# lpNTK: Better Generalisation with Less Data via Sample Interaction During Learning

arXiv: https://arxiv.org/abs/2401.08808 · HTML: https://mlsanity.com/paper/2401.08808/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 49 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentations](https://mlsanity.com/paper/2106.01548/) (2021)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)
- [Dataset Distillation with Infinitely Wide Convolutional Networks](https://mlsanity.com/paper/2107.13034/) (2021)
- [Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes](https://mlsanity.com/paper/1910.12478/) (2019)
- [DeepCore: A Comprehensive Library for Coreset Selection in Deep Learning](https://mlsanity.com/paper/2204.08499/) (2022)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [Characterizing Structural Regularities of Labeled Data in Overparameterized Models](https://mlsanity.com/paper/2002.03206/) (2020)
- [Compositional Languages Emerge in a Neural Iterated Learning Model](https://mlsanity.com/paper/2002.01365/) (2020)
- [Countering Language Drift with Seeded Iterated Learning](https://mlsanity.com/paper/2003.12694/) (2020)
- [Tensor Programs IIb: Architectural Universality of Neural Tangent Kernel Training Dynamics](https://mlsanity.com/paper/2105.03703/) (2021)
- [A Framework and Benchmark for Deep Batch Active Learning for Regression](https://mlsanity.com/paper/2203.09410/) (2022)
- [Deep Active Learning by Leveraging Training Dynamics](https://mlsanity.com/paper/2110.08611/) (2021)
- [A Fast, Well-Founded Approximation to the Empirical Neural Tangent Kernel](https://mlsanity.com/paper/2206.12543/) (2022)
- [The Emergence of Compositional Languages for Numeric Concepts Through Iterated Learning in Neural Agents](https://mlsanity.com/paper/1910.05291/) (2019)
- [Towards NNGP-guided Neural Architecture Search](https://mlsanity.com/paper/2011.06006/) (2020)
- [Iterated learning for emergent systematicity in VQA](https://mlsanity.com/paper/2105.01119/) (2021)
- [Better Supervisory Signals by Observing Learning Paths](https://mlsanity.com/paper/2203.02485/) (2022)

## Built on by (most cited first, 6 of 6)

- [Learning Dynamics of LLM Finetuning](https://mlsanity.com/paper/2407.10490/) (2024)
- [The Debate on RLVR Reasoning Capability Boundary: Shrinkage, Expansion, or Both? A Two-Stage Dynamic View](https://mlsanity.com/paper/2510.04028/) (2025)
- [Understanding Simplicity Bias towards Compositional Mappings via Learning Dynamics](https://mlsanity.com/paper/2409.09626/) (2024)
- [Alignment Dynamics in LLM Fine-Tuning](https://mlsanity.com/paper/2605.18309/) (2026)
- [Accumulative SGD Influence Estimation for Data Attribution](https://mlsanity.com/paper/2510.26185/) (2025)
- [Why Ghost Outputs Teach: A Kernel-Based Understanding of Subliminal Learning](https://mlsanity.com/paper/2609.23260/) (2026)

## Abstract (arXiv)

Although much research has been done on proposing new models or loss functions to improve the generalisation of artificial neural networks (ANNs), less attention has been directed to the impact of the training data on generalisation. In this work, we start from approximating the interaction between samples, i.e. how learning one sample would modify the model's prediction on other samples. Through analysing the terms involved in weight updates in supervised learning, we find that labels influence the interaction between samples. Therefore, we propose the labelled pseudo Neural Tangent Kernel (lpNTK) which takes label information into consideration when measuring the interactions between samples. We first prove that lpNTK asymptotically converges to the empirical neural tangent kernel in terms of the Frobenius norm under certain assumptions. Secondly, we illustrate how lpNTK helps to understand learning phenomena identified in previous work, specifically the learning difficulty of samples and forgetting events during learning. Moreover, we also show that using lpNTK to identify and remove poisoning training samples does not hurt the generalisation performance of ANNs.