Martino M. L. Pulici | Searcharxiv

arXiv2026

A Storage-Retrieval Gap in Parametric Knowledge Graph Memory

Graph retrieval-augmented generation places retrieved subgraphs into the model's context window at query time, paying a recurring token cost and exposing source data on every call. We study an alternative: compiling a knowledge graph offline into a bank of LoRA adapters, one per entity, that serve as a parametric knowledge layer queried by injecting weights rather than text, at zero query-time context cost. On the MetaQA dataset, we find that subgraph-trained adapters encode context-free factual knowledge that generalizes to unseen questions: on single-valued relations the adapter gains $+0.243$ exact-match score over a base model that is nearly blind closed-book ($0.007$), and only the correct adapter recovers this knowledge (an oracle gap of $+0.283$ over the base model). However, the stored knowledge is not recoverable by similarity: given a query with no subgraph, embedding-based and weight-space geometry retrieval both perform at chance, because a semantically neighbouring entity's adapter does not contain the answer - knowledge is stored locally and does not transfer. Weight geometry correlates with subgraph semantics ($ρ= +0.329$) but not with functional retrievability. We quantify the byte and context-token costs against graph retrieval-augmented generation and discuss deployment implications. Our results establish that parametric knowledge graph memory is feasible for storing knowledge, and identify selecting and composing the right adapters by a mechanism other than semantic similarity as the central open problem - motivating a learned, query-conditioned composition mechanism.

cs.LG↗

arXiv2026

MADA-RL: Multi-Agent Debate-Aware Reinforcement Learning for Parameter-Efficient Reasoning in Compact Models

Large language models achieve strong reasoning performance, but often at prohibitive training cost - a challenge that is especially acute for compact models ($\leq 4 \, \mathrm{B}$ parameters) trained under limited budgets. We introduce MADA-RL, a post-training framework that specializes compact models into generator and critic roles and trains them with a debate-aware learning signal, fine-tuning only a small subset of parameters via LoRA adapters. Our central contribution is a counterfactual critic advantage: a dynamic, role-conditioned baseline that redefines the critic's advantage as its reward minus the generator ensemble's per-instance accuracy. This explicitly optimizes critics to improve over generator consensus rather than to merely reproduce a correct answer, yielding more targeted credit assignment than static mean-reward normalization. At deployment, the specialized agents are composed in a lightweight multi-round protocol. Across five mathematical reasoning benchmarks, MADA-RL raises the accuracy of the DeepSeek-R1-Distill-Qwen-1.5B model from $39.9 \, \%$ to $41.9 \, \%$ ($+2.0$ points, $p < 0.001$) using $16$ times fewer trainable parameters than fully fine-tuned baselines, placing it on the accuracy-trainable-parameter Pareto front. It approaches, but does not surpass, the strongest baselines (DeepScaleR, STILL-3), which are trained on substantially larger datasets; we analyse this gap and the associated inference-time cost directly. A controlled study isolates the source of MADA-RL's gains: the counterfactual advantage produces the highest critic improvement rate of any model evaluated, indicating that trained critics learn to correct generator errors rather than to imitate them.

cs.LG↗