation is transferred to low-rank pathways.