# Sensitivity of Stability: Theoretical & Empirical Analysis of Replicability for Adaptive Data Selection in Transfer Learning

arXiv: https://arxiv.org/abs/2508.04901 · HTML: https://mlsanity.com/paper/2508.04901/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 20 of 20)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
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- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
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- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Not All Samples Are Created Equal: Deep Learning with Importance Sampling](https://mlsanity.com/paper/1803.00942/) (2018)
- [On The Power of Curriculum Learning in Training Deep Networks](https://mlsanity.com/paper/1904.03626/) (2019)
- [Dynamic Curriculum Learning for Imbalanced Data Classification](https://mlsanity.com/paper/1901.06783/) (2019)
- [Adaptive Data Optimization: Dynamic Sample Selection with Scaling Laws](https://mlsanity.com/paper/2410.11820/) (2024)
- [Stability is Stable: Connections between Replicability, Privacy, and Adaptive Generalization](https://mlsanity.com/paper/2303.12921/) (2023)
- [Are Larger Pretrained Language Models Uniformly Better? Comparing Performance at the Instance Level](https://mlsanity.com/paper/2105.06020/) (2021)
- [What is Reproducibility in Artificial Intelligence and Machine Learning Research?](https://mlsanity.com/paper/2407.10239/) (2024)
- [User-Level Private Learning via Correlated Sampling](https://mlsanity.com/paper/2110.11208/) (2021)
- [Replicable Online Learning](https://mlsanity.com/paper/2411.13730/) (2024)
- [From Model Performance to Claim: How a Change of Focus in Machine Learning Replicability Can Help Bridge the Responsibility Gap](https://mlsanity.com/paper/2404.13131/) (2024)

## Abstract (arXiv)

The widespread adoption of transfer learning has revolutionized machine learning by enabling efficient adaptation of pre-trained models to new domains. However, the reliability of these adaptations remains poorly understood, particularly when using adaptive data selection strategies that dynamically prioritize training examples. We present a comprehensive theoretical and empirical analysis of replicability in transfer learning, introducing a mathematical framework that quantifies the fundamental trade-off between adaptation effectiveness and result consistency. Our key contribution is the formalization of selection sensitivity (DeltaQ), a measure that captures how adaptive selection strategies respond to perturbations in training data. We prove that replicability failure probability: the likelihood that two independent training runs produce models differing in performance by more than a threshold, increases quadratically with selection sensitivity while decreasing exponentially with sample size. Through extensive experiments on the MultiNLI corpus using six adaptive selection strategies - ranging from uniform sampling to gradient-based selection - we demonstrate that this theoretical relationship holds precisely in practice. Our results reveal that highly adaptive strategies like gradient-based and curriculum learning achieve superior task performance but suffer from high replicability failure rates, while less adaptive approaches maintain failure rates below 7%. Crucially, we show that source domain pretraining provides a powerful mitigation mechanism, reducing failure rates by up to 30% while preserving performance gains. These findings establish principled guidelines for practitioners to navigate the performance-replicability trade-off and highlight the need for replicability-aware design in modern transfer learning systems.