Parameter-efficient methods like LoRA have revolutionised large language model (LLM) fine-tuning. ReLoRA extends this idea to pretraining by repeatedly merging and reinitialising low-rank adapters, increasing cumulative rank while keeping updates cheap. This aligns well with observations that high-capacity models learn through locally low-rank trajectories that expand over time. By contrast, recent work suggests that small language models (SLMs) exhibit rank deficiencies and under-utilise their available dimensionality. This raises a natural question: can ReLoRA's rank-expanding update rule \textit{steer} SLMs toward healthier learning dynamics, mitigating rank bottlenecks in a capacity-constrained regime? We argue SLMs are an ideal testbed: they train quickly, enable controlled ablations, and make rank phenomena more measurable. We present the first systematic study of ReLoRA in SLMs (11M-66M parameters), evaluating both performance and learning dynamics. Across loss, Paloma perplexity, and BLiMP, we find that ReLoRA underperforms full-rank training, with gaps widening at larger scales. Analysis of proportional effective rank and condition numbers shows that ReLoRA amplifies existing rank deficiencies and induces ill-conditioned updates early in training. Our results suggest that while ReLoRA's merge-and-restart strategy can expand ranks in larger models, it does not straightforwardly translate to capacity-limited SLMs, motivating adaptive-rank or hybrid-rank approaches for low-compute pretraining.

Adapting Vision-Language Models (VLMs) to new domains with few labeled samples remains a significant challenge due to severe overfitting and computational constraints. State-of-the-art solutions, such as low-rank reparameterization, mitigate these issues but often struggle with generalization and require extensive hyperparameter tuning. In this paper, a novel Sparse Optimization (SO) framework is proposed. Unlike low-rank approaches that typically constrain updates to a fixed subspace, our SO method leverages high sparsity to dynamically adjust very few parameters. We introduce two key paradigms. First, we advocate for \textit{local sparsity and global density}, which updates a minimal subset of parameters per iteration while maintaining overall model expressiveness. As a second paradigm, we advocate for \textit{local randomness and global importance}, which sparsifies the gradient using random selection while pruning the first moment based on importance. This combination significantly mitigates overfitting and ensures stable adaptation in low-data regimes. Extensive experiments on 11 diverse datasets show that SO achieves state-of-the-art few-shot adaptation performance while reducing memory overhead.

Despite the dominance and effectiveness of scaling, resulting in large networks with hundreds of billions of parameters, the necessity to train overparameterized models remains poorly understood, while training costs grow exponentially. In this paper, we explore parameter-efficient training techniques as an approach to training large neural networks. We introduce a novel method called ReLoRA, which utilizes low-rank updates to train high-rank networks. We apply ReLoRA to training transformer language models with up to 1.3B parameters and demonstrate comparable performance to regular neural network training. ReLoRA saves up to 5.5Gb of RAM per GPU and improves training speed by 9-40% depending on the model size and hardware setup. Our findings show the potential of parameter-efficient techniques for large-scale pre-training.