FlexMoRE: A Flexible Mixture of Rank-heterogeneous Experts for Efficient Federatedly-trained Large Language Models

Recent advances in mixture-of-experts architectures have shown that individual experts models can be trained federatedly, i.e., in isolation from other experts by using a common base model to facilitate coordination. However, we hypothesize that full-sized experts may not be necessary for all domains and that instead low-rank adapters may be sufficient. Here, we introduce FlexMoRE, a Flexible Mixture of Rank-heterogenous Experts, which may be either full-sized experts or adapters of a suitable rank. We systematically investigate the trade-off between expert rank and downstream task performance by evaluating $6$ experts with ranks $2^0$ to $2^{14}$ resulting in experiments covering 150 mixtures (96 with 2 experts, 54 with 7 experts) that are evaluated across $120$ tasks. For our experiments, we build on FlexOlmo and turn its pre-trained experts into low-rank versions. Our regression analysis from expert rank to downstream task performance reveals that the best-performing rank is substantially higher for reasoning-heavy benchmarks than for knowledge-heavy benchmarks. These findings on rank sensitivity come with direct implications for memory efficiency: Using optimal ranks, FlexMoRE yields improved downstream task performance (average score $47.18$) compared to the baseline FlexOlmo-style mixture of full-sized experts (average score $45.46$) at less than one third the parameters ($10.75$B for FlexMoRE vs. $33.27$B for FlexOlmo). All code will be made available.

Training Language Models to Use Prolog as a Tool

Ensuring reliable tool use is critical for safe agentic AI systems. Language models frequently produce unreliable reasoning with plausible but incorrect solutions that are difficult to verify. To address this, we investigate fine-tuning models to use Prolog as an external tool for verifiable computation. Using Group Relative Policy Optimization (GRPO), we fine-tune Qwen2.5-3B-Instruct on a cleaned GSM8K-Prolog-Prover dataset while varying (i) prompt structure, (ii) reward composition (execution, syntax, semantics, structure), and (iii) inference protocol: single-shot, best-of-N, and two agentic modes where Prolog is invoked internally or independently. Our reinforcement learning approach outperforms supervised fine-tuning, with our 3B model achieving zero-shot MMLU performance comparable to 7B few-shot results. Our findings reveal that: 1) joint tuning of prompt, reward, and inference shapes program syntax and logic; 2) best-of-N with external Prolog verification maximizes accuracy on GSM8K; 3) agentic inference with internal repair yields superior zero-shot generalization on MMLU-Stem and MMLU-Pro. These results demonstrate that grounding model reasoning in formal verification systems substantially improves reliability and auditability for safety-critical applications. The source code for reproducing our experiments is available under https://github.com/niklasmellgren/grpo-prolog-inference