MODIX: A Training-Free Multimodal Information-Driven Positional Index Scaling for Vision-Language Models

Vision-Language Models (VLMs) have achieved remarkable progress in multimodal understanding, yet their positional encoding mechanisms remain suboptimal. Existing approaches uniformly assign positional indices to all tokens, overlooking variations in information density within and across modalities, which leads to inefficient attention allocation where redundant visual regions dominate while informative content is underrepresented. We identify positional granularity as an implicit resource and propose MODIX (Multimodal Information-Driven Positional IndeX Scaling), a training-free framework that dynamically adapts positional strides based on modality-specific contributions. MODIX jointly models intra-modal density via covariance-based entropy and inter-modal interaction via cross-modal alignment to derive unified scores, which rescale positional indices to allocate finer granularity to informative modalities while compressing redundant ones, without requiring any modification to model parameters or architecture. Experiments across diverse architectures and benchmarks demonstrate that MODIX consistently improves multimodal reasoning and adaptively reallocates attention according to task-dependent information distributions, suggesting that positional encoding should be treated as an adaptive resource in Transformers for multimodal sequence modeling.

ID-LoRA: Efficient Low-Rank Adaptation Inspired by Matrix Interpolative Decomposition

LoRA has become a universal Parameter-Efficient Fine-Tuning (PEFT) technique that equips Large Language Models (LLMs) to adapt quickly to new tasks. However, when these models are scaled up, even the latest LoRA variants still introduce considerable overhead in trainable parameters. Conversely, aggressively lowering the rank to curb this overhead markedly degrades performance in complex multi-task settings. We propose ID-LoRA, a novel PEFT framework that breaks the trade-off. Its core innovation lies in extracting and reusing clustered parameter groups from the pretrained weight matrix. These groups are then used to form multiple low-rank components, all of which share only a single initialized trainable low-rank matrix. This approach cuts the number of trainable parameters while keeping the model's capacity intact. We evaluate ID-LoRA on five diverse benchmarks: Mathematical Reasoning, Code Generation, MMLU, CommonsenseQA, and Safety Alignment. ID-LoRA outperforms both full fine-tuning and existing PEFT baselines (e.g., LoRA, DoRA, HydraLoRA) while using up to 46% fewer trainable parameters than the standard LoRA. In multi-task scenarios, it surpasses LoRA and its recent variants (e.g., DoRA and HydraLoRA) on both Code and MMLU tasks, yet requires only 54% of the trainable parameters demanded by the conventional LoRA.