Paper Title
SPECTRAL GRAPH PRUNING FOR CONTEXT OPTIMIZATION IN RETRIEVAL-AUGMENTED GENERATION

Abstract
Retrieval-Augmented Generation (RAG) has become the dominant paradigm for grounding Large Language Models (LLMs) in external knowledge. Despite their effectiveness, RAG systems suffer from the context bottleneck: retrieved content fills the model’s context window with semantically similar but structurally redundant segments, increasing inference costs, latency, and degrading multi-hop reasoning performance. Existing context compression methods primarily operate on token-level statistical measures and fail to account for the global structural dependencies present in long-form documents. We present Spectral Graph Pruning (SGP), a graph-based framework for context optimization that preserves structural information. SGP models retrieved content as a heterogeneous semantic graph and applies query-biased spectral centrality analysis-specifically, a Tikhonov-regularized Laplacian smoothing formulation with thermal personalization—to identify structurally significant segments. Rather than discarding locally uninformative tokens, SGP retains the topological backbone of the document, maintaining narrative coherence while eliminating redundant context. According to experiments run on 200 multi-hop reasoning questions sampled from the HotpotQA and MuSiQue datasets, the SGP approach achieves 47.7% context compression while retaining 94.5% of Token F1 scores of full contexts (0.706 vs. 0.747). In all comparison experiments across different metrics such as Token F1, Exact Match, ROUGE-L, BERT Score, and Answer Coverage, SGP outperforms Dense Retrieval for similar levels of compression rates. These results demonstrate that structure aware spectral graph analysis provides a more effective context compression strategy than similarity-based retrieval approaches for multi-hop RAG systems. Keywords - Retrieval-Augmented Generation (RAG), Large Language Models (LLMs), Graph Signal Processing, Spectral Graph Theory, Context Compression, Query-Biased PageRank, Multi-Hop Reasoning, Tikhonov Regularization