Low-rank adaptation (LoRA) has become a widely used parameter-efficient fine-tuning method for large pretrained models. However, standard LoRA typically assigns a fixed rank profile despite layer- and stage-dependent adaptation needs, while recent adaptive-rank variants often rely on heuristic or first-order signals that provide only an indirect link between rank reallocation and local loss behavior. This leaves the rationale behind each rank reallocation insufficiently interpretable. Motivated by this gap, we propose LIRA (Loss-Informed Rank Allocation), a dynamic-rank LoRA method designed to make online rank reallocation more interpretable. LIRA scores each layer by the estimated magnitude of the local loss perturbation associated with its recent LoRA-factor movements under a second-order approximation, making the basis for each rank change interpretable term by term. By periodically applying DELTA (Displacement-Evaluated Loss-Trajectory Allocation), a displacement-based algorithm for LoRA rank reallocation, LIRA produces discrete effective ranks under matched budgets while remaining compatible with standard (A,B) adapters. On RoBERTa-base GLUE under the La-LoRA/LoRA protocol, LIRA outperforms the uniform-LoRA and adaptive-rank baselines reported under this protocol; Trajectory EMA attains performance competitive with Fixed-point Fisher at lower estimation cost.

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