Low-Rank Adaptation (LoRA) is a widely used approach to parameter-efficient fine-tuning (PEFT) of LLMs whose effectiveness depends on rank allocation. Existing adaptive LoRA methods derive ranks from local gradient, activation, or matrix statistics collected before or during fine-tuning; training-time variants add overhead, and local signals reveal little about each module's structural role in information propagation, giving weak global grounding for scarce-capacity allocation. We propose IFCLoRA, a topology-aware method for pre-fine-tuning rank allocation and adapter initialization. Using a small calibration set, IFCLoRA performs intervention tracing on the frozen model and constructs a sparse task-conditioned interaction graph over LoRA target modules. From this graph it extracts a global information-flow topology prior and fuses it with each node's local gradient sensitivity to form a topology-dominant Information-Flow Centrality (IFC) score, measuring participation in task-conditioned multi-hop propagation. The IFC scores then serve as module-level routing signals for one-shot discrete rank allocation under a rank-budget constraint. Reusing response vectors from tracing, IFCLoRA constructs a function-preserving flow-response subspace initialization, giving adapters task-relevant output subspaces. Across all settings, IFCLoRA achieves higher mean scores than standard LoRA with comparable fine-tuning time and peak memory; it requires a one-time offline calibration stage. On GSM8K, IFCLoRA attains the highest mean accuracy among compared PEFT methods on both base models, exceeding standard LoRA by 4.75 percentage points on LLaMA-3.1-8B. Resulting rank allocations are non-uniform and vary across tasks and base models, suggesting that task-conditioned global information-flow topology can serve as a useful structural prior for rank allocation in low-budget PEFT.
During the training of large Transformer models, attention masks regulate the scope and direction of information flow across a sequence. Numerous mask variants exist, and operators such as FlexAttention already support arbitrary attention masks. Nevertheless, a systematic formal analysis of the information-flow structure induced by arbitrary masks has been missing. This paper develops a complete theoretical framework. We prove that, with sufficient depth, the information flow of a multi-layer Transformer converges to a Hasse diagram -- a directed acyclic graph representing a partial order. Building on this, we recast the design of parallel training tasks as the problem of finding a minimal common supergraph of Hasse diagrams, and we establish a criterion for the minimal common supergraph. This yields a constructive method to derive attention masks directly from a family of tasks. Applying the framework, we design two novel masks: a block-generation attention mask that ensures training-inference consistency (Block Two-Stream Attention), and a fully supervised bidirectional attention mask (Butterfly Attention). These results demonstrate the framework's capacity to discover new structures.