Libra-RM Series: Dark Matter & LLM Models

• Libra-RM Series is a dual-domain research topic covering radiopurity dark matter experiments and LLM-based reward models for evaluating mathematical reasoning.
• In astroparticle physics, the series employs NaI(Tl) detectors at LNGS to capture model-independent dark matter signals through robust statistical methods.
• In AI, Libra-RM-gen integrates chain-of-thought reasoning with reinforcement learning using Libra Bench, achieving high accuracy in challenging math problem evaluations.

The Libra-RM Series refers to two distinct, context-dependent research lines present in the literature: (1) the Radiopurity-Module (“RM”) series of dark matter annual-modulation measurements performed primarily with the DAMA/NaI and DAMA/LIBRA NaI(Tl) experiments at Gran Sasso; and (2) the family of “Libra-RM” LLM-based generative reward models developed within the Libra framework for advanced mathematical reasoning evaluation and reinforcement learning. This article distinguishes the two domains, providing a rigorous overview of their experimental design, methodologies, key results, and scientific implications.

1. Experimental Contexts and Core Aims

The term “Libra-RM Series” in the context of astroparticle physics denotes the sequence of radiopurity-optimized NaI(Tl) detector modules (DAMA/NaI, DAMA/LIBRA phase1, and phase2) targeting model-independent detection of an annual modulation—an anticipated dark matter signal modulated at the Earth’s orbital period—at the Laboratori Nazionali del Gran Sasso (LNGS) (Bernabei et al., 2022).

In the natural language processing domain, “Libra-RM Series” designates a set of generative reward models. These models are trained to perform nuanced, chain-of-thought “judging,” acting as proxies for human evaluation in RL paradigms for advanced mathematical reasoning models. The family is situated within the Libra framework, leveraging the Libra Bench, a benchmark corpus curated via a “Verifiable Reasoning → Verifiable Judging” (V2V) pipeline to evaluate generative reward models in highly challenging mathematical settings (Zhou et al., 29 Jul 2025).

2. Libra-RM in Dark Matter Annual Modulation Experiments

The DAMA Libra-RM series comprises:

Phase	Detector Configuration	Mass	Years	Major Upgrades
DAMA/NaI	9 × 9.70 kg NaI(Tl), high radiopurity	≈87 kg	1995–2002	Initial deployment
DAMA/LIBRA phase 1	25 × 9.70 kg NaI(Tl), similar purity	≈242.5 kg	2003–2010	Increased mass, improved shielding
DAMA/LIBRA phase 2	25 detectors, Hamamatsu R6233MOD PMTs	≈250 kg	2011–present	High-Q.E. PMTs, sub-keV threshold, improved DAQ

The detection modules reside in LNGS hall C beneath 1,400 m rock overburden (≈3,600 m w.e.), with a multi-layered passive shield: OFHC copper, low-background lead (including ancient lead), borated polyethylene moderators, and an outer neutron-moderator. The system achieves a duty cycle of 76–86% per annual cycle, with calibrations and maintenance constituting the main sources of dead time (Bernabei et al., 2022).

3. Signal Modeling and Analysis Procedures

The event rate in each low-energy bin is modeled as:

$S(E, t) = S_0(E) + S_m(E) \cos[\omega (t - t_0)]$

where $S_0(E)$ is the unmodulated component (including background), $S_m(E)$ is the modulation amplitude, $\omega = 2\pi/\text{yr}$, and $t_0 \simeq 152.5$ d (June 2). More general two-term fits allow for phase release, introducing an orthogonal $Z_m(E)\sin[\omega (t-152.5\,\text{d})]$ term and absorbing it into $Y_m(E) \cos[\omega (t-t^*)]$, with DM-induced expectations $Z_m \simeq 0$, $Y_m \simeq S_m$, $t^* \simeq 152.5$ d. Statistical analysis includes least-squares fits, maximum likelihood estimation, and annual-frequency Fourier analysis, with rigorous background control ensuring the single-hit, low-energy modulation cannot be mimicked by known backgrounds such as muons, neutrons, radon, or long-lived isotope decays (Bernabei et al., 2022).

4. Key Results and Statistical Significance

With a total exposure of 2.86 ton × yr over 22 annual cycles—combining DAMA/NaI, LIBRA phase 1, and phase 2—the analysis in the (2–6) keVee window yields a best-fit modulation amplitude $$S_m = (0.01014 \pm 0.00074)\,\text{cpd}/\text{kg}/\text{keV}$$ (T fixed at 1 yr, $t_0=152.5$ d). If $T$ and $t_0$ are left unfixed, $T = (0.99834 \pm 0.00067)$ yr, $t_0 = (142.4\pm4.2)$ day, and $S_m$ unchanged. The significance in this dataset reaches $13.7\,\sigma$. The modulation amplitude is positive for 1–6 keVee and compatible with zero above this range; a new analysis extends this compatibility to 0.75 keV. Cross-checks confirm null modulation in multiple-hit events and at higher energies (6–14 keVee), with all detector and positional subsets showing consistent distributions (Bernabei et al., 2022).

5. Libra-RM Series in Generative Reward Model Research

The Libra-RM (Editor’s term: “Libra-RM-gen” to disambiguate) series, built on Qwen2.5-32B, synthesizes reward modeling and chain-of-thought reasoning using an end-to-end trainable LLM. The core methodology employs Libra Bench—a “V2V” pipeline utilizing challenging MATH-500 and AIME 2024/2025 mathematical questions, with at least 64 solutions per problem sampled from state-of-the-art reasoning LLMs. The data—annotated for correctness via a combination of rule-based integer matching, advanced LLM comparison, and human review—constitutes a pointwise judging benchmark: 1,360 / 1,200 / 1,200 samples in MATH-500, AIME 2024, and AIME 2025 test sets respectively (balanced for correctness and incorrectness) (Zhou et al., 29 Jul 2025).

Libra-RM-gen inference accepts a query $q$, candidate answer list $[a_1,\ldots, a_k]$, and criterion $c$, producing a generative natural-language judgment $j$. Given $c$, scalar or ranking scores are extracted. Training incorporates:

1. Rejection-Sampling–Augmented Supervised Fine-Tuning (SFT): Draws from challenging judging/answering datasets, filtered by DeepSeek-R1 for difficulty.
2. Rule-Based Reinforcement Learning (via GRPO): Refines the SFT checkpoint using a verifiable, reference-based reward and GRPO (PPO variant), with objective:

$$J_{\rm GRPO}(\theta) = \mathbb{E}\left[\sum_{t=1}^{T_i}\min(r_{i,t}(\theta)A_{i,t}, \operatorname{clip}[r_{i,t}(\theta),1{-}\varepsilon_{\rm low},1{+}\varepsilon_{\rm high}]A_{i,t}) - \beta D_{\rm KL}(\pi_\theta\|\pi_{\rm ref})\right]$$

with reward $$r(x,y,\bar y) = \operatorname{is\_correct}(y,\bar y) - \operatorname{len\_penalty}(y)$$. The training sets are large, e.g., SFT for Libra-RM-32B-MATH uses approximately 38,900 scoring and 186,700 non-judging math samples (Zhou et al., 29 Jul 2025).

6. Performance Benchmarks and Impact

On Libra Bench, Libra-RM-32B-MATH achieves pointwise accuracy of 83.4 % (MATH-500), 81.5 % (AIME 2024), 80.3 % (AIME 2025), and 81.7 % overall—outperforming comparable reward models AceMath-72B-RM (66.6 % overall) and GPT-4.1 (69.1 %). The general Libra-RM-32B model scores 80.0 % average accuracy across these subsets. Libra-RM is notably effective at rejecting incorrect solutions. On standard pairwise and correctness RM benchmarks, Libra-RM-32B records 92.9 % (RewardBench), 66.5 % (PPE Preference), 77.3 % (PPE Correctness), 72.9 % (RMB overall), and 77.1 % (JudgeBench), consistently leading contemporary discriminative and LLM-as-judge baselines (Zhou et al., 29 Jul 2025).

Downstream, fine-tuning of reasoning policies using DPO with Libra-RM rewards shows a near-linear correlation between reward model Libra Bench accuracy and AIME pass@1, e.g., DPO policy pass@1 on AIME 2024 climbs from 55.5 % to 57.7 % when using Libra-RM-32B-MATH.

7. Scientific and Methodological Implications

The Libra-RM annual-modulation results in astroparticle physics deliver persistent, high-significance, model-independent evidence for galactic dark matter signals in NaI(Tl), consistently meeting all of the field’s requirements and exhibiting rigorous control over systematic effects (Bernabei et al., 2022). The empowered configuration in phase2 introduces even lower hardware thresholds and refined energy response, with future improvements expected in low-energy coverage and discrimination of DM candidate models.

In generative reward modeling, the Libra-RM-gen approach underscores the scientific value of embedding chain-of-thought “thinking” into reward models for RL. The V2V curation paradigm and Libra Bench provide an adversarial reasoning benchmark closely predictive of downstream RL-from-unlabeled-data performance. Limitations remain in the current scope of Libra Bench—primarily high-school mathematics and integer/formula answers—with future directions focused on open-ended, process-level, and multimodal reasoning tasks, as well as integration of discriminative and generative RM architectures (Zhou et al., 29 Jul 2025).

Altogether, both incarnations of the Libra-RM Series represent methodological advancements within their scientific domains: as a unique, model-independent dark matter dataset in experimental astroparticle physics, and as a leading approach for generative reward modeling in reasoning-centric RL for LLMs.