Retrieval-Augmented Generation (RAG) grounds large language model outputs in external evidence, but remains challenged on multi-hop question answering that requires long reasoning. Recent works scale RAG at inference time along two complementary dimensions: sequential depth for iterative refinement and parallel width for coverage expansion. However, naive scaling causes context contamination and scaling inefficiency, leading to diminishing or negative returns despite increased computation. To address these limitations, we propose SPARC-RAG, a framework that coordinates joint depth–width scaling around a unified context management mechanism—a shared global context state on which specialized control agents regulate parallel exploration and sequential stopping. To optimize scaling behavior, we further introduce a lightweight fine-tuning method with process-level verifiable preferences, which improves the efficiency of sequential scaling and effectiveness of parallel scaling. Across five single- and multi-hop QA benchmarks, SPARC-RAG outperforms the strongest reproduced baseline by an average of 3.8 F1 points at 7B and 9.8 at 32B, with the largest gains on challenging multi-hop tasks.

This work aims to understand how scaling improves language models, specifically in terms of training dynamics. We find that language models undergo loss deceleration early in training—an abrupt slowdown in the rate of loss improvement, resulting in piecewise linear behaviour of the loss curve in log-log space. Scaling up the model mitigates this transition by (1) decreasing the loss at which deceleration occurs, and (2) improving the log-log rate of loss improvement after deceleration. We attribute loss deceleration to a type of degenerate training dynamics we term zero-sum learning (ZSL). In ZSL, per-example gradients become systematically opposed, leading to destructive interference in per-example changes in loss. As a result, improving loss on one subset of examples degrades it on another, bottlenecking overall progress. Loss deceleration and ZSL provide new insights into the training dynamics underlying language model scaling laws, and could potentially be targeted directly to improve language models independent of scale. We make our code and artefacts available at: https://github.com/mirandrom/zsl