# Neural Dynamic Data Valuation via Stochastic State-Adjoint Trajectories

arXiv: https://arxiv.org/abs/2404.19557 · HTML: https://mlsanity.com/paper/2404.19557/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 58 references that are in the map.
- First posted on arXiv 30 Apr 2024.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks](https://mlsanity.com/paper/1901.06053/) (2019)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [Data Valuation using Reinforcement Learning](https://mlsanity.com/paper/1909.11671/) (2019)
- [Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation](https://mlsanity.com/paper/1903.10992/) (2019)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [Maximum Principle Based Algorithms for Deep Learning](https://mlsanity.com/paper/1710.09513/) (2017)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [LAVA: Data Valuation without Pre-Specified Learning Algorithms](https://mlsanity.com/paper/2305.00054/) (2023)
- [A Mean-Field Optimal Control Formulation of Deep Learning](https://mlsanity.com/paper/1807.01083/) (2018)
- [OpenML-Python: an extensible Python API for OpenML](https://mlsanity.com/paper/1911.02490/) (2019)
- [OpenDataVal: a Unified Benchmark for Data Valuation](https://mlsanity.com/paper/2306.10577/) (2023)
- [Measuring the Effect of Training Data on Deep Learning Predictions via Randomized Experiments](https://mlsanity.com/paper/2206.10013/) (2022)
- [Data-OOB: Out-of-bag Estimate as a Simple and Efficient Data Value](https://mlsanity.com/paper/2304.07718/) (2023)
- [On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results](https://mlsanity.com/paper/2104.08015/) (2021)
- [Curriculum Learning for ab initio Deep Learned Refractive Optics](https://mlsanity.com/paper/2302.01089/) (2023)
- [An Optimal Control Approach to Deep Learning and Applications to Discrete-Weight Neural Networks](https://mlsanity.com/paper/1803.01299/) (2018)

## Abstract (arXiv)

Classical data valuation defines a data point's value through the finite marginal contribution U(Ccupi)-U(C), but estimating this quantity over coalitions requires repeated training and does not describe the contribution made along a stochastic training path. We ask whether marginal contributions of data points can be estimated from one coupled trajectory while retaining a verifiable relation to coalition-based values. To this end, we introduce Neural Dynamic Data Valuation (NDDV), which models each data point as a controlled stochastic state and computes a first-order marginal-contribution score via the adjoint equation of the Stochastic Maximum Principle (SMP). This raw sensitivity is then calibrated by a mass-preserving redistribution that increases one data point's participation while redistributing the same total weight over the remaining data points. We prove that the resulting backward adjoint recursion is the exact reverse-mode adjoint of the frozen-aggregate Euler system, bound its discrepancy from the mean-field sensitivity, and express each finite coalition marginal as an integral of local sample-weight sensitivities. These results yield pair-specific error bounds and sufficient conditions for ordering agreement with Shapley, Banzhaf, and leave-one-out values. Experiments on existing benchmarks evaluate marginal-contribution fidelity, score-release cost, corrupted-sample detection, ablations, and failure regimes. NDDV is a one-run, trajectory-conditioned estimator, not an unconditional replacement for cooperative-game values.