GIFT: Reconciling Post-Training Objectives via Variational Finite-Temperature Gibbs Initialization

arXiv:2601.09233 · cs.LG, cs.AI, cs.CL · Submitted 2026-01-14 · Read on arXiv

cs.LG, cs.AI, cs.CL

Submitted: 2026-01-14

Updated: 2026-09-07

Code: https://github.com/zzy1127/GIFT

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Benchmark — 22× in this paper · explained in 2 episodes
• Fine-Tuning — 19× in this paper · explained in 5 episodes
• Reinforcement Learning — 15× in this paper · explained in 4 episodes
• Consistency — 11× in this paper · explained in 3 episodes
• Supervised Fine-Tuning — 9× in this paper
• Accuracy — 6× in this paper · explained in 1 episode
• Regularization — 6× in this paper · explained in 3 episodes
• Generalization — 5× in this paper · explained in 13 episodes
• Alignment — 4× in this paper · explained in 1 episode
• Distillation — 3× in this paper · explained in 2 episodes
• GRPO — 3× in this paper · explained in 6 episodes
• Generalizability — 3× in this paper · explained in 6 episodes
• Gibbs Initialization with Finite Temperature — 3× in this paper
• Ablation — 2× in this paper · explained in 1 episode
• Cosine Similarity — 2× in this paper · explained in 3 episodes
• Reinforcement Learning (RL) — 2× in this paper · explained in 25 episodes
• Reward Function — 2× in this paper · explained in 2 episodes
• Verifiable Rewards — 2× in this paper · explained in 2 episodes
• AdamW Optimizer — 1× in this paper · explained in 1 episode
• Catastrophic Forgetting — 1× in this paper · explained in 5 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Dynamic Weighting — 1× in this paper · explained in 3 episodes
• Group Relative Policy Optimization — 1× in this paper
• Group Relative Policy Optimization (GRPO) — 1× in this paper · explained in 5 episodes
• Knowledge Distillation — 1× in this paper · explained in 11 episodes
• Mode Collapse — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Reinforcement Learning with Verifiable Rewards — 1× in this paper
• Robustness — 1× in this paper · explained in 5 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Supervised Fine-Tuning (SFT) — 1× in this paper · explained in 8 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes
• Verifier — 1× in this paper · explained in 2 episodes

Sources

• Training Verifiers to Solve Math Word Problems
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• DeepSeek-V3 Technical Report
• RLHF in an SFT Way: From Optimal Solution to Reward-Weighted Alignment
• Are We Done with MMLU?
• Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting
• NFT: Bridging Supervised Learning and Reinforcement Learning in Math Reasoning
• The False Promise of Imitating Proprietary LLMs
• DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning
• Step-wise Adaptive Integration of Supervised Fine-tuning and Reinforcement Learning for Task-Specific LLMs
• Measuring Mathematical Problem Solving With the MATH Dataset
• Scaling Instruction-Finetuned Language Models
• Step 3.5 Flash: Open Frontier-Level Intelligence with 11B Active Parameters
• Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge
• Rethinking Entropy Regularization in Large Reasoning Models
• Quagmires in SFT-RL Post-Training: When High SFT Scores Mislead and What to Use Instead
• Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution
• Direct Preference Optimization: Your Language Model is Secretly a Reward Model
• Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum
• GPQA: A Graduate-Level Google-Proof Q&A Benchmark

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks