Tiny Model, Big Logic: Diversity-Driven Optimization Elicits Large-Model Reasoning Ability in VibeThinker-1.5B

Abstract: Challenging the prevailing consensus that small models inherently lack robust reasoning, this report introduces VibeThinker-1.5B, a 1.5B-parameter dense model developed via our Spectrum-to-Signal Principle (SSP). This challenges the prevailing approach of scaling model parameters to enhance capabilities, as seen in models like DeepSeek R1 (671B) and Kimi k2 (>1T). The SSP framework first employs a Two-Stage Diversity-Exploring Distillation (SFT) to generate a broad spectrum of solutions, followed by MaxEnt-Guided Policy Optimization (RL) to amplify the correct signal. With a total training cost of only $7,800, VibeThinker-1.5B demonstrates superior reasoning capabilities compared to closed-source models like Magistral Medium and Claude Opus 4, and performs on par with open-source models like GPT OSS-20B Medium. Remarkably, it surpasses the 400x larger DeepSeek R1 on three math benchmarks: AIME24 (80.3 vs. 79.8), AIME25 (74.4 vs. 70.0), and HMMT25 (50.4 vs. 41.7). This is a substantial improvement over its base model (6.7, 4.3, and 0.6, respectively). On LiveCodeBench V6, it scores 51.1, outperforming Magistral Medium's 50.3 and its base model's 0.0. These findings demonstrate that small models can achieve reasoning capabilities comparable to large models, drastically reducing training and inference costs and thereby democratizing advanced AI research.

• The paper introduces a novel two-phase post-training pipeline, the Spectrum-to-Signal Principle, that equips a 1.5B-parameter model with advanced reasoning skills.
• Utilizing Two-Stage Diversity-Exploring Distillation and MaxEnt-Guided Policy Optimization, the method boosts both diversity (Pass@K) and accuracy while reducing compute costs.
• Empirical results reveal VibeThinker-1.5B outperforms many larger models on math and coding benchmarks, challenging the conventional parameter scaling rule.

Diversity-Driven Optimization Unlocks Large-Model Reasoning in VibeThinker-1.5B

Introduction and Motivation

The paradigm established by Large Reasoning Models (LRMs) has pivoted language modeling towards scaling logic and reasoning via reinforced chain-of-thought (CoT) optimization. Prevailing consensus assumes parameter scaling is essential for robust reasoning: leading models with hundreds of billions to trillions of parameters are considered necessary for superior performance in mathematics, coding, and scientific reasoning. VibeThinker-1.5B critically reevaluates this assumption by empirically demonstrating that a meticulously optimized 1.5B-parameter model can achieve near-parity with far larger competitors, even surpassing many state-of-the-art baselines in complex benchmarks.

This work introduces the Spectrum-to-Signal Principle (SSP), which explicitly decouples supervised fine-tuning (SFT) and reinforcement learning (RL) objectives and positions diversity (as maximized by Pass@K) as the cornerstone for post-training pipeline design. Through Two-Stage Diversity-Exploring Distillation and MaxEnt-Guided Policy Optimization (MGPO), VibeThinker-1.5B elicits logical reasoning competencies traditionally ascribed only to much larger models.

Methodology: SSP, Diversity-Exploring Distillation, and MaxEnt-Guided Policy Optimization

Spectrum-to-Signal Principle (SSP)

SSP formalizes a two-phase post-training pipeline:

• Spectrum Phase (SFT): Maximizes output diversity by selecting checkpoints that optimize Pass@K, rejecting the conventional focus on Pass@1. This creates a spectrum (candidate pool) of plausible correct solutions, over domains partitioned into expert subspaces.
• Signal Phase (RL): RL is tasked not with blanket improvement, but targeted amplification of the most credible solutions from the spectrum via dynamic problem prioritization.

This theoretical underpinning is operationalized by Two-Stage Diversity-Exploring Distillation.

Two-Stage Diversity-Exploring Distillation

Domain-Aware Diversity Probing: The mathematical and code domains are partitioned into $N$ subdomains. For each, intermediate SFT checkpoints are evaluated with Pass@K on domain-specific probes, and diversity-maximizing checkpoints are selected as specialists.

Expert Model Fusion: These specialist models are linearly merged, typically with uniform weight, yielding a composite SFT model $\mathbf{M}_{\text{Merge}^{\text{SFT}}$ that simultaneously maximizes both diversity (Pass@K) and accuracy (Pass@1). This construction ensures a rich solution space upon which RL can operate.

MaxEnt-Guided Policy Optimization (MGPO)

MGPO builds on GRPO, augmenting the policy optimization process with Entropy Deviation Regularization. The pedagogical value of training samples is quantified by their outcome entropy, with maximal entropy corresponding to the point of greatest uncertainty (accuracy near 0.5). A weighting function $w_{\rm ME}(p_c(q))$ penalizes deviation from maximal uncertainty, thus focusing RL updates on high-uncertainty (high-value) problems.

Formally, the KL-divergence between empirical outcome and the maximal entropy distribution $p_0=0.5$ is used to modulate the advantage estimate in GRPO:

$$w_{\text{ME}}(p_c(q)) = \exp(-\lambda ~ D_{\text{ME}}(p_c(q) \| 0.5))$$

This process generates a dynamic curriculum, concentrating policy improvement where the model is neither consistent nor fully confident, yielding disproportionately strong learning returns.

Training Data Curation

The majority of training data is open-sourced; proprietary synthetic data is used for robustness. Rigorous n-gram semantic decontamination (n=10) ensures no contamination between train and evaluation sets, reinforcing the validity of performance claims, especially since key benchmarks (AIME25, HMMT25) were publicly released only after base model finalization.

Training Pipeline and Cost

The entire training process (SFT + RL) consumed only ~3900 H800 GPU-hours, resulting in a total compute cost of under \$8,000.

Figure 1: The two-stage pipeline for VibeThinker-1.5B: domain-probing and expert fusion during SFT (spectrum), followed by curriculum-driven RL with MGPO (signal).

This is one to two orders of magnitude less than required by large models (e.g., DeepSeek R1 and MiniMax-M1, requiring \$294K to \$535K). The small model architecture supports inference on resource-constrained devices and reduces deployment cost by 20–70x compared with the largest models.

Empirical Performance and Comparative Analysis

VibeThinker-1.5B was evaluated across mathematics (AIME24/25, HMMT25, MATH500), coding (LiveCodeBench v5/v6), and professional knowledge (GPQA Diamond) benchmarks.

Figure 2: VibeThinker-1.5B's performance compared to contemporary models on mathematics and coding benchmarks. VibeThinker-1.5B exhibits significant competitiveness against much larger models.

Small Model Comparison

Relative to sub-3B SOTA models (STILL-3, DeepScaleR, ProRL, Qwen3-1.7B):

• AIME25: VibeThinker-1.5B achieves 74.4 (vs. 36.7–36.8 for largest competitors).
• HMMT25: 50.4, sharply exceeding previous best (26.0).
• LiveCodeBench v5/v6: 55.9/51.1, doubling Qwen3-1.7B's best result.

Large Model and Non-Reasoning Comparison

VibeThinker-1.5B matches and often surpasses models like DeepSeek R1 (671B), GPT-OSS-20B, Seed-Thinking v1.5 (200B), and even proprietary giants on mathematical benchmarks. For instance, on AIME25, it exceeds DeepSeek R1 (74.4 vs. 70.0).

Figure 3: VibeThinker-1.5B achieves 74.4 on AIME25, outperforming DeepSeek-R1-0120 (70.0/671B) and Seed-Thinking v1.5 (74.0/200B) despite its much smaller size.

In coding, VibeThinker-1.5B is competitive with mid-sized architectures but trails the largest coding-specialized models, highlighting its mathematically-skewed pretraining base.

However, on GPQA Diamond (graduate-level domain knowledge), VibeThinker-1.5B lags behind state-of-the-art larger models by 20–40 points, aligning with the hypothesis that general knowledge breadth is still parameter-scale dependent.

Discussion and Implications

VibeThinker-1.5B robustly challenges the scaling law assumption that logical reasoning scales monotonically with parameter count. Its competitive mathematical and coding performance, achieved via diversity-centric post-training, implies several important ramifications:

• Cost and Accessibility: Small models enable high-quality AI applications at economically viable scales, facilitating adoption even in resource-limited environments and institutions.
• Research Democratization: Lower compute requirements broaden participation in front-line model research, countering concentration of innovation in large organizations.
• Methodological Generalization: The SSP pipeline and MGPO framework are broadly applicable for balancing diversity and accuracy in RLHF for compact and large models alike.
• Model Limitations: Persistent gaps in general knowledge indicate that scaling still confers advantages in encyclopedic coverage, suggesting future research should focus on hybridization and more efficient knowledge infusion techniques for small models.

Conclusion

VibeThinker-1.5B exemplifies the realization of large-model reasoning abilities within a compact architecture. Through the explicit prioritization of output diversity in SFT, expert model fusion, and dynamic uncertainty-driven RL, VibeThinker-1.5B sets new standards for small model efficiency and reasoning robustness. The demonstrated performance, cost-effectiveness, and superior scaling properties advocate for an industry-wide revision of the "bigger is better" paradigm, with lasting implications for accessible, environmentally sustainable, and democratized AI research.