# Gradients Must Earn Their Influence: Unifying SFT with Generalized Entropic Objectives

arXiv: https://arxiv.org/abs/2602.11424 · HTML: https://mlsanity.com/paper/2602.11424/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [Documenting Large Webtext Corpora: A Case Study on the Colossal Clean Crawled Corpus](https://mlsanity.com/paper/2104.08758/) (2021)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [m1: Unleash the Potential of Test-Time Scaling for Medical Reasoning with Large Language Models](https://mlsanity.com/paper/2504.00869/) (2025)
- [Token Cleaning: Fine-Grained Data Selection for LLM Supervised Fine-Tuning](https://mlsanity.com/paper/2502.01968/) (2025)
- [Step-wise Adaptive Integration of Supervised Fine-tuning and Reinforcement Learning for Task-Specific LLMs](https://mlsanity.com/paper/2505.13026/) (2025)
- [Enhancing Large Language Model Reasoning via Selective Critical Token Fine-Tuning](https://mlsanity.com/paper/2510.10974/) (2025)
- [Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum](https://mlsanity.com/paper/2510.00526/) (2025)
- [ProFit: Leveraging High-Value Signals in SFT via Probability-Guided Token Selection](https://mlsanity.com/paper/2601.09195/) (2026)
- [Entropy-Adaptive Fine-Tuning: Resolving Confident Conflicts to Mitigate Forgetting](https://mlsanity.com/paper/2601.02151/) (2026)
- [Mitigating Forgetting in LLM Fine-Tuning via Low-Perplexity Token Learning](https://mlsanity.com/paper/2501.14315/) (2025)
- [Forgetting: A New Mechanism Towards Better Large Language Model Fine-tuning](https://mlsanity.com/paper/2508.04329/) (2025)

## Built on by (most cited first, 3 of 3)

- [From Tokens to Regions: CUDA-Sensitive Instruction Tuning for GPU Kernel Generation](https://mlsanity.com/paper/2606.16231/) (2026)
- [How Fast Should a Model Commit to Supervision? Training Reasoning Models on the Tsallis Loss Continuum](https://mlsanity.com/paper/2604.25907/) (2026)
- [Strategically Diverse Sampling for Self-Training](https://mlsanity.com/paper/2609.31571/) (2026)

## Abstract (arXiv)

Standard negative log-likelihood (NLL) for Supervised Fine-Tuning (SFT) applies uniform token-level weighting. This rigidity creates a two-fold failure mode: (i) overemphasizing low-probability targets can amplify gradients on noisy supervision and disrupt robust priors, and (ii) uniform weighting provides weak sharpening when the model is already confident. Existing methods fail to resolve the resulting plasticity--stability dilemma, often suppressing necessary learning signals alongside harmful ones. To address this issue, we unify token-level SFT objectives within a generalized deformed-log family and expose a universal gate × error gradient structure, where the gate controls how much the model trusts its current prediction. By employing the Cayley transform, we map the model's continuously evolving uncertainty onto a continuous focus trajectory, which enables seamless interpolation between scenarios involving uncertain novel concepts and those involving well-established knowledge. We then introduce Dynamic Entropy Fine-Tuning (DEFT), a parameter-free objective that modulates the trust gate using distribution concentration (R'enyi-2 entropy) as a practical proxy for the model's predictive state. Extensive experiments and analyses demonstrate that DEFT achieves a better balance between exploration and exploitation, leading to improved overall performance.